Neurobiology For Dummies. Frank Amthor
the inactivated state (refer to “Getting back to resting potential” earlier in this chapter).
The opening and closing of the voltage-dependent potassium channels, whose conductance is gK, happens more slowly than the sodium channels. They tend to drive the membrane potential toward the potassium reversal potential, usually near –75 mV. The depolarizing phase of the action potential tends to be stopped by the closing of the sodium channels (which the voltage-dependent sodium channels do on their own) and the opening of potassium channels.
Neurobiologists generally model synaptic inputs to neurons as currents injected into the dendritic tree (refer to Chapter 2) that are transformed into a train of spikes at the cell soma or axon initial segment. If the firing rate were exactly proportional to total synaptic current (above threshold), the relationship between synaptic current and spike rate would be called linear. However, in reality, this relationship is not linear for two main reasons:
Leakage currents through the membrane tend to shunt away synaptic current more for low, slowly changing current levels than for rapidly changing ones.
At high spike rates, the refractory period requires disproportionally more synaptic current to increase the spike rate. In fact, as the absolute refractory period is approached, no amount of increased synaptic input current can increase the spike rate.
One interesting result of this second factor is that the relationship between synaptic input current and spike rate in most neurons is more like a logarithmic function than a linear function. Psychophysical laws such as Weber’s and Fechner’s laws have long demonstrated that our perception of magnitude in senses such as sight, sound, and touch also follow a logarithmic relationship, where doubling the stimulus magnitude produces less than a doubling of the sensory perceptual magnitude. Direct experimental comparisons between perception of magnitude and neural firing rates have shown that the logarithmic spike compression underlies the logarithmic perception — that is, the perceptual magnitude follows the neural firing rate, which itself is logarithmically related to the magnitude of the stimulus.
Cable properties of neurons: One reason for action potentials
Neurobiologists continue to unveil new complexities about neurons, while continuously proving that we have much more to learn. Creating an accurate model of the activity of just one neuron — the complex, time-varying changes in its thousands of synapses and millions of voltage-dependent membrane ion channels — can take 100 percent of the processing power of a quite large computer.
Synaptic input current is typically divided into passive versus active conduction properties. Passive properties are those in the absence of voltage-dependent ion channels that themselves cause currents to flow through the membrane in response to synaptic input currents (and other voltage-dependent channels). Active properties involve voltage-dependent ion channels such as the voltage-gated sodium channel that can act to amplify signals.
Passive electrotonic conduction
A dendrite can be modeled (electrically) as an insulating membrane that separates an inner conductive core from the outer, extracellular fluid (which is also conductive). The membrane has resistance, which is normally very high except where ion channels and capacitance exist.
The water pipe idea can also help us to understand membrane capacitance. Suppose the pipe is not a stiff metal one, but a very stretchy rubber hose. If you suddenly turn on the faucet, the water flow creates a bulge at the end of the hose near the faucet. The water travels down and creates another bulge, and so on, until water finally begins to leave the open end of the hose. Eventually, the flow out the end of the pipe will be equal to the flow into the pipe at the faucet. Membrane capacitance works in the same way, by delaying and soothing sharp inputs at one point on a dendrite while they’re on their way to other dendritic locations.