62 



HANDBOOK OF PHYSIOLOGY 



NEUROPHYSIOLOGY I 



types of nerve fibers and neurons, the values ranging 

 from looo to approximately io,ooon-cm- for squid 

 and sepia giant fibers, respectively (49, 77), and it 

 probably lies within the range of 500 to loooli-cm^ 

 for mammalian motoneurons (15, 29, 44). Values for 

 specific capacitance of giant fiber membranes range 

 from I to 1.5 mF per cm- and for mammalian moto- 

 neurons are probably at least 3 nF per cm-. In addi- 

 tion, there is a considerable potential difference across 

 the surface membranes of neurons, including all 

 their branches, the inside being —50 to —80 milli- 

 volts relative to the exterior under normal resting 

 conditions. 



It may be claimed that only one hypothesis, which 

 may be termed the membrane ionic hypothesis, 

 attempts to account quantitatively for propagation 

 within neurons both of impulses and of the events 

 which control the generation of impulses, and also for 

 transmission across synapses. The earliest ionic 

 hypothesis was proposed by Bernstein (2) in 1902. 

 For the modern version of this ionic hypothesis, as 

 applied to the responses within a neuron, reference 

 may be made to Hodgkin (49, 50), to Hodgkin & 

 Huxley (52) and to Huxley (57). Its application to 

 synaptic transmission has been specially developed 

 for neuromuscular junctions and the synapses on 

 mammalian motoneurons (15, 16, 17, 26, 28, 29, 38, 



4i)- 



Essentially it is postulated that the resting mem- 

 brane potential of neurons and muscle fibers ( — 50 to 

 — 100 mv) is due to the relatively free diffusion of the 

 small ions, K+ and Cl~, across the membrane, while 

 the Na+ permeability is of a much lower order. For 

 example, in the giant axons of squid the resting K+ 

 and Na+ conductances are, respectively, about 0.5 and 

 of the order of 0.0 1 mmho per cm-. As a consequence, 

 an electrical potential difference is set up across the 

 membrane so that there is little or no electrochemical 

 potential gradient of the freely diffusing ions, K+ and 

 Cl~, across the membrane despite the very large 

 concentration differences that obtain, (Ki)/(Ko) and 

 (Clo)/CCli), both being of the order of 20 to 50. It 

 may be noted that subsidiary hypotheses, such as the 

 ionic pump mentioned in the preceding section, are 

 required in order to explain how these concentration 

 differences are maintained along with the very low 

 internal sodium concentration. It is further postulated 

 that, if the resting potential of the membrane is sud- 

 denly reduced by a considerable amount (say from — 50 

 mv to o), both the Na+ and K+ conductances undergo 

 characteristic increases. As summarized by Huxley 

 (57), the conductance " for Na ions rises in one or two 



tenths of a millisecond to perhaps 15 mmho, cm-, and 

 then falls to a low value with a time constant of about 

 I msec. That for K ions does not change noticeably at 

 first, but rises along an S-shaped curve, becoming 

 appreciable as the Na conductance falls from its peak, 

 and eventually flattening out and remaining at about 

 20 mmho/cm- as long as the membrane potential 

 difference is held at zero. When the membrane poten- 

 tial difference is restored to its ordinary resting value, 

 the K conductance returns to its resting value along an 

 exponential decay curve, without an S-shaped start. 

 The Na conductance remains low, but the ' inactiva- 

 tion' which caused it to fall after its peak during the 

 period at zero membrane potential difference per- 

 sists, decaying exponentially with about the same 

 time constant as the K conductance." Meanwhile the 

 Na and K ions have been moving down their electro- 

 chemical gradients. For a giant axon there is a gain 

 in Na of 3 to 4 X io~'- moles per cm- per impulse and 

 a loss of an equivalent amount of K. 



According to the ionic hypothesis, the membrane 

 may be represented by an electrical diagram (fig. 2) 

 in which the membrane capacitance (a) is shown in 

 parallel with two battery-resistance elements (6 and 

 (-) representing, respectively, the K and Na difi'usion 

 channels across the membrane. The respective 

 batteries are at the approximate equilibrium poten- 

 tials for K and Na ions, and the resistances which 

 represent reciprocals of the respective conductances 

 are both capable of variation over a wide range. For 

 the .squid axon the respective resistances of the resting 

 membrane are about 2 X lo'fi cm^ and lo^fi cm-, 

 while during activity the values are as low as 25^ cm^ 

 and loi] cm-. 



On the basis of quantitative studies of the time 

 courses of the conductance changes as produced by 

 a wide range of membrane potential changes, it has 

 been possible (52) to set up differential equations 

 which relate three parameters to the membrane po- 

 tential changes, viz. the 'turning on' of the Na con- 

 ductance, the 'turning on' of the K conductance and 

 the 'inactivation' of the Na conductance, and in which 

 all the coefficients are experimentally determined. 

 These equations give a very satisfactory quantitative 

 account of a wide range of performance of the giant 

 fibers from which the coefficients were derived. It will 

 suffice to show how the propagation of the nerve 

 impulse is explained. 



The explanation of the propagation of the nerve 

 impulse is based on measurements of the cable 

 properties of the nerve fiber in addition to the differ- 

 ential equation relating the ionic conductances to the 



