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 g_K, 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.

      

The absolute refractory period is the time during which the sodium channels are in the inactivated state, before they transition to the closed state. The relative refractory period occurs after the action potential when potassium channels remain open and sodium channels have partially recovered from inactivation. The lingering potassium current drives the membrane potential below the resting potential, and makes it harder to elicit a spike than was the case in Figure 3-2 when the cell was at the resting potential at the beginning of the plot.

      

The sodium-potassium transporter pump runs all the time, causing the imbalance in ionic concentrations between the inside and outside of the neuron. A single action potential creates a temporary current through the membrane, which changes the voltage across the membrane, but it has little effect on the total ion concentrations within the entire cell. Even if all the sodium-transporter pumps shut down (refer to the “Sodium-potassium pump” section, earlier in this chapter), up to millions of action potentials can occur before the cell starts to lose its concentration difference with respect to the cell exterior.

      

Refractory periods and spike rate coding

      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.

A major reason why the interactions among inputs to a neuron can be so complicated is that neural dendrites have what are called cable properties for transmitting signals. This means that the way synaptic signals on different points on a dendrite interact depends on the structure of the dendritic tree between the two points. This includes whether the inputs are on the same or different dendritic branches. The reason the dendritic branch structure makes so much difference is that electrical parameters of the dendrites — such as membrane resistance, membrane capacitance, and dendritic axial resistance — (which we discuss in a moment) are distributed along the dendrite or dendritic tree. Understanding how synaptic inputs interact within the dendritic tree is modeled using cable theory, which was originally developed for transoceanic submarine telegraph cables. The application of this theory to neurons was championed by Wilfred Rall, who made influential contributions to our undertanding of dendritic integration.

      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.

      

Capacitance occurs when a thin insulator separates two conductors, such as the neural membrane separating the conductive fluids inside and outside the cell. Normally, no current will flow across an insulator between two conductors. But, if the insulator is thin, and its area is large, transient current can flow due to a redistribution of charges as positive charge on one side of the insulator attract to negative charges on the other side (or vice versa).

      

To understand what membrane resistance means to spreading synaptic current, think of a water pipe. Suppose a water pipe is standing straight up and connected to a faucet at the bottom that is turned off. If you suddenly turn on the faucet, water will gush out of the top of the pipe almost immediately. The same idea applies to a neuron for a synaptic input on a dendrite with very high membrane resistance (no leakage) and no membrane capacitance between the synapse and another location on the dendrite. Now suppose the pipe has many small holes all along its length. When the faucet is turned on, some water will exit the end of the pipe almost immediately. But a lot of water will escape through the holes along the way, so the force won’t be as strong when the water gushes out of the top. In other words, the holes, like low membrane resistance, will weaken the “signal” reaching the top of the pipe from the opened faucet at the bottom.

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.

      

The highly stretchable hose is like membrane capacitance. Even if the end of the hose — which you