Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5067 

ARL-TR-2367 November 2000 

A Computational Model of 

Soman-Induced Cardiac Toxicity (I): 

Simulation at the Cellular Level 

Csaba K. Zoltani 

Corporate Information and Computing Directorate, ARL 

Steven I. Baskin 

U.S. Army Medical Research Institute of Chemical Defense 

AaDroved for Dublic release: distribution is unlimited. 
Abstract 

Under a memorandum of understanding (MOU) between the Computational and 

Information Sciences Directorate (formerly the Corporate Information and Computing 

Directorate) of the U.S. Army Research -Laboratory and the U.S. Army Medical Research 

Institute of Chemical Defense, results of a study to model the electrophysiological changes in 

the heart due to soman toxicity are reported. This, the first of a series of reports, presents a 

computational model of cardiac toxicity at the cellular level and shows the changes in 

electrical activity for a series of organophosphate (OP) dose concentrations. expressed by 

changes in the acetylcholine concentration generated membrane currents. A plausibility 

argument is advanced for the consideration of an overlooked aspect of the problem, the 

effect of extracellular potassium ion accumulation, to the understanding of soman-induced 

electrophysiological chaos. 

.: 

* 

r: 
Acknowledgments 

It is a pleasure to thank D. Maxwell and R. Sweeney for pointers on soman experimental data 

and Dr. M. Adler of USAMRICD for his comments. Special thanks go the U.S. Army Research 

Laboratory (ARL) and the USAMRICD library staffs who went the extra mile to obtain 

information requested. 
iv 
Table of Contents 

1. 

2. Methods and Materials.. . _ f.~~~......_________.f_..**.....f.._._____........ff.._.__._f......f.~f...~~ .._f..f..ff- 4 

2.1 Prior Work ........................................................................................................... 

2.2 The Electrophysiological Model .......................................................................... 

2.3 ACh Accumulation: The Purves Model .............................................................. 

3. 

4. 

5. Discussion _ . _ _ .f.**......._._.______f................_.___*.........~..~~..~~_...*......ff..~~~~~~.*........--...-...*....f 22 

5.1 Effect on the SA Node ......................................................................................... 22 

5.2 Effect on the Purkinje Fiber ................................................................................. 24 

5.3 Effect on the Ventricle ......................................................................................... 24 

5.4 Effect of Extracellular Potassium Concentration ................................................. 24 

5.5 SUmmaly.. ............................................................................................................ 26 

6. References ..________ .__ f...~.~...___.____*__.f*....~.*f__....._..__..f.*.f..ff~.._____.._.*..f.........~~~...~..f....--.--- 29 

*.* 

Acknowledgments . . . . .._.___._~..*~.~.........~~~.*..........~..._.__._..f~*f.f.~~~~__._.*........~.~~~f.f~*.....~--- 111 

List of Figures _...... _ _.__________..f.....f._.______._..........._________ff........._f___._..f...f....___...f.....ff._

vii 

List of Tables _.____.__......f ~ f._______f._ + . . . . . ..-___.___... . . . . . ..f..______............_____.__....f_.________f + +... 1x 

Introduction . . . . + .f_f__________f..f~f..f_________._._.........ff.______. + ff..f.....______ + .. . . . .._....___.........._..____ 1 

; 

13 

Computational Approach. f*..............__...._..**.......f__._._.......f.f...._.._._..f.*.....f......_..**f.f. 16 

Results ........._______.....f... _ .._.________f_._.....f..._.______.___... + f..f.f...________....f......_..____f..f...f.f.__.___ 17 

Appendix .*_._ .___. . . fff...f.__________________.*......._..._________.f..._f..______._______fff...f......_.._*....

33 

Glossary.... .ff*.....~_f.______f__f_._.f.~....f..._._____.*f.......____.__.____f...~..~....._...__f.*f,f.....~~.._.___

41 

Distribution List __. _+._.. . . . . __ _ ____-...... + .f_______._........f______._.___._. + -._. ..__..__....ff.-._. ._._.. 43 

Report Documentation Page . ..___...............____..f....f......________._.......f._______. + .. . . . .._______._ 45 

V 
vi 
List of Figures 

Fimre 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

Schematic of ACh Discharge From Nerve Endings, After Feldman et al. (2000) ..... 

Electrical Pathways of the Heart ...................................................... l_..____ .................. 

Schematic of the Synaptic Process After Hille (1992) ............................................... 

Schematic of the More Important Membrane Current Pathways of a Cell.. .............. 

Second-Messenger Pathways in the Cardiac Cell Membrane, After Hille (1992) ..... 

Action Potential of the Rabbit SA Node Under Normal Conditions ......................... 

Action Potential of a Sinoatrial Cell .......................................................................... 

Top Curve Shows the Action Potential in the Purkinje Fiber Cell.. .......................... 

Effect of ACh-Activated Potassium Current on a Ventricular Cell ........................... 

Effect of the Change in the Concentration of [K+10 on the AP of the SA Node.. ...... 

Effect of the Change in the Concentration of [‘?I0 on the AP of the Purkinje 

Fiber ........................................................................................................................... 

m 

3 

7 

8 

10 

11 

1X 

19 

19 

20 

21 

21 
. . . 

Vlll 
List of Tables 

Table & 

1. Summary of Effect of ACh on Cardiac Function f.f.f.....f.f....f_._____.__________..fff...f.. e .. . . .._ 2 

2. Simulation Studies of the Effect of ACh Concentration on Membrane Currents.... _. 14 

3. Contrast of Cell Behavior With Increase in ACh-Induced Potassium Current.......... 22 

A-l _ Rate Constants and Concentrations Used in the Simulation. f.._f_____________........... e .. . . . . . 40 

ix 
C 

I 

X 
1. Introduction 

Pulmonary and cardiac symptoms are the primary indicators of soman poisoning. The cardiac 

effects are discussed in detail in this report. The primary interests are the underlying 

electrophysiological changes at the cellular level that manifest themselves in bradycardia, 

arrhythmia, and asystole. 

Soman belongs to the class of organophosphate (OP) nerve agents that are also used in the 

civilian sector in insecticides. OP can induce a wide variety of toxic physiological changes, as 

discussed for example by Roth et al. (1993), Hassler et al. (1988), and Golomb (1999). OP binds 

to acetylcholinesterases (AChE) (Hartzell 1988), preventing hydrolysis and leading to an 

increase in acetylcholine (ACh). This overload changes the activity of the sinoatrial (SA) node 

and causes negative inotropy and arrhythmia not only in the atria (bradyarrhythmia), but also in 

the Purkinje fibers; it also produces electrical conduction anomalies. In addition, the absence of 

choline& agonists increases the calcium influx and stimulates its uptake in the sarcoplasmic 

reticulum (SR), thereby increasing the intracellular calcium. There is some evidence (Wang 

1997) that an overload of cellular Ca” within the SR can also lead to atria1 arrhythmias. 

