Creative Education
2012. Vol.3, Special Issue, 1130-1137
Published Online October 2012 in SciRes (
Copyright © 2012 SciRes.
A Computational View of the Historical Controversy on
Animal Electricity
Massimiliano Zaniboni
Department of Biosciences, and Center of Excellence for Toxicological Research (CERT),
University of Parma, Parma, Italy
Received August 27th, 2012; revised September 24th, 2012; accepted October 10th, 2012
A scientific controversy retains often some controversial sides after its fundamentals have well been ex-
plained. This is particularly true for the controversy that arose in Italy in the second half of the eighteen
century between the anatomist Luigi Galvani, and the physicist Alessandro Volta, around the intrinsic na-
ture of nerve and muscular function. The two scientists were providing, almost simultaneously from the
University of Bologna and Pavia respectively, two quite different explanations for the property of muscles
of being electrically excitable and contract as a consequence. Science seemed then to touch the very in-
trinsic mechanism of living processes. Despite the fact that one of the two explanations was explaining
better than the other, the weaker mechanism won the battle at the time. The biophysical mechanism of
nerve excitability has then been clarified in 1950 by Hodgkin and Huxley, who later won the Nobel Prize
for their work. They unequivocally showed that Galvani was right and Volta quite wrong. Only specialists
though notice that the Galvani-Volta controversy is frequently still thought wrong in schools. In this brief
essay I want to show how easy-to-handle computer models can unveil where the subtle source of the con-
troversy was hidden, and how an interdisciplinary approach can help drawing light into the multiple as-
pects of this extraordinary story.
Keywords: Animal Electricity; Galvani-Volta Controversy; Computational Physiology; Excitability
Introduction: The Controversy
The dispute between Galvani and Volta (Figure 1) for the
explanation of muscular excitability has been discussed in very
detailed articles and essays (Bernardi, 2001; Bresadola, 2008;
Piccolino, 1997; Piccolino, 1998) and I will give here only a
brief and necessarily partial report of it. In the middle of eight-
een century the “art of electricity” was moving its first steps as
a real science; interestingly, the beginning of this science coin-
cides with the beginning of the science of bio-electricity. Wil-
liam Harvey (1578-1657) had already shown in its “De Motu
Cordis” (On the Motion of the Heart) the basic mechanism of
the blood circulation through vessels, and a circulation of the
same type was believed to move some “animal spirits” through
the nerves. The eclectic Swiss anatomist Albrecht Von Haller
(1708-1777) was one of the first scientists disputing this view
and proposing, instead, the concept of an “irritability”, intrinsic
to the very nature of nerves and muscles. These were “irritated”,
in the sense that they were in a state of some high potential
energy (still unknown at that time), that some also-unknown
mechanism was able to free after stimulation. Leopoldo Caldani
(1725-1813), an eminent Italian physiologist from the Univer-
sity of Padova, was one of the most influential followers of the
Haller’s theory. I note in passing that Haller’s and Caldani’s
studies were somewhat well aligned with the eighteen century’s
zeitgeist and, not surprisingly, strongly opposed by the many,
e.g. the Scottish physician Robert Whytt (1714-1766), who
thought they were denying the role of soul in nervous activity,
and favouring a mere materialistic view of these processes. At
those times there was a constant and fruitful exchange between
disciplines; “Experimental Philosophy” was the way the Eng-
lish chemist, theologian and historian Joseph Priestley (1733-
1804) was calling his pioneeristic studies on electricity; and it
was only after reading Haller’s works that the political theorist,
politician, scientist, musician, satirist, civic activist, statesman,
diplomat Benjamin Franklin (1706-1790) started his seminal
studies on electricity. Electrostatic machines started to appear
on the working table of anatomists, chemists, and physicists,
and allowed them to produce large amount of electrical charge.
This could be stored in Leyden jars (“miraculous”, in the words
of Priestley), smart and beautiful electrical capacitors which
made this charge usefully available for their experiments with
wires, metal plates and animal preparations. What these early
experiments showed was that there definitely was a link be-
tween electricity and the ability of nerves and muscles to re-
spond to stimuli, conduct them, and contract.
