PHYSIOLOGICAL

Vol.

65, No.
Pri?ltuci

REVIEWS

2, April
1985
iw U.S.A.

Thermodynamic
Analysis ofMuscle ATPase Mechanisms
Departmentof Biochemistry,

TAKAO

KODAMA

Okayama

University

DentalSchool,Okayama,

I. Introduction..........................................................
..................................
II. Methods of Thermodynamic
Analysis
A. Thermodynamic
quantities.........................................
B. Kinetics and equilibrium
analysis..................................
.................................................
III. Reaction Calorimetry......................................................
A. Introduction
B. Instrumentation...................................................
.....................................
C. Data processing
in calorimetry
IV. Interpretationof Thermodynamic
Data ................................
A. Introduction......................................................
......................
B. Interactionof water with biological molecules
C. Conformationalchanges...........................................
.........................................
V. Energetics
of ATP Hydrolysis
A. Introduction......................................................
........................
B. Thermodynamic
analysis of ATP hydrolysis
C. Nature of high-energy
phosphate bond .............................
VI. Kinetic Mechanismof ATP Hydrolysis
by Myosin and Actomyosin......
A. Introduction......................................................
B. Contractile
proteins...............................................
...........
C. Mechanismof ATP hydrolysis
by myosin and actomyosin.............
VII. Calorimetryof ATP Hydrolysis
by Myosin and Actomyosin
A. Introduction......................................................
B. Historical
overview................................................
C. Kinetic analysis of heat production
during myosin/ATP
interaction..
............................
D. Calorimetryof myosin/ATP
interaction............................
E. Calorimetryof myosin/actin
interaction.............
VIII. Energetic Characterizationof Actomyosin
ATPase System
A. Introduction......................................................
..................
B. Thermodynamic
profiles of myosin ATP hydrolysis....................
C. Transitionof myosin head between macrostates.............................
D. Energeticsof myosidactin
interaction...
IX. Mechanismand Energetics
of ATP Hydrolysis
by Ca2+-Pump ATPase
A. Introduction......................................................
B. Structuralorganizationof Ca2+-pump ATPase in sarcoplasmic
reticulum
membrane..........................................
C. Basic propertiesof Ca2+ pump ......................................
D. Kinetic mechanism of Ca2+ pump ...................................
E. Thermodynamic
analysis of partial reactions of ATP hydrolysisbyCa2+pump....................................................
......
F. Thermodynamic
characterizationof Ca2+-pump ATPase system0031-9333/85$1.50 Copyright0 1985 the American

PhysiologicalSociety

Japan
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KODAMA...................
X. General Features of Biological Energy Transduction
A. Involvementof specific ligands and their translocationin...............................................
ATP hydrolysis
B. Alternation
between fundamental
conformational
states .............
........................................
C. Energeticsof
ATPasecycle

Volume 65
537
538
539
540

I. INTRODUCTION

Adenosine
triphosphatases
play the central roles in physiological
functions of cells as energy transducers
by coupling the chemical reactions of
ATP hydrolysis
to the other energetic processes. This review concentrates
on the two major ATPases that are characteristicof muscle: actomyosin
ATPase of the contractile
machinery
and the Ca2+-pump ATPase of thesarcoplasmic reticulum (SR). In each case the catalytic cycle of ATP hydrolysis
consists of a series of intermediate
states of the ATPase molecules. Current
research is focused on the correlationof such biochemicalmechanisms
withphysical events resulting
in the developmentof mechanicalwork in muscle
contraction
or productionof work required
for translocationof Ca2+ acrossthe SR membrane
against the chemical potentialof the cations. My mainconcern is the thermodynamic
characterizationof the intermediate
steps ofthe ATPase cycle, i.e., the evaluationof the thermodynamic
parameters
associated with these steps: changes in free energy (AG), enthalpy
or heat(AH), entropy (AS), and heat capacity at constant pressure (AC*).
There are two major goals of such thermodynamic
studies. First, evaluation of the free-energychanges for transitions
between different
intermediate states provides an energetic basis to correlate intermediatesof theen zyme in a catalytic cycle with its physical states in doing work. This goal
iS to ult ,im .ately identify
th e most c rucial step or steps in the energy-transduction process. The problem in the actomyosin
ATPase, for example, is todecide which transition
between the intermediates
is energeticallyfeasiblefor force generationin muscle contraction.
Considerable
progress has been
made during the last IO years owing to the extensive kinetic studies supported
by a wide range of new analyticaltechniques.
Indeed it is now possible toprofile for the actomyosi n ATPase in solution.
depict a reasonable free-energy
The next step is to extend such in vitro ana lysis to th e actomyosin
systemin a more organized structure so that the coupling of chemical and mechanicalphenomena
can be investigated.
There have already been several studies inwhich serious efforts were made in this direction(46, 97, 189, 212).
In the case of the Ca2+-pump ATPase, the relative
free-energy
levelshave not been evaluatedunequivocallyfor all of the major intermediate
states. However,investigationof the Ca2+ pump has the advantagethat its
usual experimental
system in vitro, the SR vesicles preparedfrom muscle
homogenate,
can performthe coupling of chemical work and ion transport.
In addition the ATPase alters its affinity for Ca2+ when facing opposite sidesof the membrane
during its catalytic cycle; this is thought to be the mostfundamental
feature shared by active transportof ions across a membranein general. Thus the basic problem of this ATPase reaction is well defined,AprilENERGETICS1985

OF MUSCLEATPASE

REACTIONS

469

and intermediate
states can reasonably
be assigned to those having different
directions
and affinities in Ca2+ binding. Thermodynamicrefinementof sucha mechanismof the chemiosmoticenergy transduction
is now in progress.
Second, from the assessment of enthalpy
and entropy contributions
tothe free-energychange, it is possible to have an insight into the nature ofa given chemical reaction. The signs and magnitudesof enthalpy and entropychanges are good measures of the nature of the various forces, their relative
strength, and their importancein the reaction. If the heat-capacitychangeis also evaluated,
the insight is deepened, as described in this review. Thiskind of information,
brought
by thermodynamics,
is difficult
to obtain byother methods. In addition it is complementary
to that obtained by structuraland spectroscopic
studies. X-ray diffraction,
electron microscopy,
and otherrelated techniques are essential to describe the gross morphologicalchangesaccompanying
the energy-transduction
processes, particularly
in muscle contraction. A wide range of spectroscopic methods probes the microenvironmentof a specific residue or residues of ATPase proteins; hence, in combination
with kinetic methods, they are also essential to identify
and characterize
the intermediate
states of the ATPase reaction cycle.
In this review, a description
is given of the methods for experimental
evaluationof the major thermodynamic
parametersof the intermediate
stepsof the ATPase reactions. I emphasize calorimetry,because instrumental
improvements
recently have been made enabling
one to apply it to the two
muscle ATPase systems. Because the kinetic knowledge
and related information about these systems are essential for the calorimetricanalysis as
well as thermodynamic
discussion, recent results are also summarized.
I discuss implicationsof the results obtained by these methods in relation
to the mechanismsof the ATP hydrolysis
coupled with other energetic processes. Based on these results, I discuss certain general features of chemomechanicaland chemiosmoticenergy transductions.
Even if the range of topics to be covered is confined as described above,the scope of the thermodynamics
of biological energy transduction
is enormousand requires a vast accumulationof knowledge
and information
obtainedfrom various types of studies. However,this review is by no means intended
to be a comprehensive
coverage of the literatureon such studies. Hence,taking advantageof the fact that several reviews concerning
the energytransducing
ATPase systems are publishedevery year (for a very recent,comprehensive
collection of reviews see ref. 219), only a limited number oforiginal
papers publishedearlier than 1977 are cited.
II. METHODSOF THERMODYNAMIC

A. Thermodynamic

ANALYSIS

Quantities

Principal thermodynamic
parameters
and their interrelations
are briefly
summarized
here.’ For a more formal treatmentof biothermodynamics
and’ 1 cal = 4.184 J.

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related physicochemical
subjects, readers are referred
to many excellent
textbooks (e.g., refs. 68, 152, 198, 211). A recent book writtenby Edsall and
Gutfreund(66) is especially concerned with analysis and interpretationofdata obtained from biochemical
reactions, ligand binding, and calorimetricmeasurementsof biologicalsystems.
1. Free-energychanges

The Gibbs free-energychange (AG) is a fundamental
criterion
for thedirection and extent of a chemical process, and the magnitudeof its decrease(-AG)
is the direct measure of the maximum
capacity of the process totransfer
energy as useful work at constant temperatureand pressure. For
a given chemical reaction, which is held away from equilibrium,
AG is givenbY
AG = -RT

In (K/Q)(1)

where R is the gas constant (8.314 J. K-l mol-‘), T is the thermodynamic
temperaturein Kelvin scale, K is the equilibrium
constant that equals the
mass-action
ratio of concentrationsof the products to those of the reactants
at equilibrium,2and Q is the observed mass-action
ratio relating to the concentrations
when the reaction is displaced from equilbrium.
Hence AG, referred to as the actual free-energychange, has a value that is a functionofthe displacementfrom equilibrium.
The standard
Gibbs free energy (AGO)
is defined as the value of AG when the value of Q is unity. Thus by definitionl

AGO = -RT
By substituting
this relationshipfree-energychanges are related

In K

into Equation(2)
1, the actualand standard

AG=AG’+RTlnQ
Consequently
the actual free-energychange can be calculated for any reaction
if the concentrationsof the reactants
and products are analyticallydetermined, provided
the appropriate
value of AGo is known for the conditions(pH, ionic strength, temperature,etc.) under which the reaction will occur.
Hence the first step of thermodynamic
analysis is to evaluate
AGo by determining
K.

2 Strictly speaking, thermodynamic
discussion
should be in terms of activities
instead ofconcentrationsof reactants and products. However, there may be no serious consequence in theuse of concentration
as long as both Q and K for the reaction are evaluated under comparable
conditions.

April1985

ENERGETICS

2. Basic free-energy

OF MUSCLEATPASE

471

REACTIONS

changes

Both the actual and standard free energy refer to the system as a whole.
In considering
the bioenergetics,
particularly
the energy-transducing
processes, it is often necessary to define the relative
free-energy
levels of theintermediatesof the reaction. These intermediates
are different
states of anindividual(time-averaged)
macromolecule,whose free-energy
levels are referred to as the “basic” free-energy
levels by Simmons and Hill (253). This
concept is useful to describe the energy transductionof biological processes,
muscle contraction
in particular(73, 74).
Consider, as an example, the reaction

where M is a macromolecule(e.g., myosin) and N is a ligand (e.g., ADP),
which form a complex M l N (see sects. IIICI and VICZ). Let kf and kb be theforwardand backward
rate constants, respectively.
kf is the second-order
rate constant with the unit M-?-l,and kb is the first-orderconstant withthe unit t-l, where t is an appropriate
unit of time. Because at equilibrium
the rates will be equal for both directions,employingequilibrium
concentrations(denoted by subscript e)MWe(N)ewlthis equation,

kb(M

’ N)e

=

JCf’kb=N)e(&f),(N),By rearranging=

K

one obtains

which is the equilibrium
ratio of probabilitiesof the two states of the macromolecule,
M l N (complexed)
and M (free), at a given (equilibrium)
concentrationof the ligand. This ratio is called the basic or effective equilibrium
constant, Kbasic. Thus
K basic
and the basic free-energy=change

(M

l

wmf)e

(AGba;ici,) for the reaction

AG asic = -RT
Note also the relationshipbetween
K basic=

isln Kbasic
Kbasic and the rate constants

kf(N)e/kb

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Because kf(N), has the unit t-l, it is referred
to as the pseudo-first-order
rate constant. In other words, the basic equilibrium
constant is the ratio of
the first-order
rate constants for both directions;hence the basic free energy
is directly related to the rate of the process.
As is obvious from the definition,
the actual concentrationof the ligand
is taken into account for AGbasic. This fact is relevantto the argumentinterms of the drive of the energy-transducing
systems in which the concentrations of ligands involved(ATP as reactant and ADP and Pi as products)
are kept rather constant, as in the muscle cell. Incidentally,
for reactions
not involving
the binding or release of a ligand such as isomerizationof amacromolecule,the basic free-energychange is numericallyequal to thestandard
free-energychange.
3. Enthalpy

and entropy

The energy-entropy
pressure ischanges
relationfor changes

AG = AH-TAS

at constanttemperature

and
(3)

where AH and AS are the changes in enthalpy
and entropy, respectively.
If
AHcan be evaluated, it becomes possible to make the assessment of enthalpic
and entropic contributions
to the free-energychange. The value of AS iscalculated with a rearranged
form of Equation
3
AS = (AH - AG)/T
For most biochemical
reactions that take place in solution, the volume
changes (AV) are negligible.
The AH is identical with energy change (AE),as is evident from the equation defining AH
AH=AE+PAV
where P is the pressure on the system. Also by definition,
AH equals theheat change (reactionheat) accompanying
a reaction at constant pressure.
AH is negative for an exothermic
reaction (heat lost from the system) andpositive for an endothermic
reaction (heat gained by the system).3

3 The sign convention
to be used in this review is the same as that used by Wilkie (303)and Curtin and Woledge (47). Heat produced by the system is considered to have a positive signand, by definition, AH values have a negative sign for reactions that produce heat. Therefore
the heat produced equals -AH for any reactions when no external work is done.

AprilENERGETICS

1985

4. Unitary

quantities

OF MUSCLE

of thermodynamic

ATPASE

REACTIONS

473

parameters

In the thermodynamic
arguments
of a reaction occurringin a solution,
it is often necessary to exclude a complicationthat arises from changes in
the number of solute particles
in the reaction. In other words, a thermodynamic parameteris composed of two distinct terms, the unitary and thecratic (66,109,150). The unitary term is fundamentally
relevant to the natureof the reaction, whereas the cratic term is only related to the mixing ofsolute molecules with solvent, hence independentof the nature of the solutes.
For reactions
in aqueous solution
such as the bindingof a nucleotide
tomyosin (see sects. IIICI and v1C2)
M+N+MoN
the cratic

termof the entropychangeAScratic(ASc,,,ic) is=RlnX

where Xis the change in the total mole fraction of solutes. For the standard
state of 1 M, Xis numericallyequal to the reciprocal of the molar concentrationof water (l/55.5) in diluted aqueous solution, and the value of AScratic is -33.4
by subtracting
this cratic contribution
J K-l M-l. Hence A& is calculated
from the value of the standard entropy change (AS’)
llas, = AS0 - AScra+--c
The unitary
free-energychange (AG,) can then be calculatedon the basisof a reasonable assumptionthat observed m is a unitary quantity.
For thereaction described, the value of AG, is more negativeby ~10 kJ/M thanAGo for the standard state of 1 M at w20°C.

5. Detailed balance of thermodynamic

parameters

For a cyclic process consisting of n steps of reactions, if the equilibrium
constant for the ith step is defined as & referringto the clockwise direction,
the product of all n equilibrium
constants is equal to unity. Thus

KIK2..

.K,=lThis is called the detailed balance of equilibrium
cyclic process (66). From Equation z it is evident
change (AGP) for the same cyclic process
c AG; = 0

constantsin the closedthat for the free-energy

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Likewise the sums of the enthalpies,
entropies,
and heat capacities definedin the same way as AGY are numericallynil. These relations are useful because
thermodynamic
parameters
for one of the steps in a cyclic process canbe evaluated
if the others are known. Examples
are found in sections VI
and VII.
B. Kinetics

and Equilibrium

Analysis

In principle
it is possible to obtain all the information
about energetics
for a given reaction from kinetic analysis, because it reveals the rates andhence the equilibrium
constant. However,
all the necessary kinetic data arerarely obtained, particularly
for complex reactions consisting of a sequenceof more than two steps. In some cases, equilibrium
analysis of partial reactions
in multistep
reactions provides invaluable
data that complement
kinetic information(110).
If the equilibrium
constant is measured over a range of temperaturesand In K is plotted against l/T, AH can be estimatedby the van’t Hoff
equation for the variationof the equilibrium
constant with temperature4d(ln K)/d(l/T)= -AH/RIn many cases, however, the slope is not linear, because AH also varies
with temperature.
This tendency is quantitatively
expressed by the change
in heat capacity (ACJ

AC,= d(AH)/dT
In theory the magnitudeof ACP can be estimatedfrom the degree of
curvaturein the van’t Hoff plot based on data of sufficient precision. Thus
measurementof the equilibrium
constant for a given reaction by kinetic andequilibrium
methods over a temperature
range could provide the data necessary to evaluate all principal
thermodynamic
parameters
for the reaction.
However,
there is a major practical difficultyin this type of approach.
In most cases, values of K, whether
estimatedby kinetic or equilibrium
analysis, are not precise, and it is fair to say that the errors accompanying
these estimates usually exceed tlO%. Thus the evaluationof AH from thetemperaturedependence of K with van’t Hoff plots may have a large error,
which is often not properly
appreciated.
It is still harder to estimate AC’,from the curvatureof the van’t Hoff plots.
In studying the reactions consisting of a series of intermediate
reactions4 To a good first approximation,observed AH is independent of concentrationof reactants,
hence equated with A&
Also note that, in the strict sense, the van’t Hoff equation is basedon a two-statemodel of equilibrium
and will not be applicable to a highly cooperative
and/ormultistateprocess (239).

AprilENERGETICS1985

OF MUSCLEATPASE

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475

such as the ATP hydrolysis
by myosin, actomyosin, and Ca2+-pump ATPases,
the values of AGO are estimated by the kinetic methods in combinationwiththe equilibrium
analysis as outlined in sections VI and IX. The direct calorimetric measurementof m, known as reaction calorimetry(sect. III), should
be used to evaluate the contributionsof @ and AS0 to AGo for these reactions.

III.

REACTIONCALORIMETRY

A. Introduction
Calorimetry
is a thermodynamic
method used to measure heat quantities
or heat effects. It may be divided into reaction calorimetry
and differential
temperature-scanningcalorimetry.
The former is the measurementof heatchange accompanying
a given chemical or physical process initiated by mixing
two or more reactive components in the calorimeterat constant temperature.
The latter is the measurementof the heat capacity of a substance, be it
solution or solid, and its variation
with temperature.
It provides useful information
about the thermodynamic
principles
of organizationand stabilization of the unique three-dimensional
structureof biologicalmacromolecules (163, 227, 228).
B. Instrumentation
1. Generalconsideration

There are several calorimetricprinciples
and a large variety of different
practical designs suitable for reaction calorimetry.
Many of these are describedby Brown (32) and in several reviews (167, 256, 257, 259, 285). Some of these
instruments
are commerciallyavailable
and have been widely used to study
the interactionof proteins and nucleic acids with their ligands (16, 25, 70,
236, 285).
Calorimetric
instruments
are classified into two types, depending on how
the reacting components
are mixed to initiate the reaction: the batch calorimeter and flow calorimeter.
In a batch calorimeter
the two reactant solutions
are first somehow separated in the calorimeter
cell and mixed after thermal
equilibration,then the accompanying
heat effect is measured. A high sensitivity is the major advantageof this type of instrument.
Althoughpractical
sensitivity
is limited by various factors not inherent
to the instruments,aheat change as small as 0.05-0.1 mJ produced in 1 ml of reaction mixture
can be measured at best in some cases. Hence tl pmol of reactant is sufficient
for a single experiment,
providedthat the enthalpy
change exceeds 10 kJ/
mol (256).

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For thermodynamic
analysis in general, however, a set of data obtainedby repetitionof such experiments
is required.
The whole experiment
would
then extend for several days because the thermal equilibration
usually takes
several hours for each calorimetricrun, whereas the heat measurement
itselftakes little time compared with that for the equilibration.
On the other hand, in a flow calorimeter
the reactant
solutionsarepumped into the calorimeter
cell where they are mixed, and a steady-stateheat effect is observedthat greatly facilitates
the accumulationof data.
However,
this method requires
much more material
and is less sensitive
than batch calorimetry.
2. Calorimetrictitration

A titration
device was developed by Woledge (304) to speed up the experimentwith a batch calorimeter
without
sacrificing
its high sensitivity.
This device adds one reactant to the other in the calorimetercell. This improvement
has markedly
reduced the time required
to study the process ofprotein saturation
with a specific ligand in a number of steps. Thus data for
determinationof a binding curve (the equilibrium
constant, enthalpy change,and stoichiometric
relationshipbetween the reactants)
can be obtained bya single calorimetricrun. Furthermore,
if such a calorimetrictitrationisrepeated over a range of temperaturesat an appropriate
interval,
not only
can the heat-capacitychange (ACJ be evaluated,i.e., the temperaturedependence of AH, but so can that of Cp and the equilibrium
constant (see,e.g., refs. 154, 159, 308).
3. Rapid-response

calorimeters

To estimate individual
reaction heats for the intermediate
steps of theATPase reaction, such as myosin ATP hydrolysis,
it is necessary to follow
the time course of heat production
immediately
after initiationof the reaction.
This demands a rapid-response
calorimeterwith high sensitivity.
There havebeen several designs of fast calorimeters,
and the continuous
rapid-flow
calorimeter
developed by Hartridge
and Roughton
in 1923 (24, 240) should be
noted. Althougha time resolution
in the millisecond
range can be obtained,
it suffers from the disadvantagethat large volumes of solution are needed.
Some recent stopped-flow
calorimeters
have time resolutionsof 1 s to 1 ms
(15, 24, 29, 213), but the sensitivity
is inadequate
by at least one order ofmagnitude.
A rapid-response
calorimeterwith a compromiseof the response andsensitivity
was recently constructed(160, 305). In this instrument
the thermocouple detectors connected in series provide
a sufficientsensitivity
tomeasure heat effects as small as 0.2 mJ. In addition, they are placed so they
make a close contact with the reactant solution to minimize heat-conductionApril1985

ENERGETICSOF MUSCLEATPASE

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477

delay. Thus the response is 90% complete in 1.5 s. Although
this calorimeter
is not as fast as the stopped-flow
type, it has been successfully used for the
analysis of ATP hydrolysis
by myosin and Ca2+-pump ATPase. In addition
this instrument
has proved to be suitable for calorimetrictitration(154).
Apart from time required for thermal equilibration
after loading the sample,
a whole titration
process can be completed within several minutes, compared
to several hours requiredin earlier studies (158, 159).

C. Data Processing in Calorimetry
Biltonen and Langerman(25) gave the subject more general treatment.
The two most basic points in calorimetricexperiments
are mentioned
here.
First, the heat observed in a calorimeteris a complex effect composed of agenuine heat effect (h) accompanying
the reaction under investigation
andthat from several nonspecific sources. Second, the value of h is proportional
to the extent of the reaction ([) in the calorimeter,
so independent
analyticalexperiments
are usually necessary to estimate the [ values.

