Membrane biophysics of neurons

Membrane biophyiscs is a broad area of research to which entire textbooks have been devoted. The discussion below is derived mainly from two sources: Bioelectricity: A Quantitative Approach, by Plonsey and Barr,6 and Principles of Neural Science, 3rd ed., by Kandel et al.7 Nerve cells have a measurable electrical potential that exists across the cell membrane. Typical

Table 4.1 Concentration, Permeability, and Nernst Potential for Various Ions in Squid Axon

Concentration (mM/l)

Relative Permeability

For Active

Nernst

Ion

Intracellular

Extracellular

At Rest

Membrane

Potential

K+

280

10

1.0

1.0

-83.9

Na+

61

485

0.04

20.0

52.2

Cl-

51

485

0.45

0.45

-56.7

resting potential is -60 mV measured inside with reference to outside. The electrical potential exists due to active and passive cell processes that maintain a difference in the chemical concentration of various ions that exist in the intra- and extracellular fluids.

The ions most responsible for maintenance of membrane potential are Na+, Cl-, and K+, although in some cells (cardiac and photoreceptor) Ca2+ plays a major role in signaling. The concentrations of these ions are different inside and outside the cell. Potassium (K+) has a higher concentration inside the cell, and sodium (Na+) and chloride (Cl-) have higher extracellular concentrations. Table 4.1 shows the concentrations in the squid axon.6

In human nerve cells, the absolute numbers are two to three times lower, but the ratio of intracellular to extracellular is similar. The cell membrane at rest is not equally permeable to all ions; that is, some ions diffuse more readily than others. The diffusion force will drive the ions toward equal concentration inside and outside the cell. However, taking an extreme example, if only positively charged ions could cross a membrane and negatively charged ions were completely blocked from diffusing, the diffusion of only positive charge would create an electrical imbalance that would slow and then halt the diffusion. The potential at which the diffusion force is equal and opposite to the electrical force is called the Nernst potential and can be calculated from Eq. (4.1),

where Vmp is the membrane voltage for the pth ion; Zp is the charge of the pth ion, [Cp]e is the extracellular concentration of the pth ion, and [Cp] is the intracellular concentration of the pth ion. The Nernst potential is for a single ion. The various ions in the intra- and extracellular fluid each have Nernst potentials. The resting permeabilities and Nernst potentials for each ion are listed in Table 4.1. By weighting the Nernst potential of each ion with the membrane permeability for that ion, it is possible to calculate the membrane potential at steady state using the Goldman equation:

where Px is the permeability of the membrane to ion x. Though this equation is only valid if the membrane is at rest (net current is zero), qualitatively it is clear that a change in permeability for one or more ions will alter the membrane potential.

Electrical charge moves across the cell membrane through ion channels and ion pumps. The rest of the cell membrane is impermeable to ion flow. The number and nature of ion channels in the membrane determine the permeability of the membrane. Ion channels can always be open or can be opened and closed in response to a stimulus, but once they are open they act as pores that allow ions to flow to equilibrium. Ion channels can be specific to particular ions but are otherwise passive; that is, the chemical or electrical driving forces will determine the direction of the net ion flow through the channel. In contrast, ion pumps move ions against the driving force gradient, consuming energy in the process.

Signals are initiated by changes in the membrane permeability, which change the membrane potential (see Eq. (4.2)). Membrane permeability can be changed in a variety of ways depending on the type of cell. If the cell is a sensory transducer, such as a photoreceptor in the retina, then the presence of the excitation signal results in a change of membrane potential. The photoreceptors are unusual in that they are depolarized (excited) in the absence of light. Other sensory receptors, such as the hair cells of the cochlea and olfactory cells of the nose, are depolarized in response to their excitation, either sound or odor. The excitation signal might trigger a chemical cascade that opens ion channels or the ion channels may be mechanically opened. The second way that membrane potential can be modified is by synaptic transmission, that is, through a signal transmitted from a connecting neuron. Chemical neurotransmitters released by a nearby neuron bind to a specific protein on the membrane of the target neuron, leading to the opening of chemically gated ion channels.