ACh dramatically alters gating properties of cellular membrane channels, such as iki 

channels. It increases intracellular Nd activity. The physiologic changes are not uniform in all 

cardiac structures. The Purkinje fibers and the SA node experience different degrees of 

impairments than the ventricles and atria. Other factors may also enter the picture. A rise in 

plasma acetylcholine is accompanied by a fall in coronary blood flow. According to McKenzie 

(1996), OP toxicity is thought to lead to “vasospasm followed by myocardial ischemia and 

cardiac dysfunction.” The cardiac muscle is mainly aerobic. An excess of acetylcholine at 

muscarinic myocardial receptors sites results in an increase in oxygen uptake in the muscle. 

Blocking these muscarinic sites with atropine can lead to myocardial infarction in hypoxemia. 

High concentrations of ACh also elicit negative inotropic effects. Ancillary manifestations 

are lesions in the atrium, hypotension, and vasodilatation. In rats, soman-produced ECG changes 
include reduced P-wave height, prolonged P-Q interval, a QRS complex, and AV-block. There 

is scant in vivo data in man, but cholinesterase inhibition is known to cause increased electric 

systole and, in some cases, torsade de pointes (Baskin and Whitmer 1991). 

At the cellular level, ACh increases K+ permeability (conductance) via G-protein-gated 

channels leading to 

(1) opening activation gates of iK,*ch, 

(2) decreasing amplitude and duration of action potential, and 

(3) slower pacemaker depolarization. 

Table 1 shows the effect of ACh on cardiac function. OP agents antagonize (AChE) at cardiac 

sites, leading to an excess of ACh and atria1 modulation of the negative chronotropic effect of 

ACh. The basic assumption is that since AChE is vital to survival, once its concentration falls 

below a certain limit, which varies among animal species, the subject dies. Green (195X) 

suggests that LD50 be defined as 10% of the essential level needed for survival in the absence of 

an acetylcholine antagonist. 

Table 1. Summary of Effect of ACb on Cardiac Function 

I SA Node Decreases rate of spontaneous diastolic depolarization. Hyperpolarizes node. 

AV Node Slows conduction. Lengthens refractory period. I 

Atrium Shortens AP and refractory period duration. 

Purkinje Fibers May shut be shut down by excess. I 

II Ventricle Induces inotronic effect. II 

There is a parallel between soman and flouxetine (Prozac group of antidepressants), or for 

that matter cocaine. Prozac boosts serotonin by blocking reuptake of the neurotransmitter into 

the cells that originally released it. This leads to elevated levels of serotonin and other 

neurotransmitters, such as dopamine, while soman acts as an “ACh uptake inhibitor.” Figure 1 

provides a schematic of ACh discharge from nerve endings modeled after Feldman et al. (2000). 

2 

F 

: 
Synaptio 

Clef4 

Choline * 

Figure 1. Schematic of ACh Discharge From Nerve Endings, After Feldman et al. (2000). 

In the present project, a mathematical model of cardiac toxicity induced by OP is under 

development. Given an LD50 dose of soman and the ancillary overload of ACh, the question 

addressed is: What are the effects on the electrophysiology of the heart? 

Since cardiac toxicity fmds a marked expression in the rabbit, it was adopted as the animal 

model (Dokos et al. 1998). Where available, references to experiments with other animals are 

also made. The manifestations of the presence of OP is an ACh overload. In recognizing this, 

single-cell calculations of the effect of ACh overloading are presented using the Oxford Heart 

3 
program, Oxsoft Ltd. (1997). Particularly, calculations are presented showing how ACh 

overload affects the individual membrane currents and its overall effect on the resulting action 

potential. The approach is to gauge the effect of changes in potassium conductance (gk) and two 

of the membrane currents important in pacemaking (if and ik,ACh) on the electrophysiology of the 

cardiac cell (i.e., the development of the action potential). 

It is known that [K+],, the extracellular potassium concentration, influences the 

transmembrane resistance in Purkinje fibers. Elevated concentrations result in 

higher-than-normal conductance. Hyperkalemia can also result in sudden cardiac death. There 

is a direct causality between soman poisoning and changes in action potential (AP) of the heart, 

and the connection is investigated in this report. This investigation leads us to suggest the 

importance of the overlooked aspect of soman intoxication, excessive potassium extracellular 

concentration, and propose possible new avenues for therapy. 

The answers to several subsidiary and important questions are deferred for later. These 

include the effect of the toxic environment-induced gene mutation of ion channel configuration, 

the effect of the “aging” process affecting AChE-OP complex, and the presence of OP 

scavengers on the ionic currents. 

2. Methods and Materials 

2.1 Prior Work. Baskin et al. (1991) summarized much that was known about cardiac 

toxicology due to OP agents. Subsequently, experimental observations of the effect of soman in 

general have appeared, but Little related specifically to the heart. Computational models remain 

scarce; with few exceptions, those existing address ancillary issues such as the effect of ACh 

pulses on the membrane ion dynamics. 

i 

The effect of ACh on individual sinoatrial node cells includes activating the 

acetylcholine-activated potassium current, iK,ACh, which indirectly decreases the L-type calcium 

current and the hyperpolarization-activated current, ir. Using this formalism, Sears et al. (1999) 

4 
studied postexercise heart rate mimicked by higher potassium concentration and its effect on ir 

and iK,AChSeveral research groups have presented mathematical models of the effect of repeated pulses 

of ACh on the action potential on pacemaker cells. Yanagihara et al. (1980) showed that for the 

rabbit SA node, an ACh-induced K current (ik,Aci,) with ACh concentrations of 5 x lo-* and 10m7 

decreased the spontaneous frequency from 173 to 132 and 79 beats/min, respectively. At a 

concentration of 2 x lo-‘, it ceased completely. They noted that the hyperpolarization was 

caused by a gradual activation of i A& with a time constant of 110 ms. 

Michaels et al. (1984) showed the phase dependence of a brief (50 ms) ACh pulse on the 

action potential. A pulse introduced at 127 ms produced a hyperpolarization of 4.9 mV, and the 

cycle was lengthened by 112 ms. The same pulse applied later at 280 ms hyperpolarized the 

membrane by 17.5 mV and prolonged the cycle to 548 ms. This was in line with earlier 

experimental findings that introducing the pulse later produces longer cycle times. Higher 

concentrations of ACh elicit larger phase shifts. It was also noted that at very late times in the 

cycle, a “latent” period is observed (i.e., the ACh pulse effects are postponed until the following 

cycle). Repetitive acetylcholine input synchronization of the sinus pacemaker was observed. 