I. Heat of mixing
Suppose a reaction started in a calorimeterby mixing solutions 1 and
2, which contain reactants A and B, respectively(A and B react to form C).
The observed heat effect (bobs) equals the sum of the heat due to solution
mixing (h,ix) and the heat effect (h,,,) accompanying
the reaction. The happ
includes the heat of ionizationof the buffer compound used (this problem is
discussed in sect. ~3).
Strictly speaking, hmixconsists of two components, the heat due to dilutionof reactants and the heat dissipated by any physical processes accompanying
the mixing of two solutions and mixing itself. The value of hmix is determinedin separate experiments
by mixing solution 1 containing
A with solution 2
not containing B, or vice versa. However, if appropriate
precautions
are taken
to adjust pH, ionic strength,
and compositionof two solutions to be mixed,
the correction
for the hmix will be relatively
small.

2. Extent of reaction
The value of happthus obtained (h,,, = bobs- hmix) is proportionalamount of C formed &), which is related to an apparent
enthalpyof the formationof C(AHa,,) byh app
The determination
reaction mixture after=of & should
calorimetry.

tmmapp)l

to thechangetC

be made from a chemica #l analysis of the
If difficult, the analysis can be made in

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separate experiments
for the reaction under conditions
otherwise
the same
as calorimetry.
In titration
calorimetry
the problem of determining
the extent
of the reaction is replaced by the curve-fitting
procedure.
There is a usefulway to control the extent of reaction in some special cases. If the binding
constant is known to be very large and the reaction
is carriedout in acalorimeterwith one of the reactants in excess of the other, the reaction of
the latter can be regarded
as complete. The results can be analyzed by assuming that the extent of reaction equals the initial concentrationof reactant
not present in excess. An example of this is found in the analysis of myosin/
ATP interaction(see sect. VIIC).
3. Heat of bqfler

ionization

In many reactions
involving
biologicalmacromolecules,
some protons
are liberated
or absorbed through the shift of pK values of certain ionizing
groups. Therefore
the heat produced by interactionof these protons withthe buffer present in the reaction system is included in the values of AHa,,.
There are two methods of correcting
for this heat. One is to measure in
separate experiments
the amount of hydrogen liberated or released (no) witha pH electrode and the heat of protonationof the buffer (AHbuffer). The true
enthalpy change for the reaction (AH) then will be given by

AH = AH,,, - nHAHbuffer
Another method is to repeat the calorimetricexperimentswith buffers having
different
protonation
heats. Assumingthat the nH value is the same in two
different
buffers, both AH and nH can be determined.
The Ca2+-pump ATPasereaction has been analyzed with this method (sect. 1xlZ-4).
The protonation
heat values of buffers widely used in biologicalexperiments can be found elsewhere (87, 128). The temperature-dependence
tableof buffer pKvalues
is also useful because the protonation
heat can be worked
out with the van’t Hoff relation(98, 113, 221).
IV. INTERPRETATION

OF THERMODYNAMIC

DATA

A. Introduction
This subject is discussed in detail by Eftink and Biltonen (70) in a recent,comprehensive
review, and the results relevant
to my review are briefly
summarized.
It is possible to foresee how far a chemical reaction proceeds if the initialconcentrationsof the reactants and the standard free-energychange of thereaction are known. However,the standard
free-energychange value mayApril 1985

ENERGETICSOF MUSCLEATPASE

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REACTIONS

be relatively
insensitive
to variationin the molecular details of the reaction,
because the enthalpy(AH) and entropy (Z’AS) contributions
tend to compensate for one another (70, 174). The situation
is often encounteredwhen
a protein/ligand
interaction
is studied as a functionof ionic strength,pH,or temperatureor with different,
but structurally
related, ligands. Whatever
the actual mechanismof such an “enthalpy-entropy
compensation
effect”(69), it is of fundamental
importanceto evaluate the enthalpy
and entropy
contributions
to the free-energychange in thermodynamic
analysis.
Current research suggests that the sign and magnitude of thermodynamic
parametersconstitutevery importantdiagnostic
molecular
mechanismsofmany biochemical
processes (70, 239, 260). Several
possible interand
intramoleculareffects are summarizedin Table 1, some of which are discussed below.
B. Interactionof Water with Biological

1. Importanceof hydration/dehydration

Molecules

Hydrophobic
and electrostatic
effects are the two major effects by which
the state of water is altered by its interaction
with biologicalmolecules,
thereby making large contributions
to the thermodynamic
state of the system.
Althoughthese effects are different
in nature, both are related to the hydration/dehydrationof the solute molecules in water. In an enzymatic process
therefore
they play importantroles in the transfer
of reactantsfrom thebulk-waterphase to the surface of the enzyme protein, their interaction
withspecific protein groups at the catalytic site, and concomitantconformational

1. Major sources of thermodynamic
reactions involving
proteins

TABLE

changes in

Sources

Exposure of nonpolar groups to water
Exposure of charged groups to water
Van der Waals interaction
Formationof H+ bond
Increase in intramolecularmotionsof protein
Increase in number of isoenergetic
conformationsof protein
Shift of equilibrium
between macrostatesof protein*+ or -

-

-

+
-

+

+

+

0

+

0

+

AH, change in enthalpy; AS”, change in entropy; AC,,, change in heat capacity.
* Signs
and magnitudes
depend on system (see text).
[Based on data from Ross and Subramanian(239) and Sturtevant(260).]

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Volume 65changes of the enzyme proteins that are most 1ikely to change the degreeof exposure of charged and/or nonpolar
protein groups to water WV .
2. HydrophobicefectThe importanceof this effect in biologicalprocesses is now well appreciated, and it can be quantitatively
treated in physicochemicalterms (21,96, 269).
Qualitatively
the hydrophobic
effect refers to the tendency of nonpolargroups in water to associate preferentiallywith themselves or other nonpolargroups, because “cages” of structured
water are formed around nonpolargroups. Similar to its state in ice, water in such a state has a low entropy
and a high heat capacity. The association of nonpolar groups in the aqueous
environmentor the transfer
of nonpolargroups from the aqueous to nonaqueous environmentis accompaniedby the breakdownof the water cages.
These processes are therefore
energeticallyfavorable
ones, characterizedbya large positive entropy (AS @ 0) and large negative heat-capacitychanges(Ac, < 0).
The AH for the hydrophobic
effect is usually small and often makes anegative contribution
to the free-energychange. For example, the transfer
of ethane from water to chloroform
is accompanied
by a slightly unfavorable AH of +7.5 kJ/mol, and the process is entropicallydriven with AS of
79 J K-l mol-’ at 25OC (269). It should be noted, however,that because
ACP < 0 in the hydrophobic
effect, AH becomes more negative with an increasein temperature,making AS less positive at higher temperatures.
This arises
because of the diminishingwater structure
at higher temperatures.
ll

3. Electrostaticinteractions

When charged molecules are introduced
into water, several water molecules are attracted,
oriented,and compressed by the intense electrostatic
field around the charged molecules (see ref. 68, p. 450-457). Those watermolecules are in a low entropy state, but their heat capacity is also lowered
because their structureis less labile than it would be in pure water (269).
The AH for the interactionof charged molecules with water shows either anegative or positive sign, but its magnitude
is not large as long as no net
change occurs in the number or strengthof hydrogenbonds. On the basisof the thermodynamic
nature of the interaction
between charged molecules
and water, the strong interaction
between a charged molecule and a countercharged
molecule in the aqueous environmentis driven primarily
by anincrease in entropy due to the release of water from around the charged
molecules. Enthalpy
changes (of either sign) are small, and ACP is positive.
A good example illustrating
the contributionof the electrostatic
effectto the thermodynamicchange may be provided by the interactionof divalentAprilENERGETICS1985

OF MUSCLEATPASE

REACTIONS

481

charged groups of proteins,
cations such as M$+ and Caz+ with negatively
nucleic acids, and related molecules. As expected from the state of the reacting
groups in an aqueous solution in which they are surroundedby water molecules, the binding of M8+ to ATP, for example, is totally driven by a large
positive entropy change that dominates
the slightly
unfavorable
enthalpy
change (4).
C. ConfOrmational
1. Unfolding

Changesof protein

Of the conformationalchanges possible for proteins, the most extreme
is probably
the unfolding
accompanying
denaturation.
This is a transitionof the polypeptide
chain from its state of a certain compact structure
to astate that is close to a random coil. As a result of intensive thermodynamic
studies, particularly
by Privalov with a scanning-calorimetrictechnique (227,228), it is now possible to evaluate
thermodynamic
parameters
for protein
unfolding.
Roughly speaking, for a typical globular protein with a molecularweight of 25,000, denaturation
occurs with a AH of 200-400 kJ/mol,
AS of
0.4-1.5 kJ. K-l mol-‘, and ACp of 4-17 kJ K-l. mol-l.
These thermodynamicchanges are explainedin terms of the changes
induced on unfolding.
A large AHis probably due to the disruptionof hydrogenbonds and van der Waals contacts, which contributeto the stabilizationofcompact structure,
whereas a large positive AS can largely be attributedtothe accompanying
increase in configurational
freedomof the polypeptide.
The most important,
if not the only, source of the increase in heat capacity
is the interactionof water with nonpolar groups that are exposed on unfolding.
Bearing in mind that unfoldingis the extreme of protein conformationalchanges and that it occurs with such large thermodynamicchanges, more
subtle conformationalchanges relevant to the enzymatic mechanism are now
described.
l2. Protein/water

intramolecularlinteractions
followedchanges of proteinsbY

As described above, when an enzyme protein interacts with its reactants
and goes through different
intermediate
states in the catalytic process, its
hydration
should change considerably.
For example, if some hydrophobic
residues exposed to water become sequesteredin the interiorhydrophobic
regions of the enzyme protein or assembled while remaining
on the exteriorof the protein (see, e.g., ref. 272), the cages of water around the hydrophobic
residues are disrupted.
The extent of hydrationis also changed in the formation of protein molecules from subunits and in the interaction
between

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65

different
proteins. When protein surfaces come into close contact with each
set free.
other, a large number of water molecules are probably
effect is disorderingof the water
In these cases therefore
the primary.inated, the sign ofeffect predom
structure;
hence AS > 0. If theth e hydrophobic
predominated,
AH. However,
the observed thermoACP would be negative with positive
dynamic changes are often hard to explain on this basis alone. In fact, notonly AC, but also AH and AS are predominantly
negative in many reactions,particularly
ligand binding and self associationof proteins (239).
To overcome
this difficulty
it seems necessary to consider the intramolecu
molecularlar changes of proteins as a consequence of disruptionof the hydration
layers of proteins and ligands. Sturtevant(260) suggested the importanceof the contributionof changes in intramolecularmotions of proteins to ACP
and AS, including vibration
and rotation of side chains and backbone bending,which are characterized
by force constants weak enough to be readily perturbed by ligand binding or partial unfolding.
On the other hand, Ross andSubramanian(239) emphasizedthat the strengtheningof hydrogenbonds
in the low-dielectric
protein interior
and van der Waals interactions(see
Table 1) are the most importantfactors contributing
to the observed negativevalues of AH and AS. Apart from the large negative
ACP, both theories
predict that with an increase in temperature,enthalpic
contribution(more
negative or less positive)
becomes dominant
in stabilizing
a conformationof many proteins (239).
3. Shiftin equilibrium

betweenproteinmacrostates

With the accumulationof data from direct calorimetricmeasurements
on many processes involving
proteins, a strong temperaturedependence ofthe heat-capacitychange has also been detected (82,X53,154).
This phenomenon is difficult
to explain on the basis of the hydrophobic
effect or othersources described above, because they are observed within a small temperature range.
If a protein exists in different
macroscopic
structuralstates that are
distinguishedby their peptide-folding
patterns in at least part of the structure
and the equilibrium
between these macrostates
is temperaturedependent,
their redistribution
caused by interaction
with other molecules could be asource of a large ACP and temperaturedependence of ACP (69, 70).
In the case of a protein/ligand
interaction,
elements of this hypothesis
are: I) a protein exists in (at least) two macrostates,
one of which is in ahigh-enthalpy
state and the other in a low-enthalpy
state; 2) the transition
between these states is controlled
by a substantial
enthalpy change (AH,,,,,)
and a relatively
small equilibrium
constant (&,,)
that is in unity withinor near the experimentallyfeasible range of temperature;and 3) the affinity
for a ligand is different for the two macrostates. By mathematicalformulation

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483

the apparent
enthalpy change for the ligand binding (AHa,,) can be shown
as a functionof the intrinsic
heat of the ligand binding(AH*,,>, AH,,,,,,
K trans F and temperature(69,70,82).
The apparent heat-capacitychange (AC1 tapp) and its temperaturedependence are, of course, the first and second temperature
derivativesof AHa,, . The most important
prediction
made by thishypothesisis that even if both AHtrans and AHli, were temperature
independent, the ligand binding would apparently
be accompanied
by a negative
heat-capacitychange ( ACp app < 0) also showing a temperaturedependence.
The nucleotide binding to myosin is probably best explained by this hypothesis,
described in section VIIIC.
In summary,
there are many possible sources for the thermodynamicchanges accompanying
processes in which proteinsplay the primaryrolethrough the interaction
with other molecules. One wishes to relate particularsources to the experimentallyobtained thermodynamic
parameters.
However,
because they are the sums of contributions
from several different
sources,quantitativeevaluation
is difficultat present. Nonetheless,comparisonsofthermodynamic
data with information
on mechanisticchanges obtained byother analyticalmethods will definitely
provideuseful insight into theseprocesses involving
biologicalmolecules.
V. ENERGETICSOF ATP HYDROLYSIS

A. Introduction
From the kinetic viewpoint
ATP is relatively
conditions, but it is unstable in the thermodynamicof the hydrolysis
reaction
ATP + Hz0 + ADP

stable under physiologicalsense that the equilibrium+ Pi

lies far to the right. Thus the ATP-ADP
system serves as a carrier of chemicalenergy from metabolic reactions for use in most energy-requiring
processes
in cells.
Since its discovery, ATP and related compounds have been the subjectof extensive studies from various aspects. There are many good articles andreviews about the history of the discovery of ATP and subsequent developmentof the “high-energy
phosphate bond” concept (83), chemical kinetics of polyphosphatehydrolysis(71, 142), quantum
chemistry(229), theoretical
thermodynamic
analysis (94, 95), and calculation
methods of thermodynamic
parameters
for ATP hydrolysis
as a function of metal ion concentrationandpH (3-5). The results that are relevantto this discussion are briefly summarized.

484
B. Thermodynamic
1. Equilibrium

TAKAO

Analysisconstant

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KODAMAof A TP Hydrolysis

and free-energychange

The thermodynamic
analysis of the ATP hydrolysis
is complicatedfor
two reasons. First, the reaction involves a variety of molecular species, because
all the reactants and products are weak acids having more than two dissociable
protons (polybasic
acids). They are partiallyionized at physiologicalpH,
formingvarious anionic species. In addition,these anions form complexes
with metal ions of different
affinities.
The complex formation
with Mg?+ isparticularly
importantbecause of its high affinity for the ionized forms ofthese phosphate compounds. It is not negligible when the hydrolysis
reactionis studied under physiologicalconditions
for which a relatively
high concentrationof the cation (0.6-l mM; ref. 108) is required.
For this complicatedsituation,
the ATP hydrolysis
reaction is treated,by convention,
as having an apparent
equilibrium
constant (K,,,; often as
K’ or KObs in the literature)
K app = [ADP]l[Pi]/[ATP]where the concentrations
are those determined
analyticallyand include all
ionized and M8+-complexed
species of each component. In other words, any
effects of ionizationor chelation are ignored, so a value of Kapp is only valid
for a given pH and [Mg?]. The method of calculating Kapp based on information
about these conditions
has been formulatedby Alberty(3, 4).
The second difficultyis that it is almost impossible
to evaluate the Kappand hence the apparent
standard free-energychange of ATP hydrolysis
ina straightforward
fashion, because in the hydrolysis
reaction only a traceof ATP would remain at equilibrium.
Thus, indirect methods have been used
in which two or more reactions are coupled. The net effect is the hydrolysis
of ATP together with another reaction, the equilibrium
constant of whichis exactly known. The glutaminase-glutaminesynthetase reactions (22, 238)
and acetate kinase-phosphate
acetyltransferase
reactions (111) have beenused so far.
2. Heat of A TP hydrolysis
As for AE& direct measurement
is possible by calorimetry
with an appropriate
preparationof ATPase, which should be active under a variety ofconditions and behave as a true catalyst that does not bind either reactantsor products to an appreciable
extent at the end of the reaction.
Myosin was used in earlier studies (151, 225).5 In fact, myosin shows a

6 The AH value obtained in these studies (-20.0
has been used as the basis in var ious thermodynamic+ 0.5 kJ mol-‘) at pH 8.0 without
calculati .ons (Eqs. 3-5).

M2+

April
TABLE

1985

ENERGETICS

2. Enthalpy

OF MUSCLE

change f&r ATP

ATPASEhydrolysis

determined
AH/kJ

Temperature,

“C

pH

4
8
12
20

by calorimetry

mol-’

7.0

pH

8.0

16.8”
18.5
19.0”
20.3

25.2
26.9

Values obtained by Kodama et al. (155) with
6 PM A23187.
* With 10 mM MgCl,.

485

REACTIONSSR vesicles

in presenceof 4 mM MgCI, andhigh affinity for ADP and a low catalytic
activity(see sect. VI). Recently,
Kodama et al. (155) showed that the Ca2+-pump ATPase of SR vesicles isquite useful for the determinationof AH for the ATP hydrolysis
underphysiologicalconditions!
AlthoughCa’+, which is necessary to activate the
enzyme, is taken up by the vesicles, there is no net accumulationof thecation in the presence of a Ca ionophore such as A23187 or X537A when ATPhydrolysis
has been completed. In addition, the interactionof Ca2+ with ATP,
ADP, and Pi is negligible
comparedwith that of Mg2+, because a cation
concentration
as low as 10 PM is sufficient for full activationof the enzyme.
Thus the net effect may be regarded
as the ATP hydrolysis
when MgATP
is added to the SR vesicles in the calorimetricexperiment.
Althougha systematic study of the variationof AH with temperature,
pH, [M$+], and ionic strength has not been made, the values obtained so far
under various conditions are useful for the present analysis and summarizedin Table 2. The calorimetricresults are generally
in good agreementwiththose obtained by calculation,
providinga valuable confirmationof the correctness of the latter values and vice versa, and ACp for the ATP hydrolysis
could be calculated for the first time from the calorimetricresults. The best
estimate is 0.17 t 0.03 kJ. K-l mol-‘, which also agrees with the value assumed by Alberty (5).
l

C. Natureof High-Energy

Phosphate

Bond

Since Lipmann(170) proposed the concept of “energy-rich”
phosphatebonds, much experimental
and theoreticaleffort has been made to explain
why ATP as well as some other phosphate compounds are thermodynamically

6 In this work, P’,P’-di(adenosine-5’)pentaphosphate,enylate kinase (169), was used to prevent further breakdownof ATP (164).

which is the potent inhibitorof adof ADP formed from the hydrolysis

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KODAMA

unstable. In previous formulations
the high-energy
propertyof these compounds was thought to be mainly intramolecularin origin. Thus either singly
or together intramoleculareffects such as opposing resonance, electrostatic
repulsion,and electron distribution
along the P-O-P backbone might play
an importantrole in the large negative free energy of hydrolysis
of highenergy compounds.
George et al. (95), however, pointed out that the importanceof the solvent
water had been overlookedin these earlier studies. Analyzing
the thermodynamics of hydrolysis
of different
pH forms of pyrophosphate(PPi), acetyl
phosphate,and phosphoenol
pyruvate,
they suggested that differencesinsolvationenergy of reactants
and products made the predominant
contributions to the large negative free energies of hydrolysisof these compounds,
whereas the intramoleculareffects were of secondary importance.
This suggestion was later confirmedby the quantum chemical calculationof Haynes
et al. (117).
These studies indicate that if the hydrolytic
reactions of various highenergy compounds
took place in the gas phase (nonaqueous
environment),
reactionenergies would be strongly
positive.
In contrast,in the aqueous
phase the reaction energy would be negative, having values that are in good
agreement with available
experimental
reaction enthalpies.
The importanceof the solvation(hydration)effect has a most intriguing
bearing
on thereaction mechanisms of ATPases, because the enzyme proteins would probably
provide a catalytic environment
for the reaction that is grossly different
from those in the bulk aqueous phase. This problem is discussed in sections
VIII
and IX.

VI.

KINETICA.

Introduction

MECHANISMOFATP

HYDROLYSIS

BY

MYOSINAND

ACTOMYOSIN

The molecular entities responsible for muscle contraction
are the proteins
myosin and actin, which are arranged
separately
into the thick filaments
and the actin filaments in living muscle. The thick filaments have regularly
spaced projections
consistingof the globular
head of the myosin moleculethat contains the sites for ATP hydrolysis and interaction
with actin. During
muscle contraction
these projectionsof myosin heads form cross bridges
with the actin filaments, which attach and detach cyclically. As a result of
the interaction
the relative sliding force is developed between these filaments.
The energy for this physical process is provided
by ATP hydrolysis,which
is catalyzed by the molecularcomplex of myosin and actin. This is the actomyosin ATPase activity in vivo, which can be studied in vitro with purified
myosin and actin.

April1985

B. Contractile

ENERGETICSOF MUSCLEATPASE

REACTIONS

487

Proteins

The myosin molecule is large (M, 500,000) and consists of a long tailregion carrying
two globular
heads that can be visualized
by electron microscopy (76, 172, 215). The tail is insoluble
at low ionic strengthand isresponsible
for the aggregationof myosin into thick filaments.
Each of theglobularheads has an enzymatic site that binds ATP and subsequently
hydrolyzes it, and each has a binding site for actin. These two sites are distinct
but can interact with each other (see sect. vIIB3).
The myosin molecule from skeletal muscle consists of two polypeptide
chains with molecularweight of 200,000 (heavy chains) and four smaller
peptide chains with molecularweights from 16,000 to 27,000 (light chains)(84, 296). The light chains are divided by operational
convention
into twoclasses. One class of light chains can be selectively
released by treatment
with the thiol reagent DTNB. The other class of light chains is dissociatedat high pH and therefore
called the alkali light chains. Two distinct alkali
chains exist, alkali 1 (A,) and alkali 2 (AZ) with molecular weights of 21,000
and 17,000, respectively.
These two chains are the same except for an extra
40 amino acid residues in the NH2-terminal
region of A1 chain. There arethree types of light-chain
combinations
in myosin molecules: (DTNB)2+(Ad29 (DTW2+ @2)2 uw,
and (DTNB)2 + (Al) + (A2) (13~).
For many biochemical
purposes, the heads are separated from the tailby proteolytic
digestion (172), and studies can then be made on heads either
singly (subfragment
1, SF-l) or in pairs joined by a short part of the tail(heavy meromyosin,
HMM). These proteolytic
subfragments
are soluble ator below physiologicalionic strength, unlike parent molecules. Evidence obtained so far indicatesthat they retain the enzymaticand actin-binding
properties
almost unchanged
compared with those of the intact myosin?
The unique enzymatic property of myosin is its low ATPase activity thatis strongly activated by actin (see sect. VI@). The turnoverrate of the catalytic
cycle is around 0.03 s-l at 20°C under physiologicalconditions(0.15 M KCl,
5 mM Mg2+, at neutral pH). The situation may be analogous to that in restingmuscle in which interaction
with actin is prevented.
Actin is a relatively
small, globular
protein (& 43,000). The monomers(G-actin)have a strong tendency to form double-stranded
linear polymers(F-actin)at physiologicalionic strength.
It is this form of actin that exists
as the thin filament
in muscle and is used for experiments
in vitro. The
unique propertyof actin is its ability to activate
the ATP hydrolysisbymyosin. Under appropriate
conditions
the actin activationis several lOO-

7 Recently it has been shown that the heavy chain alone contains the catalytic
site forATP hydrolysis
and that neither class of light chains is essential for activity (254). From thispoint on, myosin refers to its head portion unless otherwise
specified.

