S3-5
シンポジウム3: 「物質間境界層に於ける環境適応機能の発現」
水溶液中における生体分子自己組織化過程の統計熱力学

Statistical thermodynamics of biological self-assembly in aqueous solution
木下正弘
M. Kinoshita
京都大学エネルギー理工学研究所
Institute of Advanced Energy, Kyoto University
1. Introduction
A material element exhibits high function when it is incontact or mixed with other material elements rather than when
it is independently present. We refer to a system comprisingmultiple material elements as a “complex system”. For example,
a complex system is formed by the contact of a metal withaqueous electrolyte solution or the dissolution of solute
molecules in solvent. The biological system is a typical complex
system. Biomolecules, a great diversity of molecular and ionicspecies, or water is simply material when each of them isseparately present. When they form a system, however, theircomplicated correlations can lead to life. In this talk, though theprincipal subject is the microscopic self-assembly or ordering
process in the biological system, it is argued that studies on
general complex systems are quite challenging and important.
2. Nonlinear behavior of complex system
The behavior of a complex system is far from thesuperposition of behavior of its individual elements. It is often
highly advanced and beyond imagination. When solute
molecules are immersed in solvent, for example, the interface
region whose structure and properties are quite different fromthose of the bulk solvent is formed near each solute molecule.
The structure and properties of the solvent confined between
two solute molecules are even more different. Moreover, thepresence of a solute molecule generates a space from which thecenters of solvent molecules are excluded. Upon the formationof a complex system, drastic changes such as the appearance of
these matters occur, leading to the exhibition of nonlinear
behavior. In studies on any complex system, it is necessary tocombine the concepts and approaches which have beendeveloped independently in different fields. Take themetal-aqueous electrolyte solution interface, for example. The
metal is a quantum system treated in solid-state physics. Bycontrast, the solution is a classical system requiring liquid-state
theory. It presents a new, difficult problem where these twosystems must be combined in a self-consistent manner. The
studies enlighten the creation of innovative areas. A complex
system is a treasure house of exhibition of novel and highfunctions leading to the development of new functional
materials and technology. I am a biophysicist with the skill of
liquid-state theory and collaborated with metal physicists,
electrochemists, and structural biologists. In these collaborations,
we could construct a new theory of the metal-aqueous
electrolyte interface [1], develop a new method for constructing
electrode structure for a fuel cell using the concept of“surface-induced phase transition” [2], and elucidate themechanism of molecular recognition [3].

3. Biological system
Multilevel problems must be solved in studies on life
phenomena: a molecular-level problem related to the structureand function of a biomolecule, properties and functions
exhibited by an ensemble of biomolecules, a cell-level problem,an organ or system comprising a number of cells, and a living
body. Multiscale analyses are thus required. A variety ofself-assembly and ordering processes are sustaining life. They
are microscopic, mesoscopic, or macroscopic. We have been
investigating those of a microscopic scale which occur only by asingle biomolecule or several biomolecules. Typical examplesof biological processes occurring at microscopic levels areprotein folding, protein traffic, ordered aggregation of proteins,
molecular recognition, unidirectional movement of alinear-motor protein along a filament, and exclusion of toxic
solutes from a cell by a protein complex. These processes can beargued on the basis of equilibrium thermodynamics for a closedsystem. By contrast, the problems of the cell level and larger
scales are expected to require the concept of “dissipativestructure” formed in a nonequilibrium and open system, just likethe macroscopic self-assembly in the plasma system.
The features of our study are as follows. We emphasize thecrucial importance of “entropic effect” and “entropic force”
originating from the translational displacement of watermolecules. Upon the biological self-assembly, the number ofaccessible translational configurations of water in the systemincreases considerably, leading to a large gain in water entropy.
The concept of the entropically driven self-assembly is thensuggested.
We
havedevelopedvery
efficientstatistical-mechanical approaches treating water andbiomolecules in atomic details [4-6] and succeeded in
elucidating a variety of biological processes [7]. As aninteresting example, in this talk I give some informative
calculation results obtained for the extrusion of toxic solutes(drugs) from a cell by ABC transporter [8].
4. Extrusion of toxic solutes (drugs) from a cell
The transporter first inserts the solute and then releases it. It
is quite mysterious that the two apparently opposite events,insertion and release, successively occur in the same system.
The structural change caused by the ATP binding to thetransporter should play essential roles in the switch from
insertion to release. In the bulk solvent, there is no spatial
distribution of the potential of mean force (PMF) formed.
However, in the solvent confined on the scale of a nanometer,
there is a spatial distribution in which the PMF becomes largely
positive and largely negative with the periodicity of the solvent
diameter dS. Here we analyze the entropic component of thePMF scaled by kBT (kB is Boltzmann’s constant and T is theabsolute temperature), S/kB. S is rather insensitive to theproperties of the solute and vessel surface (i.e., hydrophobic orhydrophilic). Figure 1 illustrates the entropic insertion of a soluteinto a cylindrical vessel. In the figure, S becomes lower as thecolor approaches dark blue and it becomes higher as the color
approaches dark red. The solute motion is severely influenced
by the distribution of S, and the solute is spontaneously
inserted into the vessel and confined within its cavity without
contacting the vessel surface. Once the solute is inserted, asillustrated in Fig. 2, it can be released by changing the spatial
distribution of S using continuous variation of the vesselgeometry caused by the ATP binding. In this case, the exit of thevessel is opened, and the diameter of a portion in the entranceside is made smaller by 2dS and the portion is continuouslylengthened. After the solute release, Pi and ADP (products ofhydrolysis of ATP) are dissociated, the transporter structure
returns to the other one, and the next solute insertion occurs. We
have shown that a variety of solute sizes can entropically behandled.

A serious problem in medical practice is that a drug quickly
looses its efficacy. The “multidrug efflux”, which means that thetransporter is capable of extruding a variety of drugs, can beelucidated when the entropic component dominates as describedabove. However, our result may imply that even useful solutes
such as sugar and amino-acid molecules are extruded. To solve
this problem, we have to account for the energetic component of
the PMF scaled by kBT, E/(kBT), as well. E is largely
dependent on the properties of the solute and vessel surface. If
the solute is hydrophilic and the vessel surface is not, forexample, the solute insertion does not occur because the soluteprefers to be hydrated in the bulk [9]. We intend to perform asystematic analysis accounting for both of E/(kBT) and S/kB
so that we can design a drug which cannot be extruded.

5. Future outlook
Though intimate collaboration by experts in different fields
is required in studies on the complex systems, suchcollaboration cannot readily be realized. Therefore, the studieshave lagged behind. In other words, there are lots of unresolved,important problems which are solvable only by interdisciplinary
research. The research leads to the systematization of new fields,
exploration of innovative areas, and development of novel

functional materials, drugs, and technology. The biologicalsystem, electrochemical system, and first wall-plasma interface
in a fusion reactor are typical complex systems. To accomplish
the biological research, the connection between problems of themolecular level and those of the cell level and larger scales isrequired. The theoretical approach toward the formation ofmacroscopic ordered structure and spatiotemporal pattern in the
biological and electrochemical systems are relevant to those in
the plasma system. Biophysicists, electrochemists, and plasma
physicists could collaborate on such subjects as the treatment ofhighly nonlinear problems, theoretical methods for the interfaces,
self-assembly in a nonequilibrium and open system, andmultiscale analyses and simulations. For example, some aspectsof the theoretical approach for the metal-aqueous electrolyte
solution interface might be applicable to that for the firstwall-plasma interface. Such collaboration, which has never been
performed, presents very much challenge.

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