Dexter et al. (1989a, 1989b, 1994) developed a mathematical model to predict the rate of 

degradation of ACh in the neuroeffector junction. A decline of the sinus period in anesthetized 

dogs was observed. 

Dokos et al. (1996) presented a single-cell model of the chronotropic response of the SA 

node to brief-burst vagal stimulation by acetylcholine. The three submodels discussed were the 

ACh release by vagal stimulation at the SA node and activating ik,Ach when ACh binds to 

muscarinic receptors. These rely on data taken from guinea pig myocytes. The second 

submodel is a three-compartment model of ACh kinetics at the neuroeffector junction. Finally, 

ACh-inhibited if, operative only in cardiac tissue capable of spontaneous activity, and iCa,L in SA 

cells are discussed. Data taken on rabbit SA node cells were used. The effect of ACh was 

5 
shown by Dokos to result in strong hyperpolarization of the membrane and a prolonged cycle in 

a phase-dependent manner. In a related paper, Dokos et al. (1997) showed for a cycle length 

recovery after prolonged vagal stimulation for a single-cell rabbit SA node. Refer to Table 1 for 

a summary or see Dokos et al. (1998) and Demir et al. (1994). 

These models rely on the Hodgkin-Huxley (HH) formalism whereby the experimental ionic 

current data is curve-fitted and coupled to first-order activation equations of the form 

Y 

du/dt =(x, *(l-u)-& *u, (1) 

where u is a gating variable, and the coefficients of opening and closing, a,, and pU, are functions 

of the ACh concentration. Dokos et al. (1997) has subsumed the effect of the G-protein into this 

formulation. 

Other related works are those of Trautwein and Dude1 (1958), Magleby and Stevens (1972), 

Bristow and Clark (1983), and Egan and Noble (1987). Ancillary chemical effects of ACh 

inhibition of the SA node were examined by Kale et al. (1999). They were able to demonstrate 

the suppression of CAMP by acetylcholine by G-protein effects. 

Sweeney and Maxwell (1999) presented a single compartment model of an OP interaction 

with AChE and CaE, OP scavengers. They obtained an “OP toxicity surface” that shows, for 

example, relative initial concentrations of OP/AChE as a function of the binding rate of 

CaE/AChE, where hydrolysis and CaE protect against OP poisoning (see also Maxwell et al. 

1988, 1991). 

Though useful contributions to the general understanding, none of these authors offer a 

comprehensive and quantitative approach to the changes induced in the cellular dynamics and 

the resulting pathologies caused by soman. This report contributes to establishing that 

quantitative relationship. 
2.2 The Electrophysiological Model. The SA node may be considered the most important 

component of the heart due to the centrality of its function. This node mnsists of a group of 

specialized cells at the superior portion of the junction between the right atrium and the superior vena 

cava, and it controls the rhythm of the heart, see Figure 2. In turn, the behavior of its constitutive 

cells depends on the synchronous functioning of at least eight membrane curreuts. Thus, examining 

the vulnerability of these cells to OP toxicity is a logical starting point in these studies. 

Figure 2. Electrical Pathways of the Heart. 

The parasympathetic innervation of the cardiovascular system occurs through the vagus 

nerve. The innervation is thought to be limited to the SA node and the atrioventricular (AV) 

junction. The ventricles participate little, if at all, in this process, although ACh binds to the 

receptors in the endothelium, the layer of cells that line the heart. ACh binds to the muscarinic 

receptors of the target tissues (i.e., the SA node), the AV junction, and the endothelium. 

7 
Nerve impulses into the axon terminal trigger the processes that lead to release of ACh, 

followed by interaction with the acetylcholine receptors, and conductance increase of specific 

ion channels in the postsynaptic membrane (Rosenberry 1979) and postsynaptic endplate 

currents, see Figure 3. These sequence of events then contribute to the processes that result in the 

action potential and, ultimately, the expansion and contraction of the heart muscle. 

Figure 3. Schematic of the Synaptic Process After Hille (1992). 

Katz (1992) defines pacemaker activity as “an instability of diastolic (resting) potential that 

initiates a propagated action potential.” The pacemaker activity is the result of the decay of the 

delayed, outward rectifier current (ik) that appears during the plateau of the action potential. The 

inward, anomalous rectifier current (iK1) also contributes to the pacemaker activity. 

t 

There are two primary inward currents (ica) active at the end of repolarization; they regulate 

cardiac contraction and if, the most important pacemaker current. The sodium current mediates 

8 
f 

. 

* 

the heart rate by the autonomic nervous system. This is apparent from the changes in the slope 

of the diastolic depolarization. 

Heart rate is slowed by vagal stimulation and increased by P-adrogenic agonists. In turn, 

these are mediated by Gi and G, proteins on channels that carry if. Gi is inhibitory and 

dominating and causes vagal slowing. 

Both the Na and the K conductance change during depolarization. While Na permeability 

rises rapidly before decaying, R conductance attains a plateau and subsequently decreases 

rapidly to resting levels during repolarization. 

One of the earliest works on ik,Ach was by Osten-ieder et al. (1980, 1981). Of the five 

muscarinic receptors, he noted that the MZ and M receptors inhibit adenylate cyclase @DC) 

activity. These receptors preferentially couple the Gil0 family of G proteins. Inhibiting ADC 

reduces the phosphorylation of the L-type Ca” channel, reducing icaL, and reducing the 

hyperpolarization activated current if. Cholinergic inhibition of ica,L was also observed (Demir 

et al. 1999) due to cGMP-stimulated CAMP. Phosphodiesterase (PDE) hydrolyzes CAMP, thus 

inhibiting 

CAMP-dependent phosophorylation of L-type Ca” channels, see Figure 4. 

In muscarinic ACh-dependent channels, activating iK,Ach requires splitting a CTP-binding 

G-protein. When both Gi and G, are antagonized, ikJ,ch is eliminated. 

The direct effect of ACh is expressed by activating the ACh-sensitive Ki channel. Binding a 

muscarinic agonist to a receptor results in a configuration change, and a signal is sent to the 

G-protein in the membrane lipid bilayer. GTP binds to an a-subunit and activates the G-protein. 

In the process, the G-protein dissociates into the a, /+y subunits, which enable, the channel 

opening. The deactivation results upon the hydrolysis of GTP to GDP, and the channel closes as 

a result. 

9 
5 

Figure 4. Schematic of the More Important Membrane Current Pathways of a Cell. 