In the second half of the century, Luigi Galvani was con-
ducting his experiments on the so called “frog preparation”,
where the spinal cords, crural nerves, and lower limbs of the
little amphibian, were dissected as a unit. One of the Galvani’s
findings, achieved by a fortunate chance, was that, when the two
extremes of a bi-metallic arc were made to touch the two ex-
tremities of the preparation, the muscle contracted (Figure 2).
Galvani knew well Haller’s and Caldani’s works: he concluded
that nerves were electrically charged, and that the bi-metallic arc
only let this charge flow, excite the nerve, and contract the
muscle; detailed mechanisms were still to uncover but the prin-
ciple seemed to be found. The fact that a bi-metallic arc was
required and that a simple one-metallic arc did not the job was
initially not explained by Galvani. He performed several ver-
Figure 1.
Luigi Galvani, anatomist from the University of Bologna
(1737-1798), and Alessandro Volta, physicist from the
University of Pavia (1745- 1827).
Figure 2.
The bimetallic-arc experiment. When an arc, made half of
copper and half of zinc, touches the extremities of the frog-
preparation, the limb suddenly contracts.
sions of this experiment as well as many others, that he lately
detailed in his “De viribus electricitatis in motu muscularis”,
published in 1791; for the purpose of this paper, I will focus on
this one only. The bi-metallic nature of the arc was indeed the
very point were Galvani’s theory was disputed by Alessandro
Volta. His discovery that piles, made of plates of two different
metals separated by salted solutions (Voltaic pile), were able to
generate differences in electrical potential (measured after his
name in Volts) and thus able to drive electrical current flow,
seemed perfect to take the Galvani’s explanation and turn it
upside down. There was no animal electricity as Galvani claimed,
no irritability nor any potential energy stored in tissues; only the
bi-metallic arc in Galvani’s experiments was a rudimentary
Voltaic pile, making electrical current flow through muscles and
providing the force needed for contraction. The mechanism
responsible for contraction was obscure to both scientists and
was not object of the dispute anyway. A complete account of the
controversy can be found in a recent book of Piccolino and
Bresadola (Piccolino & Bresadola, 2003). I want here to point, as
these authors detail in their work, to the persisting misinterpre-
tation of the controversy: both in schools and in popular scien-
tific handbooks, it is still thought frequently that the wrong
Galvani’s hypothesis of an “animal electricity” had only served
the successful Volta’s theory of an external force driving nerve
conduction and muscle contraction, which eventually started the
immense technological revolution of electricity. In this article I
will shortly describe the theory of nerve excitability as it has
been explained in the 20th century. The explanation can be
summarized into an equation system that can easily be solved by
means of tools from modern computer science. A compact
computational view of one of the Galvani-Volta’s experiments
can help teachers and students to better dissect the critical points
of this instructive controversy.
The Hodkin and Huxley Theory of Excitability
As I have summarized in the introduction, whereas Galvani
retained that the source of “animal electricity” was inside the
animal, Volta’s explanation put this source externally. The
impact that Volta’s discoveries had on science and not only on
science (think what electricity has done to human history), is
one of the reasons, not the only one, for its success over the
dispute with Galvani. Excitability has been explained in detail
through a bio-physical model developed by Hodgkin and Hux-
ley (Figure 3) 150 years later; Galvani, as they showed, was
right, Volta was wrong, but the story was not over. By means of
the newly developed voltage clamp technique, which allowed
them to control the voltage difference across the nerve mem-
brane and measure the corresponding flow of ion current
(Hodgkin & Huxley, 1952a; Hodgkin & Huxley, 1952b), the
two English physiologists could tell the exact plot of the story
(of excitability) without knowing the protagonists. These, the
ion channel molecules, were indeed discovered only about 20
years later, and the molecular confirmation of the Hodgkin and
Huxley (HH) theory has been a further coup de théâtre in the
history of animal electricity. I will briefly summarize HH the-
ory as it is known now, assuming therefore the knowledge of
ion channels.
