Properties of Neurons

Neurons can be classified using different criteria like polarity, length of synaptic projections, functional mechanism, and electrophysiological activities. However, most of the neurons can be classified by their polarity. They are mainly of three types: (i) unipolar or pseudounipolar, (ii) bipolar, and (iii) multipolar [138]. Neurons can also be classified by their functional mechanism as (i) afferent or sensory neurons (it transfers the information from tissues and organs to central nervous system), (ii) efferent or motor neurons (it transmits the signals from central nervous system to effector neurons), and (iii) interneurons (the cells which connect the neurons with the central nervous system). To study the activities of any neuron, it is important to know the particular action of this neuron on other cells. The synapses and neurotransmitters respond to these activities. The excitatory neurons depolarize the target neurons, and inhibitory neurons hyperpolarize the target cells. The activity of the presynaptic neuron on the postsynaptic neuron depends not only on the neurotransmitters but also on the receptors of the postsynaptic neuron. The modulatory neurons often release dopamine, serotonin, and acetylcholine. This type of neurons has more complex effects which are known as neuromodulation.

Electrophysiological Properties of Neurons

The difference between the electrical potentials (or voltages) of extracellular and intracellular potentials is a crucial measurement of the neuronal cell's activity (membrane potential or voltage) (see [66,67]). The neurons have passive electrical properties which do not influence sensitively on the activity of neurons. It affects the membrane capacitance and resting membrane resistance. To compare membrane properties of neurons of different sizes, the resistances of unit area of the membranes are often used (specific membrane resistance). It depends on the densities of the resting ion channels and their conductance. The cell membrane behaves like a capacitor. The polar head directs to the intracellular cytoplasm and extracellular region, separating the external and internal conducting solution by an insulated layer of 35-50 A. From physics, we know that if a thin insulator is charged, it acts like a capacitor. The voltage V across the capacitor is proportional to the charge Q which is stored inside it, Q = CV. In membrane dynamics, the capacitance is referred as the specific membrane capacitance C„„ whose unit is in microfarad per square centimeter of membrane area. When the voltage changes across the capacitance, current flows and the current equation is given by 1 = C„,[dV„,(f)/df]. The value of capacitance depends on the dielectric property of a medium and the conductance on either side. If we consider a capacitor as consisting of two parallel plates of area A, which is separated by thickness d and an insulated dielectric constant e, then the capacitance is given by С = e0A/d, where e0 is the electric constant (e0 ~ 8.854187 x 10~12F/m). This measures the polarization of free space universal constant. Polarization plays a major role in signal transmission [26,85]. A section of the neuronal membrane with two ion channels embedded in it as given by Hille [64] is reproduced in Figure 6.2a. A schematic diagram of voltage-gated ion channels as given by Izhikevich [80] is reproduced in Figure 6.2b.

Ionic Conductance

The active properties of the neuron are its excitability, the specific properties of generating action potential and transmission of signals [25]. The cell membrane acts as a capacitor,


(a) A section of the neuronal membrane with two ion channels embedded in it. (Reproduced with permission from Hille, B. Ion Channels of Excitable Membranes, 3rd Edition, Sunderland, MA: Sinauer Associates [64]; and from Oxford Publishing Limited, Copyright 2001.) (b) Schematic diagram of voltage gated ion channels. (Reproduced with permission from Izhikevich, E. M. 2007. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Cambridge, MA, London, England: MIT Press [80], Copyright 2007.) and it can conduct the electrical signal through ion transmission. The ionic conductance across the cell membrane increases during the emission of action potential. Action potential arises due to the effects of ionic fluxes through the ion channels (Figure 6.2). Alan Hodgkin and Bernard Katz [69] observed that the amplitude of action potential reduced when the concentration of external Na+ ions becomes low. Thus, the flow of sodium ions inside is responsible for the rising of action potential. The authors' experiment suggested that the phases of action potential fall due to the effect of increase in K+ permeability. To test this proposition, the authors varied the membrane voltage systematically of a squid giant axon and measured the changes in Na+ and K+ conductances across the membrane (see also Hodgkin and Huxley, [68]). Their experiments showed that four types of ionic currents, sodium ions (Na+j, potassium ions (K+), calcium ions (Ca+2), and chloride ions (СГ), are responsible for the electrical activity of a neuron. The concentrations of these ions are different on the outside and inside of the cell membrane. The extracellular medium is highly concentrated with sodium and chloride ions and it has also a high concentration of calcium ions. The intracellular medium is highly concentrated with potassium ions and other different negatively charged molecules which are confined in the intracellular medium. The motions of calcium and sodium ions have no significant effects at resting condition. However, the movements of potassium and chloride ions have significant effects. There are two types of ionic conductances across the membrane. They are the following:

a. The impermeable anions attract more potassium ions inside the cell and repel more chloride ions outside the cell. It creates the concentration gradients.

b. The Na+ -K+ ion channels pump three sodium ions outside the cell for every two potassium ions which is inside the cell, and it creates the concentration gradients.