The indirect action of ACh is expressed when ACh binds to muscatinic receptors and 

activates the Gi protein, resulting in the inhibition of the activation of ADC. This step slows the 

activation of CAMP-dependent protein kinase and reduces the phosphorylation of Ca” channels. 

There are two paths, direct and indirect. In the direct pathway, the neurotransmitter ACh 

activates the GTP-ase of the Gi protein. h subunits bind to the KAch channel, causing an 

increase in the muscarinic current iAct+ See Figure 5 and Accili et al. (1998). 

The intracellular second messenger, CAMP, mediates the indirect effect. Changes in CAMP 

produce if. In summary then, the SA node pacemaking potential results from 

(1) the decay of the outward flowing K’ current ik, which was activated during the 

previous action potential cycle (the decay mediates inward background current to 

depolarize the cell); 

(2) if’s contribution to the depolarization becoming prominent as the diastolic potential 

becomes more negative; 

10 
Figure 5. Second-Messenger Pathways in the Cardiac Cell Membrane, After Hille (1992). 

(3) the ica current becoming important in the later portion of the cycle; and 

(4) the possibility of the Na-K pump currents and Na-Ca exchanger currents playing 

secondary roles. 

11 
During prolonged exposure to ACh, the level of iK,ACh fades from desensitization. This 

current is thought to be directly activated by the G-protein GK that links the muscarinic receptor 

to K+ channel; thus, it has been postulated that desensitization is a result of modifying the GK 

protein or the K+ channel. Zang et al. (1993) reported a reduction to 22% of the peak value over 

time of the current when muscarinic receptors are activated by ACh (see also Boyett et al. 1995). 

5 

In this, the first of a series of communications, the changes in the electrophysiology of a 

single cell of the SA node, Purkinje fiber, and ventricle are considered. The effect of an overload 

of ACh is examined, as expressed by the membrane currents, which are in turn responsible for 

the action potential in these cells. The initial calculations consider only ACh overload based on 

soman LD50 data for rabbits. 

Cell models continue to evolve. For the SA node, the models of Demir et al. (1994, 1999) 

are the most up to date. Until 1985, the Purkinje fiber cell models did not treat the pacemaking 

currents correctly. The DiFrancesco-Noble formulation, which comes in several forms, is now 

accepted as the closest to experimental observations. For ventricular cells, the Noble et al. 

(1991) model and its improvements are most widely used. 

When the vagal nerve is continuously stimulated or ACh is applied to a tissue sample, ACh 

has a negative chronotropic, inotropic (influencing contractility), and dromotropic effect (factors 

that change the time needed to complete one beat). Due to phosphorylation or 

dephosphorylation, these fade over time as a result of desensitization. On the other hand, if and 

i,, are unaffected. In particular, note the following: 

(1) A low dose of ACh inhibits if by the indirect pathway. The if activation curve is shifted 

in the hyperpolarization direction. 

(2) High doses of ACh (10e6 - 10m3M) activate the muscarinic K.” current i,,,,h by the 

indirect pathway. 

12 
. 

(3) ACh produces conductance change, whereby the K’ ionic channels are enabled. 

(4) ACh affects if at concentrations lower than that required to affect iK,ACh. 

(5) The effect of ACh on iK,ACt, shows rapid desensitization. 

(6) ACh inhibits the L-type calcium current, iCa,L. 

Table 2 summarizes the simulation studies that included the effect of ACh on membrane 

currents. 

2.3 ACB Accumulation: The Purves Model. The amount of ACh present in the synaptic 

cleft is one of the crucial variables in the problem. The hypothesis undergirding this study is that 

the persistence of an excess of ACh is a direct measure of the effect of soman on the heart. Thus, 

it is important to establish the expected concentration of ACh for a given soman loading. 

ACh is stored in a large number of vesicles in the presynaptic endplate terminal whose area is 

taken to be typically to be around 2,000 pm2, and the density of receptors on the average is 

around 2 x lo7 (Michelson and Zeimal 1973; Katz 1969; Koelle 1963). Assuming the number of 

AChE molecules near the neural effector junction to be of the same order as the number of 

receptor sites, the presence of 10’ soman molecules would deprive all sites of AChE and thus 

from hydrolyzing ACh. It follows that a concentration of soman of the same order or greater 

would mediate the maximum effect in iK,*Ch and if. 

Purves (1977) showed that the ACh concentration after a single stimulus to the vagus nerve 

can be expressed as 

(2) 

13 
Table 2. Simulation Studies of the Effect of ACh Concentration on Membrane Currents 

Reference Animal Model ACh Concentration Pulse Effect(s) Noted Tools Used 

Width 

Yanagihara et al. (1980) Rabbit SA 5x10-‘M - Heart Frequency ACh Concentration 

1~10-~ M 

ZX~O-~ M 

Bristow and Clark (1983) Rabbit SA - - Cycle Length Bursts of ACh 

Michaels et ai. (1984) Rabbit SA 1~10-~ M 50 ms Cycle Length Single, Repetitive ACh Pulses 

Noble and Noble (1984) Mammalian SA - Frequency I& Concentration Change 

Egm and Noble (1987) Rabbit SA 1~10-~ M, 2x@ M - Cycle Length K-current 

Arrest Condition Conductance Change 

ACh Conductance Change 

Dexter et al. (1989a) - 5OllM - Half Life Vagal Stimulus 

Dokos et al. (1993) Rabbit SA 0.001 n-&f to 0.01 - Cycle Length ACh Pulse 

Zhang et al. (1999) Rabbit SA 0.09mMandO.l mM - Shift ACh Concentration 

Sears et al. (1999) Guinea Pig iK,AC set at 50 pA - Frequency Extracellular I( at 3,4, 8, 10 n&l 

Demir et al. (1999) Rabbit SA 0, 10,100 nM - Frequency Bath, Vagal Stimulus 
where U = 1 for t > to, and 

U(t - t 0 ) = 0 elsewhere. (3) 

Here, to is the time of the quanta1 release, and M is the amount of ACh. The total ACh is 

the sum over all the bursts. The equation takes both diffusion and chemical change into account. 

There, x is the distance between release sites, typically 7.5 x 10m6 cm, and D is the diffusion 

constant. Bristow and Clark (1983) give a value of 5.14 x lo-” cm2/s for the diffusion constant. . 

They found an ACh concentration per pulse of 0.1 pM. This is considerably higher than the 

lo-l7 moles per nerve impulse (or 5 x lo6 molecules of ACh liberated) cited by Michelson and 

Zeimal (1973). The latter authors also state that between 200 and 300 vesicles are discharged in 

the synaptic cleft in 1 ms. 

