PSpice Simulation of Cardiac Impulse

Propagation: studying the mechanisms of action

potential propagationSomayeh Mahdavia, Shahriar Gharibzadehb*, Mostafa Rezaei-TaviraniC, Farzad Towhidkhahd, Soheil Shafieeea Department of Cellular and Molecular Biology, Khatam University, Ferdous Boulevard, Sazman Bamame, Tehran, Iranb Neuromuscular Systems Laboratory, Faculty of Biomedical Engineering, Amirkabir University of Technology (Tehran

Polytechnic), Somayyeh, Hafez, Tehran 15875-4413, Iranc Faculty of Medicine, Ilam Medical Sciences University; & Asre novin Institute of Research and industrial Services, Tehran, Irand Biological Systems Modeling Laboratory, Faculty of Biomedical Engineering, Amirkabir University of Technology (Tehran

Polytechnic), Somayyeh, Hafez, Tehran 15875-4413, Iran

e Speech Processing Laboratory, Faculty of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic),

Somayyeh, Hafez, Tehran 15875-4413, Iran

Abstract - For many years, local circuit current through gap junctions has been seemed to be the main fundamental route for

impulse transmission. In the last few years, some different evidences suggest another view on action potential propagation via

myocardial cells. Some researches offered that myocardial cells may not require low-resistance connections for successful propagation

of action potential. It seems that some other mechanisms are involved in the action potential propagation. Electrical field has been

suggested as the main effective mechanism in action potential propagation. It is demonstrated that in the lack of gap junctions, electrical

field is sufficient for action potential propagation. We simulated the mechanism of electrical field and local circuit current separately,

studied the effect of these mechanisms on action potential propagation and compared them with each other. Our results demonstrate

that although the mechanism of electrical field alters the resting potential of the post-junctional cell, but it is not sufficient to excite the

post-junctional cell. These results offer a new view on action potential propagation in which both of the abovementioned mechanisms

are necessary for normal cardiac functioning, but in different times of a cardiac cycle. It seems that gap junction has a dynamic

behavior in each cardiac cycle, managing different routes of propagation in the diverse moments of normal cycle. Closure of gap

junctions allows the negative cleft potential to develop and enhance the cell excitability by reducing cell potential. Then opening the gap

junction produces AP. Based on this view, we think that most of the paradox about the role of gap junctions in cardiac impulse

propagation will be solved.

* Corresponding author. Tel.: +9821 6454 2369; fax: +98216649 5655.E-mail address: gharibzadehgaut.ac.ir (S. Gharibzadeh).

I. Introduction

The electromicroscopic and electrophysiological studies

show the presence of gap junction as a kind of cell connection

between adjacent myocyte cells [1]. Gap junctions are

composed of two subunits entitled connexon, which are

located along each other in the neighboring cells. Each

connexon is formed by six subunits, which are named

connexin [2]. To date, the connexin gene family comprises 21

members in the human genome [3].

Protein oligomers (connexon) of gap junctions form

conduits for intercellular communication that allow the

exchange of nutrients, metabolites, ions, and small molecules

up to 1,000 Dalton [4]. Gap junctions create a low resistance

pathway, functioning as a fundamental route for impulse

transmission [1]. Therefore, they are the major determinants of

intercellular resistance to current flow [5]. Several

experiments on mice lacking gap junctions show abnormality

in action potential (AP) propagation [6, 7]. Alteration of gap

junction organization and connexin expression are now well

established as a consistent feature of human heart diseases

accompanied by an arrhythmic tendency [8, 9, 10]. Acute

myocardial ischemia is the major cause of cardiac death,

related to gap junction uncoupling and abnormality [11].

These evidences suggest the importance of gap junction in AP

propagation. In addition, some simulations confirm this role

for gap junctions [12].

In the last few years, some different evidences suggest

another view on AP propagation via myocardial cells. Kucera

et al. demonstrated experimentally that for greatly reduced

coupling, the sodium current in the prejunctional membrane

leads to facilitated and accelerated conduction [13]. In

addition, Sperelakis proposed some evidences against the role

of gap junction in AP propagation.

According to these evidences, it seems that some other

mechanisms are involved in the AP propagation. Therefore,

different mechanisms, which probably induce AP propagation,

were suggested in different studies [14,15]. Sperelakis

presented models, indicating that myocardial cells may not

require low-resistance connections for successful propagation

of the AP [16]. He offered electrical field (EF) as the main

effective mechanism in AP propagation and demonstrated that

in the lack of gap junctions, EF is sufficient for AP

propagation [16, 17, 18]. This mechanism, in contrast to the

pervious one, claims that following sodium current into the

prejunctonal membrane, the negative electrical potential

developed in the narrow junctional gap leads to electrical

transmission between contiguous excitable cells, without any

need to direct electrical current through gap junctions [14, 15].

Here, we simulate the mechanism of EF and local circuit

current separately, study the effect of these mechanisms on AP

propagation and compare them with each other.

II. Methods

In order to produce electrical circuits, we used the software

PSpice 9.2. The myocyte was assumed to be a cylinder 150

,tm long and 16 ,tm in diameter. The cell capacitance was

assumed to be 100 pF, and the input resistance to be 20 MQ. A

junctional tortuousity (interdigitation) factor of 4 was assumed

for the cell junction. Calculations indicated that the area of one

junctional membrane was about one-fifth that of the entire

surface membrane [16].Therefore, we assumed the surface as

5 units and the junction as 1 unit. A basic unit is demonstrated

in Fig. 1.

