3.1 Physiology and Electrical Activity of Muscle and Nerve Cells

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in the form of adenosine triphosphate (ATP) and is thus able to transport substances

even against these existing gradients. Both forms are caused by the conformational

change of the proteins, which in the case of the pore causes the opening/closing

and in the case of the transporters a folding over. The conformational change of the

proteins can have different causes: For example, there are channel proteins which

open or close due to the change in electric field gradients; others react to mechanical

stimuli or docking-mechanisms of messenger substances. The passive sodium or po-

tassium channels of the nerve cell, for example, can be activated electrically, while

the potassium-sodium pump is concentration-controlled. Channels usually have a

signalling function due to their high transport rates, in contrast the much smaller

transport rates of the transporters are counted as the housekeeping function of the

cell [47, 67].

However, both types allow the passage of ions across the membrane wall, indu-

cing a conductance like an ohmic resistor, which can change with time depending on

the actual state (open/closed). The current flow of charged molecules or ions across

the biomembrane (electrogenic transport), is the basis for most cellular signals such as

the emergence and propagation of the action potential or local changes of field gradi-

ents etc.. Since the electrical conductivity of the cell membrane is very low, by Ohm’s

law ULDS = RLDSILDS even small ionic currents lead to reasonable high potential dif-

ferences of ULDS ∼mV across the cell membrane [47, 67]. Besides the ion selective con-

ductivities or permeabilities of the membrane wall, the electrical activity of nerve and

muscle cells is also based on asymmetric ion distributions (for Na⁺, K⁺, Ca²⁺ and Cl⁻)

between the intra- and extra-cellular space. Assuming the cell in thermodynamic equi-

librium, ion concentrations and permeabilities can be considered as constant quant-

ities and the resting potential is given by the Goldmann-Hodgkin-Katz-equation (de-

tailed derivation in [13, 47])

URP = ^RT

F ^{ln ( PNa+ce}

Na^{+ + PK+ce}

K^{+ + PCl−ci}

Cl⁻

PNa⁺cⁱ

Na^{+ + PK+ci}

K^{+ + PCl−ce}

Cl⁻

) .

(3.1)

R and T are the ideal gas constant and the absolute temperature respectively. Given

the concentration gradients between the intracellular i and extracellular space e of

the individual ion species cNa⁺, cK⁺ and cCl⁻and the permeabilities PNa⁺, PK⁺ and PCl⁻

the resting potential can be calculated, concentrations of the mammals given in Fig-

ure 3.9 lead to URP ∼−70 mV. The generation of nerve impulses (action potentials) is

limited by a temporal exchange of these charges according to time varying membrane

conductivities (cf. Figure 3.9).

3.1.2 Analogy to Electrical Circuits

The basic principles of the electrical activity of cells in the previous section led to a de-

scription via the electrical membrane capacitance and the membrane resistance. Even