The hydrolysis rate constant, kh, has a value of 50 s-l. Enzymatic hydrolysis of ACh 

terminates the action. Also, frequent stimulation results in exhausting the ACh stores in the 

nerve endings. 

In the effective stimulus, S in a plane, where the receptors cover a plane of radius r, with r 

very large 

’ = (KDt)‘.’ 

BM exp(-x2/4Dt), (4 

where B is a constant and, as stated by Purves (1977), “relates to the sensitivity, etc., of the 

receptors and whose dimensionality is appropriate to the particular circumstances.” M, as 

before, is the amount of released ACh. 

Maxwell et al. (1991) noted that, for the rabbit SA node, E&, for contraction in the atria, the 

concentration necessary to produce 50% of the maximum response was 4.1 x 10m6 M for ACh. 

15 
At the same time, they reported that soman concentration of 10m6 M or greater produced 

complete ACh inhibition. Thus, for the rabbit SA node, it is not unreasonable to hypothesize that 

ACh concentrations exceeding EC 50 are of special interest and would mediate the maximum 

effect in ik,Jch and if . 

3. Computational Approach 

The computational model is based on the electrical representation of the cardiac cell by a 

system of equations expressing the electrical and chemical activity of the cell. 

The presence of OP was simulated by an increased presence of ACh, as reflected in ik,Ach, if, 

and a change in the potassium conductance. In addition, simulations were run with varied 

extracellular potassium concentrations. The rate of change of the membrane voltage, 

equation (A-26) was solved, with the membrane currents depending on a model such as 

equations (A-l)-(A-32). 

A Runge-K&a-Merson integration with automatic step-size adjustment based on error size 

was used to solve the system of eq,uations. Single cell calculations were run on an NT 

workstation. Simulations encompassing large arrays of cells, in preparation at the present time, 

require the 12%node Origin 2000 of the MSRC. 

In the first series of calculations of a SA-node cell, the potassium current induced by ACh 

was increased from the normal condition up to where soman was thought to have neutralized in 

excess of 95% of the AChE. 

The calculations were repeated, but with the external (to the cell) potassium concentration 

changed from the normal state of 5.4 mM to 10.0 mM. The ACh overload calculations were also 

16 

r 

repeated for the Purkinje fiber and the ventricular cells. 
4. Results 

This computational study was directed at examining how membrane currents change in 

response to concentration changes in ACh induced by the presence of soman. This allows for 

determining the critical conditions that culminate in the shutdown of the action potential. The 

sensitivity of the SA-node, the Purkinje fibers, and the ventricular cells could then be contrasted 

and compared with experimental data from the literature. Oxsoft Heart, version 4.8 (Oxsoft Ltd. 

1997), was used in the calculations. 

The result of the set of runs is shown in Figures 61 l_ Changes in concentration of ACh 

were expressed in the induced currents and approximated the effect of a soman level 

corresponding to LDso. 

The important observations of this study are the following. 

(1) An ACh overload can suppress the action potential of the Purkinje fibers. 

(2) In line with and in addition to earlier experiments and published data, ACh overload not 

only produces bradycardia, but can also arrest the heart at high levels of induced K’ 

current. 

(3) In the animal model used in this study, the action potential in the sinoatrial node 

terminated whenever iACh,k exceeded 0.0023 nA. 

(4) In the presence of elevated ACh, if is depressed. 

(5) In the presence of ACh, iCa,L is depressed. 

17 
(6) ACh overload in the ventricle shortens the action potential a notch in the voltage in 

phase 2, and ultimately ceases the calcium current. This suggests incipient onset of 

fibrillation. 

The action potential of the rabbit sinoatrial cell and calcium membrane current, iCa, are 

shown in the first panel of Figure 6. The resting potential is at -50 mV, and after a gradual rise 

for 0.1 s, there is a steep rise, though much gentler than the corresponding rise in the ventricle. 

Following the plateau region, the drop steepens as repolarization takes place. Increasing the 

acetylcholine concentration lengthens the period, as shown in Figure 7, a 20% increase. The 

action potential ceases at a value of ix,Ach = 0.02 nA. 

Figure 6. Action Potential of the Rabbit SA Node Under Normal Conditions. The Top 

Curve Shows the Action Potential, the Lower Trace icp . 

; I 

Figure 8 shows the behavior of the Purkinje fibers to ACh overload induced by iK,Ach. The 

action potential is totally suppressed when the current increases to 9 nA. Purkinje fibers under 

ACh overload exhibit bradycardia, and the action potential eventually disappears. 

18 
Figure 7. Action Potential of a Sinoatrial Cell. The Second Displaced Curve Shows the 

Effect of ACh-Activated Potassium Channel. The Current is 0.0018 nA. When 

the Current Reaches 0.0024 nA, the Action Potential Ceases, Shown by the Flat 

Trace. 

Figure 8. Top Curve Shows the Action Potential in the Purkinje Fiber Cell. With Increase 

in the ACh-Activated Potassium Current, the Curve is Shifted, Increasing the 

Period. The Values of the Activating Current Are 1,5, and 9 nA, Respectively. 

At 9 nA, the Action Potential Ceases, Shown by the Flat Trace. The Lower 

Traces Show the Corresponding ir (Grey) and iK Currents. 

In Figure 9, the response of a ventricular cell is illustrated. Shutdown occurs at 0.8 nA. The 

change in dv/dt in phase 1, at the peak of the curve, is remarkable. The shortening of the period 

of the action potential, tachycardia, is quite pronounced. 

19 
l 

Figure 9. Effect of ACh-Activated Potassium Current on a Ventricular Cell. As the 

Current Increases From 0.01 to 0.3,0.6, and Finally, 0.8 nA, the Period Shortens 

Continuously, Effectively Extinguishing the Action Potential. 

The magnitude of the calcium current, ica, is also smaller. A notch appears in the action 

potential curve. With further increase in acetylcholine concentration (not shown), the calcium 

current practically ceases and the period shortens further. 

Figures 10 and 11 show the effect of the extracellular potassium concentration change on the 

action potential. Note that the magnitudes of the concentrations are considerably different in the 

two cases. In Figure 10, at a concentration of 30 mM/liter, the action potential is terminated, as 

shown in flat trace. The green curve represents the calcium current (gray if and violet iK), and 

iNaCa is given in blue. 

In Figure 11, the flat voltage trace is for [K”10 = 8 n-M; the right-most and the trace to its left 

have [K’10 = 2 and 4 mM, respectively. The gray trace represents if and the purple iK. The 

negative going if is for {K+JO = 8, and the second largest purple trace is for the starting condition, 

[I+& = 4 mM/l. Table 3 shows the contrast of cell behavior with an increase in ACh-induced 

potassium current. 