The cell membrane is electrically polarized: a difference of
electrical potential (Vm) exists between its intra- and extra-
cellular face (of around 80 mV for example in neurons), being
negatively charged inside and positively outside. Responsible
for such polarization are ion channels, proteins embedded into
the membrane lipid bi-layer and endowed with a pore, selec-
tively permeable to ions, which are differently concentrated
into and out of the cell. When, for example, a potassium ion
tends to flow out through a channel along its concentration
gradient (around 150 mM inside and 4 mM outside the cell), it
leaves a negatively charged protein residue inside, which can-
Figure 3.
Alan L. Hodgkin (1914-1998) and Andrew F. Huxley
(1917-2012). They developed a mathematical model for
the membrane excitability from their electrophysiological
studies on nerve membranes.
Copyright © 2012 SciRes. 1131
not permeate the channel’s pore and which, in turn, operates an
attractive electrical force on it. The condition when the work
generated by the concentration gradient balances that of the
electrical gradient is called electrochemical equilibrium of a
given ion, and is described by the Nernst equation:
ln o
The pre-logarithmic factor (including the gas constant R, the
temperature T in Kelvin, the Faraday constant F, and the ion
charge z) is constant at a given temperature: thus, if a mem-
brane (biological or not) is selectively permeable to an ion S
which is differently concentrated (i.e. the argument of loga-
rithm is different from 1) across it, Vm tends to assume an elec-
trical polarity (ES), in general different from zero. Trans-mem-
brane ion flow leads to a current that can be expressed, from
Ohm’s law, as:
If channels are open (conductance GS 0), ion will flow (IS
0) until their Nernst equilibrium is reached (Vm = ES). Molecu-
lar pumps, driven by metabolic energy, maintain several ion
gradients across the membrane and several families of ion
channels permeable to them are present as well. Vm is therefore
determined by the combination of all the electrochemical gra-
dients, each weighted by the corresponding permeability of the
membrane to it. The total ion current can thus be written as:
ionNaKNa mNaKmK
IIIGVE GVE  (4)
Let’s call Vr the resting value of Vm. When Vm value de-
creases, membrane is said to depolarize. When membrane re-
stores Vr value after depolarization, it is said to repolarize.
When Vm exceeds Vr, hyperpolarization is said to occur.
Hodking and Huxley knew that, when the nerve membrane
was stimulated by injecting a brief (few ms) current pulse, if the
amplitude of the pulse was large enough, Vm rapidly depolar-
ized, inverted its polarity of about 20 mV, and more slowly
recovered Vr value: this transient Vm displacement, the action
potential (AP), was first described by the German physiologist
du Bois-Reymond in 1848. They also knew that depolarization
was accompanied by sodium entry into and potassium exit from
the cell. They found that the membrane permeability to ions
(and therefore GS values) is voltage dependent, i.e. it changes
when Vm changes, and, what is more important, this voltage
dependency is, in general, not instantaneous, but takes time to
develop. Now we know that time dependency is due to the
opening and closing properties of molecular gates that regulates
ion trafficking through membrane channel pores (Figure 4).
Also, being made by a thin (few nm thick) insulating lipid
bi-layer separating electrically charged compartments, the cell
membrane per se can be represented as an electric capacitor of
capacitance C (the parallelism with Leyden jars is striking). The
current flowing through a capacitor is given by:
Thus, ion channels are embedded into the capacitive mem-
brane, their conductance G is voltage and time dependent and,
when they are open, ion current flows according to Equation (4).
All this can be incorporated into the equivalent electrical circuit
reported in Figure 5. E terms represent the Nernst batteries for
the different ion species (Equation (1)), and the G terms the
corresponding electrical conductances (the arrows means “vol-
Figure 4.