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fold, which compares with a factor of ~1,000 for the relative turnoverrates
of muscle shortening
at maximum
velocity and resting muscle (see ref. 81).
Physiologicalinvestigationof muscle contraction
has largely concentrated
on frog muscle, whereas rabbit muscle has been the subject of extensive
biochemical
studies. It is desirable to correlate physiologicaland biochemical
data obtained with material
from the same biologicalsource for better understandingof the mechanismof muscle contraction.
Recently some efforts
have been made to isolate contractile
proteins from frog muscle and characterize their kinetic properties(79-81). Althoughfrog muscle myosin andits subfragment
are too labile to perform
extensive biochemical
studies (79),the data obtained so far indicate that the mechanismof frog myosin ATPhydrolysis
is similar to that of rabbit myosin.
C. Mechanismof A TP Hydrolysis

by Myosin

and Actomyosin

Kinetic studies have revealed
that the hydrolysis
of ATP in vitro bymyosin and actomyosin is complex and consists of a sequence of intermediate
reactions, which may be simplified
for this discussion as the cycle of reactions
shown in Figure 1. For more information,
excellent reviews are publishedalmost every year (e.g., refs. 1, 140, 184, 255, 274, 278, 281).
1. Myosin

when

ATPasereaction

The most characteristic
the reaction is started

feature of the myosin ATP hydrolysis
is that,by mixing an excess of ATP with myosin and

FIG. 1. Kinetic scheme for myosin and actomyosin
ATPase reaction. Inner circle represents
myosin ATPase cycle in absence of actin. Outer circle represents
ATP hydrolysis
by complexof actin and myosin. A, actin monomer in F-actin filament; M, single myosin head; T, ATP; D,
ADP. For simplicity,
all Z-step processes involving binding and release of ATP, ADP, Pi, andactin are shown as single steps.

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ENERGETICSOF MUSCLEATPASE

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489

then quenching
it with acid at intervals
to measure the progress of thereaction, one observes a rapid burst of Pi formation.
This phenomenon,
calledthe early phosphateburst, proved to be due to the acid denaturationof theprotein, releasing Pi from the myosin product complex that undergoes slow
dissociation
during the normal enzyme catalytic
cycle. Thus the myosin
ATPase cycle can be divided into two parts, the steps in hydrolysis
and thesteps in product release. This unique property
has facilitatedthe kinetic
analysis.
An importantfeature shared with a number of enzyme reactions is thatthe binding of a ligand occurs in at least two steps (for reviews see refs. 110,
143,144): collision-controlled
association followed by an intramolecularchangein the protein (isomerization).
The collision intermediate
is in rapid equilibrium with free forms of the enzyme and the ligand; the equilibrium
constant
is usually on the order of 103-lo4 M-l. The next step, isomerization,
usually
has a large equilibrium
constant, resulting in the tight binding of the ligand.
It is in this step that a unique change in protein conformation
takes place,dependingon the nature of the ligand. Note that in the scheme shown in
Figure 1, steps involving
interactionof the protein with the ligand are known
to occur by such a two-step mechanism(9, 17, 42).
The first step in the reaction between ATP and myosin is the binding(step 1 in Fig. 1). In this reaction the forward
rate of the isomerizationisvery fast (>l,OOO s-l; see refs. 44, 145) and the reversal is very slow (~0.01s-l), so the overall equilibrium
constant is on the order of 1011 M-l (35, 101).
In addition
the rate of ATP dissociationfrom myosin is much slower than
the rate of ATP hydrolysis(step 2) and release of products (steps 3 and 4).
Thus the binding of ATP to myosin is effectively
irreversible.
The next hydrolysis
step is characterized
by a rather small equilibrium
constant that ranges between 1 and 10 depending on conditions(12,45,273).
This is a remarkable
contrast to the situationin free solution, in which theequilibrium
strongly favors the hydrolyzed
state (see sects. v and VIIIBZ).
The forward
reaction is moderately
rapid; the rate constant is in a range
between 20 and 200 s-l (45, 92, 145, 275). Thus the hydrolysis
is faster by atleast two orders of magnitude
than the rate of the overall catalytic cycle.
When the ATP is hydrolyzed
on the myosin site, changes in microenvironments
of protein side-chaingroups take place, as detected by various
methods. These include a varietyof spectroscopic
methods (19, 204, 300),
measurementsof the deuterium-hydrogenexchange rate (310,311), and reactivity of protein side-chain groups toward the specific modifying
agents (210,289). Results of recent kinetic studies favor the view that the hydrolysis
step,rather than the binding, is responsible
for the proton release (41, 43) that
occurs through the shift of pK values of the ionizing groups in or near thecatalytic site of the protein (274).
The conformationalchanges in the myosin molecule associated with thehydrolysis
are partiallyreversed when the myosin-productcomplex slowly
dissociates Pi and converts to the myosin-ADP(Me D) complex (step 3). This

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reactionis the rate-limiting
step in the ATPase cycle at temperatures>lO”C (13). Interestingly,
however, its apparent rate shows little temperaturedependence.
On the other hand, the rate of subsequent
ADP dissociation(step 4) is strongly dependent on temperature(Q10 > 4 between 10 and ZO”C),
and indeed it becomes comparablewith that of step 3 at temperatures
6°C.
The isomerizationthat precedes the dissociation
is probably the stepthat is influenced
by temperaturein such an extraordinaryway (see sect.
VIIICI).

As for the H+ release, the major contribution
is made by step 3, whichis accompanied
by Pi dissociation,
but a fractionof H+ is liberated
in step
2, and the same amount of H+ is absorbed in step 4. In Table 3 the equilibrium
constants for the intermediate
steps of the myosin ATPase cycle are listed.

2. Interactionof myosinwith ATPanalogues

A large variety of ATP analogues has been synthesized during the lasttwo decades (321). The analogues with modified triphosphatemoiety havebeen widely used in studying the mechanismof ATP hydrolysis
by myosin
and actomyosin(281) and the structuraland mechanicalpropertiesof glycerinatedmuscle fibers (102). Relevantto the present analysis are adenyl5’-yl imidodiphosphate(AMPPNP)and adenosine 5’-0-(3-thiotriphosphate)(ATP+).
In the former the nonbridging
y-phosphoryl
oxygen atom of the original
ATP is replaced by sulfur, so that the kinetics of hydrolysis
by myosin isaltered. The hydrolysis products are ADP and thiophosphate.
Thus the bindingof ATPyS to myosin is as fast as that of ATP, but its hydrolysis
rate isreduced by some two orders of magnitude
and is in fact rate limiting(10,
13, 92, 100). The predominantsteady-stateintermediateof the myosin-catalyzed hydrolysis
is the myosin-substratecomplex M ATP+in contrast
with the myosin-products
complex Me ADP Pi in ATP hydrolysis.
However,the subsequent product release takes place much faster than the corresponding
step in the ATP hydrolysis.
In the calorimetricexperiments
this analogue
was used to study the substrate-binding
step, as described in section VII.
The structureof AMPPNP
is very similar to that of ATP except thatthe ,&y-bridging
oxygen atom of the latter is replaced by an imino (NH)group (322); hence the analogue is nonhydrolyzable(323).
ll

3. Actomyosin

ATPasereactionOn the basis of pre-steady-statekinetic experiments,
Lymn and Taylor(175) proposed a simple mechanismof the ATP hydrolysis
by actomyosin,
which is essentially the pathway of ATP hydrolysis consisting of the following
steps from Figure 1. In this mechanism,
ATP causes rapid dissociationofApril1985

ENERGETICSOF MUSCLEATPASE

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491

actomyosin (steps 5 and IO), which is followed by ATP hydrolysis
on myosin(step 2). The myosin-products
complex then reassociates with actin (step ll),
and the actin causes rapid release of the products (steps ‘7 and 8). Because
this product release is much faster than the corresponding
step with myosin
alone, the rate-limiting
step of myosin ATP hydrolysis
is bypassed in thepresence of actin.
Thus this scheme elegantly explains the apparently
contradictory
classic
finding that actomyosin is essentially dissociated at ATP concentrations
normally used to measure the ATPase activity,
although the rate of hydrolysis
is much higher than for myosin alone. In addition a very attractive
featureof the model is that myosin and actin undergo dissociation-association
reactions for each catalytic cycle of ATP hydrolysis,
providinga possible way
to correlate
the biochemical
events (intermediate
steps of ATP hydrolysis)
with structural
events during muscle contractionthat involve cyclic dissociation and reassociationof the cross bridges.
Althoughsubsequentstudies confirmedthat the originalLymn-Taylor
scheme fits the kinetic behaviorof actomyosin
at low actin concentrations,they faced serious difficulties
in explaining
the steady-state
ATPase rate asa function of actin concentrationand kinetic behavior of various intermediate
states at higher actin concentrations.
The scheme has been modified
andexpanded by kinetic experiments
and equilibrium
studies have been performedin recent years.
The addition of a step in which ATP is hydrolyzed
on actomyosin(step
6 in Fig. l), i.e., without
dissociationof actomyosin,
is fundamentally
important (258). This nondissociating
pathway was, in fact, originallyindicatedby Tonomura
and his collaborators
as early as the late 1960s (see ref. 278,
p. 191-235). Now there seems to be little doubt that the ATP hydrolysis
occurs without dissociationof actomyosin, particularly
under conditions with
low ionic strength.
Another modificationthat has long been claimed by Eisenberg
and coworkers (1, see also ref. 274) is an inclusionof the refractory
state. This
state originallyreferredto the myosin state, which cannot interact
withactin, and was introduced
to explain the steady-state
ATP hydrolysisbyactomyosin(75) but now refers to the state before the rate-limiting
step,
whether myosin is dissociated or associated (1). It is still controversial,
however, whether the refractory
state is really needed.
It must be admitted
that the present state of our understandingof theactomyosin ATP hydrolysis
is by no means complete and that rate constantsfor various steps, particularlytransitions
between nondissociatedstates, have
not yet been determined
unequivocally.
However, many attempts have recently
been made to determine
the equilibrium
constants (Ki values) for the steps
at which actin binds to the various
myosin intermediate
states. If thesevalues were known, those for transitions
between undissociatedactomyosinintermediates
could all be estimatedby applying
detailedbalance to thecyclic processes (sect. IIkt5).

492

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65

Actin binding to nucleotide-free myosin has, of course, been most thoroughly studied under various conditions. Recently, accurate kinetic analysis
has also been made possible (188). The second-best-studied step is the actin
association to the M l D complex (step 12). The reported values of Klz (105,190) agree well with each other. Thus the dissociation constant of ADP fromthe A M D (step 8) can be calculated. The remaining two actin association
steps are hard to analyze precisely. Semiquantitative
estimation of KIO andKll, however, may be made based on the results obtained by Stein et al.
(258). They observed that the actin binding is weakened -3,OOO-fold in thepresence of ATP or ADP + Pi, where the nucleotide site is probably occupied
either by ATP or its hydrolysis products. Thus a reasonable estimation isll

Klo 11 Kll N lo4 M-l

This estimation is close to the value obtained by a study with a techniqueof fluorescence-correlation
spectroscopy (27). Accordingly, the equilibrium
constants for the ATP hydrolysis on actomyosin complex (step 6) and the
Pi dissociation (step 7) can be estimated. The equilibrium constants estimatedin this way are listed in Table 3.
A most crucial aspect of the actomyosin ATP hydrolysis is that thenucleotide and actin-binding sites on a myosin head are functionally linked

3. Equilibrium
constants for intermediate
and actomyosin ATPase reactions

TABLE

steps of myosin

Equilibrium
Steps

Reactions

Constants

1
2
3
4
5
6
7
8
9
10
11
12
Completionof cycle

ATP binding to M
ATP splitting on M
Pi dissocitition
from M ADP Pi
ADP dissociationfrom Ma ADP
ATP binding to A l M
ATP splitting on A M
Pi dissociationfrom A M ADP Pi
ADP dissociationfrom A. M ADP

5 x lO+‘l M-’
10
0.1 M
lO-‘j M
5 x lO+8 M-’
10
10 M
lo+ M
1O+7 M-’
1O+4 M-’
lO+4 M-’
1O+6 M-’
5 x 1O+5 M

l

l

l

l

l

l

l

.pi
~M=ADP
ATP hydrolysis

Refs.

35, 10112, 45, 281
281
154, 281, 288

104, 105, 120, 190
1, 27, 258
1, 27, 258
105
238

Keeping overall consistency(i.e., Kapp of ATP hydrolysis),
equilibrium
constants
wereestimated on round numbers from reported values that were obtained under different conditions.
Values are referred to conditions of 100 mM KCl, l-5 mM MgC&, pH 7-8, and 20-25°C. Equilibrium
constants
for steps 5-8 were calculated as described in section IIA5.

Aprilzwi

ENERGETICSOF MUSCLEATPASE

493

REACTIONS

so that binding at one site influences the other antagonistically.
For example,
as described above, the strong interaction
between actin and myosin is weakened by about three orders of magnitudein the presence of ATP or ADP +Pi (27, 258). Actin in turn weakens the association of the products with thenucleotidesite. Much weaker reduction
is seen with ADP alone (105, 189).
On the basis of these findings together and those obtained with PPi or ATP
analogues
such as AMPPNP
and ATPyS, it can be generalizedthat theaffinity of myosin heads for actin is altered cyclically while they pass througha series of intermediate
states during the ATP hydrolysis
cycle. In addition,actin bound to a distinct site modulates the chemistry of ATP hydrolysisatthe nucleotide site and thus facilitates
product dissociation.
In other words,
the myosin intermediates
are roughly divided according to their affinity for
actin into states that bind actin strongly (M and M D) and weakly (M ATP
and M D Pi). These correspond,
respectively,
to strongly
actin-associatedstates (A M D and A M) and weakly associated states (A M ATP andA M D Pi) (72).
A kinetic difference
between weakly and strongly associated states isthat the former dissociates from actin much faster than the latter (188). As
in the case of the interactionof myosin with nucleotide ligands, the bindingof actin to myosin occurs by a two-step mechanism regardless of the natureof the ligand bound to the myosin nucleotidesite. It involves
a collisioncontrolled
association followed
by a protein isomerization(102). Again it is
the isomerization
step that is affected by the nature of the bound nucleotide
and determines
whether
the association with actin is weak or strong.
l

l

l

l

VII.

l

l

l

l

l

l

l

l

CALORIMETRY

OF ATP HYDROLYSISBY MYOSINAND

ACTOMYOSIN

A. Introduction
To evaluate the enthalpy
and entropy contributions
to the free-energychanges of intermediate
steps of the myosin ATP hydrolysis,a few efforts
have been made to obtain necessary informationfrom the temperaturedependence of the equilibrium
constants with the van’t Hoff relation.
For example, Arata et al. (8) did such an analysis for the ATP hydrolysis
by HMMand noted that the formationof a myosin-productcomplex from myosin(HMM) and ATP was associated with a large increase in entropy. As often
suggested, however, kinetic measurements
are not generally
precise enoughfor evaluationof the enthalpy changes (see sect. III); hence more quantitativearguments
may be difficult.
Thus the requirementof calorimetricanalysishas become obvious.
In this section, results of calorimetricstudies of the myosin ATP hydrolysis performedby my laboratory(153, 154, 158-160) are summarized
together with an historical
overview
and brief descriptionof the method ofanalysis.

494
B. Historical

TAKAO

KODAMA

Volume 65

Overview

The pioneeringcalorimetricwork on myosin ATPase was reported
byYamada et al. (312). They mixed stoichiometricamounts of HMM with ATP
or ADP in an LKB precision calorimeterand followed the subsequent
heat
production
with a time resolutionof -10 s. When ADP was added, a rapid
heat production was seen. As ADP binds tightly to HMM, this heat presumably
comes largely from their binding reaction (the reverse of reaction 4 in Fig.
1). When ATP was used a similar rapid heat production
was seen, followed
by a slower exponential
heat production.
The time constant of this slow phase
was the same as for the release of Pi from the myosin-productcomplex(reaction 3). This seems to show that reaction 3 is strongly exothermic.
The
rapid heat production
comes presumably
from reactions 1 and 2 together.
The implicationfrom the results of Yamada et al. (312) that the ADP
binding is strongly exothermic
was challenged
by Goodno and Swenson (99)in a detailed calorimetricstudy. They reported that the heat of this reaction
was small, between -4 and -12 kJ/mol. The question was reexaminedbyKodama and Woledge (159) using a calorimetrictitrationtechnique(sect.
IIICI).
Their result clearly showed that the ADP binding to native myosin
is strongly exothermic
and that the heat of reaction was definitely
greater
at 12°C than that at OOC. However,
the observations
at 25°C suggest thevalue does not continue to increase with temperature.
They suggested that
reliableresults were hard to obtain at 25°C because of instabilityof theprotein at this temperature.
Measurementof the heat of ADP binding tomyosin at 25°C was later made by Banerjee
and Morkin (18) with a flow
calorimeterthat can reduce the exposure time for myosin at high temperatures. The result indicates that the binding heat at 25°C is indeed similar
to the value obtained at 12°C by Kodama and Woledge (159). Kodama et al.
(158) extended the calorimetrictitration
study to HMM, SF-l, and myosin
filaments and obtained the same results for myosin in these different
states.
These results have left little doubt that the ADP binding, i.e., the reverseof reaction 4 of the myosin ATPase cycle, is exothermic and hence the forward
reaction is endothermic,
which is in fact consistent with the classic observationby Martonosi
and Malik (193) that the equilibrium
constant of the ADP
binding to myosin markedly
decreases with temperaturerise. The effect oftemperatureon the thermodynamics
of the nucleotide binding was recently
reexamined
by Kodama (154; sect. VIIIC~).
As for the interactionof myosin with ATP, a Calvet calorimeter
was
initially
used, which gave a time resolutionof ~20 s (304). Subsequentlyacalorimeterwith improved
time resolution
was used (sect. IIIBQ; 160). Thesestudies confirmed
the exothermicityof reaction 3 as suggested by Yamada
et al. (312). On the other hand, Swenson and Ritchie (262) observed a rapid
heat absorption
and a subsequent slow heat production
on addition of ATP
to native myosin. The rapid heat absorption
at the beginningof the myosin/
ATP interaction
has not been confirmed
by more recent work with a tem-

Apd

1985

ENERGETICSOF MUSCLEATPASE

495

REACTIONS

perature
range between 4 and 23”C, which indicates rapid heat production
at the beginning(153).
There is another point to be noted for calorimetricstudies of myosin
and other contractile
proteins. It has been known for 10 years that part ofthe energy produced during contractionof skeletal muscle does not comefrom the hydrolysis
of ATP, the hydrolysis
of creatine phosphate,or thereactions that resynthesize
these energy sources (47,132,166).
A hypothesis
has been suggested that this chemically“unexplained”
energy comes fromchanges in muscle proteins on activation.
The results of calorimetricdetermination
show large heat changes accompanying
various changes in the stateof the actomyosin
system and support the hypothesis(47, 132).