20 
Figure 10. Effect of the Change in the Concentration of [K’], on the AP of the SA Node. 

I I Figure 11. Effect of the Change in the Concentration of [K’10 on the AP of the Purkinje 

Fiber. 

21 
Table 3. Contrast of Cell Behavior. With Increase in ACh-Induced Potassium Current 

Cell Type 

SA Node 

Purkinj e 

Ventricle 

ik,Ach at Shutdown if at Shutdown 

of Action Potential of Action Potential 

(I-LA) (nA) 

0.0024 - 

9.0 -0.2 

0.8 - 

AP Duration With 

Increase in ik,Ach 

lengthens 

lengthens 

shortens 

5. Discussion 

Animal studies show that at lLD50 of soman, the accumulated acetylcholine concentration is 

high enough to arrest the heart. The SA node, the ventricles, and the Purkinje fibers are affected 

unequally. Evidence points to the SA node cells and the Purkinje fibers as determinants of the 

outcome. 

The primary objective of this study was to elucidate the behavior of the action potential in 

face of changed membrane currents due to soman-induced ACh concentration change, especially 

that expressed by ik,Ach and if. The former current is the best gauge of the effect of acetylcholine 

overload. In addition, cell environmental changes, such as extracellular [KflO, were also 

examined. 

5.1 Effect on the SA Node. The first series of runs on the SA node cells reported here 

showed that at a constant high level of ACh, the induced K” current, ik,Ach, lengthens the period 

of the action potential. With the current at 0.0018 nA, the period is extended by 15%; at 0.0024 

m4, the action potential ceases. 

A secondary response to ACh is that the inward peacemaker current, if, is inhibited by the 

G protein. The G-protein inhibits cyclic AMP production, which in turn inhibits the calcium 

current that plays a role in depolarizing the SA node. One possible outcome is SA block. 

22 
These results concur with the findings of Yanagihara et al. (1980) and the data of Ostenieder 

et al. (1980). They noted that the spontaneous frequency of the heart rate decreased from 

173 beats/min to 132 beats/min at an ACh of 5 x lo-’ M, and to 79 beats/min at 10m7 M, ceasing 

completely at 2 x lo-’ M. Zhang et al. (1999), studying the rabbit sinoatrial node with their 

computer model, found that an ACh concentration of 7.4 x 10 -’ M induces a decrease of 50% in 

the heart rate, and that iLACh is mainly responsible with the shift in if opposing the decrease. 

Egan and Noble (1987) studied the variations in the SA node activity in response to AChactivated potassium channels and calcium current permeability. The concentration of ACh, 

which produced noticeable effect, was 2 x 10m6 M. The maximum potassium current of 

O-2-0.3 nA was found at an ACh concentration of 10m4 M. Increasing the current to 2 nA 

lengthened the cycle, while 10 nA arrested the heart. Altering if by increasing the conductance 

of K’ and Na’ from 612 ,uS accelerated the heart, while decreasing it to 0 lengthened the 

cardiac cycle. 

The computations were run under the premise that the level of soman in the environment 

does not noticeably change in the short run. The trends observed from experiments with doses 

applied for various periods concur with these findings. Bristow and Clark (1983) studied the 

effect of 1, 2, 3, 5, 7, and 9 pulses per burst of ACh at different times within the cardiac cycle. 

They showed that when the stimulus is delivered near the peak of the diastolic potential, the 

cycle length increases to 874 ms from baseline. The channel blocking was simulated by setting 

g& or gi to zero. Michaels et al. (1984) induced changes in pacemaker rhythm by single and 

repetitive applications of ACh pulses. The pulses were simulated by adding ACh-activated 

potassium current, iK,ACh, to the membrane equation. An ACh concentration of 10m6 M applied at 

280 ms of the cardiac cycle shifted the pacemaker cycle duration from 3 18 to 548 ms. 

Considering that the effect of ACh declines over time, the “aging effect” (Dexter et al. 1989a, 

1989b) working with dogs found the half-life of ACh after vagal stimulation to be 2.7 s. The 

sinus period decreased from 550 ms to 410 ms in 15 cardiac cycles after stimulation. The 

concentration of ACh was 50 nM, and the change in the sinus period depended on the rate of 

release of ACh. 

23 
5.2 Effect on the Purkinje Fiber. In contrast to the SA node, considerably larger values of 

the ACh-induced current, 9 nA, is needed to shut down the action potential. With an increase of 

the current, there is a gadual shortening of the period starting at baseline. When the current has 

increased five-fold, the period has lengthened by less than 20%. 

This is in line with the experimental work of Carmeliet and Mubagwa (1986). They showed 

that bath-applied ACh to rabbit Purkinje fibers caused an increase in K’ conductance, 

hyperpolarization, and an inhibition of spontaneous activity. In addition, they noted a decrease 

in K’ and Na4 conductance. 

5.3 Effect on the Ventricle. The ventricle has no pacemaker activity; but still, an ACh 

overload can arrest its action potential. The cells of the ventricle respond considerably less to 

changes in ACh concentration than the other two cell types considered, the SA-node cells and the 

Purkinje fiber cells. The increase in the ACh-activated potassium current has two marked 

manifestations: shortening the AP period and steepening the slope of the action potential at 

phase 1, the point of the highest value of the voltage. At a value of 0.8 nA, the AP is not 

recognizable; it is but a blip of a hundredths of a second duration whose amplitude stays below 

- 50 mV. For all practical purposes, it has been extinguished. 

Dokos et al. (1993) also noted that ACh lowers the rate of impulse generation by activating 

potassium channels, and it also inhibits the hyperpolarized-activated L-type current. An 80-ms 

ACh pulse of 1-uM concentration increased the cardiac period up to 10%; a concentration of 

5 pM lead to an increase of 35%, while an ACh concentration of 10 uM yielded a change of up 

to 50%. The simulations were made with the modified DiFrancesco-Noble model with imch 

included. 

5.4 Effect of Extracellular Potassium Concentration. Changes in K+ ion movement are 

central to expressing soman-induced cardiac toxicity. An ancillary aspect is proposed here that 

the accumulation of K” ions in the interstitial space may play an important role in the overall 

behavior. The reasoning is as follows: excessive parasympathetic stimulation results in 

24 
excessive ACh release. ACh binds to M2 muscariuic receptors, activates the G-protein, and 

hyperpolarizes the SA node. When ACh activates ik,Aeh, K” exits the cell. The soman-induced 

ACh overload results in more receptors than usual being bound, also leading to an increase in the 

external concentration of potassium ions.* 

Y 

The two cases shown in Figures 10 and 11 show the effect on the SA node and the Purkinje 

fibers if the elevated K” concentration outside the cell is maintained. 