Voltage dependent ion channel. An ion channel is a pro-
tein made by several sub-units that span the cell mem-
brane and surround a central pore, which is selectively
permeable to a given ion species. In the case of voltage-
dependent channels, the opening of the pore is regulated
by Vm. Charged residues on the inner or outer side open
or close following Vm changes and making the voltage-
dependency time-dependent as well.
tage and time-dependent”). The total current flowing into the
circuit (across the membrane) is therefore:
tot Cion
For a single cell, it is found that Itot is always zero, i.e. Iion
deposits all its ions on the membrane surface, causing Vm to
change and generate, according to Equations (5) and (6) an IC
equal and opposite to Iion. This can be rewritten as:
ion st
 (7)
where the constant term Ist can represent the external current
injected by the electro-physiologist in order to study membrane
properties, or it can simulate what happens in nature when
neurons or muscular cells are stimulated by different biological
mechanisms leading to current flow.
The HH theory explains that the voltage dependency of ion
conductances (GNa, GK, etc.) develops in a time dependent
manner, due to the kinetics of the open probability p of chan-
nels gates. When membrane depolarizes, some gates open (acti-
vation gates), other close (inactivation gates). An ion channel
can be endowed with none, one, or n activation and/or inacti-
vation gates, and the corresponding open probability will be p0,
p1, pn respectively, where:
 
dpm pm
pVp V
Hodgkin and Huxley happen to work on a particularly simple
biological membrane, that of the squid giant axon (Figure 6),
where only three types of ion channels where presents: 1) So-
dium channels with 3 activation gates (their open probability is
classically called m) and 1 inactivation gate (open probability is
called h); 2) Potassium channels with 4 activation gates (n) and
none inactivation gates; 3) Leakage channels, no activation nor
inactivation gates, and with a constant (ohmic) conductance.
They derived the constant terms G and the exponential func-
tions αp (Vm) and βp (Vm) for Na and K conductances with a series
of elegant voltage clamp experiments (Hodgkin & Huxley,
1952a; Hodgkin & Huxley, 1952b), and summarized the mem-
brane dynamics into the following equation system:
Copyright © 2012 SciRes.
Copyright © 2012 SciRes. 1133
 
 
 
 
 
 
 
 
tNamNaK mKLmL
mm mm
hm hm
nm nm
mmm m
mm mm
hm hm
hmh m
nm nm
nmn m
mVm Vm
hVh Vh
nVn Vn
 
Figure 5.
Electrical equivalent circuit for an excitable membrane. Cell membrane
can be considered as a parallel combination of a capacitor C, represent-
ing dielectric properties of the lipid bi-layer, and several ion conduc-
tances G, in series with the corresponding Nernst batteries.
Figure 6.
The squid giant axon. The giant axon is a very large (up
to 1 mm in diameter) and long (several cm) projection
of a single neuron that controls water propulsion in this
cephalopods. (image taken from Memorial University at
This is an ordinary differential equation (ODE) system.
Whereas the solution of an algebraic equation system is a given
set of numbers, the solution of an ODE system is a set of func-
tions of the differentiated variables. When the embedded con-
stants are accurately derived from in vivo experiments and the
system “stimulated” with appropriate Ist values, its solution
provides a set of functions, including the AP and the time
course of the corresponding ion conductances (Figure 7). The
system reproduces the dynamics of the excitable nerve and
allow to dissect the underlying mechanisms. When Vth is reached,
INa dynamics becomes auto-regenerative: sodium channels
(their activation gates) start to open abruptly and let sodium
ions enter the cell (following Equation (2)). Sodium entry de-
polarizes the membrane (towards ENa) and depolarization, in
turn, open more m gates and lets more ions in. All this happens
in less than 1 ms, while AP reaches its peak. Eventually h gates,
also triggered by depolarization, close sodium channels. At the
same time depolarization also open n gates of potassium chan-
nels. Potassium ions rapidly exit the cell following their elec-
trochemical gradient and repolarise the membrane (towards EK).