The stimulus that creates a change in the membrane permeability affects the equilibrium equation and thus alters the cell membrane potential, which triggers the opening of a special type of ion channel that is sensitive to transmembrane potential. These ion channels are called voltage-gated ion channels, and depolarization changes membrane permeability by opening voltage-gated channels. Initially, the stimulus will result in a proportional response from the cell. In this case, the cell membrane will respond with what is called a graded potential. This means that there is a proportional relationship between the amount of depolarization and the strength of stimulus. Graded potential cells, such as the bipolar cells in the retina, transmit information over short distances; the space constant for signal propogation is small (the signal will decay over distance). Some cells have the ability to "spike," to produce an action potential, a self-propogating signal that transmits over great lengths. The anatomical structure that serves as the transmission line for the action potential is the cell axon, a relatively long projection from the cell body (soma). The action potential is generated when the cell depolarization exceeds a threshold. Once a cell is depolarized beyond that point, a process begins that will generate an action potential, even if the stimulus that produces the initial depolarization is removed.

Hodgkin and Katz determined the permeability of the squid axon membrane to sodium, potassium, and chloride ions, both at rest and at the peak of the action potential. They obtained the data by altering the extracellular ion concentrations and monitoring the current. The results suggested that the action potential generation is due to a dramatic change in the permeability of the membrane to sodium. The permeabilities from this work are shown in Table 4.1.

This sequence of events that occurs during an action potential was described in detail by Hodgkin and Huxley,1 who won the Nobel Prize for their seminal work in membrane biophysics. The initial depolarization (from synaptic transmission or sensory stimuli) will cause voltage-gated ion channels to activate (open). Voltage-gated ion channels exist for both sodium and potassium, but the sodium channels have a much shorter time constant. The quick response from the sodium channels results in an increase in the outward current, which depolarizes the membrane even further. The ion channels cannot open or close instantaneously, so, once opened, they will stay open for a finite period of time. This allows the depolarization to continue even after the stimulus is removed. An action potential is generated when the depolarization exceeds a threshold, at which point the outward current exceeds the inward current, creating a positive feedback situation (i.e., more outward current, more depolarization, more open sodium channels). The depolarization is quickly (within 1 to 2 msec) reversed by two mechanisms: inactivation (closing) of voltage-gated sodium channels and activation of voltage-gated potassium channels. Sodium activation and sodium inactivation are accomplished by two distinct, voltage-sensitive mechanisms. The sodium inactivation mechanism and the potassium activation mechanism have longer time constants than sodium activation, but they work together to restore membrane potential to resting potential.

After the action potential, it takes several milliseconds for the voltage-gated ion channels to return to their resting state. The voltage-gated sodium channels will change from inactive (cannot be opened) to resting (closed, but will open in response to voltage change). The potassium channels will change from active (open, thereby making the membrane highly permeable to inward potassium current) to resting (closed, but will open in response to depolarization). This transitional period is called the refractory period and has two stages. The absolute refractory period is the time during which the increased potassium permeability prevents an action potential generation regardless of the stimulus. The relative refractory period follows, during which time an increased stimulus is needed to generate an action potential. Hodgkin and Huxley quantified the behavior of sodium and potassium currents with mathematical equations. This work, and that of Frankenhauser and Huxley, remains the basis for much of the neuron modeling that is performed today.

The action potential has been described as an all-or-nothing phenomenon, implying that information on stimulus strength cannot be communicated by these cells. However, the firing rate of the neuron, the number of spikes per second, can be used to code information about stimulus strength. In addition, it has been demonstrated in the retina that cells may work in concert to transmit more information than if they worked independently

In summary, the basic steps of transient ion channel response to depolarization are: (1) initial depolarization; (2) voltage-gated sodium channel activation, leading to more depolarization; (3) more voltage-gated sodium channels being open due to continued depolarization and net outward current; (4) inactivation of sodium channels and activation of potassium channels; (5) repolarization of cell membrane; and (6) ion channels return to the resting state. Ion channels are sophisticated structures built from transmembrane proteins. The study of ion channel membrane biophysics is a field unto itself and a detailed discussion is beyond the scope of this chapter. While the description above is a generalization of membrane behavior to demonstrate how the neuron is capable of signaling by transiently altering its membrane properties, the basic mechanism of action potential generation is shared by most neurons.

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