Excessive concentration of K” ions changes the concentration gradients and the functioning 

of the Na-K pump. In the initial stages of the accumulation of the potassium ions, the cells are 

more excitable, but as the membrane potential drops below the excitation threshold, the 

generation of an action potential is no longer possible. A two- or three-fold change in the 

extracellular concentration from the baseline of 4-5 mM can paralyze muscles and arrest the 

heart. In fact, the rapid loss of potassium ions into the extra cellular fluid can be lethal. It is 

known that [K*10 below 2 mM and above 9 mM stops the heart. Hyperkalemia suppresses the 

automatic@ of the heart, slows conduction, and leads to bradycardia. It is also characterized by 

negative inotropy. In man, 98% of the potassium is held intracellularly; thus, a shift of 2% to the 

extracellular space doubles the concentration of the ion with profound implications. 

, 

Indications of hyperkalemia include a flattened P wave on the ECG and, more importantly, in 

many cases, a tall and narrowed T wave. The literature (see Side11 et al. [ 19971 for example) 

does not connect hyperkalemia with soman poisoning, but there is persuasive circumstantial 

evidence for the case. Some of the changes in the ECG of soman-affected mammals certainly 

point in that direction. With hyperkalemia in the picture, a number of new antidote strategies 

suggest themselves. 

f 

Though not connected to soman-induced ACh overload, external potassium concentration 

variation has been studied earlier. Noble and Noble (1984) found that variations in the 

l The number of receptor sites available can be very large. Hille (1992) notes that in the frog neuromuscular junction, “there are 

almost 20,000 binding sites per square micrometer in the top junctional folds of the postsynaptic membrane that lie opposite the 

active zone of the nerve terminal” (p. 142). 

25 
extracellular potassium influenced the frequency of the pacemaker activity. Increasing [K’10 

from to 26 mM lengthened the cardiac cycle. If [Na]i was increased from 7.5 mM to 30 mM, 

the pacemaker activity was stopped. Sears et al. (1999) studied the effect of the changes in the 

extracellular potassium on the heart-rate frequency. An increase in [K”], led to a decrease in the 

heart rate. iKAch was set at 50 pA. 

This is in line with the work of Carrneliet and Mubagwa (1986) and, more recently, Cordeiro 

et al. (1998). They reported that reducing @*I0 from 5.4 mM to 2.0 mM resulted in 

hyperpolarization of the action potential. 

5.5 Summary. The computer runs simulated the development of the action potential and the 

apparent induced physiological abnormalities corresponding to the soman concentration and 

accompanying ACh overload. While the SA exhibited bradycardia at the same concentration 

level of ACh, the ventricles exhibit tachycardia. The shape of the. action potential of the 

ventricles also changes, a notch appears at phase 1. With increase in [ACh], the notch becomes 

more pronounced. Also, negative inotropy of the cardiac muscles becomes apparent. All 

electrophysiological activity was ceased for soman concentrations exceeding Lx)50 > 50% in all 

parts of the heart. 

No conclusive evidence was found for or against the postulate that increased iuch 

suppresses if(Boyett et al. 1995; DiFrancesco 1994). 

The ACh overload effect on the Purkinje fibers, as expressed through the increase in ik$.ch, is 

the most critical. When the Purkinje fiber fails, cardiac arrest ensues. 

It remains to be determined whether the Zwaardemaker-Libbrecht effect, when rapid changes 

in [K’10 produce transient arrest of pacemaker fibers, hyperpolarization, and shortened action 

potential, takes place when large doses of soman are suddenly introduced. 

26 
These data suggest that hyperkalemia may play a role in the electrical chaos at the cellular 

level in soman poisoning. Experiments in the near future should enable a conclusive evaluation 

of this conjecture. 

27 
INTENTIONALLYLEFTBLANK. 

28 
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32 
Appendix 

33 
INTENTIONALLYLEFTBLANK. 

34 
Membrane Ionic Model 

Yanagihara et al.,’ using the Hodgkin-Huxley formalism for the rabbit SA node, used the 

following membrane current models. 

(1) Slow Inward Current 

i, = (0.95d + 0.05)(0.95f + O.OS)i 

l.O45~lO-~(E+35)) 3.125~10-~E 

ad = 1-exp(-(E+35)/2.5)+1-exp(-E/4.8) 

4.21~1O-~(E-5) 

” = exp((E - 5)12.5)- 1 

3.55~1O-~(E+20) 

af = exp((E + 20)/5.633)- 1 

9.44~10~1E+60 1 

Pf = l+exp(-(E+29.5)/4.16) 

T, = 12.5(exp(E -30)115)-l) 

(A-1) 

(A-2) 

(A-3 

(A-4) 

(A-5) 

(A-6) 

’ Yanagihara, K., A. Noma, and H. Irisawa. “Reconstruction of Sinoatrial Node Pacemaker Potential Based on the 

Voltage Clamp Experiments.” JQP. J. PhysioZogy. vol. 30, pp. 841-857, 1980. 

35 
(2) Fast Sodium Current 

IN, = m3hiNa 

E+37 

am = l-exp(-(E+37)/10) 

f3, =40exp(-5.6x10w’(E+62)) 

P, = 

1 

exp(-(E+30)/10)+1 

: I,, = 0.5(E - 3) 

(3) Hyperpolarization-Activated Current 

i, =qT, 

3.4~10-~(E+lOO) +4 95Xlo-5 

aq = exp((E + 100)/4.4) - 1 . 

5~10-~(E+40) 

‘, = 1 - exp(- (E + 40)/G) + 8-45 x lo-’ 

i, = 0.4(E + 25) 

36 

(A-7) 

(A-8) 

(A-9) 

(A-10) 

(A-l 1) 

(A-12) 

(A-13) 

(A-14) 

(A-15) 

(A-16) 
(4) Potassium Current 

i, =pi, (A-l 7) 

9x1o-3 

l-t- exp(- (E + 3.8)/9.71) 

p = 2.25~10-~(E+40) 

’ exp((E + 40)/13.3)- 1 

; 

k 

= 0.7(exp(O.O277)(E t 90))- 1 

exp(0.0277(E + 40)) 

(5) Leak Current 

i, = O.S(l - exp(- (E + 60)/20)) 

Acetylcholine-Activated Potassium Current 

: 

‘,.A,, = %A,, 

12.32 x 1O-3 

ax, = 1 + (4.2 x 1 O-4 /[ACh]j ’ 

where [ACh] = acetylcholine concentration 

0, = O.Olexp(0.0133(E + 40)) 

lK,ACh = 0.27(E + 90) 

(A-l 8) 

(A-19) 

(A-20) 

(A-2 1) 

(A-22) 

(A-23) 

(A-24) 

(A-25) 

37 
The membrane potential, V, , under isopotential conditions is given by 

(A-26) 

where C, is the membrane capacitance, and ij s are the individual membrane currents. 