The entire AP waveform lasts (in the case of the squid giant
axon) about 2 - 3 ms (Figure 7). Action potentials underlie
nervous activity, and trigger cardiac and skeletal muscular con-
traction in higher organism; they are also present in prokaryotes,
protists, green algae, and practically in any form of life, when
the cell generates an all-or-none response to any sort of stimuli
coming from its inside or outside environment. For more in-
formation on HH theory see (Hille, 2001; Aidley, 1998).
Figure 7.
HH action potential model. Numerical solution of HH model showing
sodium and potassium components of membrane conductance (g) dur-
ing action potential (V). Note that Vm scale was shifted vertically in
order to make Vr = 0. (From HH original paper: Hodgkin & Huxley,
Computational Solutions of HH Systems
Since the time of its formulation, the HH equation system
has been a powerful tool to reproduce and study membrane
excitability. Unfortunately, the solutions of the system, func-
tions of Vm and time (later came also space, i.e. spatial conduc-
tion of excitability), cannot be written analytically. No discrete
combinations of sin(Vm,t), exp(Vm,t), nor any analytical function
can, in general, describe the time course of the AP, nor that of
the underlying ion currents. Numerical computation, based
essentially on Euler’s method (Borse, 1997), allow to do the job;
such methods have preceded the computer technology but
greatly advanced with it. The principles of Euler’s integration
of ODE, like those of HH, can easily be thought in high schools;
I will not discuss them here but note that their knowledge is not
irrelevant for “computationally thinking” many physiological
problems. The computing steps needed to solve ODE systems
are nowadays incorporated into easy-to-handle routines that can
be run from many mathematical computing environment. One
of the most popular for both teaching and research purposes is
definitely Matlab (MathWorks, Natick, Massachusetts, USA),
where commands to solve the HH system can be written into
straightforward scripts, and solutions obtained by means of
built-in ODE solvers. Equations system (9) can be re-written
into the following Matlab script:
1. function dY = hodgkin_huxley_model(time, Y)
2. Cm = 1.0;
3. g_L = 0.3; g_K = 36.0; g_Na = 120.0;
4. E_L = -64.387;
5. E_Na = 40;
6. E_K = -87;
7. stimulus_amplitude=4;
8. if ((time >= 1) && (time <= 1.5))
9. Ist = stimulus_amplitude;
10. else
11. Ist = 0.0;
12. end;
13. i_L = g_L*(Y(1)-E_L);
14. i_Na = g_Na*Y(4)^3.0*Y(3)*(Y(1)-E_Na);
15. i_K = g_K*Y(2)^4.0*(Y(1)-E_K);
16. dY(1, 1) = -(- Ist +i_Na+i_K+i_L)/Cm;
17. alpha_n =
18. beta_n = 0.125*exp((Y(1)+75.0)/80.0);
19. dY(2, 1) = alpha_n*(1.0-Y(2))-beta_n*Y(2);
20. alpha_h = 0.07*exp(-(Y(1)+75.0)/20.0);
21. beta_h = 1.0/(exp(-(Y(1)+45.0)/10.0)+1.0);
22. dY(3, 1) = alpha_h*(1.0-Y(3))-beta_h*Y(3);
23. alpha_m =
24. beta_m = 4.0*exp(-(Y(1)+75.0)/18.0);
25. dY(4, 1) = alpha_m*(1.0-Y(4))-beta_m*Y(4);
Line 1 defines the name of this script (“hodgkin_huxley_
model”) which, in Matlab language, is considered as a “func-
tion”. Lines 2 - 12 define membrane capacitance (I will not
discuss here scaling and dimensional details), ion channels
maximum conductance values, amplitude and timing of the
current stimulus Ist (amplitude = 4, starts at time 1 ms and stops
at 1.5 ms, lasting therefore 0.5 ms). Remaining lines report
explicitly the exponential functions for α and β described above
for each gate and their dynamics (Equation (8)). Line 13 - 16
contain Equation (7). The function “hodgkin_huxley_model”
will be called from a second script. I name it “main_HH”and
report it here:
1. tMax = 10;
2. Y = [76.0, 0.325, 0.6, 0.05];
3. options=odeset('reltol',1e-8,'abstol',[1-8, 1-8, 1-8, 1-8]);
4. [tData, YData] = ode15s(@hodgkin_huxley_model,
[0 tMax], Y, options);
Line 1 sets duration of simulation in ms, line 2 initial condi-