The electric potential and concentration gradients drive the ions across the membrane channel. Potassium ions diffuse outside the cell as the external concentration of the ions is lower than the internal concentration. If we excite the cell, potassium ions carry a positive charge and flow outside the cell and leave a negative charge inside the cell. It generates outside current flow across the membrane. The positive and negative charges separate on both sides of the cell membrane which produce an electrical potential difference across the cell membrane. It is called the membrane voltage or transmembrane potential. The potential slows down the diffusion process of potassium ions as the ions are attracted to the negatively charged molecules inside the cell and they are repelled from the positively charged ions outside the cell. The concentration and electrical potential gradients apply equal and opposite forces which balance the two forces, and equilibrium is formed where the cross-membrane current becomes zero. It is denoted by the Nernst equation (see [64]):

where t is the equilibrium potential (Nernst potential) for a given ion, i< is the universal gas constant, Г is the temperature (in degree Kelvin), and z is the valency of the ionic species and has no units. For example, z is 1 for Na+ and K+; -1 for CP; and +2 for Ca2+. F is Faraday's constant and is equal to 96485 C/mol (Coulombs per mole), and [ion]out5ide and [ion]inside are the ion concentrations outside and inside of the cell [54]. Membrane conductance provides a measure of how the ions flow through the membrane channels. The permeability of the membrane for a specified ion is denoted by P (cm/sec). A Nernst potential develops across a membrane if the following two criteria are met: (i) a concentration gradient exists across the membrane for a given ion, and (ii) selective permeation pathways (i.e., selective ion channels) exist that allow transmembrane movement of the ion of interest. For some ion channels, where the selectivity filter strongly favors the permeation of one ion over other ions, the Nernst potential also predicts the reversal potential (Vrev) of the current-voltage (I-V) relationship. David Goldman [54] proposed a formula which relates the equilibrium potential, permeabilities of ions, and extracellular and intracellular ionic concentrations. The formula is known as Goldman-Hodgkin-Katz (GHK) equation [54]. Hodgkin and Katz [69] (see [64]) provided a method to compute the reversal potential. For the membrane separating potassium ions, sodium-positive ions, and chloride negative ions, the GHK equation is given by

where PNa, PK, and Pa are the permeabilities of the ionic species. The equilibrium potential is reached when the ionic currents flow across the cell membrane and balance it. As a result, the net current flow is zero across the membrane. For neurons, the value of the equilibrium potential ranges from -70 to -30 mV [36].

Generation of Action Potential, Its Activity, and Signal Propagation

The signals produced and propagated along the neurons are called action potential or spikes. It is the elementary unit of signal transmission. The electrical impulses transmit rapidly through the neurons. Axon potential is transmitted at a speed of around 1100 m/s. The amplitude of the impulse throughout the axon remains almost a constant. Axon potential is regenerated at the region known as Ranvier's nodes which is a thick insulating myelin sheath in axon. The action potential has the following properties [80]:

a. An axon potential is initiated by a sufficiently strong depolarization of the membrane potential in the axon hillock region. The depolarization occurs due to the injection of sodium ions inside the cell, and it comes from various sources such as synapses and sensory neurons. The membrane permeability is low for potassium ions. The depolarization triggers the voltage-gated potassium and sodium ion channels to open so that the ions can flow across the membrane. If depolarization becomes small, the potassium current dominates the sodium current, whose flow is toward the inside of the cell and the membrane starts repolarizing to its normal state of resting potential (around -70 mV). When the depolarization is strong enough, the flow of sodium current inside the cell increases and becomes more than the flow of potassium current. The voltage causes more sodium channels to open, which stimulates the membrane voltage toward the reversal potential of sodium channels. This process continues until sodium channels are completely open and the membrane voltage V converges to the sodium channel reversal potential.

b. When the phase falls, the voltage which opened the sodium channels slowly decreases and the sodium channels close. During this process, voltage-dependent potassium channels open and it increases the membrane's potassium permeability. These changes simultaneously repolarize the membrane and action potential falls down.

c. Next, hyperpolarization occurs. Not all potassium channels which opened due to increase in voltage close while the membrane voltage comes back to the normal resting potential. The permeability of potassium channels becomes high, and it acts on the membrane voltage to reach the value of equilibrium potential of potassium channels. Hyperpolarization exists until the permeability of potassium channels returns to the base value.

d. The switching of the potassium and sodium channels during the process of action potential generation may leave some of them in refractory period. In this state, the channels will not be able to open until these are recovered. When absolute refractory period occurs, many ion channels cannot work, and at this time, no action potential is produced. Recovery of the process requires that membrane voltage remains hyperpolarized for certain duration of time. Sufficient number of channels is recovered in the relative refractory period so that an action potential can be generated with a sufficiently strong stimulus than usual.

The action potential is produced in the cell body of the neurons and travels as a wave along the axon. The membrane of axon also consists of voltage-gated ion channels as soma's membrane which allows transmission of electrical impulses. The signals are propagated by different ions carrying the charges. The ionic currents move toward the intracellular medium along the axon when the axon potential is generated, and depolarize the adjacent region of the membrane to evoke an action potential in the neighboring membrane patches. The flow of current passively travels from one Ranvier's node to another. It increases the conduction velocity of action potential. In an unmyelinated axon, the axon potential propagates continuously along the axon. The signal is propagated from soma to the axon terminal.

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