Enzyme Kinetics Formalism 

Michaelis-Menten kinetics was used for the interaction of OP with AChE, i.e., 

kz k3 

S+Ee ES-E+P, 

kl 

(A-27) 

where 

E = enzyme,AChE, 

S = substrate (i.e., reactant, here OP), 

ES = enzyme-substrate complex, and 

P = product. 

Here, ki’s are the elementary rate constants. Using the mass-action law, the concentration of 

each of the four species changes according to the following equations. 

d[E]/dt = -k, * [E]* [S]+ k, *[ES]+ *[ES] (A-28) 

d[S] /dt = -k, * [E] * [S] + k 2 * [ES] (A-29) 

d[ES]/dt = k, * [E]* [S]- k, *[ES]- k, *[ES] (A-30) 

38 
d[P]/dt = k, *[ES] (A-3 1) 

Initial conditions and rate constants need to be appended to solve the equations. 

Michaelis-Menten kinetics allows simplification in that only two parameters, which represent 

enzyme properties, need to be specified. These are K, and V, defined as follows: 

(A-32) 

The K,,, of the enzyme is the concentration of the substrate at which the rate of generation of 

the product is half maximal. V, is ‘knaximum velocity of the enzyme” (i.e., the rate of 

formation of the product when there is a saturating amount of substrate present). All the enzyme 

is complexed with the substrate so V, is equal to k3. 

h 

39 
Table A-l. Rate Constants and Concentrations Used in the Simulation 

Reduction Rate 

Reverse 

Reduction Rate 

Hydrolysis Rate 

Initial ACh 

Concentration 

ACh Diffusion 

Constant 

Michaelis-Menten 

Constant 

Symbol 

h 

kz 

k3 

Whlo 

D 

Knl 

Estimate Reference 

2 x lo7 M-‘s-’ Rosenberry” 

5 x 102s-’ Rosenberry” 

1.5 x 104s-’ Rosenbed 

1.62 x 10m3 ms-’ Bristow and Clarkb 

6 x lo-‘h/i Dexter et al.” 

Rosenbed 

1 x lo-6 to 0.5 X IO-~ M Michaels et aLd 

1 x lo-%m2/s Rosenbed 

9.15 x 10-‘2cm2/ms Bristow and CXarkb 

0.14 x 1o-3 Demir et al.” 

0.012 ms-’ Bristow and Clarkb 

. 

F 

aRosenberry, T. L. “Quantitative Simulation of Endplate Currents at Neuromuscular Junctions Based on the 

Reaction of Acetylcholine With Acetylcholine Receptor and Acetylcholinesterase.” Biophys. J, vol. 26, 

pp. 263-289. 

bBristow, D. C., and J. W. Clark. “A Mathematical Model of the Vagally Driven Primary Pacemaker.” Am. J, 

Physiol., vol. 244 (Heart Circ. Physiol., vol. 13) pp. H150-H161, 1983. 

‘Dexter, F., G. M. Saidel, M. N. Levy, and Y. Rudy. “Mathematical Model of Dependence of Heart Rate on Tissue 

Concentration of Acetylcholine.” Am. J. Physiol., vol. 256 (Heart Circ. Physiol., vol. 25), pp. H52GH526, 1989b. 

dMichaels, D. C., E. P. Matyas, and J. Jalife. “‘A Mathematical Model of the Effects of Acetylcholine Pulses on 

Sinoatrial Pacemaker Activity.” Circ. Res., vol. 55, pp. X9-101, 1984. 

eDernir, S. S., J. W. Clark, and W. R. Giles. “Parasympathetic Modulation of Sinoatrial Node Pacemaker Activity 

in Rabbit Heart: a Unifyins Model.” Amer. J. Physiol., vol. 276, pp. H2221-H2244, 1999. 

40 
Glossary 

ACh 

AChE 

B 

CAMP 

cm 

D 

E 

ib,L 

ka,r 

if 

iK 

ha 

k,ACh 

gK,ACh 

ki 

Ll 

M 

OP 

P 

S 

acetylcholine 

acetylcholinesterase 

constant 

cyclic AMP 

membrane capacitance 

diffusion coefficient of ACh 

potential also enzyme 

L-type calcium current 

T-type calcium current 

hyperpolarization-activated current 

delayed rectifying potassium current 

leak current 

sodium current 

ACh K” current 

conductance of iK,ACh channel 

first-order rate constant for hydrolysis of ACh 

Michaelis-Menten constant 

amount of ACh release 

organophosphate 

product 

substrate 
t 

u 

V 

X 

Greek letters: 

a 

P 

time 

gating variable 

membrane potential 

average distance between ACh release sites 

gating coefficient of opening 

gating coefficient of closing 

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44 
REPORT DOCUMENTATION PAGE Form Approvtxl 

OMB No. 07WO18.9 

Zellular Level 

Zsaba K. Zoltani and Steven 1. Baskin* 

J.S. Army Research Laboratory 

“IT-IN: AMSRL-a-HA 

4berdeen Proving Ground, MD 210055067 

REPORT NUMBER 

ARL-TR-2367 

TJ.S. Army Medical Research Institute of Chemical Defense 

12a. DlSTRlBUTlON/AVAllABlLlTY STATEMENT 

4pproved for public release; distribution is unlimited. 

12b. DISTRIBUTION CODE 

13. ABSTRACT(Maximum 200 words) 

Under a memorandum of understanding (MOU) between the Computational and Information Sciences Directorate 

:formerly the Corporate Information and Computing Directorate) of the U.S. Army Research Laboratory and the US. 

4rmy Medical Research Institute of Chemical Defense, results of a study to model the electraphysiological changes in 

he heart due to soman toxicity are reported. This, the first of a series of reports, presents a computational model of 

:ardiac toxicity at the cellular level and shows the changes in electrical activity for a series of organophosphate (OP) 

lose concentrations expressed by changes in the acetylcholine concentration generated membrane currents. A 

)lausibility argument is advanced for the consideration of an overlooked aspect of the problem the effect 01 

:xtracellular potassium ion accumulation, to the understanding of soman-induced electrophysiological chaos. 

4. SUBJECT TERMS 

ioman, cardiac toxicity, computer simulation 

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48 

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