tions, lines 3 and 4 call the Matlab ODE solver “ode15s” and
make it to solve the equations listed in the script “hodg-
kin_huxley_model”. When, from the Matlab prompt, we simply
type “main_HH”, the system will be solved numerically (note
that simulating 10 ms of membrane dynamics was taking about
a week for the 1950’s analog computers, it takes much less
than1 s now on my laptop). The ODE solver generates in this
case a vector tData which is the time of the simulation, and a 4
columns matrix called YData, where the time courses of Vm, m,
h, and n are reported in columns 1 to 4 respectively. These 5
vectors contain all we need to know about AP dynamics. We
can try simulating the application of a sodium channel blocker
known (from experiments) to reduce sodium conductance by
50%, simply multiplying g_Na by 0.5, or see what happens
when some genetic disease leads to a 30% increase in potas-
sium channel conductance (simply multiply g_K by 1.3). We
have just to type: “plot(tData, YData(:,1))” and Matlab will
produce a graphic representation of the AP. We can type:
“plot(tData, YData(:,2))” to see the time course of m; or, again,
we can type:
to see the time course of Sodium current (note that when simple
algebraic operation are applied to vectors, a dot should be
placed between the vector and the operator). Same for potas-
sium or leakage current. Ready to use scripts containing HH-
type equations systems like that discussed here can be found on
different web sources, like, or di-
rectly from the MathWorks website at
http://www.mathworks. com/matlabcentral/fileexchange.
Back to the Controversy
“In order to save something of the Galvani’s hypothesis on
animal electricity, which I consider to be wrong through a
number of experimental evidences, and which I have replaced
with the principle of a purely artificial electricity where the
cause is all extrinsic to the animal, it would be necessary that
the followers of Galvani showed me contractions in frogs elic-
ited by arcs made by metals of the same species; they will never
be able to do so”. These are Volta’s words from a letter to a
colleague in 1795 (Piccolino & Bresadola, 2003: p. 391). Too
bad at his time he could not experiment on the electrical activ-
ity of cardiac pacemaker cells, nor on the rhythmic firing of
pacemaker neurons, where the electrical excitability develops
without any external stimulus. In the HH model that I reported
above, the external stimulus is indicated by Ist. In the Gal-
vani-Volta bi-metallic arc experiment, it was the “battery-like”
Copyright © 2012 SciRes.
nature of the arc that made Ist flow across the membrane. Ist
elicited in turn an AP on the crural nerves, and the AP was then
conducted to the muscle where it triggered contraction. We can
play around with Ist in the model, and see where the core of the
controversy is hidden. If we go to the script “hodgkin_hux-
ley_model” in Matlab, we set stimulus_amplitude = 4, and we
run main_HH, we obtain the sub-threshold voltage trace re-
ported in Figure 8. Vm slightly depolarizes (about 2 mV) dur-
ing the current injection, and slowly recovers its Vr value after
injection stops. We can try different amplitudes (8, 4, +4, +8,
+12) and obtain Vm deflections reaching each time a value (at
time 1.5 ms, when the pulse ends) proportional to the injected
current (Figure 9): membrane is, in this Vm range, ohmic, i.e. it
behaves like a passive RC circuit. Now, if we give Ist a value of
16 and we run main_HH, Vm reaches its threshold value Vth
(arrow in figure) and an AP is elicited (Figure 10). The intrin-
sic nature of AP is all-or-none, i.e. it does not depend on the
stimulus, as we can easily verify by playing around with higher
Ist values. During the AP the membrane dissipate energy asso-
Figure 8.
Sub-threshold voltage response. The trace is obtained by setting stimu-
lus_amplitude = 4 in the Matlab script.
Figure 9.