C. Kinetic Analysis of Heat Production

During Myosin/ATP

Interaction

In the following
discussion AHi denotes the reaction heat of the ith stepin the simplified
kinetic scheme of myosin ATP hydrolysis(Fig. 1).
Accordingto the kinetic mechanism
outlined in section VICZ, when ATP
is mixed with excess myosin, a mixture of M ATP and M .D Pi complexes
forms instantaneously
in terms of the time scale of calorimetry.
The heat
produced by this rapid phase (hfast) is described by
l

hfast

=

(-AHI)+

K2/(K2+l

1J(-A-H2)(4)

Because the dissociationof M .D would be negligible
under the conditions
where myosin is in excess over ADP, the heat produced during the slower
phase (hslow), is given by

hslow

=

WG

+

~Fmd

+

(-Am

(5)

The rate of this slow heat production
is controlled
by the rate constant of
this step (k3). The heat produced by time (t) after mixing myosin with ATP
is then described by

hohs

=

hfast

+

hs10w[~-

exp(-k3t)1(6)

Because the heat for the hydrolysis
of ATP (-AH*&
equals the sum of theheat of four intermediate
steps, the total heat produced (ht,tal), is expressedby combining
Equations 4 and 5

htotal

=

hfast

=

(-AH,,,)

+

h3low

-

(-aN,)

This equ ation indicatesthat AH, can be d eterm .ined from htotal, because
AHATP is evalu ated in se parate experim .ents (sect. 1vB2). Thus, cal .orimetric

496

TAKAO

KODAMA

Volume 65

experiments
will yield estimationof k3 and AHd, and provided
that the K2
value is known, Equations 4 and 5 give estimates of AH1 + AH2 and AHS.
Appropriate
values of Kz have been provided by Taylor (273) and Chock andEisenberg(45).
Another type of calorimetricexperimentthat is possible to perform andwould provide useful information
is to follow the heat production
after mixing
ATP with M ADP, which can be generated in the calorimeterby the reaction
just described. The reaction sequence is similar but preceded by the dissociation of M D (step 4), and the overall reaction is simply the hydrolysisofATP. The time course of heat production
is divided into two phases-the
rapid phase, equal to (-AHd)
plus hfast given by Equation 4, and the slow
phase, equal to the hslowof Equation 5.
With the calorimeter,
the response time of which is -1 s (sect. III&?),
separate evaluationof AH1 and mz is not possible with ATP itself because
the cleavage reaction (step 2) is too fast (see sect. VICI). One way of obtaining
an estimate of AH, is to use an ATP analogue that is split more slowly. If
the rate of splitting/& < 0.3 s-l, which is the upper limit for the calorimeterto follow, the time course of heat production
would be composed of hfast andhslow. The fast phase should correspondto binding
and the slow phase to
splittingand product release together. ATPyS was used in our work (153,
160) because the rate of splittingof this analogue is ~0.2 s-l (lo), which iswithin the possible time resolutionof the instrument,
and the estimate of
AH1 was thus obtained as described below.
It is, of course, desirable to measure the heat of binding of ATP itself,
but this is one of the most challenging
problems
in the energeticsof themyosin ATP hydrolysis
as well as calorimetry
in general, because one needs
to construct a stopped-flow
calorimeterwith a time resolution
within 50 ms
and sufficient sensitivity
to measure a heat pulse as small as 0.5 mJ.
Finally a correction
to the AHi values thus obtained must be made forthe heat produced by interactionof the buffer components with proton released
or absorbed (see sect. IIICZ). The magnitudeof such proton movementshasbeen determinedwith a pH electrode in separate experiments
via the protein
solution with a reduced buffer concentration(160). The amount of H+ released
for the ATP binding or splitting,i.e., the rapid phase, is -0.3 mol/molofATPase site, and the same amount is absorbed by ADP dissociation(step4). The Pi dissociationis accompaniedby H+ release of l.O/site. These results
agree well with those obtained by other workers (274). The necessary corrections to AHi values can then be made accordingly.
llD. Calorimetryof MyosidATP

Interaction

Woledge and I (160) observed that on interactionof ATP with excess
SF-l there was a rapid heat production,
followed by a slower heat production,
as in the reaction sequence shown in Fig. 2A. The slow heat production
couldAprilENERGETICS

1985

A

M + ATPOF MUSCLE

MeADPa+ ATP

497

REACTIONS

fast
I

M*ADP

ATPASE

Pi

b

slow
I b

NADP

fast
M eADP* Pi

MeADP

t*

fast
ATP/S

M-ATPIS

slow

M*ADP

I

FIG. 2. Schematic
diagrams of calorimetricresults of interactionof myosin with ATP and
5’-0-(3-thiotriphosphate)
ATPTS. Reactions were started in calorimeteras indicated at far left.
Myosin (M or M ADP) was excess over ATP or ATPyS so that end-productwas Me ADP in allcases. Up arrow represents
heat absorption
and dcnon arrows represent
heat production.
Figs.
in ellipses refer to heat values in kJ/mol of ATP at 23°C and are correct within&5 kJ/mol.
[Based on data of Kodama (153) and Kodama and Woledge (160).]lbe fitted by a single exponential,
as expected from Equation
6. The heat of
ADP binding was estimated by subtracting
the value of (-AH*&
from thetotal heat. The value of AH4 thus obtained is +83 kJ/mol at 23”C, which isin excellent agreement with that obtained by a calorimetrictitration
method(154). The slower heat production
accounts for about two-thirdsof the totalheat observed, and the rate of this phase agrees with that for the dissociationof Pi from the M l D.Pi complex (step 3), as confirmedby the measurementof the UV-absorptionchange (160) and the H+ release (153).
When ATP was added to myosin, which should have existed as the M D
complex, a fairly rapid heat absorption
was observed at the beginning;it
was then followed by a slower heat production(Fig. 2B; 153). By quantitative
analysis one finds that the total heat equals the heat of ATP hydrolysis,
andthe time course of the second slower phase is approximately
the same as
when myosin withoutbound nucleotide(M) is the starting
material.
ATPbinds to myosin much more strongly than does ADP, so the former will chasethe bound ADP from the myosin. Because the ADP dissociation is endothermic
and is faster than the Pi dissociation,
the heat record obtained on the additionof ATP to Ma ADP is interpreted
as indicatingthat the rapid phase of thel498

volumeTAKAOKODAMA

65

myosin ATPase catalytic
cycle (steps 4 + I + 2) is endothermic
and theslower phase (step 3) is strongly exothermic.
(Note that it is merely a conventional
practice to take the free enzyme as the starting
point of the catalytic cycle.)
In contrast to a relatively
small heat productionin the rapid phase of
the ATP/myosininteraction,a large heat burst was observed on the additionof ATPTS, which was followed
by a slower heat production,
as shown in
Figure 2C (153,160). The time constant of the slower phase showed reasonableagreementwith that for the rate of ATPyS splitting(10; T. Kodama, D.
Gower, and R. C. Woledge, unpublishedobservatioh).
These results indicatethat the binding of ATPrS to myosin is strongly exothermic and that splitting
and the subsequent release of the product leading to the formationof M .D
complex is also exothermic,
but only moderately.
The heat of ATPyS binding
was evaluated,
as in the case of hfast for ATP hydrolysis.
On the basis ofremarkablesimilarities
in the kinetic behaviorof the actomyosin
systeminteractingwith ATP and with ATPyS (sect. VICZ), it is concluded that thebinding heat thus obtained is an estimate of AM, for ATP.
The calorimetricresults calculated with Equations 4-s are summarizedin Table 4. Two remarkablefeatures are thus revealed by calorimetry.
First,
large enthalpy changes, compared with the enthalpy change for the overall
reaction, accompany intermediate
steps of the catalytic cycle, and an exothermic step alternateswith an endothermic
step. Notice particularly
that
the actual splitting of ATP on myosin is strongly endothermic,
which contrasts
with the hydrolysis
in free solution that is moderately
exothermic.
Second,the enthalpy change for each step shows a large temperaturedependence,i.e., large heat-capacitychanges accompany the intermediate
steps. In addition, on close inspection it can be seen that the heat-capacitychanges show
peculiar
temperaturedependencies.
The implicationsof these results are
discussed in section VIIIC.
TABLE

myosin4. Reaction heats for
ATPase reaction

intermediate

steps of

Temperature,
Steps

1
2
3
4
1+2+3+4

Reactions

ATP binding
ATP splitting
Pi dissociation

ADP dissociation
ATP hydrolysis

“C

4

12

23

-65
67
-73
54
-17

-92
82
-81
72

-89
51
-52
70
-20

-19

Data for 100 rnM KCl, 10 mM MgCl,, pH 8.0. All values (kJ/mol)were corrected for heatfrom reaction of protons released or absorbed with buffer, assuming that -0.3 mol H+ is released
by step 2 (41) and the same amount is taken up by step 4, and 1.0 mol H+ is released concomitantwith step 3. Heat values for ATP hydrolysis
are from Table 2.

1985

ENERGETICS

E. Calorimetryof Myosin/Actin

April

OF MUSCLEATPASE

499

REACTIONSInteraction

Relatively
little calorimetricwork has been done on the reactions of theactomyosin cycle. The fact that actomyosin hydrolyzes ATP much more rapidly than does myosin alone is the major difficulty in such calorimetricstudies.
In addition,a simple calculation
illustrates
anotherdifficultyin the experiment.
Suppose a calorimeter,
which could measure a heat productionof 2 mJover a period of a few seconds, were used to measure the heat effect of -40
kJ/molaccompanying
an intermediatestep (or steps) of the actomyosin
cycle. The amount of actin needed to produce a detectable heat would thenbe calculated to be on the order of 50 nmol, which is equivalent
to 2 mg actin
in 1 ml of reaction in the calorimeter.
As is well known, the actin solution
is too viscous to achieve effective mixing suitable for kinetic analysis of heatproduction.
To date, only some preliminary
experiments
have been performedby Woledge and colleagues (personal communication;
see also refs. 47, 304).
The interactionof myosin with actin in the absence of a nucleotide
isprobably not an essential step in the actomyosin cycle, but the understandingof its thermodynamics
is importantfor various reasons. Because the reaction
strongly favors the bound state, the calorimetrictitrationtechnique can be
In an actual calorimetricrun, a highly concentrated
solutionused (sect. II&Z).
of SF-1 or HMM was added stepwise to the F-actin solution. The reaction
is moderately
endothermic,
AH is +30 to +40 kJ for each mole of myosinsite binding actin at 12°C. The AH is more positive at OOC. Thus the bindingof actin to myosin is driven by a large increase in entropy and accompanied
by a substantial
decrease in heat capacity. A preliminary
estimate of ACp
is about -3 kJ/mol. These large changes in entropy and heat capacity areprobably due to expulsion of water from the area in which the two proteinsapproach close to each other.
The reverse of reaction 8 (ADP binding to A M) also has been studied
by the calorimetrictitration
method. In this experiment,
however, it is moredifficultto obtain quantitative
data as the extent of the reaction, i.e., theformationof the ternary complex A M D must be determinedin a separate
experiment.
The result obtained indicates that the heat effect is very small(<lo kJ/mol) in contrast with the large heat productionin the corresponding
reaction of the myosin cycle (the reverse of step 4).
l

l

VIII.

ENERGETICCHARACTERIZATIONl

OF ACTOMYOSIN

ATPaseSYSTEM

A. Introduction
With all the results for the equilibrium
constants (Table 3) and reaction
heats (Table 4) of the intermediate
steps, it is now possible to depict thethermodynamic
profiles of the myosin and actomyosin
ATPase reactions.

500

TAKAO

The free-energy
been considered

KODAMA

Vohmechanges for the intermediate
steps of these reactions
previously(73, 102, 255, 274, 302).

1. Basic free-energy

levels of myosin

ATPase65

haveintermediates

The basic free-energy
levels of the myosin ATPase intermediatesareshown in Figure 3 on the basis of the values of the equilibrium
constants
listed in Table 3, with an assumptionthat concentrationsof ATP, ADP, andPi are taken as 5, 0.05, and 1 mM, respectively.
These values pertain
toconditions in muscle in vivo and are generally thought to be effectively clamped
constants (47, 48, 90).
As described in section IIA~, the basic free-energychange is closely
related to the kinetics of the transitions
between the different
intermediate
states. According to Simmons and Hill (253), in the basic free-energy
diagrama downwardchange favors flux throughthe system in the directionof theoverall drive (ATP hydrolysis
into ADP and Pi), whereas an upward change
opposes it. It is the downward
basic changes that constitutethe stochastic
drive at the level of the intermediatein a reaction. Two main features ofthe myosin ATP hydrolysis
are illustrated
in the basic free-energy
diagram(Fig. 3): I) the binding of ATP to myosin constitutes
the major drive of theoverall reaction; 2) the Me ATP and M ADP l Pi states are essentiallyinequilibrium(isoenergetic).
l

2. Basic free-energy

levels of actomyosin

ATPaseintermediates

The basic free-energy
diagram of actomyosin
ATP hydrolysis
is shown
in Figure 4. In addition
to assuming the same values of ATP, ADP, and Pi

AG

I

for

ATP hydrolysis

T
p M-T
1

20 kJ mol

-1

FIG.
3. Basic free-energy
diagramfor
myosin
ATP hydrolysis.
Basic free-energychanges for transitions
between reaction intermediates
were calculated
as describedinsect. IIA~ with equilibrium
constants
listed inTable 3. Concentrationsof ATP, ADP, and Pi
were assumed to be 5, 0.05, and 1 mM, respectively.

April 1985

ENERGETICS

Non-dissocia

OF MUSCLE

REACTIONS

Dissociating/reassociatingt ing pathway

AG

ATPASE

501
pathwayfor

ATP hydrolysis

A*M

ATP hydrolysis.
Calculation
was made
FIG . 4. Basic free-energy
diagram for actomyosin
in same way as described in Fig. 3, except actin concertration
was assumed to be 1 mM.

concentrations
as in the myosin ATPase diagram, it is necessary to assume
a value of the actin concentration.
The value of 1 mM is used in accordancewith Sleep and Smith (255) and Goody and Holmes (102). This value is notmuch different from the overall average concentrationin muscle fibers (-0.2
g actin/g myofibril
protein, equivalent
to 0.7 mM) (64,320). As seen in Figure
4, there are two major steps that are associated with large falls in the basic
free-energy
level, ATP binding to the A. M complex and Pi dissociationfrom
the A. M D Pi complex. These two steps correspondto the transition
fromthe strongly to weakly associated states of actomyosin
and to the transitionin the oppos lite direction.
An attractive
hypothesisthat comes out from this fact is that thesetransitions
would be possible candidates for the cross-bridge
movement
that
actually produces force in contracting
muscle. This should be considered,however, in taking into account the constraints
introducedby the lattice oforganized myofibril structure and the observed mechanical behavior of muscle.
Discussion of this problem is beyond the scope of this review, and readers
are referred
to several recent reviews (72, 73, 102, 280).
It is obvious that the large equilibrium
constant for the binding of ATP
to the actomyosin complex is primarily
ascribed to the intrinsic strong bindingof ATP to myosin. On the other hand, the thermodynamicallystable natureof the M D Pi state is responsible
for the relatively
large energy fall at the
Pi dissociation
step in the actomyosin
ATP hydrolysis.
Thus it seems quite
appropriate
to concentrateon these two steps in the actomyosin
ATP hydrolysis. In addition, the nature of the strong association between actin and
l

l

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l

502

TAKAOKODAMA

Volume 65

myosin and the mechanismof interaction
nucleotide site within the myosin molecule

between the actin site and theshould be considered.

B. Thermodynamic

ProLfiles of Myosin

A TPase Hydrolysis

How then are these characteristicfeatures of the myosin ATPase hydrolysis accounted for in thermodynamic
terms? This question is the thermodynamic inquiry into the nature of the various forces involved in stabilizingthese myosin states and their relative
strength.
The unitary
quantitiesofthermodynamic
parameters
for the intermediate
steps of the ATPase cycle
are listed in Table 5 for this purpose.
I. Nucleotide

binding

The fundamental
reason that ATP binding to myosin is the major driveof the myosin ATP hydrolysis is the extremely large value of the equilibrium
constant (loll M), which is equivalent
to AGu of about -80 kJ/mol. This large
unitary free-energychange is completely
accounted for by a large favorable
enthalpy
change (AH, = -90 kJ/mol).
Because the accompanying
A& issmall, the Me ATP is described as a state stabilized by a large decrease ofenthalpy (internalenergy). A favorable
AG, for the binding of ADP to myosin(the reverse of the dissociationin the ATPase cycle) is also dominatedby alarge negative
enthalpy
change, but the opposingchange of entropy(AS, < 0) is much larger in this case.
As described in section IVB, thermodynamics
of the binding of ATP or
ADP to myosin, like the ligand binding to proteins in general, is conveniently
treated in the following
four processes (which do not necessarily take placein sequence).
5. Thermodynamic
parametersof myosin ATPase reaction

TABLE

for

intermediate

steps

ReactionsAG,*kJ mol-’mu
kJ mol-’AS,,*
kJ K-’ mol-’ATP binding
ATP splitting
Pi dissociation
ADP dissociation
ATP hydrolysis

-76
-6
+15
+44
-23

-89
+51
-52
+70
-20

-0.04
+0.19
-0.23
+0.09
+0.01

kJ

l

AC,, ,t
k-l
mol-’
l

-0.45
-2.8
+2.6
+0.4
-0.2*

Values are expressed in unitary quantities
and for 100 mM KCl, 10 mM MgClz, pH 8.0,
* Calculated from Table 3 as described in section II.
and 20-24OC. See Table 1 for definitions.
$ Calculated from data of Kodama et al. (155).
0 Calculatedt Calculated from Table 4.
from values for other reactions.

AprilI.WS

ENERGETICSOF MUSCLEATPASE

REACTIONS

503a) Trunsji3r $ n?ccleoticjleJ’ror~~, h& soZ?)enf f;o myosiz site. Accompanying
this process,’ water molecules that have probably
been oriented around theMg2+ nucleotide and protein groups constituting
the myosinsite are releasedI(as, > 0).
b) Inte~ractim
tcf ‘r/t yosin site. A part of the enthalpy loss for the nucleotide
binding could be ascribed to the interactionof the purine ring of adeninewith the protein moieties. However,
because myosin does not have an appreciable affinity for AMP, it seems that the pyrophosphate
structureplays
a far more importantrole in both the binding and the binding-induced
conformation
change of the protein. In fact the relatively
strong binding of PPi(AG N -50 kJ/mol; ref. 105) is also accompanied
by a large negative
AH,(R. C. Woledge, personal communication).
’
Recently, Matsumotoand Morita (195) made a spectroscopic
study ofthe mode of binding of Mg”+ to myosin. The result indicates that, althoughstrong binding of the cation only occurs in the presence of a nucleotide (e.g.,
ATP, ADP, or AMPPNP),
the free cation is bound to the active site independentlyof the bound nucleotide.
This seems to contrast with the generalview that the Mg2+ -complexed form of ATP is the true substrate of myosin
ATPase (234, 297). If in fact this were the case, one should take into accountthe energy changes accompanying
the dissociationof the Mti+ and ATP fromthe complex on the enzyme-abtivesite (i.e., an exothermic
process in aqueous
environment;
see ref. 4) and those for the binding of the cation and the Mg2+free nucleotide to the site. No calorimetricexperiment
relevant
to this point
has been made.
c) Buryin~gsite *withbow&
nucleotide
in ,interior
qj’ protein molecule.
Several lines of evidence indicate that the Mg2’-nucleotide
complex boundto myosin is buried within the protein and inaccessible to bulk solvent (11,185). This process is probably a part of a binding-induced
conformation
changeand may involve some dehydration
phenomenon(AS;, > 0).
ccrr&mutitm
chlange. Judging
from the fact that ATPd) Bin(~,irL;c/-irlduced
binding to myosin dramaticallyweakens the binding to actin, it is generally
believed that a certain conformationalchange must accompany the formationof the Ma ATP complex. However,
because it is not easy to trap the M ATP
state for conformational
analysis because splitting of bound ATP is too fast,
there has been little evidence that this state assumes a unique conformation.
On the other hand, the M ADP state has been rather well studied by various
methods, as described in section VICZ, and it may be inferredthat the overall
conformationin this state is more compact than that in the nucleotide-free
M state. If a protein molecule takes up a compact conformation,
it would be
associated with a net increase in weak interactions
within the molecule (e.g.,ll

8 In regard to the unitary quantities of the thermodynamic
parameters,
the thermodynamic
contribution
from the loss of rotational
and translational
freedom of the ligand may not betaken into account in the first approximation(ref. 70, p. 367).

504

TAKAO

Volume 65

KODAMAhydrogenbonds, van der Waals contacts, charge-chargeinteractions)that
contributes
to a negative value of AH,. Such a change would be expected toresult in a decrease in freedomof intramolecularmotions,
and hence
AS, < 0, as seen in the nucleotide
binding.
2. A TP hydrolysis

on myosin

Using the oxygen-exchange
technique, Trentham
and colleagues (92,93,
290-293) have shown that ATP hydrolysis
at the myosin site is a single stepwith direct transferof the terminal
phosphorus
from ATP to water. Thus
the M ADP Pi contains chemicallydistinct ADP and Pi, so the energetics
can be concerned only with the on-enzyme equilibrium
l

l

M*ATP

+ Hz0 + M*ADP*Pi

where Hz0 denotes a water molecule directly
involvedin the reaction to
distinguishit from those in the bulk aqueous phase (see below). As is clearlyshown in Figure 3 and Table 5, although the Me ATP and Me ADP Pi states
are essentially
isoenergetic,the latter is stabilized by a large entropy gain
with a concomitantdecrease in heat capacity. By comparison
with the valuesof AS, and AC, accompanying
protein unfolding(sect. IvCI), one may havesome idea how large these thermodynamicchanges are for an intermediatestep of the enzyme catalytic cycle in which the enzyme-boundsubstrate andbound products are in a rapid equilibrium.
This characteristicfeature of theenergetics of the ATP hydrolysis
step is considered in reference
to the following two aspects.
a) ATP hydrolysis in hydrophobic
environment.
As described in section
VIIIBI, bound nucleotide is buried in the interior of the myosin and inaccessible
to the bulk solvent. If the hydrolysis
of ATP occurs under such conditions,
neither reactants nor products would be hydrated;
hence the energetics ofthe hydrolysis
should differ from that in the aqueous environment.
In otherwords, gas-phase energetics probably
govern the reaction.
There are several high-energy
compounds whose mvalues
for hydrolysis
are favorably
negative in the aqueous environment
but less negative or rather
positive in the gas phase (117). These changes in energetics
of hydrolysis
may be attributed
to the differencesin hydrationenergy of reactants andproducts (95, 117). The point may be illustrated
by the hydrolysis
reactionof pyrophosphatel

H3P207 + HZ0 -H3P04 + H2P0i

The calculated value of the energy change for this reaction in the gas phaseis -4.2 kJ/mol, whereas the m value obtained by calorimetry
in solutionis -30.5 kJ/mol(117). Althoughno such theoretical
calculation
has been
made yet for the hydrolysis of ATP in the nonaqueous environment,
becauseApril1985

ENERGETICSOF MUSCLEATPASE

RJ3ACTIONS

505

of the complexityof calculation,
there would be an intriguing
speculationthat a similar change in the energetics would apply to the ATP hydrolysis
on the myosin and in the aqueous environment.
The endothermic
nature ofthe hydrolysis
could then be explained in part by the endothermichydrolysis
at the expense of an entropy increase accompanying
the protein conformation
change, as described below.
As for the rate enhancementof ATP hydrolysis
at the myosin site, it
has been suggested on the basis of theoretical
calculationthat the electrostatic-repulsion
force contained in P-O-P bonds may play a substantialrole
in lowering the activationenergy for the hydrolysis in the largely nonaqueous
environment(117). Such intramoleculareffects are damped by hydration
effects and hence are of secondary importancein the aqueous environments.
Geeves et al. (93) showed in their oxygen-exchange
study that the P-phosphateof ADP formed by the cleavage is highly constrainedin the protein. This isprobably
another consequenceof the catalysis in the hydrophobic
region:coordinationof P-oxygen of ATP to electrophilic
sites would increase thelabilityof the terminal
O-P bond, thus facilitating
rapid cleavage.
b) Microenvironments
of protein side-chain groups. As first suggested byMorita (204) on the basis of her measurementof the ATP-induced
UV-spectrum change, subsequently
confirmedby measurementof intrinsic
proteinfluorescence (300), it seems that some tryptophan
as well as tyrosine residues
are buried in the interiorof the protein when the Ma ADP.Pi
is formed but
become more exposed again on the conversionof M ADP. Pi into Me ADP
by Pi release. Thus the microenvironmentsof these protein side-chain groups
are probably most hydrophobic
in the M ADP Pi states. In agreement
withthis, Yamada et al. (311) found that the rate of hydrogen-deuterium
exchangeof the tryptophan
residues markedly
decreased when the Me ADP l Pi wasformed from the reaction of the myosin with ATP but increased again at
the step of M*ADP*Pi
to M*ADP+ Pi.
If tryptophan
residues are buried in the hydrophobic
region within the
myosin molecule, there would be a possibility
that some water moleculesthat have surroundedthese hydrophobic
residues are set free, resultinginAS > 0 and ACp < 0. A similar effect could also be expected to occur in thechange of the affinity of myosin toward actin. The affinity in the Me ADP Pi
state is as low as in the Ma ATP state (258). Because the interactionof these
two proteins is strongly hydrophobic
as well as electrostaticin nature (seesects. VIIE and VIIIDQ,
some hydrophobic
and charged residues are likely
to be involvedin the interaction.
If these residues were transferredfromthe protein-solvent
interfaceto the interiorof the protein accompanying
either binding of ATP to the catalytic site or its subsequent hydrolysis,
theaffinity for actin would decrease and concomitantly
a large increase in entropy
would be expected.
However,
all the changes do not necessarily
favor the observed thermodynamicchanges. The change of the microenvironmentof other proteingroups, in a way that is reciprocal
to that described above, has also been
l

l

l

l

506

TAKAO

KODAMA

Vdume

65

suggested (187, 243, 244, 310, 311). Thus one must bear in mind that themagnitude
and sign of the thermodynamic
parametersreflect a balance between opposing effects that result from the distinct,
local conformation
changes of the myosin molecule in the accompanying
transitions
betweenthe M.ATPand M.ADP*Pi
states.
C. Transition

of Myosin

Head

BetweenMacrostates

So far this section has been limited to the data obtained at temperatures
around 20°C. However, once the range of temperatures
is broadened, anotherinteresting
feature of the myosin ATPase can be seen, which is probably
directly relevant to the role of myosin in the energy-transduction
mechanism.
1. Effect

myosinof temperature
on proportion
ATPase intermediatesof different

Bagshaw and Trentham(13) showed that, although
the M ADP Pi is
the predominantsteady-stateintermediatein the ATPase cycle at around
ZO”C, the Me ADP state also becomes significant
among the intermediate
species at temperatures
below 10°C. This shows that the rate of the processcontrolling
ADP dissociationfrom the myosin is markedly
temperaturedependent (rate = 1.4 s-l at 21°C and 0.07 s-l at 5°C). Subsequently,
the temperature-dependent
shift of spectral propertiesof myosin-productcomplexduring the steady-state hydrolysis of ATP was noted by Morita and colleagues(141, 206) and Bechet et al. (19). Thus the spectral properties
observed at
low temperaturesare similar to those induced by ADP. The results could beinterpreted
in terms of the equilibriuml

