Step 2 is difficult. Chapter 5 of "The Book of GENESIS" ("the BoG"), which was assigned as reading for this lecture, gives some useful information for answering the two questions. This chapter (Segev, 2005) is also very mathematical, and it is easy to get lost in the equations and forget what they are used for. I wanted you to read it in order to get an overview of the theory of passive propagation in dendrites. Now, I'll list what I think is important for you to remember. There are three things that can be measured experimentally and are related to the parameters that we need for a model:
- The attentuation of voltage with distance, and the "space constant" or
"length constant".
- The membrane time constant.
- The input resistance of the cell, measured at the soma.
This slide gives a summary of the electrical properties of a uniform section of passive dendrite having length l and diameter d.
The conducting cytoplasm inside the neuron, the insulating neural membrane, and the liquid (similar to salt water) surrounding the neuron form a cable with a capacitance Cm. The inner conductor, the cytoplasm, is a poorer conductor than the copper wire used in an undersea cable, and it has an resistance along the length of the cable Ra, the "axial resistance". The membrane in not a perfect insulator due to the ion-conducting channels that pass through it. It is convenient to make a distinction between the "passive channels" that do not vary in conductance, and the "active channels" that have conductances varying with voltage, calcium concentration, or synaptic input. The passive channels account for the membrane resistance Rm and the associated leakage current Ileak. The active channels are represented by the various variable conductances that are labeled as Gk in the neural compartment diagram and the differential equation for Vm that we described in the previous section on compartments.