More sub-threshold traces. Stimulus_amplitude was set, in turn, to 8, 4,
+4, +8, +12.
Figure 10.
Sub- and supra-threshold responses. When stimulus_amplitude is set to 16,
Vth (arrow) is reached and an AP elicited. Full scale on the left panel, and
expanded scale on the right.
Figure 11.
Spontaneous activity. It is enough to slightly increase extracellular potas-
sium (i.e. setting EK = 80 mV) for inducing spontaneous pacemaker
activity even in the absence of any external stimulus (stimulus_amplitude =
ciated to the electrochemical gradients that sustain its electrical
polarity. This gradients are maintained by ion pumps and other
molecular transport mechanisms. Gradients (and ion pumps as
well) can also be incorporated into the Matlab script by assign-
ing physiological values to [Na+]o, [Na+]i, [K+]o, [K+]i, and
explicitly adding equation (1) for each ion species. In our sim-
plified script though, gradients and their required metabolic
energy are all contained into lines 4 - 6. Also, we have focused
here only on nerve excitability. The membrane of the muscle
cell is excitable as well and transduces AP into mechanical
activity through a mechanism known as excitation-contraction
coupling, which is also included with its dynamics into very
recent and more complex mathematical models.
In conclusion, it is useful to look at the bi-metallic arc ex-
periment and, through it, at the all controversy, from the Matlab
script of the HH model. We can observe that the Haller’s irrita-
bility lies into the potential enegy associated with metaboli- r
Copyright © 2012 SciRes. 1135
Copyright © 2012 SciRes.
Figure 12.
The key points of the controversy can be discussed by playing around with the Matlab
script of the HH model.
cally maintained electrochemical gradients (ENa, EK, etc.), the
Galvani’s excitability is indeed given by the flux of an “animal
electricity” (Itot) through ion channels, as their non-ohmic dy-
namics (voltage and time dependency of m, h and n) is trig-
gered. The external intervention, the trigger, is present in the
model through the Ist term, what Volta thought as the source of
the all phenomenon and which, in the bi-metallic arc experi-
ment, was indeed due to the current flow driven by the different
electro-negativity of metals. As mentioned above, pacemaker
activity of some excitable membranes is the clearest example of
how Volta’s thinking was wrong. We can make Ist equals zero,
i.e. we can completely turn off the stimulus (Volta was sug-
gesting so in the words that opens this paragraph) and simply
simulate a slight change in potassium gradient across the mem-
brane (equation 1) resulting in a 7 mV depolarization of EK
(hyperkalemic conditions are not uncommon in physiology and
pathology). We do so by assigning a value of 80 instead of
87 to EK into the script “hodgkin_huxley_model”. We obtain
that the simulated membrane generates APs spontaneously and
repetitively (Figure 11). Again, we can play around with EK
value and see how pacemaker activity changes accordingly.
Automatic firing is achieved in nature thanks to the presence of
particular ion channels expressed in pacemaker cells (they gen-
erate the spontaneous heart beat and a number of fundamental
neurological functions), which are not included in the original
HH model, but this is not the point here. The point is that ex-
citability is indeed a form of “animal electricity”; the cell
membrane contains the fuel necessary to the AP (ion gradients)
and the engine to generate it (ion channels); there are conditions
in which an external current (Ist) is required for the process to
take place, but this is not necessarily required (see scheme in
Figure 12).
Computational techniques are increasingly gaining impor-
tance into modern biological (Fall, Marland, Wagner, & Tyson,
2010) and physiological (Keener & Sneyd, 2008; Zaniboni,
2012) research and, according to my experience, they can be
successfully approached also in high schools and in under-
graduate courses. What a mathematical model does is to trans-
late our logical knowledge of a phenomenon into a synthetic
series of commands; in doing so, the HH model of the AP is
shown here to be a useful tool for removing ambiguities that
still concern one of the greatest controversies in the history of
science. The study of this controversy can also be a great op-
portunity to combine history, physiology and technology into
an interdisciplinary dialog fruitful for both teachers and stu-
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