M*ADP*Pi+ M*ADPl+ Pi

As temperature
falls, the equilibrium
shifts toward the right-handside,
due to the marked decrease of ADP dissociation
rate. Note that this interpretation
is apparently
consistent with the thermodynamics
of this step inthe myosin ATP hydrolysis(AH < 0 for the reaction from left to right; seesect. VI@).
Similar temperature-dependent
spectral changes with ATP analogues were also observed by these authors (19, 205). The complex formed
with AMPPNP
at high temperatures
was similar to the Ma ADP.Pi
state
in spectral properties but to the M ADP state at lower temperatures.
Morita(205) analyzed the result assuming that in the interaction
with myosin thisATP analogue mimics ADP at low temperatures
and ADP + Pi at higher
temperatures.
Thus the interpretationis that temperaturechange causes anequilibrium
shift between the chemical states of myosin, i.e., the distinct
states of the myosin defined by the nucleotide
bound to the myosin site.
lApril1985

ENERGETICSOF MUSCLEATPASE

507

REACTIONS

Recently,
are hard

however, reports have appeared that show that observed phenomena
to explain on this basis alone (153, 154, 249-251).
a) Temperature-dependent
anomalies of heat capacity changes for intermediate steps of myosin ATP hydrolysis.
Table 4 shows the result of acalorimetricstudy of myosin ATP hydrolysis
at different
temperatures(153).
As can be seen, the reaction heats for the binding of ATP and ADP to myosin
become more strongly
negativeas temperaturerises from 4 to 1z”C. The
apparent
heat-capacitychange (ACp.,,)is calculated
to be about -3
kJ K-’ . mol-‘, which agrees with the’ earlier result for the ADP binding
obtained by calorimetrictitration(159). The binding heats, however, show
little temperaturedependence
between 12 and 23OC. On the other hand,hydrolysisof bound ATP is positive in the lower
AC, ,w-wfor the endothermic
temperature
range (+2 kJ K-l mol-‘) but strongly negative in the higher
temperature
range (-3 kJ K-l. mol-‘). Just the opposite effect is seen forthe step of Pi release from the M ADP *Pi state.
A more detailed thermodynamic
study was subsequently
made on the
ADP and AMPPNP
binding at 4-K intervals(154). The results, which are
shown in Figures 5 and 6, indicate that large negative values of AC,.,,? accompany the nucleotide
binding
to myosin, and the ACp shows a marked
temperaturedependence like that for the myosin ATPase intermediate
steps.
b) Temperature-dependent“P-NMR
spectra of myosin-nucleotide
complexes. The 31P-NMR spectroscopy
provides useful information
concerning
the chemical environmentsof the phosphorous
atom and hence its compounds(89, 233). Using this technique,
Shriver and Sykes (249) observed that ADP
l

l

l

l

l

FIG. 5. Variation with temperatureof enthalpy change
and equilibrium
constantfor ADP binding
to myosin
subfragment
1. l , Data from Kodama (154); A, data from
Kodama and Woledge (159). Lines were fitted to points byan iterative least-squares
analysis according to Eqs. 7 and
8 as describedin sect. VIIICZ (see Table 6).

I
260

280

320
T/K

508

TAKAO

KODAMA

Vdume

65

FIG. 6. Variation
with temperatureof enthalpy change
and equilibrium
constant for AMPPNP
binding to myosin
subfragment
1. Lines were fitted as described in Fig. 5. [Basedon data from Kodama (154).]binds to myosin to form one type of M ADP complex at 25”C, but at O°C
there are two different
forms of the Me ADP complex present in nearly equal
concentrations.
On the contrary, at least two forms of the AMPPNP complex
are observed at 25”C, whereas only one form is observed at 4OC. Subsequently,
they performed
a 31P-NMR study of the ADP binding to myosin over a wide
temperature
range at smaller temperatureintervals
and showed that there
is a temperature-dependent
shift of the equilibrium
between the two formsof the Ma ADP complex (250). More recently, using “F-NMR
of SF-l labeledwith a fluorine-containing
reagent, they also showed that the myosin exists
in at least two conformational
states even without bound nucleotide(251).
How can all these results be explained?
To explain temperaturedependence of heat-capacitychanges, the two fundamental
conformationsof myosin
were assumed, one of which would be favoredby low temperature(ML),
whereas the other (Mn) would exist predominantly
above some critical temperature(153, 154). A temperature-induced
transition
between these states
would be expected to modify the thermodynamics
of nucleotide binding. Independently,
Shriver and Sykes (249,250) proposed a similar model to explain
their NMR results, in which they claimed that the relative
populationsofMn and ML should be determined
not only by temperature
but also by the
nucleotide in the myosin site. It is evident that this hypothesis is essentiallythe same as the one described for the ligand-induced
shift of the equilibrium
between two macrostatesof proteins (sect. IVc4).
The equilibrium
between the macrostates
can be analyzed based on thedata obtained by NMR studies, whereas reaction calorimetry
providesthethermodynamic
information
about the equilibrium
between the chemical
states with different
nucleotides
in the active site. Thus these two methodslAprilENERGETICS1985

OF MUSCLEATPASE

complement
each other in the thermodynamic
nucleotide
and induced conformationalchange2. Thermodynamic

509

REACTIONS

analysis of the bindingof myosin.

ofschemeThe simplest scheme for the two macrostatesof myosin, the equilibrium
between which varies with temperatureand nucleotide
binding, is given by
M,+N

,A

M,+N
1

1

KH
1
MnN

KL
1 +
MLN

In this scheme, K0 and K1 are equilibrium
con.stants for the isomerizationof either the free or the nucleotide- -bound myosin from the low-temperaturefavored state (ML and MLN) to the high-temperature-favoredstate (Mn and
MnN). The KL and Ku are the binding
constants of N to ML and Mn, respectively. Likewise, other thermodynamic
parameters(AH and AS) are defined for these processes. These parameters
are interrelatedwith each other,as described in section II. It is assumed that neither isomerization
nor nucleotide binding involves a measurable
AC& From the thermodynamic
pointof view, the two routes taken for the formationof MnN from ML
ML + N + MLN + MnN
ML + Mn + N + MnN
are equivalent
to each other.
The values of K0 and K1 and their temperaturedependencies
have been
determined
by NMR studies, hence the corresponding
enthalpies(AH0 andAH1) and entropies (A& and A&) have been estimated(250). The apparent
binding constant K’
K’ = KL(land apparent

heat of binding+ KI)/(l

+ KO)

(7)

AH’

AH’ = AHL + AHIK,/(l+ Kl) - AH&*/(1

+ KO)

(8)

can be calculated
from calorimetrictitration
data (154). Note that KL isrelated to AHr, and A& by Equations
2 and 3. Therefore,taking AHL andA&, as adjustableparameters,
Equations 7 and 8 can be fitted to the observed
values of K’ and AH’ by an iterative least-squares
method. The thermodynamic
parameters
thus obtained are given in Table 6. With these values, the theoretical variations
with temperatureof K’ and AH’ for ADP and AMPPNP

mol-’

+103
+64
+18

AH/kJ

parameters

276
271
298

T,/K

for nucleotide

Nucleotide
bindingbindingin different

MH

ML

Macrostates

to myosin

ADP
AMPPNPADP
AMPPNP

Nucleotides

macrostates
AH/kJ

-35
+33
-74
-52

mol-’

AS/J

-18
+244
-155
-69

K-l

mol-’

Left table is conformationaltransitionof myosin from low to high (ML to Mu) states with different bound nucleotides.
T,, temperature
atwhich standard free-energychange for macrostatetransition
would be nil (i.e., K,, or Kl = 1). Its values were assumed according to Shriver andSykes (250, 251) to fit Equations
7 and 8 with data shown in Figures 5 and 6 by an iterative least-squares
analysis. Right of table is nucleotide
binding to myosin in different macrostates.
AHo, ML, and A& were adjustable parameters
for ADP binding, and AI&, AHL, and AS;, were those
for AMPPNP
binding.

None
ADP
AMPPNP

Bound
Nucleotides

6. Thermodynamic

Transitions
betweenmacrostates

TABLE

k
+

8

Pi

0

j!

R
*

April1985

ENERGETICSOF MUSCLEATPASE

511

REACTIONS

binding were drawn (Figs. 5 and 6). For both parametersof either nucleotide,the cu rve fitted the actual data well, which clearly sh .ows th at the ‘ ‘macrostateshift” model could accoun t for the otbserved AH’ and . K’ for nucleo tide binding.
The variation
with temperatureof the populationof the two macrostateswith and withoutbound nucleotide
was calculated
from the best-fit values
and is shown in Figure 7. In a lower range of experimentallyfeasible temperatures,a shift of the myosin macrostatefrom ML to Mn takes place on
ADP binding, but the magnitudedecreases as the proportionof Mn in theabsence of nucleotide
increases with temperature.
In marked contrast to the ADP binding, AMPPNP binding elicits a large
shift from the Mn to the ML state, which beco mes more prominent
as temperaturerises. This resu It indicates that the magnitudeof the trans ition
from one macrostate
to another differs for these nucleo tides at a gi ven temperature.
For example, at 30°C almost no macr lostate shift takes place on
ADP binding, because >90% of the myosin exists in the Mn state whether.
ADP is bound or not. In contrast, about half of the total POPUlate .on of themyosln in the MH state undergoes a conformational
than ge to the ML state
when AMPPNP binds.
An i mportant
conclusionfrom the analysis described above is that achemical change at the nucleotidesite of myosin elicits a shift of one macrostate to another, and i ts magni tude depend .s on the nature of the chemical
reaction. Although there has been no di rect evi dence of whether shifts between
the myosin macrostates actually occur during the ATPase cycle, the observed
temperaturedependenciesof ACp for the intermediate
steps suggest that it
is indeed the case, and the magnitude could be very large in some intermediate
steps (153). Thus the macrostate-shiftmodel could show the role of myosinin the transductionof chemical to physical energy in muscle contraction.

FIG. 7. Populationof a myosin macrostate(high -temperature favored, MH) as a function of temperatureand effectof nucleotide binding. It was calculated with values of AH
and T, given in Table 6.

260

280

300
T/K

320

512

TAKAO

KODAMA

Volume 65

3. Energetics
As indicated by Equation 7and the relation of K&n = KIKL, the apparent
binding constant K’ will always be lower than the intrinsic binding constantof the state with higher affinity for the ligand. This is the manifestationof
preferential
binding of a nucleotide
to one of the myosin macrostates(see
sect. IVES), which causes a shift in the distributionof those states. In otherwords, part of the total intrinsic
free energy available
for the interaction
between myosin and nucleotide is expended to drive the shift of the equilibrium
between macrostates.
To illustrate
this point, temperaturedependencies
of KH, KL, and K’ for
AMPPNPbinding
are shown in Figure 8 on the basis of thermodynamic
parameterslisted in Table 6. At temperatures
above 30°C (which may be
more or less physiologicalfor contractionof rabbit muscle), K’ is lower than
KL by more than an order of magnitude.
Hence the apparent
free-energychange for AMPPNP binding is more positive by 6 kJ/mol or more than the
intrinsic free-energychange. At the expense of that much energy, about halfof the total populationof myosin undergoes a shift from the Mn to the ML
state when it binds AMPPNP.
This is the coupling of a chemical change toa protein conformational(physical)
change that has a certain biochemicalconsequence, as described below. In the case of ADP binding, which does notcause a large shift in macrostates,
the difference
between K’ and KH or KL
is not large.
4 Biochemical

implications

As discussed by Shriver and Sykes (249), the macrostate-shiftmodel isof particular
relevance to its interaction
with actin. AMPPNP
reduces the0'..-*5\.\*\ T,./.-*
..
.\
..
..
5

\.

l .

..

AG =Z4
kJ mol-’‘\*.. ‘\. ‘*
l .
.

‘.
‘.

‘.

‘. 1
\

‘.
l\.

.

‘\.

.
‘.

‘.
.

I

‘.

‘$obs

‘.
l .

l .

‘\
l .

l *. .

‘\

‘\ *<

FIG.
8. Variation
with temperatureof binding
constantsof AMPPNP
to myosin. Observed binding
constant(K,b) and intrinsic
binding constantstoM&&)
and to ML(&)
were calculated with values
given in Table 6.

April1985

ENERGETICSOF MUSCLEATPASE

REACTIONS

513

affinity of myosin for actin -lo-foldmore than ADP does at 25”C, but theiractomyosin dissociating
effects are not much different
at 4°C (105). According
to the scheme given here, at 45OC approximately
half of the total myosin
population
converts from the Mn to the ML state in the presence of this ATP
analogue, in contrast to a few percent shift induced by ADP. On the other
hand, there is no marked difference
between the macrostate
distributions
induced by these nucleotides
at low temperatures.
Thus the macrostate-shiftmodel is also consistent with the nucleotideinduced modulationof the myosin/actin
interaction.
The ML state could be
the myosin state with a reduced affinity for actin. In this context, it is interesting
to note the report of Marston et al. (189), who observed changes
in the tension of muscle fiber in a rigor state in response to the binding of
AMPPNP
and ADP without
appreciabledissociationof cross bridges.
AMPPNP is far more effective in this action than ADP. Their interpretationis that there are two states of the actin/myosininteractionthat differ intheir affinity and cross-bridgeorientation.
AMPPNPbinds to myosin andstabilizes one of these states, resulting
in a decrease in the interprotein
affinity and a length change without
dissociation.
On the other hand, ADP
preferentiallybinds to anotherstate but does not induce an appreciablechange in the mode of myosin/actin
interaction.
The exact relationshipofthese actomyosinstates to the myosin macrostates
is not certain.
Apart from this direct bearing on the mechanism of muscle contraction,
the macrostate-shiftmodel could provide the basis for interpretationof various temperature-dependent
phenomena
involving
myosin. These include thechanges in spectral propertiesof myosin-nucleotide
complexes (19, 205) anda biphasic fluorescence response in kinetics of mixing of SF-l with nucleotides
under certain conditions(91, 282). Probably
the temperature-induced
shiftof the UV spectrum of the myosin ATPase steady-statecomplex (206) could
also be explained in terms of the macrostate
shift.
In summary,the macrostate-shiftmodel based on the observations
by
NMR and calorimetry
can provide a unified view to account for many of theresults from a wide variety of experiments
and has important
implications
for considering
the mechanismof coupling between chemical events and amechanicalmanifestationin muscle contraction.

D. Energetics

of MyosidActin

Interaction

It has long been known that the interaction
between myosin and actin
is weakened with increasingionic strength,
decreasing
temperature,or inthe presence of ATP, PPi, or ADP (190, 295). Because of improvements
inanalyticaltechniques,
quantitative
data have recently been accumulated,allowing
discussion of the thermodynamic
aspects of this fundamental
interaction
between the two principal
muscle proteins.
In addition,
understanding of the substructureof the myosin head has also been enhanced.

514

TAKAO

Volume 65

KODAMA

Several lines of evidence suggest that it consists of at least three structural
domains, and the interactionof these domains appears to be altered when
myosin and actin bind together.

1. Entropic

nature of interaction

Using the method of time-resolved
fluorescence depolarization,Highsmith(120) made a systematic study of the association
constant of actin and SF1 as a functionof temperatureand ionic strength.
He obtained
a linearrelationshipbetween log K and the reciprocalof temperature
over the range
between 4 and %“C, from which the van’t Hoff enthalpy
was calculated
tobe +39 kJ/mol(O.l5
M KCl, pH 7.0). This value can almost completely accountfor the apparent differencein the K values determinedat different
temperatures but at similar ionic strength(e.g., refs. 119, 190). The calorimetricresult at 12°C (304) is in good agreement with this van’t Hoff enthalpy. Thus
it is clear that the actin/myosininteraction
is endothermic,
and, like many
protein-protein
association
processes (sect. Ivc3),
it is entropy driven (thestandard entropy change Aso = 0.3 kJ* K-l mol-’ at 25°C).
Because there is no evidence that myosin undergoes the delocalized changeof conformation,
one of the most likely sources of such a large entropy
increase seems to be displacementof water from surface areas of two proteinsthat come in close contact during association.
As discussed in the thermodynamic changes for the myosin ATPase reaction, charged and/or hydrophobic side-chaingroups are presumably
involvedin the interaction.
The
importanceof the surface charge can be inferredfrom the strong ionicstrength dependence of the binding constant. Highsmith(120) also showedthat the log K was proportional
to the square root of the ionic strength.
However,interpretationof this result in terms of the Debye-Hiickel
theoryfor the behaviorof strong electrolytes
in solution is not easy, because thelarge size and unique shapes of the proteins should be taken into account.
Borejdo (28) recently attempted
to map hydrophobic
sites on the surfaceof myosin and actin with a fluorescent hydrophobic
probe, cis-parinaric
acid,
which is known to report the surface hydrophobicity
of a variety of proteins(149). The result indicates that this probe binds to the region distant fromboth actin- and nucleotide-bindingsites in the myosin molecule, whereas
there is little binding to actin. This result, however,does not necessarily
preclude the involvementof the hydrophobic
interactionin the binding ofactin to myosin, because release of water molecules around only several
aliphatic
chains on binding could be sufficientto account for the observed
entropy change. Preliminary
results of a calorimetricstudy indicate thatthe actin binding to myosin is most likely accompanied
by a negativeAC,(sect. VI@). This suggests that either hydrophobic
interaction
is importantor actin binding induces an equilibrium
shift in the macrostateof myosin
like that in nucleotide
binding to myosin.
lApril1985

2. Intramolecular

ENERGETICSOF MUSCLE

changes of myosin

ATPASE

REACTIONS

515&YLactin binding

Recently, two totally different
approaches
have been made to this problem: high-resolution
proton NMR (for review see ref. 122) and a proteolyticdigestion method.
Using the former technique,Akasaka et al. (2) found that myosin had
a high side-chain
mobility
within its molecular
structure.
In a subsequent
study, it was shown that the mobile region is almost completely
within the
myosin head and accounts for ~20% of its structure and that actin quenches
these mobilities(123). This effect of actin is not ascribed to a reduced rateof overallmolecular
rotationon actin binding
but rather to the myosinstructurechange induced by actin binding (124).
The intact heavy chain of SF-l (Mr 95,000) is rapidly split by mild treatment with trypsin into three discrete fragmentswith molecularweights of
27,000, 50,000, and 20,000 (14, 209, 313, 316) that are aligned in this orderfrom the NH2-terminalof the heavy chain (173). These fragments
remainassociated in the protein after tryptic digestion but are separable on SDSgel electrophoresis.
A photaffinity-labelingstudy suggested that the nucleotide-bindingsite is contained in the 27,000-M, fragment(263). On the other
hand, the 20,000-M, fragment
contained two reactive cysteine residues (SH1and SH2), a chemical modificationthat drasticallyalters the enzymatic properties of myosin (14, 286).
It has been shown that when the tryptic digestion is performedin thepresence of actin (actin-SF-lcomplex is thus subject to proteolysis),ohly
the 27,000- and ‘70,000-M, fragments
are produced from the SF-l, indicatingthat actin induces the structuralchange within the SF-l molecule to reduce
the susceptibilityof the joint connecting
the 50,000- and 20,000-M, peptides
to tryptic attack (209, 313). A slight increase in resistanceto the tryptic
digestion was also noted for the alkali light chains (313). On the other hand,the 27,000- to 50,000-M, joint seems to become more susceptible
to tryptic
digestion(313, 314). Mornet et al. (207, 208) argued that the region, themobility of which is quenched on actin binding as observed by proton NMR,
may reside in or near the actin-bindingsite and that the 50,000- to 20,000Mr joint is probably part of this mobile structure. Hence actin binding would
cause the conformationalchange of SF-l, resulting in protection of the 50,000to 20,000-M, joint from proteolytic
attack, and concomitantly
the oppositechange would occur at the 27,000- to 50,000-M, joint.
3. Energetics
interaction

and mechanismof myosin/actin
in presence of nucleotide

As described in section VIC, the nucleotideand actin-bindingsites onmyosin are functionallylinked in such a way that binding at one site influences
the other antaganistically.
This is an example of heterotropicinteractions

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of proteins with interacting
sites (306). Because this interaction
is fundamentally
importantto the coupling of chemical and mechanicalevents inmuscle contraction,
recent results concerningenergetics and the mechanism
are summarized
here. A different
but interesting
view of the subject has
been presented by Morales and Botts (203).
The interaction
between myosin and actin (A) in the presence of a nucleotide or a nucleotide
analogue may be described as
A+M+N,AA+M*N

A*M+N
If three out of fourchange of interaction(306)
AGnter\K4’ A*MmN

association
constants are determined,
the free-energy( AGinter) can be calculatedwith the Wyman method=-RT In (KJKJ= -RT In (K3/K2)

This equa tion describes the strength of interaction
between the nucleotide
and actin sites. Note that AGinter num eri tally equals the difference
betweenthe free-energychanges for binding of either actin or nucleotide
to myosinwith and withoutbinding of the other.
Table 7 summarizes the values of AGinter reported (119,129) and calculated
from the association
constants(27, 301) for the interactionof actin andmyosin in the presence of ADP, AMPPNP,or PPi. Partly because of the
difficultyof the measurements
and the variationin experimental
methods
and conditions,
there are some discrepancies
between the AGinter values fora given nucleotide.
Nonetheless,if the comparison
is made for the values
obta ined at the same or simi lar ionic strengthand temperat ure, it is clearthat when the nucleotide site is occupied with a nucleotide or analogue thathas the stronger dissociation
power of actomyosin,
its interaction
with theactin site is stronger. The dissociation
power is on the order of AMPPNP
N
PPi > ADP.
Only limited information
is available
for the enthalpy and entropy contributions
to the free energy of the site-site interaction.
The ADP binding
to the A l M complex is almost thermallyneutral (see sect. VILE).
This isconsistent with an observationthat the binding constant is fairly insensitive
sh ould thento temperatu re (30 11). The enthal PY than .ge for the interaction
be about the same magnitude
as fo r the ADP bind .ing to myosin. Thus theinteraction
enthalpy
is estimatedto be -70 kJ/mol. This implies that theinteraction
between the actin and nucleotide sites is accompanied
by a large
decrease in entropy. It is of great interest to know how such negative entropicApril1985

ENERGETICSOF MUSCLEATPASE

7. Free-energy changes for interaction
and actin sites of myosin head

TABLE

517

REACTIONS

between nucleotide

Ionic
Nucleotides- AG/kJ

mol-’

Conditions

Temperature,

“C

Refs.