Since the EF, as explained above, is produced following the

depolarization phase, this study focuses on depolarization and

its propagation. To make the circuit as simple as possible, all

other ion channels (e.g., CaL, CaT, Cl-, Na slow, KATP, KCa)were omitted. We utilized only those channels that set the

resting potential and predominate during the rising phase of

the action potential.

Voltage-dependent Sodium channel operates as a variable

resistance, the amount of which alters in specific voltages. We

simulated it as an S-voltage dependent switch. The on/off

voltages of the switch were selected due to the activation and

the resting voltage of the channel, and the resistances were

chosen from physiological conditions.

Because other resistances in the cell, e.g. longitudinal

resistance of the cytoplasm, are not considerable in

comparison with the huge main resistance of channels, to

make the circuit as simple as possible, we did not present them

here. Moreover, our initial studies demonstrated that they do

not have considerable effect on the results.

The function of EF can be simulated as a capacitor located

in the junction. In this view, the operation of the voltage

dependent sodium channel induces negative potential in the

gap without any current between cells. If the negative voltage

is capable to fill the capacitance sufficiently, it considerably

verifies the post junctional cell potential and excites it. The

value of the capacitance is supposed to be 0.05 microfarad

(pF).Figure 2 illustrates the equivalent circuit for two cells and

their connection, which is assumed a capacitor. This capacitor

connects the last unit of pre-junctional cell to post junctional

first unit. S voltage dependent switch induces negative charge

in the capacitor during AP rising phase.

Figurel: a myocardial basic unit

Figure 2: the equivalent circuit for simulation of electric filed between two

myocytes

Another model was prepared to study the AP propagation in

the presence of gap junction. Here the inner surface of the pre-

junctional cell was connected to the inner surface of post-

junctional cell by a resistance, which simulates the low

resistance pathway, i.e. gap junction. Figure 3 demonstrates

this connection.

III. Results

According to the sinoatrial (SA) node physiological

properties, the model of SA node was produced and was

applied to stimulate a chain of cells. This model is not

presented here for shortening). SA stimulates the first unit up

to thereshold. The voltages were measured across each unit.

Fig. 4 shows the propagation of AP in the model of EF. As it

was expected, the function of voltage dependent sodium

channel of the pre-junctional cell produces

pre-juncioa cell posst- ictionl cell

gap junction

Figure 3: the equivalent circuit for simulation of local circuit current

between two myocytes

pre-juntiona cell post-junctonaI cel

I- Cjc

0

RNa|ROFF = 1 oDDo g

Rk1DDK?Ig RON =20Mveg

c20 P

. I --J- %/V3-~~ ~ ~ Dm

9~4r

100

10

1 10 100 1,000 10,00number of gap junction

Figure 6: ability of gap junction for impulse propagation

Figur4: propagation ofAP by the EF mechanism (each curve related to the

unit of the cell)-EF alter the resting potential of the post-junctional cell but it

is not sufficient to excite the post- junctional cell

negative voltage in the cleft. Also this voltage alters the

resting potential of the post-junctional cell but it is not

sufficient to excite the post-junctional cell. Fig. 5 displays the

propagation of AP in the presence of gap junctions as low

resistance pathways. The results show that the local circuit

current is able to stimulate the post junctional cell.

The ability of gap junction for impulse propagation was

studied by changing the number of gap junctions (Fig. 6).

Although the small number of gap junctions can alter the post-

junctional cell voltage, but it can not exactly stimulate the

post-junctional cell. This figure also shows that increasing the

number of gap junctions increases the probability of AP

propagation.

IV: Discussion

Gap junctions have been detected Since half a century ago

as a low resistance pathway which allow direct

communication between adjacent cells [1] Most of evidences

approve the role of gap junction in AP propagation

[1-7]. They also demonstrate the role of gap junction in

regulation of the AP propagation velocity and its safety,

which is called safety factor[19].

The role of sodium channels in the upstroke phase of AP

and its relation to AP velocity are distinguished [19, 20].

However, it is already considered that this effect is because of

altered conduction velocity along the cells [21 ] but nobody has

paid attention to the effect ofjunction transmission. Sperelakis

interest to this effect created a new perspective on the cardiac

AP propagation. This hypothesis, although is in opposition

with previous evidences, is confirmed in Sperelakis

simulations [14, 17].

Although Sperelakis offered a mechanism, which is

effective in junction potential, it needed to be quantitized. As

we previously confirmed mathematically, the ion changes

during a single AP can alter the post junctional cell potential,

but the alteration is not sufficient to excite the post junctional

cell [22]. The results of this study also indicate that the

function of sodium channels can cause negative potential in

the cleft and depolarize the post junctional cell partially, but it

cannot cause AP (Fig.4). Fig. 5 demonstrates that in theFigure 5: propagation ofAP in the presence of gap junctions- the local circuit

current excited the post-junctional cell

existence of gap junction, AP is propagated successfully,

indicating the critical role of gap junctions.

Although our results do not verify the sperelakis hypothesis

about the effect of gap junction on AP propagation, but

confirm his hypothesis on the effect of negative cleft potential.

Our results support the results of Kucera et. al about

conduction facilitation by the sodium current. The results of

present study also support our previous hypothesis on AP

propagation in which we proposed that both of the

abovementioned mechanisms are necessary for normal cardiac

functioning, but in different times of a cardiac cycle. It seems

that gap junction has a dynamic behavior in each cardiac

cycle, managing different routes of propagation in the diverse

moments of normal cycle. Closure of gap junctions allows the

negative cleft potential to develop and enhance the cell

excitability by reducing cell potential. Then opening the gap

junction produces AP [23]. Based on this view, we think that

most of the paradox about the role of gap junctions in cardiac

impulse propagation will be solved.

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