Nerves and the Resting Potential


  1. The Neuron
The basic cell unit of the nervous system in the neuron. Neurons come in a variety of shapes and sizes – there are over a billion in the human body.

Supporting cells are about 5 times more plentiful than the neurons themselves.

Each neuron is composed of a cell body, or perikaryon which contains the nucleus, mitochondria and the endoplasmic reticulum. Cell bodies are frequently clustered together. In the brain and spinal chord (CNS) the clusters are called nuclei, in the peripheral area they are called ganglia.

The dendrites or dendritic branches are extensions that carry an impulse toward the cell body. Usually dendrites are highly branched to provide connections to up to 100 other neurons.

Axons are longer processes that carry impulses from the cell body. Axons vary in length from 1 mm to several meters. Side branches are call colaterals.

Proteins are transported rapidly down an axon from the cell body. Axoplasmic flow (slower) results from rhythmic waves of contraction that move the cytoplasm. Axonal transport uses microtubules to move selected substances.

The neurons themselves may be afferent or sensory and conduct impulses to the CNS; motor conducting impulses from the CNS or associative interneurons between the two.

Supporting cells include :
Schwann cells (neurolemmocytes) of the peripheral nervous system. These cells form myelin sheaths as they grow around the peripheral axons
Satellite cells or ganglionic gliocytes support ganglia of the PNS
Oligodendrocytes – from sheaths around axons in the CNS
Microglia – phagocytotic cells of the CNS
Astrocytes – ion regulators of the CNS
And Ependymal cells – line the ventricles of the brain and spinal chord.

In the PNS axons are surrounded by sheaths of Schwann with The outer surface of the layer is encased in a glycoprotein basement matrix. ( there is no continuous basement membrane in the CNS). Nerves in both CNS and PNS are insulated with a myelin sheath formed by successive wrappings of the neurolemmocytes or oligodendrocytes.

The supporting cells themselves remain alive. The oligodendrocytes surround more than one axon – with extensions rather like an octopus to form the white matter of the CNS.
 
 

If an axon in the PNS is cut. The severed part degenerates and the myelin sheath forms a growth tube, secreting factors that allow the original cell to regrow. Injury in the PNS stimulates the growth of the colateral branches – but these cells do not regenerate as well . Further cells of the neighboring area also degenerate. But there are several nerve and myelin growth factors that are present in the fetal brain and can promote CNS regrowth. These factors are being applied to spinal chord injury in an attempt to heal damage.

The Resting Potential
The Nernst Equation Revisited.

In the section on transport and the movement of ions, we examined the way in which an impermeant ion could cause an uneven distribution of permeant ions across a membrane in Donnan equilibrium. We also noted that the charge as well as the concentration gradients affect this distribution. The Nernst equation allows us to examine the concentration and charge forces acting on a particular ion to see if that ion is in passive equilibrium or is actively moving.

The equation states that the equilibrium potential for an ion (E) is equal to the gas constant (R) times the absolute temperature (T) divided by the charge on the ion (z) times Faraday’s constant (F) ; this quantity is multiplied by the natural log (ln) of the concentration ratio inside and outside the membrane.

E = RT/zF ln [C1]/[C2]

Faraday’s constant is 96,500 coulombs/ mole. Charge is measured in coulombs. A coulomb is a charge equivalent to 1/96,500 grams of electrons. The charge on one electron is –1.6 x 10-19coulmbs. If this is multiplied by Avagadro;’s number, the total charge is one faraday or –96,487 coulombs/mole.

The gas constant is 8.314 joules/ degree Kelvin/ mole.

So E = 8.314 joules/ degree/ mole x degrees x ln [C1]/[C2]
            96,500 coulombs/mole x charge

E = joules/ coulomb and a joule/ coulomb is equal to a volt.
( or a potential difference x a charge = energy)

If we assume a temperature of 18 Centigrade and a monovalent ion and convert the natural log to log base 10 then

E = .058/z log [C1]/[C2]

In squid nerve the intracellular potassium concentration is 410 mM and the external concentration is 22 mM, the measured membrane voltage is – 70 mV. Is potassium in equilibrium ?
( by convention the membrane voltage (Vm) is inside with respect to outside and all animal cells have a membrane potential of –20 to –120 mV.

Note that the equilibrium potential for potassium is negative. This means that the interior of the cell would have to be –70 to –75 mV negative in order to prevent the outward movement of potassium given these concentration gradients.

The Goldman Equation

More than one ion contributes to the overall potential of a membrane and because the membrane is selectively permeable to different ions, when the membrane potential is calculated, the permeability of the ions must be taken into account. The Goldman equation expands the Nernst equation with the addition of several ions and their relative permeabilities.
Vm = RT/F ln PK [Kout] + PNa[Naout] + PCl[Clin]
                    PK[Kin] + PNa[Nain] +PCl[Clout]
 
 

Resting Potential

The resting potential of a neuron is approximately – 70 mV. Ion concentrations affect the resting potential, but the nature of the biological membrane itself is also important.

Membrane Capacitance

The bilipid membrane of the nerve is not very permeable to the movement of most ions. The rate at which ions traverse membranes is as little as 10-8 times the rate at which they cross an equivalent distance of 50-100 A in the cytoplasm. In fact we can think of the membrane as a narrow strip of insulation between two plates where charge accumulates. We can say then that the membrane has a capacitance. Capacitance is measured in farads and a farad is equal to a coulomb per volt. The capacitance of a nerve membrane is about one microfarad.

Membrane Conductance

Conductance is the release of the charge difference on either side of a membrane, through pores, channels or carriers, ions are allowed to move across a membrane and conduct the current from one side to another. Conductance is the reciprocal of resistance G = 1/R and the units of conductance are siemens. Resistance (R) = E/I so he voltage across the membrane is proportional to the current passed through the membrane and inversely proportional to the conductance. E = I/G. For each ion the conductance of that ion will be equal to the current carried by that ion divided by the potential difference or emf acting on that ion.

Permeability

 If the axon  potential becomes  more negative than the resting potential, the cell is hyperpolarized, if the potential becomes more positive the cell is depolarized.  Ion channels contribute to changes in permeability of individual ions. The ion channels for Na and K are fairly specific . There are two basic types of K channels; one is not gated and always open, but the other is gated and closed in the resting cell. Sodium channels are gated and are closed in the resting cell. So the cell is more "leaky " to potassium than sodium and the membrane potential is just slightly less than the K equilibrium potential .

Over the long term, Na is removed from the cell and K is added by Na/K ATPase and the ion gradients are maintained.