ADP

4.7
12.2
7.5
12.9
13.1

A
A
B
C
C

4
4
22
20
23

119
105
105
301
129

AMPPNP

12.8
14.0
14.0”
19.4

A
B
A
C

4
22
4
23

105
105
119
129

PPi

10.8*
16.2
15.7

A
A
B

4
4
22

119
105
105

Ionic conditions:A, ~1 (ionic strength)8.0. PPi, pyrophosphate.
* Approximate= 0.17, pH 7.0; B, p = 0.22, pH 7.0; C, p = 0.12, pH
value.

contributiondiffers for different nucleotides with more favorable
free energies
of interaction.
The importance of the mobile structure in the mediation of the interaction
between the nucleotide and actin sites has been suggested by the proteolytic
approach (207, 209, 315), showing that PPi and ADP only partially
impairthe protective
effect of actin on the tryptic cleavage of the 50,000- to ZO,OOOM, joint (a complete loss of the protection
was observed in the presence ofATP, but this was attributable
to the dissociation of the actomyosin complex).
Furthermore,when SF-1 was treated by trypsin in the absence of actin so
the 50,000- to 20,000-M, joint was cleaved, its Mg-ATPase activity was retained,
but there was little actin activation.
On the other hand, SF-1 digested in thepresence of actin showed unalteredactin activationin the ATP hydrolysis.
These results suggest that the 50,000- to ZO,OOO-1M,joint plays an importantrole in activationof myosin ATP hydrolysis
by actin.
Chemical modificationof the two reactive SH groups in the 20,000-2M,
domain affects the propertiesof myosin ATP hydrolysis,
the site for which
resides on the 27,000-M, domain. This fact suggests that there is a close
spatial disposition
between these domains. In fact, Wells et al. (298, 299)
found that when ADP was bound to the nucleotidesite (either on additionof ADP or ADP formed from ATP), these SH groups were brought
closeenough to be cross-linked
with bifunctional
reagents with cross-linkspansof 5-14 A. The nucleotide
was in turn trapped in the active site in a stablemanner with a half-lifeof >7 days at OOC. Interestingly,
however, the trappednucleotide was rapidly released on the addition of actin. These results suggest

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that the chemical event at the catalytic site induces a certain local conformationalchange in the other domain or domains that are responsibleformyosin binding to actins (see ref. 203).
4. Bindingof single- and double-headed

myosinsubfragments

to actin

Apart from the functionalsignificanceof the double-headed
structureof the myosin molecule that has been disregardedin most theories of muscle
contraction,
considerationof the binding of single-headed(SF-l) and doubleheaded (HMM) subfragmentsof myosin to actin is of interest from the energetic viewpoint.
Althoughit has been known for some time that HMM binds to actin
more strongly than does SF-l (121, 186), the binding process has not beentreated quantitatively.
The complexity
in the analysis of the HMM/actin
interaction
arises from the “parking
problem”(104, 125, 126). This occurs
because HMM binds to two actin sites, and as the sites of the F-actin filament
become occupied with HMM, the number of pairs of adjacentactin sites
available
for binding decreases more rapidly than the total number of freeactin sites. However,the problem is not of serious consequence when actin
filaments are far from being saturated
with HMM.
The binding of HMM to F-actin was studied by the competition
method,in which HMM and SF-l compete for sites on F-actin (104, 106). The data
were analyzed with the mathematics
for the parking problem worked out
by Hill (125). Their results indicate the following:
1. In the absence of nucleotide,
HMM binds lOO- to l,OOO-fold morestrongly
to F-actin than does SF-l, suggestingthat both of the heads of
HMM can bind strongly to actin. But the increase in the strength of binding
due to the second head is much smaller than what might be expected if eachof the two HMM heads bound independently
to actin (126, 186).
2. In the presence of ADP or AMPPNP, on the other hand, the bindingof HMM to F-actin is not much stronger than that of SF-l. Thus the secondhead binding seems to be very weak and in fact does not seem to take placeat all in the presence of AMPPNP.
A possible physiologicalimplicationofnucleotide-weakened,second-headbinding of double-headed
myosin is discussed by Goody and Holmes (102).
3. Quantitatively,
the effect of ionic strength, temperature,and nucleotides on HMM bindingis the square of the effect on SF-l binding.
Thissuggests that the first- and second-head bindings are affected by these agentsto the same extent, which implies that the energetics of the intrinsic
bindingto actin is probably
the same for either of the HMM heads as well as for
SF-l. Therefore
it seems that a smaller contributionof the second head tothe free energy for HMM binding to actin would be due to an expenditureof part of the binding energy for protein deformation
for two heads to bind
actin sites simultaneously
under geometricalconstraint(cf. ref. 186).

April1985

IX. MECHANISMENERGETICSANDOF MUSCLE

ENERGETICS

ATPASE

519

REACTIONSOF ATP HYDROLYSISBY C&PUMP

ATPaseA. Introduction
The SR serves as the intracellular
sink of Ca’+, which has the capacity
to release and to reaccumulate
the cations. The former is an energeticallypassive process that is triggered
by depolarization-induced
redistributionofcharges within the muscle fiber membrane and the subsequent similar change
in the SR adjacent to the transverse
tubule (for reviews see refs. 34, 77, 85,
162, 245). On the other hand, the Ca’+ accumulationis the translocationofthe cations across the membrane
against a chemical potential
of Ca2+ andhence requires energy input. The molecular entity responsible for this functionof the SR is the membrane-boundCa2+-pump ATPase.
Ever since the pioneering
work of Ebashi and Lipmann(63, 65) and
Hasselbachand Makinose (115), the mechanismof Ca2+ accumulationhas
been extensively
studied with the fragmented
SR isolated as a microsomal
fractionby differential
centrifugationof muscle homogenate.
The isolated
microsomes consist of small vesicles, 100-200 nm in diameter, and are called
the SR vesicles. MacLennan(176) solubilized
SR vesicles with deoxycholate
and obtained a functional
Ca2+-dependent
ATPase preparation
in a highly
purifiedstate. Such purified
ATPase preparations
have been used for the
structural
analysis of the ATPase protein. They have also been used in studiesof the kinetic mechanismof ATP hydrolysis,
the interactionof the ATPaseprotein with phospholipids,
and the reconstitutionof SR vesicles with Ca2+pump activity.
In this section the mechanismof the Ca2+ pump is characterized
inthermodynamic
terms on the basis of experimental
data obtained by recent
kinetic, equilibrium,and calorimetricstudies. For more details of the structure
and mechanism of the Ca2+-pump ATPase see several recent reviews (23,52,
58, 114, 116, 134, 136, 137, 177, 192, 264, 317). The mechanismof free-energy
coupling in Ca2+ pump and other ion-transportsystems has been recently
discussed by Tanford(270).
B. Structural
Organization
Sarcoplasmic
Reticulum
I. Membraneof Ca2+-Pump
Membrane

ATPaseinsidedness

When the vesicles are incubatedin a medium
containing
Ca2+ andMg ATP, free Ca2+ rapidly disappear from the medium, and the cations areaccumulated
in the interior of the vesicles (vesicular lumen). This observation
indicates that the medium in this in vitro experimental
system corresponds
to the cytoplasm in the muscle cell (sarcoplasm).
In addition,
ATP and its
l

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65hydrolysis
products ADP and Pi react solely from the medium side and do
not penetrate
the vesicularlumen. Other agents such as ethylenediaminetetraacetate(EDTA)and ethylene glycol-bis(~-aminoethylether)-N,N’-tetraacetateacid (EGTA),
which are experimentally
useful metal-chelating
agents, also remain outside the vesicle (294). For convention,in this review
the medium and lumen sides are referred
to as out and in, respectively.

2. Asymmetricdispositionof Ca2+-pump

ATPasein SR membrane

The ATPase protein, which has a molecularweight of 100,000, accounts
for 60-70% of total protein in the SR membrane(177). The gross asymmetry
has been indicated for its dispositionin the SR membraneby biochemical
and ultrastructural
studies (for reviews see refs. 23, 134, 136, 137, 177, 178,
192, 246, 264). The relatively
polar portions of the amphiphilic
polypeptide
chain of the ATPase protein protrude
from the cytoplasmic
surface of themembrane. The primary structure of these protein parts has been determinedby Allen and colleagues (6, 103; see also refs. 134, 178, 179), whereas the
nonpolar portions are largely buried within the membrane, which is probably
responsible
for a strong interaction
with the membrane
lipids.
It has been shown with a purified ATPase preparationthat -30 phospholipid molecules are associated with each polypeptide
chain of the enzyme(118). These lipids are called annulus or boundary
lipids (146, 242). Theirinteraction
with the enzyme protein is stronger
than that of other phospholipids, and their removal from the ATPase by detergent treatment
resultsin the irreversible
loss of the enzyme activity.
Tanfordet al. (50, 51, 168),
however, showed that these boundary
lipids can be replaced by a nonionicdetergent, dodecyl octaethylene
glycol ether [C12H25(OCH2CH2)sOH],
without
loss of the enzyme activity.
Results of recent studies on the interaction
between the ATPase moleculesin the SR membranesuggest that the ATPase molecules form a complex(dimer) within the membranethat may be the functional
unit for the Ca2+pump (36, 214).
The SR vesicles also contain several minor protein componentsthat arebound much more loosely to the membrane
and are easily extracted
by arelatively
mild treatment
with detergents(33, 37, 177). Of these proteins,calsequestrin(M, 50,000) accounts for lo-20% of the total protein (177), whichis generally
assumed to be localized on the internalsurfaces of SR. Because
this protein has a number of Ca2+ -binding sites, although its binding constantfor the cation is low ( -lo3 M-l), it seems likely that calsequestrin
molecules
confer an increased internal
Ca2+-binding
capacity on SR. It is known fromreconstitution
studies that this protein is not essential for Ca2+-pump activity (231).

April1985

ENERGETICS

C. Basic Properties
1. Coupling

OF MUSCLEATPASE

REACTIONS

521

of Ca2+ Pumpof Ca2+ transport

to A TP hydrolysis

The SR vesicles perform rapid Ca2+ accumulation when incubated withMg ATP together with Ca2+. The maximum capacity of Ca2+ accumulation
within the vesicle is usually 120-180 nmol Ca2+/mg protein in the presenceof excess ATP. The free [Ca”‘] inside the fully loaded vesicle is 1.5-2 mM,
assuming an average water space of 10 pl/mg protein and the content ofcalsequestrin in SR and its Ca2+ affinity (see above; 217, 218a, 264). Thus
most of the intravesicular
Ca2+ accumulated by the Ca2+-pump activity ispresent in a bound form.
The rate and the maximum capacity of Ca2+accumulation show a similar
dependence on [Ca2+] in the incubation medium: half maximum is observed
at pK ~6 and the maximum at pK < 5.5. The Hill coefficient of the saturation
curve is ~2. In the absence of ATP, Ca2+ also binds, although to a muchsmaller extent, to the SR vesicle that has high- and low-affinity sites for thecation. The high-affinity sites are attributed to the ATPase protein that has
two binding sites per molecule. The binding constant of these sites is -lo6
M-l. On the other hand, the low-affinity Ca2+ sites may be attributed in partto proteins other than ATPase and polar groups of the membrane phospholipids, and it is unlikely that they are directly involved in the Ca2+-pumpsystem.
The ATP hydrolysis rate is very low in the absence of Ca2+ (pK > 8)
but is significantly stimulated by low [Ca”‘] in essentially the same manneras the Ca2+ transport. The stoichiometric ratio of Ca2+ transported per molecule of ATP hydrolyzed has been measured by a variety of methods uhderdifferent conditions, and the value is usually two. The same stoichiometricratio also holds for the translocation of Ca2+ coupled to the phosphorylationof enzyme (see sect. IXBZ).
Thus it is concluded that two Ca2+ bind to the high-affinity
sites of an
ATPase molecule, which then activates the catalysis of ATP hydrolysis, andthe completion of the catalytic cycle results in translocation of both cations.
[Lower values of the stoichiometric ratio have been reported under certain
conditions, in particular at low temperatures, e.g., O°C (23, 134).]
One of the important properties of the Ca2+ pump of SR is that it canbe reversed under certain conditions (183). When the Ca2+-preloaded SR
vesicles are transferred to the medium deprived of Ca2+ with EGTA, but
containing ADP and Pi together with Mg+, there is a rapid Ca2+ release towhich ATP synthesis is coupled. This is an important demonstration of thereversibilityof chemiosmotic energy transduction (58, 114). Note that thestoichiometric ratio of ATP synthesized to released Ca2+ is also two, as in
the forward mode of the pump function (for more details see sect. IXD3).
l

TAKAO522

2. Ion movement

accompanying

KODAMA

Volume 6.5

Ca2+ transport

For ion movements
accompanying
the functionof the Ca2+ pump, themain concern from the viewpointof energetics
is to know whether
activeCa2+ transport
by the pump is electrogenic(net charge displacement)
or isaccompanied by a displacementof other ions and electricallycounterbalanced(for reviews see refs. 116, 201).
Results of recent experiments
indicate that some protons are ejected(39, 155, 180, 282a).
into the medium in exchange for the Ca2+ translocation
Note that this proton movement
is quite distinct from the net formationof
H+ in the ATP hydrolysis
reaction. In addition, when the SR membraneismade permeable
to Ca2+ by a detergent
or a Ca ionophore
such as X537A
and A23187 proton ejection is not observed, and when the Ca2+ gradient
formed by the activityof the pump is collapsed by the additionof a Ca
ionophore, the released protons are reabsorbed. On the basis of these findings,
the proton ejection is attributable
to the Ca2+ binding to the internalsitesof the SR vesicles. Thus the ratio of the H+:Ca2+ exchange depends on thepK values of these sites and intravesicular
pH. The value is ~1 at pH 6.0(39) and -0.2 at pH 7.0 (155).
As for the movement of other ions, M$+ is not countertransported
duringthe Ca2+ movement(39, 40, 216). Monovalentions such as K+, Na+, and Clare permeable
throughthe SR membrane(40, 116, 201). Thus there is apossibility
that the Ca2+-pump activity is electrogenic
in itself. However,thebuildupof an inside-positive
potential
across the SR membrane
may belargely offset by the inward movementof Cl- and the outward movementof
K+ under physiologicalconditions.
D. Kinetic

Mechanism

1. Kinetic

analysisof Ca2+ Pump

A characteristicfeature of the ATPase reaction of the Ca2+ pump is the
rapid formationof a protein-boundacyl phosphate intermediate(phosphoenzyme) followed by its slow decomposition(181, 318, 319). Therefore,
like themyosin ATP hydrolysis,
the overall reaction is divided into two parts, thesteps to the formationof phosphoenzyme
and the steps involved in its breakdown and regenerationof the original
enzyme state.
Soon after the complete reversalof the Ca2+ pump was demonstrated
in 1971, it was found that the Ca2+-ATPase could be phosphorylatedwith Piin the absence of ATP and Ca2+ (with EGTA). The phosphoenzyme
formedwas subsequently
confirmed
to be an intermediatein the usual sequence ofreaction with ATP (264).
Taking advantageof the acid-stable
nature of the acyl phosphate bondof phosphoenzyme
on the acid denaturationof the enzyme and participation

April523

ENERGETICSOFMUSCLEATPASEREACTIONS1985

TABLE 8. Kinetic
data forCa’+ pump of sarcoplasmic

partial reaction
reticulumof ATPhydrolysis

Apparent
Hydrolysis

Steps

Reactions

by

Rate

Constants/s-’

Refs.

1+2

Formationof E E and ATP

P from80-15038, 86, 218,
261, 283

5Dephosphorylation

of

40-60

139, 23560

86, 139*E 3+4+5+6+(7)Completecycle

P

Decay of *E - P
Steady state
ATP hydrolysis

8-9$

139

l-26

218

Values are referring
to conditionsof KC1 100 mM, MgCl,, 5 mM, pH -7, and 20-20°C.
The term *E - P represents
ADP-insensitive
phosphoenzyme.
t Reaction steps shown in
Fig. 9.
* In the absence of net Ca2’ accumulation.
0 For intact sarcoplasmic
reticulum
vesicles.

of Ca2’, a wide variety of techniques are available for transient kinetic studies(38, 86, 136, 137). Several kinetic steps have been identified
in the formation
and breakdownof phosphoenzyme
as shown in Figure 9 (for reviews see refs.
52, 58, 134, 136, 137, 264, 317). Kinetic and equilibrium
data for the partial
reactionsconstituting
the ATPase cycle are given in Tables 8 and 9, respectively.
The important
point here is that during the ATPase cycle, the enzyme
protein alternates
between two distinct conformational
states, referredtoas the E and *E states. These two states are distinguishedby the propertyof Ca2+-bindingsites and reactivities
toward ATP and Pi (58,134). The Ca2+binding sites in the E state have high affinity for Ca2+ and have an outside

9. Equilibrium
constants forhydrolysis by Ca2’-pump A TPaseintermediate

TABLE

Steps

1 Ca2+ binding
1 ATP binding

2E - P formation
3E-P
+*E-P
4 Ca2+ release
5 “E - P +* E-Pi
6 “E Pi dissociation‘7*E+El

Equilibrium

Constants

0.5-6 X lo6 M-‘t
105-lo6 M-’
lO-2 M
0.5
0.6-l

steps of ATP

x 1O-3 M-j-

Refs.

20, 58, 61, 133, 138, 284
60, 114, 138, 139, 200, 283
224
139, 247
58, 133
59, 147, 148, 191

0.6-2.2
l-4 x 1O-3 M

59, 191, 230

l/30-l/1,000

191, 271, 284

The terms E - P and *E - P represent
ADP-insensitive
phosphoenzyme.
values should be squared for interactionof 2 Ca2’ with single ATPase molecule.

t These

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KODAMA

orientation(facing the external surface of the SR vesicle). In the *E state
the Ca2+-bindingsites have low affinity and an inside orientation(facing theinternalside of the vesicle membrane).
In the E state, which is stabilized
in the presence of Cite+, the enzyme reacts with ATP to give rise to one formof phosphoenzyme,
E - P but not with Pi. On the other hand, Mg? stabilizes
the *E state, in which the enzyme is phosphorylatedby Pi in the absence ofCa2+ forming
the other type of phosphoenzyme,*E - P (see below for distinction between E - P and *E - P).
2. Intermediate

steps of ATPhydrolysis

coupledto Ca2+ transporta) Bindingof ATP and Ca2+ (step I). ATP as the complex with Mg?
interactswith the ATPase in the presence of Ca2+ to form Ca2* E 6ATPcomplex. Because of its inherent
complexity(two Ca2+ and one Mg ATP
complex participate
in the reaction) and subsequent rapid phosphoryltransfer
reaction (step 2), kinetic resolutionof the process is not yet satisfactory.
Evidence for the existence of Ca2. E ATP complex was only recently obtained(224, 248). From equilibrium
analysis, however, it has been shown that two
Ca2+ bind to the enzyme with high affinity in the absence of ATP (see sect.
1xG1). A reasonableguess of the ATP-binding
constant can also be made on
the basis of several lines of circumstantial
evidence (114, 136, 137). Hencethe overall equilibrium
constant for the formationof the Ca2 E. ATP complex
can be estimated(see Table 9).
b) Phosphorylationof the enzyme (step 2). The terminal
phosphateof
ATP is transferred
to a specific aspartyl residue of the enzyme formingaprotein-boundacyl phosphate (E - P) and releasing ADP into the medium.
By analyzing the ATP-ADP
exchange reaction, which is a dynamic reversalof steps 1 and 2, it has been shown that free ADP (not complexed with M8’)
is released (182, 218, 309).
From the viewpointof Ca2+ transport,
the most important
effect accompanying the phosphorylationis that Ca2+ initiallybound to the external sitesof the enzyme with high affinity is brought into the occluded state in which
the cation is inaccessible to EGTA (60, 266-268).
c) Inward orientationand decrease in a$inity of Ca2+-binding sites (steps
3 and 4). The rapid formationof the phosphoenzyme
is then followedbymuch slower conformationalchange of the enzyme (step 3), by which theCa2+-bindingsites become oriented toward the inner surface of SR vesicle,
and concurrently
the affinity for Ca2+ decreases by three orders of magnitude.
These changes lead to a release of Ca2+ into the vesicularlumen (step 4).
The reactivityof the phosphoenzyme
with ADP is also altered. As noted
above, phosphoenzyme
in the E - P form transfers
its phosphoryl
groupback to ADP (ADP-sensitive
phosphoenzyme),
but it becomes unable to reactwith ADP in step 3 (ADP-insensitive
phosphoenzyme,*E - P). It is wellknown that when the [Ca”‘] is increased inside the vesicle by Ca2+-pumplllApril1985

ENERGETICSOF MUSCLEATPASE

525

REACTIONS

activity, the rate of the pump and ATPase is markedly decreased. This rate
limitation
is imposed primarily
by the “pushingback” of the equilibriumofstep 4 by Ca2+ and the consequent buildup of the phosphoenzymes.
d) Hydrolysisof phosphoenxyme(steps 5 and 6), outward orientation
andincrease in ajinityof Ca2Qindingsites (step 7). Among all of the partial
reactions of the Ca2+-pump ATPase reaction, the best studied is the hydrolysisof phosphoenzyme.
It has been investigatedby kinetic and equilibrium
analysis of its reversal, phosphorylationof the enzyme with Pi as described below.
The hydrolysis
occurs rapidly and is followed
by a relatively
slow reversalof the conformationalchange from the *E to the E state (step 7). The Ca2+binding site is reoriented
to face the outer surface of the vesicle, and thehigh affinity for the cation is restored. This conversionof the enzyme stateis activatedby ATP throughbinding to a low-affinity
noncatalytic
site (54,58,264). Interestingly,
the other nucleoside triphosphates
such as inosine 5’triphosphateor other phosphateesters exhibit little stimulatoryrole, eventhough they can support the Ca2+-pump activity.
3. Experimental

reversalof Ca2+ pumpBecause the original
experiments
were performedin the presence of anapparent
Ca2+ gradient(the Ca2+-loaded vesicles incubatedin the Ca2+-deprived medium),the finding of the reversalof the Ca2+ pump with Ca2+
release coupled to ATP synthesis led to the hypothesisthat osmotic energy
derived from a transmembrane
Ca2+ gradientcould be utilized for a phosphorylationof ADP. However,subsequentstudies (for reviews see refs. 58,
114, 264) have shown that 1) the Ca2+ -ATPase can be phosphorylated
with
Pi in the absence of a transmembrane
Ca2+ gradient under certain conditions(see below); and 2) ATP can be formed by first phosphorylating
the enzyme
with Pi in the absence of Ca2+ (with EGTA) but in the presence of M2+ andthen raising the Ca2+ level in the presence of ADP. This indicates that thetransmembrane
Ca2+ gradient is also unnecessary for the phosphoryltransferfrom the phosphoenzyme
to ADP.
At present the mechanismof the reversalof the Ca2+ pump can be
explained, if not conclusively, as follows (55,58). The enzyme is phosphorylatedwith Pi only in the *E state, where the Ca2+ -bindingsites are internallyoriented
with low affinity for the cation. As is evident from the ATPasescheme (Fig. 9), Ca2’ shifts the equilibrium
between *E and E states toward
the latter, as a consequence of formationof the E. Ca2+ complex, and hence
makes the phosphorylation
less favorable.
The phosphoenzyme(*E - P) thus
formed is in equilibriumwith E - P, which has high affinity for Ca2+. The
equilibrium
constant does not deviate much from unity and is effected byvarious factors such as the dielectric constant of the medium, temperature,and pH. Subsequently,
E - P reacts with ADP to form ATP. Thus the
enzyme-ATPcomplex with Ca2+ bound to the high-affinity
site (Ca2 E. ATP)
l

526

TAKAO

2 Ca2+(wt)

ATP

t

t

2

9

Ca,eE*P

17

*E

31

,6,

*E*Pi
2

Pi

Volume 65

ADP

Ca2mE l ATP

E-i-

KODAMA

5*E - P + 4

hydolysis
FIG.
coupled
9.
Reactionto Ca2+schemetransport
for ATPby
Ca2+ pump of sarcoplasmic
reticulum.

