Biomedical Engineering Reference
In-Depth Information
The di cult part in this approach is the titanic work needed to unveil the
nature of the currents I ionic . Hodgkin and Huxley were capable precisely of
writing down phenomenological models for these.
The two major voltage-dependent ionic currents involved in the gener-
ation of spikes are a sodium current and a potassium current. These are
characterized by conductances G Na and G K , respectively. A smaller “leak”
current, characterized by G L , is also important in the description. Therefore,
I ionic = I Na + I K + I L ,
(8.2)
where
E i ) G i ( V,t ) . (8.3)
Here E i are reversal potentials, typical of each of the ionic species ( i =
Na, K, L). The conductances G i ( V,t ) are typically expressed as products
of maximum values g i and nonlinear functions of coe cients that describe
macroscopically the fraction of open ionic channels.
The equations end up being quite intimidating, but the dynamics dis-
played by such a system are not complex to describe, at least for one unit.
The most remarkable property of the axonal membrane is its capacity to re-
spond in two qualitatively different ways to depolarizing perturbations. What
could be the origin of these perturbations? In its natural environment, the
origin is the currents that occur when neurotransmitters are released by an-
other neuron in a synapse, and ionic channels are opened. The qualitatively
different responses can be described as either (a) a small depolarization fol-
lowed by a return to the resting potential, or (b) a pulse-like action potential,
whose shape is somewhat independent of the perturbation. The last response
will occur whenever the perturbation exceeds a threshold.
In order to communicate, neurons have specialized contact zones called
synapses . In what is known as a chemical synapse, a spiking presynaptic
neuron releases neurotransmitters , chemicals which are capable of opening
channels that allow the passage of ions through the membrane of a post-
synaptic neuron. When the synapse is an excitatory one, the postsynaptic
membrane potential rapidly depolarizes, finally to return to its rest value.
When the synapse is inhibitory, a hyperpolarization takes place. Therefore,
the result of spiking activity in a presynaptic neuron is reflected in the onset
of a postsynaptic current
I i =( V
I syn =( V ( t ) − E syn ) G syn ( V pre ,t ) ,
(8.4)
where G syn ( V pre ,t ) is determined by the presynaptic state. The details of the
function G syn ( V pre ,t ) depend on the nature of the synapse. Most of the fast
excitatory synapses are regulated by a neurotransmitter called glutamate,
and various receptors are sensitive to it (with different synaptic properties
associated with different receptors). The inhibitory synapses are regulated by
γ -amino butyric acid (GABA), the most common inhibitory neurotransmitter
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