Ca2FE - P

!

2

“20

2 Ca2+(in)is formed, which dissociates rapidly when Ca2+ is released into the low Ca2+
medium (i.e., in the presence of EGTA).
From this explanation
it is clear why ATP can be synthesized by meansof the two-step procedure described above. The ATP synthesis is facilitatedby lowering
the temperature,for example, in the second step. On the other
hand, for the ATP synthesis in the presence of an apparent
Ca2+ gradient,
the large differenceof Ca2+ concentrationon the two sides of the membrane
is only needed to meet the differences of affinities of the external and internal
Ca2+-bindingsites (57, 58). In other words, repeated cycles of ATP synthesis
coupled to Ca2+ release from the SR vesicle require alternate
exposure of
the Ca2+ sites to an outside medium in which the Ca2+ level is sufficiently
low to facilitate
the phosphorylationof the enzyme with Pi and to an insideenvironment
in which the Ca2+ level is sufficiently
high to push back theequilibriumfrom a Ca2 E - P to a Ca2. E - P state (137, 139).
l

E. Thermodynamic
Analysis of Partialof A TP Hydrolysis
of Ca2+ Pump
1. Bindingof Ca”

to Ca2+-pump

Reactions

A TPaseIn agreement with the earlier suggestions based on the Ca2+ dependenceof the enzyme activity, Ca2+ binding occurs in a cooperative
manner involving
binding to a first site, followed by binding to a second site with a magnitude
increase of two orders in the binding constant (138, 284). Kinetic resolutionof these two binding processes has been made (61,135). It has been suggested
that the interactionof the enzyme protein with phospholipids
and/or theinteraction
between the enzyme molecules may underlie
the apparent
cooperative
binding of Ca2+ (134, 252, 284).
Inesi et al. (138) originallyexplained
the cooperative
Ca2+ bindinginterms of two interacting
bindingsites. Hill and Inesi (127) subsequently

April1985

ENERGETICSOF MUSCLEATPASE

527

REACTIONS

proposed a more elaborate model that involves interaction of more than twosites, as well as H+ competition with Ca2+ for the binding sites, to explain
pH dependence of both the affinity and the cooperativity (287). An alternative
explanation for the cooperative character of the Ca2+ binding is the shift ofthe equilibrium between two basic conformational
states of the ATPase, E
and *E (Fig. 9), which is described below.
Ikemoto (133) and Watanabe et al. (287) found little variation of theapparent binding constant with temperature, whereas Pick and Karlish (223)
reported that an increase in the temperature slightly decreased the affinity
for Ca2+. Interpretationof these results should be made with caution because,
as just described, the Ca2+ binding is a cooperative process. In fact, thetemperature-induced
shift of the equilibrium between the *E and E states
may overshadow the actual temperature dependence of the Ca2+-binding
constant. In view of these situations it is hardly possible to estimate thevan’t Hoff enthalpy for Ca2+ binding to the Ca2+-pump ATPase.
2. PhosphorylatimofCa2+-ATPaseby Pi

This reaction proceeds by way of a ternary complex, Mg *E . Pi, that isformed by random addition of reactants as described by a scheme shown in
Figure 10 (161). Equilibrium analysis of this reaction provides thermodynamic
information about intermediate steps 5 and 6 of the ATP hydrolysis scheme(Fig. 9).
Using the detergent-solubilized
SR vesicles, Kanazawa (147) studied thephosphorylation
step (Mg *E Pi + Mg . *E - P) and found that the equilibrium constant is very small (4) and strongly dependent on temperature;
the equilibrium favors the phosphoprotein state at higher temperatures. The
reaction is thus strongly endothermic, and the phosphorylated
enzyme is
l

l

*E”Pi

4

-I- Mg2+

‘!‘/
2’ +

Pi

k4

+ *E

Mg?CE*Pi

MgpE

refer

l

-k

Kg
+

Mg*%-P

Pi

FIG. 10. Reaction scheme for phosphorylationof Ca’+-ATPaseby Pi. All equilibrium
to direction of Mg *E - P formation.
Hence KS4 = KzKs.
lconstants

528

TAKAO

k?~?um 65

KODAMAstabilized by a large increase in entropy compared with the enzyme-phosphatecomplex. This important
finding has been confirmedwith different
preparations of the enzyme in several laboratories(20,148,191,194,235).
Kanazawa
et al. (148) studied the reaction over a wider range of temperatures(6-38°C)at small intervals and obtained a nonlinear van’t Hoff plot. The slope decreases
with temperaturerise. This result may suggest that the reaction is accompanied by a negative A& Considering
the difficultyof the experiment,
however, further
quantitative
discussion may not be warranted.
The AH for theformationof Mg . *E - Pi complex (reaction 6 in Fig. 9) has been estimatedby equilibrium
analysis of the reactions shown in Figure 10 and their temperature dependencies. Thermodynamic
parameters
obtained by these studiesof the phosphorylationof Ca2+ -ATPase by Pi are summarizedin Table 10.
Epstein et al. (78) made a calorimetricstudy of the interactionof Ca2+ATPase with M8+ and Pi. This work was an extension of their previous
study on the Na+-K+-ATPase(165). The result indicated that the binding ofeither M8+ or Pi to the enzyme was accompanied
by an extraordinarily
large
negative enthalpy change. The values of AH for reactions 1 and 3 in Figure
10 were -96 and -318 kJ/mol, respectively(78). Similar large enthalpy values
were obtained for the corresponding
reactions of the Na+-K+-ATPase(165).
On the basis of these results, Racker (232) argued that ion binding induces
a conformationalchange in the enzyme that is prerequisite
for phosphorylation by Pi.
Martin and Tanford(191) raised a doubt that the AH values obtainedby Epstein et al. (78) are not genuine thermodynamic
parameters
for theprocesses described by reactions in Figure 10 for several reasons, because
the values are not consistent with a modest temperaturedependence of theequilibrium
constants. For example, an enthalpy change of -318 kJ/mol for
Mti’ binding to the enzyme (reaction
3 in Fig. 10) would correspond
to adecrease of the equilibrium
constant for the reaction by a factor of 74 for atemperaturerise of 10 K (at 20°C). This would represent
an unusuallyhightemperaturedependence for an ion-protein
interaction.
Martin and Tanford(191) suggested a possibilityof a reversible
denaturationof the enzyme thatmight have occurred during lengthy incubationof the unliganded
form ofthe enzyme required for calorimetry.
Because transitionsof proteins between

TABLE

10. Thermodynamic
parameters
A TPase by Pi

forreactionsin phosphorylationof Ca2+-pump
Reactions“E + Pi - *E*Pi*E*Pi - “E - P

Stepsin Fig.

1+4or2+3
5

10

AH/kJ

mol-’

-4.21
+29 to +67$

$ Reportedt Data from Martin and Tanford (191).
on experimental
conditions (147, 148, 191, 235).

AS/kJ

K-’

mol-’

78-f
10-40

values vary considerably,

dependingApril1985

ENERGETICSOF MUSCLEATPASE

REACTIONS

529

native and denatured
states may involve large positive AH values (sect. IV),
reversal of denaturation
by addition of M8+ or Pi might give anomalously
large negative AH values for the apparent
enthalpy change of ion binding.
Note that from a thermodynamic
point of view, two routes taken for theformationof the ternary complex Mg *E Pi, 1 + 4 and 2 + 3, are equivalent,and hence A HI + A H4 should equal A Hz + A H3. However,the data presented
by Epstein et al. (78) indicate clearly that this was not the case.
l3. Transition
between two fundamental
states of Ca”-ATPaselconfmmational

Apart from the reactivities
toward ATP and Pi and the sidedness andaffinity of the Ca2+ -binding sites, there is now strong evidence that, whether
phosphorylated
or not, the ATPase exists in two distinct conformational
states.
a) Thermodynamics
of conformationaltransitionof unphosphorylated
enzyme (step 7 in Fig. 91. There is as yet no way to make a direct approach tothis transitionin isolation from other steps of the ATPase cycle. Arguments
therefore
are usually made on the basis of analysis of Ca2+ bindingandaccompanying
changes (61,223,252,284)
or on studies of M8+ binding (171,271) and vanadate binding (223).
An important
point suggested from these studies is that the equilibrium
between the E and *E states of unphosphorylated
enzyme consistently
explains the kinetic and equilibrium
data of apparent cooperative
Ca2+ binding.
Thus if there is more *E than E in the absence of Ca2+, the first Ca2+ binding
would involvea conversionof *E to E and hence have a smaller binding
constant. The second Ca2+ binding would occur on the enzyme already in the
E state, and the observed binding constant would therefore
be much larger
than the first one. In this case, even if the two binding sites have an identical
intrinsic
affinity for Ca2+, the observed cooperativityof Ca2+ binding can be
explainedby assuming a small value of the equilibrium
constant for thetransition
from the *E to E state, i.e., K7 N 10m3 (271). A similar small valueof K7 has also been inferredfrom the analysis of M$+ binding (171). On theother hand, a much larger value (KY II 10A2) would be acceptable provided
that the ratio of the Ca2+-binding
constants between the E and *E states islarge, say larger than 3 X 103. Thus the *E-state conformation
is more stable
than E-state conformation
by lo-17 kJ/mol.
In an earlier study, Masuda and de Meis (194) suggested that the transition from the *E to the E state is exothermic.
Pick and Karhlish(223)
estimated an accompanying
van’t Hoff enthalpy to be -85 kJ/mol. However,their study was performed
with a fluorescein-labeled
enzyme in which Ca2+ATPase activity and phosphorylation
by Pi are severely impaired.
Therefore
the observed value may not be the genuine thermodynamic
parameterforthe native enzyme.

530

TAKAO

KODAMA

Volume 65b) Conformationaltransitionof phosphorylated
enzyme (step 3 in Fig. 9).
The fact that the equilibrium
constant of this step is not far from unity was
first suggested by the presence of two populationsof phosphoenzyme
duringthe steady-state
ATP hydrolysis
by Ca2+ &ATPase (247). Inesi et al. (139) madea kinetic estimationof the ratio of the two phosphoenzyme
species andobtained an approximate
value of 0.5, which indicates the isoenergetic
natureof the two forms of phosphoenzyme.
De Meis and Inesi (55) examined theconditions
that favor the conversionof phosphoenzyme
formed by phosphdrylation
with Pi to the ADP-sensitive
form. They found that when the
enzyme was first phosphorylatedwith Pi at pH 5-6 at 30°C and then transferred to an alkaline medium of pH 8 at O”C, a large fractionof the phosphoenzyme
was converted
to the ADP-sensitive
form, as judged by thesynthesis of ATP. This result may indicate that the transition
from the*E - P to the E - P state is exothermic.
The method is not suitable, however,for estimationof the van’t Hoff enthalpy of this transition.
4. Calorimetricstudies of ATPhydrolysis

by SR vesicles

During the steady state of ATP hydrolysis
by SR vesicles in the presenceof Ca2+, nearly all the Ca2+ -ATPase proteins remain phosphorylated,becausephosphorylation
is much faster than hydrolysis.
Hence it seems that if acalorimetricmeasurement
is made of heat production
during the ATP hydrolysis, the total heat observed should be composed of two components,
asgiven byh 0b9 = ~ATP(-AHATP)+ ~EPGHEP)(9)where [ATp is the extent of ATP hydrolysis,and [Er is the level of phosphoenzyme in the reaction mixture, whereas AHATr and AHEp are the heats
of ATP hydrolysis
coupled to Ca2+ transportand of the phosphoenzyme
formation, respectively.
Thus, [ ATr (-AHATP)
is due to ATP hydrolysis,and&p(-AHEp)
comes from the formationof phosphorylated
enzyme and accompanying
changes such as occlusion of Ca2+. The measurement
has to bemade at low temperatures(<lZ”C)to slow down the overall rate of ATPhydrolysis
and also in the early phase in which the heat contribution
fromthe phosphorylation
would be significant
to the total heat production.
Kodama et al. (112, 156) performed
such a calorimetricstudy. Using thesame microcalorimeteras for myosin ATP hydrolysis(sect. IIIBQ), they observed that there was a rapid heat absorption
at the start of the reaction,
followed by a slower heat production.
They also found that during the first
few turnoversof the ATPase cycle, the observed heat was much smaller thanthe expected heat from the amount of ATP hydrolyzed.
This result implies
that the formationof phosphoenzyme
by the reaction of the enzyme with
ATP is endothermic(AHEp > 0), because Kodama et al. (155) earlier showedthat the ATP-driven
Ca2+ transport
inclusiveof Ca”+ binding
to internalApril1985

ENERGETICSOF MUSCLEATPASE

531

REACTIONS

sites is associated with little heat change after correction
for the heat due
from theseto the ATP hydrolysis.
The value of AH EP can be determineddata with Equation
9, and the heat for the phosphoenzyme
breakdown
canthen be calculated
as the difference
between heats for ATP hydrolysis
andfor the phosphoenzyme
formation.
In this earlier work, however, no correction
was made for the observed
heat from the interactionof buffer used with protons released on ATP hydrolysis coupled to Ca2+ uptake (see sect. IxC~). This correction
can be madeeither by measuring
H+ production
accompanying
the formation
and breakdown of phosphoenzyme
or by determining
the heat values with other buffers
having different
heat of protonation
values, as described in section IIICZ. The
latter approach has been adopted in the recent work with MOPS (AHbuffer= -21.0 kJ/mol) and BTP (A HbuRer = -43.4 kJ/mol) (157). The results indicatethat the heat of phosphoenzyme
formationis essentiallythe same in these
two buffers, suggesting that the decompositionof E - P is mostly responsible
for the liberationof protons accompanying
the ATP hydrolysis.
The reaction
heats for formationand decompositionof E - P corrected for heat fromthe interactionof buffer with these protons are given in Table 11.
F. Thermodynamic

Characterization

1. Thermodynamic

e$iciencyof Ca2+-Pump

A TPase System

of Ca2+ pump

The coupling of a transport
process to another spontaneous
processa plausible definitionof active transport.
The spontaneous
process, which

11. Possible sources of large enthalpy
Ca2’-pump A TPase reaction

TABLE

Reaction

Phaseschanges in

Sources

AH/kJ

mol-’

Fast, endothermic,t
AH = +55 kJ mol-’ATP binding
Splitting of ATP bondFormationof acylphosphate
ADP release
ADP + &I$+ - MgADP
Ca2+ occlusion

?
?
?
?
+15*
?

Slow, exothermic,t
AH = -70 kJ mol-’

E - P to *E - P transition
Ca2+ release*E - P - *E + Pi
*E to E transition
Ca2+ binding

Endothermic?
-249
Exothermic?

(4).

?, Value unknown.
t See sect.
6 Calculated from data of Martin

IxE&$ Calculated
and Tanford (191).

fromvaluesused by Alberty

is
is

532

TAKAO

KODAMA

Volume65

often ATP hydrolysis,is the drive for the transport.
Accordingto this definition, the total free-energychange for the Ca2+ transport
into SR by theCa2+ pump ( AGtotal) is
AG total= AGATP + nAGca

where AGATP is the free-energychange accompanying
the hydrolysisof 1
mol of ATP, and AGca is the minimum
work required to pump 1 mol of free
Ca2+ against the concentration
gradient, assuming the absence of an electricalpotential(see sect. IxCZ); n is the number of Ca2+ taken up per mol of ATPhydrolyzed
and is assumed to be 2. In living muscle cells, AGATP is constantand equals -61 kJ/mol at 25°C (sect. VIIIAI).
On the other hand, for thetransport
process
AGCa= RT In ([Ca”‘],,t/[Ca”‘]i,)

where the [Ca”‘] refers to the free-cation
concentrations
in both sides of the
SR membrane.
With these equations,the efficiency of free-energy
coupling
can be estimatedif a Ca2+ gradient([Ca2+]in-[Ca2+]oUt ratio) maintainedby
the Ca2+ pump is known. It must be recognized that the observed gradientis not a true equilibrium
ratio but rather a ratio brought about by the Ca2+pump and passive fluxes in physiologicalsteady states. It is also possible topredict the maximum
or thermodynamicallypossible limit of Ca2+ gradientthat the pump can achieve.
The physiologicallevel of Ca2+ loading of the SR is estimated to be onefourth to one-thirdof its maximum filling capacity (77). If it is assumed that
calsequestrin
is solely responsible
for Ca2+ binding and buffering
inside theSR (see sect. IX&?), [Ca2+]i, is calculated
to be 0.3-0.5 mM. It is estimatedthat the free [Ca”+] in myoplasm is --lo-? M or lower in resting muscle but
increases to -10V5 M when muscle is stimulated(26, 77). In resting muscle
therefore
the Ca2+ pump should achieve and maintaina Ca2’ gradientoflarger than 3 X 103, which is much lower than the theoreticallypossible limitof Ca2+ gradient(112 X 104). In other words, the efficiency of energy couplingin the Ca2+ transport
by SR is ~‘70%. This is probably
because as [Ca2+]i,
increases, passive Ca2+ leak through the SR membrane
becomes significant
with concomitant
slowdown of the Ca2+-pump activity (see sect. IxD;Z). Notethat at [Ca2+LUt below 10B7 M, the initial rate (in the absence of Ca2+ accumulation)of Ca2+ uptake and ATP hydrolysis
is markedly
decreased (217,294). [It has been mentioned
in other reviews that the coupling efficiency of
the Ca2+ pump is much higher, and the calculated
Ca2+ gradientis close to
the theoreticallimit (116, 270). However,the values of [Ca2+]in and [Ca2+lout
used in the calculation
are different
from those in my analysis.]On the other hand, only 20% of the free energy available
from ATPhydrolysis
is converted
into useful work to take up Ca2+ into the SR at[Ca2+loUt of 10B5 M, and the remainder
is used for rate accelerationand dis-AprilENERGETICS1985

OF MUSCLEATPASE

533

REACTIONS

sipated as heat. In fact, the SR vesicle shows the maximum
rate of Ca”+
uptake and ATP hydrolysis
at pK 5 (217, 294).
With the data for the maximum
Ca2+ -filling capacity of SR vesicles asa function of [Ca2+10Ut (217, 218a, 294), the Ca2+ gradient produced and maintained in vitro can be calculated.
The result indicatesthat the gradientsimilar to that for conditions in resting muscle are produced and maintainedby isolated vesicles.
2. Basic free-energy

levels of Ca”+-pump

ATPaseintermediates

The basic free-energy
diagram of the Ca2+-pump ATPase intermediates
is shown in Figure 11, which is derived from the values of equilibrium
constants listed in Table 9.
Three importantfeatures of the Ca2+‘-pump reaction are clearly illustrated
in this diagram: 1) there are two major steps that are associated with large
falls of the basic free-energy
level, the formationof Ca2 E ATP complex,
and the subsequentphosphorylationof the enzyme; 2) different
forms ofphosphoenzymes
are essentially
an isoenergetictransition
between whichtranslocationof Ca2+ and hydrolysisof phosphoenzyme
takes place; and 3)
the reversal of the conformationalchange, *E - E, is the major energeticallyunfavorable
process of the Ca2+-pump cycle.
The fundamental
reason that the formationof Ca2 E. ATP complex is
l

l

l

E
4

T
20 k J mol

-1

I

AG

FIG. 11. Basic free-energy
diagram for Ca2+-pump ATPase reaction of sarcopl .asmic reticulum(SR). Bas ic free-energychanges for transi tions between reaction intermediates
were calculatedwith equilibrium
constants listed in Table 9 with [Ca”+] of 10s6 and 10T3 M for outside and insideof SR vesicles, respectively.

534

TAKAO

KODAMAVohme

65

the major drive of the Ca2+-pump reaction is the large equilibrium constantsfor Ca2+and ATP binding to the enzyme whatever the actual binding sequencein the catalytic cycle. It is understandable that the high affinity for Ca2+ ofthe pump protein facing the external surface of the SR membrane should
be prerequisite for binding the cation, particularly when the [Ca2+loutis <10S6
M. The high affinity for ATP seems to be essential for the pump to operate
when the external Ca2+ is lowered further to a level ~10~~ M, such as in theresting muscle where the equilibrium of the Ca2+ binding is apparently notfavored.
A substantial fall of the basic free-energy level in the subsequent phosphoryl transfer reaction is mainly due to the dissociation of ADP into themedium that usually (both in the physiological situation and in the ordinary
assay system of the Ca2+-pump activity) contains a low concentration of thenucleotide. Indeed, the equilibrium constant for the actual cleavage of the
ATP terminal phosphate coupled to phosphorylationof the aspartyl residueof the enzyme is small (Table 9). Thus it is evident that if the ADP concentration in the medium were increased for some reason, the fall in the freeenergy level accompanying the phosphorylation would be decreased, and thefunction of the Ca2+ pump would be affected considerably. In fact, Dawson
et al. (49) showed in their 31P-NMR study of fatiguing muscle of the frogthat the decrease in mechanical relaxation rate is linearly related to anincrease in ADP concentration.
Because free ADP is dissociated at step 2 (see sect. IxDZ), it is desirable
to see whether the calculation of the free-energy change of this step is affectedby taking this fact into account. Usually, as in this review, concentrationsof ATP, ADP, and Pi represent all ionized (free) and Mg%omplexed
speciesof each component (see sect. III@. With the values of the acid-dissociation
constants and stability constants of free and Mg%omplexed
species of ADP(4), free-ADP concentration can be calculated, which turns out to correspondto -65% of the total concentration in the presence of 1 mM M2+ at neutral
pH. Thus this figure does not seriously affect the calculation of the freeenergy change for step 2. On the other hand, the contribution of interaction of free ADP with Mg+ to the heat change will not be negligible (seesect. IxF3).
The conformational change from *E to E does not proceed spontaneously.
Thus energy input is required for the pump to enter into the next cycle. This
energy deficit is compensated for by expenditure of a part of the large favorable free-energy change accompanying the Ca2+ and ATP binding followedby phosphorylation.
The rate acceleration is another matter, however, andATP may stimulate the transformation of *E into the E state through binding
to a low-affinity, noncatalytic site, as described in section IXDZ. [Boyer et al.
(31, 199) recently proposed the regulatory role of ATP in Ca2+ pump andother ion-transporting
ATPases.]AprilENERGETICS

1985

3. Natureof forces

stabilizing

OF MUSCLEATPASE

REACTIONS

Ca2’-pumpintermediates

535

An attempt is made here to assess which step or steps may contributeto the observed enthalpy changes for the rapid formationof phosphoenzyme
and its subsequentslow decay in the Ca2+-pump reaction (Table 11). The
calorimetricresults indicate that the phosphoenzyme
formationis endothermic and hence driven by a large increase in entropy, whereas the slow
phosphoenzyme
decay is strongly exothermic
and thereby makes the overall
Ca2+-pump reaction (ATP hydrolysis)
exothermic(see sect. 1xE4). In addition,
possible sources for large entropy changes during the Ca2+-pump cycle are
discussed.
a) Phosphoenxyme formation. Of reactions involved in the phosphoenzyme
formation,
association of free ADP (released on E - P formation)with M$+in the medium is the only reaction for which the enthalpy
change can be
estimated. It is evident, however, that its magnitude
is too small to accountfor the overall
endothermicityof the phosphoenzyme
formation.
Judgingfrom calorimetricresults of binding of nucleotides to various enzyme proteins
includingmyosin, it is likely that the M$+-ATP
binding is itself exothermic.
The enthalpy change for the dissociationof ADP uncomplexedwith M$+on E - P formationis also unknown.
Accordingto a recent study of ADP
binding to myosin subfragment
1 under various conditions(288), the binding
constants in the presence and absence of Mg? show similar temperaturedependencies,
suggestingthat the dissociationof ADP uncomplexed
with
M$’ from the myosin site may be endothermic.
Althougha simple extrapolation of this result to the Ca2+-pump reaction is not warranted,
it is intriguingto speculate that ATP binding
and ADP dissociation
thermallycancel each other (at least partially).
If this were the case, the remaining
three reactions (cleavage of the ATP-terminal
phosphate, formationof acylphosphate bond and the occlusion of Ca2+ bound to the high-affinity
sites)
together would be strongly endothermic.
Although the nature of the occlusionof Ca2+ is not yet known, it can be regarded as a manifestationof a certain
conformationalchange within the Ca2+ -ATPase molecule accompanying
theEP formation.
Thus there is a close analogy with the ATP-cleavage
stepof the myosin ATP hydrolysis,
which is endothermic
and accompanied
by acertain local conformation
change, as described in section VII.
b) Phosphoenxyme
decomposition.
The overallvan? Hoff enthalpy
forthe process of acyl-phosphatehydrolysis
and dissociationof the ternarycomplex, *E Mg . Pi (191), can explain about half of the observed enthalpy
change of this slow phase of the Ca2+-pump cycle. In addition,
the major
conformationalchange, E - P - *E - P, seems to be endothermic(139).
Thus other exothermic
steps should be looked for.
As described in section IxE3, the reversalof the conformational
state*E - E is probably
exothermic.
At present even the sign of the reaction
heat for Ca2+ binding to the high-affinity
sites of the Ca2+ pump cannot be
l

536

TAKAO

KODAMA

speculated. From the enthalpic
point of view, there are two classes of Ca”+binding
proteins.
TroponinC (226, 307, 308) and parvalbumin(202) show
exothermic
Ca2+ binding. On the other hand, recently, Tanokura
and Yamada(272) have shown by calorimetrictitrationthat Ca2+ binding to calmodulin
is endothermicand driven by a large increase in entropy. An importantpoint
is that the binding-site
structuresare very similar for these three proteins.
Thus the differencein the thermodynamic
propertiesof Ca”’ binding may
reflect the differencein the overall conformationalchanges of the proteins.
It is interesting
to see whether the structuresof binding sites of the pumpproteinshow any similarity
to those of other Ca2+-binding
proteins
andwhich class of the Ca2+-binding
proteins it belongs to. In this context thethermodynamic
nature of the reductionin the affinity for Ca2+ in the *Estate conformationis also of interest.
c) Sources for large entropy changes. Although quantitative
assessmentof enthalpic
and entropic contributions
to the free-energychanges for individual
steps of the Ca2+-pump cycle is not yet possible, it can be concluded
that several intermediate
reactionsare characterized
by large changes inentropy. Especially phosphoenzymes,
formed either by the interaction
withATP in the presence of Ca2+ or with Pi in the absence of Ca2+, are stabilized
by a large increase in entropy.
One possible source of such an entropy gain is a loss of water structure
as a conformationalchange in an enzyme molecule or a conformational
rearrangement
within its oligomeric
structure,
which takes place when theprotein-boundacyl phosphate
is formed
at the catalytic
site. Indeed, an
involvementof hydrationand dehydration
phenomenaat the protein-waterinterfaceof the Ca2+-ATPase has recently been suggested (52, 53, 56, 62).
De Meis et al. (56) found that phosphorylationof the enzyme is greatly
facilitatedin a dimethyl
sulfoxide (DMSO) and water mixture. De Meis (52)
proposed the hypothesisthat the catalytic site is more hydrophobic
in theabsence of Ca2+, favoring
Pi and the P-carboxyl group of the aspartyl residue
to react to form the acyl phosphate bond spontaneously.
The reaction would
proceed as if in a gas phase, where the hydrolysisof acyl phosphates would
be unfavorable,
as indicatedby large positive AH values calculated
on atheoreticalbasis (117; see sect. IV). The major effect of DMSO is to increase
the hydrophobicityof the medium and thereby further
favor the phosphorylation. Agreeing
with this hypothesis,
the van’t Hoff enthalpyof phosphoenzyme formation,i.e., the reversal of the hydrolysis
in the presence of
40% (v/v) DMSO, is strongly exothermic(AH = -85 kJ/mol and AS = -270
J l K-l mol-’ at pH 6.0) (59). This is a remarkable
contrast to the thermodynamics of phosphorylation
by Pi without DMSO (IxEZ).
In this hypothesis,
some water molecules should be released from the catalytic site on phosphorylationof the enzyme by Pi. DuPont and Pougeois (62) made a detailed
analysis of the water-activity
dependenceof the stability
constant of thephosphoenzyme
and obtained a result indicatingthat as many as 18 waterlApt-it 1985

ENERGETICSOF MUSCLEATPASE

REACTIONS

537

molecules are released from the catalytic site on phosphorylation.
In agreement with this observation
they also found that the phosphorylationis accompanied
by a decrease of the polarity
in the catalytic site.
The phosphoenzyme
formed is of course the ADP-insensitive
form. To
confer ADP sensitivity on it, reduction of the DMSO concentrationis necessary
together with addition of Ca2+ (56). This result indicates that water participates in the transition
from the *E - P to the E - P state. Althoughtherole of this water is not known, one possibility
is that the water would enter
the catalytic site on *E - P to E - P transition.
This view is consistent
with the observationthat the polarityof the catalytic
site of the ADPsensitive phosphoenzyme(formed by ATP) is not much different
from thatof the free enzyme (62).
Note, however, that such a differencein the polarity of the catalytic site
between the *E - P and E - P forms does not necessarily
negate the involvementof water-molecule
movement
in the formationof the latter phosphoenzyme
in the normal catalytic
cycle. For example, occlusion of Ca2+
bound to the high-affinity
transportsites of the enzyme, which accompanies
the E - P formation,must involvecertain changes in the interactionofprotein groups with water. Another possibility
for hydration
or dehydration
to be involved
would be changes in the interaction
between the ATPase
molecules, which exist as an oligomer(see sect. 1X&3), during the catalytic
cycle (222).

X. GENERALFEATURES

OF BIOLOGICAL

ENERGY

TRANSDUCTION

This review concentrates
on the mechanismand energetics of the two
major energy-transducing
ATPases in muscle, actomyosin of the contractile
machinery
and the Ca’+ pump of SR membrane,
which controls the activityof the actomyosin. Besides these muscle ATPases, ATPases of other energytransducing
systems essential for physiological
functionsof cells have beenstudied intensively
in recent years.g
On the basis of reaction mechanisms,
these ATPases are conventionallyclassified into either the actomyosin
or Ca’+-pump
type. During the ATPase
cycle, an enzyme-product(ADP + Pi) intermediate
dominates in the former,
as does the phosphoenzyme
intermediatein the latter. The dynein-tubulin
system belongs to the actomyosingroup (265, 276, 277). This system is theg Prof. Y. Tonomura, who died on November 28,1982, was a pioneer in studying the mechanisms of ATPase reactions in biological energy transduction.
We should appreciate that muchof the recent progress in this area originated from his idea, which has been developed over thelast three decades, when his first paper concerning the kinetics of actomyosin
ATPase reaction
was published (279).

538

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KODAMA

Volume65

molecular
entity responsible
for chemomechanicalenergy transduction
byflagelli in eukaryoticorganisms.
On the other hand, in a number of ion-transporting
systems of cell
membranes and intracellularorganelles, phosphorylated
forms of the ATPaseproteins play a key role in chemiosmoticenergy transduction.
An intriguing
exception for the membrane-boundATPases is the ATP-synthetasesystemsin mitochondria,
chromaffin
granules,chloroplasts,
and bacteria(7, ZZO),
which utilizes the proton-electrochemical
gradient
across the membranetoproduce ATP from ADP + Pi. In these systems, a myosin ADP Pi-like(107, 196,
intermediate
is formed rather than phosphorylated
intermediates
197, 241).
Apart from such a chemical difference in the major reaction intermediate
between these ATPase types, they share several common features that areprobably
directly relevantto the energy-transduction
mechanisms.
In thefinal section of this review, some of the salient points are emphasized, mainly
based on the present analysis of the muscle ATPases, but also referringtoother ATPases where appropriate.
l

A. Involvement
Translocationof SpeciJic Ligands
in A TP Hydrolysisland Their

A fairly complex and highly ordered piece of apparatus
is a prerequisite
for any energy-transducing
processes (303). In biological energy transduction
this is required
so that an ATPase molecule interacts with specific partner
molecules or ions in such a way that chemical potential is not merely dissipatedas heat but rather converted
into a useful work. Here these molecules andions are referred
to as ligands. For example, actin and Ca2+ are ligands formyosin and the Ca2+-pump ATPase, respectively.
The essential structuralrequirement
for the ATPase is that they have a specific site for binding aligand that is distinct from the catalytic site where ATP hydrolysis
occurs.
Thus the catalytic and ligand sites are physicallyseparated, and their interaction
is mediatedby distortionof a peptide chain within
an ATPase
molecule and/or change if any in interactionof subunits.
From an enzymologicalpoint of view, these ligands are enzyme activators.
In the absence of their respective
ligands, ATPases only catalyze the hydrolysis of their substrate slowly. Usually an ATPase has high affinities for
its specific ligands. A crucial point, however, is that to fulfill its role as anenergy transducer,
the ATPase should change affinities for ligands in a cyclic
way during the catalytic cycle. For example, the Ca2+-ATPase shows a highaffinity for Ca2+ to bind the cation at a low concentration
on one side of the
SR membrane(the myoplasm)
but subsequently
reduces its affinity to dissociate them into the other side where the cation level is much higher. The
effect of such affinitychanges is the translocationof Ca2’ across the SR
membrane. A similar principle may operate in the H+-translocating
ATPaseApril1985

ENERGETICSOF MUSCLEATPASE

REACTIONS

539

system, where the molecular complex of ATPase is disposed across the membrane, which separates two aqueous phases with different
proton-electrochemical potentials.
An actin filament may be regarded as a linear track of ligands. During
muscle contraction
the myosin molecules take states with low and high affinities for actin alternately
and tend to associate with and dissociate fromactin in a cyclic fashion. Thus myosin and actin filaments
slide past one
another
if muscle is allowed to shorten or produce isometricforce if notallowed.
Thus it seems a general property of energy-transducing
ATPases to have
intrinsic
affinities for their ligands, which are changed during the ATP hydrolysis cycle to translocate
ligands. A plausible hypothesisis that the affinities are changed at the expense of the chemical potentialof ATP. To be
more specific, however,
it is necessary to introduce
the basic concept that
the ATPase can inherently
assume two distinct conformational
states thatdiffer from one another in the propertiesof the ligand-bindingsite and thecatalytic site.
B. Alternation

BetweenFundamental

Conformational

StatesSpectroscopic
and other structuralevidence indicates that protein conformationalchanges do occur during the catalytic cycle of energy-transducing
ATPases. An orthodox view is that such conformationalchanges are inducedby chemical changes at the catalytic site, and a unique conformational
state
corresponds
to a specific intermediate
state of the enzyme.
On the basis of recent studies of the ATPase and some other enzyme
systems, however,it seems more plausiblethat the ATPase proteins exist
in two fundamental
conformational
states that are alternatedduring theenergy-transduction
process; changes in the state of ligand-bindingsites arefunctional
manifestationsof these conformational
states. A hypothesisis
proposed here that their relative populationis governed by chemistry of thecatalytic
site and occupancy of the ligand site. On one hand, a chemicalchange will result in a redistributionof the state population.
The catalytic
cycle is composed of a series of chemical changes. Some of these changes
cause significant
redistributionsof the state population(at least two of which
are in opposite direction for a cycle to be completed),but others do not. Theinteractionof the ATPase with ligands is then stabilized
and destabilized
in a cyclic manner during the ATPase cycle. Actomyosin(sect. VIII) and Ca2+pump (sect. IX) are good examples.
On the other hand, if a ligand stabilizes one of the two conformational
states of the ATPase protein that is not predominant
in the catalytic cyclein the absence of the ligand, its binding could result in the accelerationofthe catalytic cycle, provided
that ATP reduces the affinity for the ligand.
This is the activationof ATPase by a ligand.

540

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Thus the hypothesis provides a basis for explanationof the indirect link
between the catalytic event and ligand translocationand hence for energetic
coupling of chemical and physical processes.
C. Energetics

of ATPase

Cycle

In the proposed hypothesis
a series of chemical changes accompanying
ATP hydrolysis
at the catalytic site induces conformationaltransitionsofthe ATPase protein that bring the ligand sites into different
orientations
and affinities
in a cyclic fashion. For the myosin-ATPasereaction, some ofthese chemical events and accompanying
changes in protein conformation
can now be characterized
in thermodynamic
terms. In short, the major freeenergy change in ATP hydrolysis
is the binding of ATP to myosin, whereas
the free-energychange for the hydrolysisof myosin-boundATP is negligible.
The rest of this review is a discussion of how far these characteristicfeaturesof myosin-ATPhydrolysis
can be generalized
among various ATPases inreference
to their implicationin the energy-transducing
mechanisms.
1. Hydrolysis

of ATPon enzyme

Hydrolysis
of ATP into ADP + Pi under physiologicalconditions
is atypical exergonic reaction, and its major drive is the decrease in enthalpy.
In contrast with the situationin free aqueous solution, the hydrolysisof
E ATP andATP on myosin is virtuallyisoenergetic;
i.e., the intermediate
E (ADP + Pi) are in equilibrium.
Direct kinetic evidence has recently beenobtained that this also applies to the F1-ATPase reaction (107).
It is obvious that energy release on hydrolysis
of free ATP does not takeplace when the terminal
phosphateof ATP is split at the catalytic site ofthese ATPases. It is most likely that E. (ADP + Pi) is a key transit form
through which the energy is switched from chemical to physical form or viceversa. In muscle contraction,
ATP is bound to myosin with an extraordinarily
high binding constant. This may be referred
to as energy trapping.
On hydrolysis of the enzyme, the trapped energy is converted into the transit form,
which is then used to produce force when the cross-bridgetransition
occurs,probably from A Me ADP . Pi to the A M state. On the other hand, in synthesizing ATP on energy-transducing
membranes
where F1-ATPaseis themachinery
to make an anhydrous
bond between Pi and ADP, energy neednot be supplied to convert E*(ADP+ Pi) into E ATP. Thus, once ADP and
Pi bind together to the catalytic site of F1, a protein-boundATP is formed
almost spontaneously.
The complex is as stable as the myosin-ATP
complex,and energy input is required
to dissociate the complex, which is just the
opposite of the energy trapping
in myosin/ATP
interaction(30, 237).
What occurs in ATPases that form phosphorylated
intermediates?
For
the Ca2+-pump ATPase, the actual step in which the protein-bound
acyl
l

l

l

l

l

April1985

ENERGETICSOF MUSCLE

phosphate
is formed by transfer
specific aspartyl residue
Ca2eE*ATPATPASEof the terminal.- Ca2*E

541

REACTIONS

phosphateof ATP

to a- PeADPis also in equilibrium(see ref. 224). Accompanying
this reaction, Ca2+ boundto the high affinity
sites of the ATPase are brought
into a state that is
occluded from the bulk aqueous phase of either side of the membrane.
When
the phosphoenzyme
is transformed
into another form (*E - P), the Ca2+
sites are exposed again, but this time to the other side of the membrane,
and the affinity is reduced. This step of Ca2+-pump function
is critical to thetranslocationof the cations across the membrane, and probably is the energytransducing
step. Thus the phosphoenzyme
with occluded Ca2+ can be regarded
as the transit form of the energy-transduction
process. In the Na+-K+-ATPasesystem, the free-energychange for phosphoenzyme
formationfrom theE ATP is also suggested to be very small (88).
l

2. High-entropy

state of transit

forms

in biologicalenergytransduction

One of the most important
contributions
made by calorimetricstudiesof muscle ATPases is that the isoenergetichydrolysis
of ATP on myosin isendothermic.
This is of considerable
significancebecause it implies that the
M ADP Pi intermediateis stabilized by a large increase in entropy. In otherwords, the transit form in the chemomechanicalenergy-transduction
process
is in a high-entropy
state, whereas the strong binding of ATP to myosin andhence energy trapping
is driven solely by a large decrease in enthalpy.
It is important
to know if the E ADP. Pi intermediateis also stabilized
by entropy gain in the process of ATP synthesis by F1-ATPase. On the other
hand, formationof the phosphoenzyme
with occluded Ca2+ by interaction
ofthe Ca2+-ATPase with ATP has been shown to be endothermic
by calorimetry.
Althoughfurthercalorimetricstudies are required to resolve steps involvedin the phosphoenzyme
formation,evidence suggests that the transit form of
ion transport,
at least in the Ca2+ pump, is also in a high-entropy
state.
lll

3. Natureof transit

state withhigh entropy

Again in the case of myosin ATP hydrolysis,
it has been suggested that
there is a large loss of ordered water structurearound the hydrophobic
residuesof the proteinwith isoenergetictransition
from
M ATP toM ADP*Pi(sect. VIII@.
It is still too early to identify
which parts of the
myosin-waterinterphaseare mainly dehydrated.
An attractive
speculationis that the catalytic site becomes more hydrophobicon ATP hydrolysis.
Assuggested by theoretical
calculation,energetics
of hydrolysis
of so-called
high-energy
compounds in a hydrophobic
environment
is different
from that
l

l

542

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Volume 65

KODAMA

in an aqueous environment
in that the equilibrium
between reactants
andproducts would not be much favoredfor the latter. Thus the high-energy
phosphateester bond could be made spontaneously
in hydrophobic
environments. This is obviously
a very attractive
idea that could explain the spontaneous formationof ATP on F1-ATPase; i.e., energy input is not needed forformationof ATP itself but for its release.
In this context, note that the Ca2+-pump ATPase and Na+-K+-ATPaseare phosphorylatedby Pi under appropriate
conditions.
This is a typicalexample of spontaneous
formationof high-energy
acyl phosphatebond. In
the case of Ca2+-pump ATPase the reaction occurs in the absence of Ca2+ as*E + Pi + *E*Pi+ *E - P(Note that M$+ is essential for this reaction but for simplicity
has not been
written.)
Thermodynamic
analysis indicates that formationof *E Pi is accompanied by a rather large favorable
free-energychange (AG < 0) and isdriven by a decrease in enthalpy.
In contrast, the free-energychange over
the acyl phosphate-formation
step is almost nil (AG _N0), which is endothermicand hence driven by an increase in entropy. Thus, from a thermodynamic
point of view, the reaction sequence is analogous to that for the interaction
between myosin and ATP. An important
point is that an increase in themedium hydrophobicity
caused by adding certain organic solvents such as
DMSO strongly facilitates
the phosphorylation.
This is also the case for ATP
synthesis on F1-ATPase (241). In addition,evidence, althoughindirect, hasbeen obtained for the increase in hydrophobicityof the catalytic site of the
enzyme by releasing water during phosphorylation.
Because the reaction is
the reversal of phosphoenzyme
breakdownin the Ca2+-pump cycle, hydrophobicity of the catalytic site must increase at some step or steps preceding
the breakdown
in the forward
mode of operationof the pump. The most
likely step is the formationof phosphoenzyme
with occluded Ca2+.
Thus there is a general possibility
that hydrationand dehydrationatthe catalytic site is a crucial mechanism for the formationand decompositionof the transit state through which the energy is transformed
between chemicaland physical forms during biologicalenergy transduction.
l

I am grateful for all the help I received from N. A. Curtin, F. Morita, Y. Ogawa, .I. A.
Rall, and K. Yamada, who kindly read an earlier version of the manuscriptand gave manysuggestions
and comments. K. Kometani spent a great deal of time going over various draftsof the manuscript
and made many useful remarks.
Discussions
with M. Endo were extremely
valuable. Special thanks go to R. C. Woledge and Y. Ogawa for collaborationand stimulating
discussions
during my tenure in their laboratories.
I also wish to express my sincere gratitude
to S. Ebashi, who first advised me to take part in muscle protein calorimetry
and has given me
continuous
support and encouragement
since then.
My original work over the past several years, which is discussed
in this review, wassupported by grants from the Medical Research Council of the United Kingdom, the Ministryof Education, Science, and Culture of Japan, and the Naito Science Foundation.

AprilENERGETICS1985

OF MUSCLEATPASE

543

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