CONICAL

Channels & Synapses

The membrane of a neuron (or, for that matter, any cell) is mostly impermeable to most substances, including single ions such as sodium (Na+), calcium (Ca++), and potassium (K+). However, the membrane contains tiny pores or channels which allow ions to pass through. These channels are formed by proteins which have evolved to allow only certain ions to pass through, and to exclude others.

When charged ions flow through a channel, it results in a current in the direction of the positive charge. Ions will flow due to diffusion (from a region of high density to a region of lower density), and due to electrostatic force (positive ions will flow towards a region with a more negative electrical potential). In a neuron, these two forces are frequently in opposition; which one dominates depends on the concentration of ions inside and outside the cell (which is relatively constant), and on the membrane potential -- that is, the difference in electric charge between the inside and outside of the cell (which is highly variable). At some membrane potential, diffusion and electrostatic pressure exactly balance each other, resulting in zero net flow of ions. This point is called the reversal potential or equilibrium potential of the channel.

The equilibrium potential (E) of a channel depends on the exact mix of ions which it allows to pass. Rather than keeping track of ion concentrations, CONICAL simply allows you to set the equilibrium potential of a channel (or any other current) directly, via SetE() method. In addition, a set of ion channels has a particular conductance (G), which describes how quickly ions can flow through. This depends both on the individual channel conductance, and the number of channels in a particular compartment. Any set of passive channels (see below) can be described completely as a current with a certain E and G.

Active Channels

So far, we've described channels as if their properties are fixed: the combination of ions which are passed by such a channel never changes. These are called passive channels, and they do indeed exist in neurons. However, many more dynamic channels also exist, who change their properties in response to a variety of signals; these are called active channels. Active channels may respond to chemical signals, such as neurotransmitters, hormones, or intracellular messengers. More commonly (at least in our modeling), active channels respond to the membrane potential; these are called voltage-gated ion channels.

It's fairly easy to understand how voltage-gated ion channels work. They are composed of proteins which are imbedded in the membrane, forming a tunnel through it. Sticking into the tunnel are a variety of knobs and protrusions with various electrical charges; these give the channel its selectivity to certain ions. When the membrane potential changes, it exerts a force on the proteins, which can cause some parts to rotate or bend in (or out) of the tunnel, changing its conductivity.

In CONICAL, all active channels are derived from Channel, which is a Current with a Step() method. This method adjusts the current's conductance (G) at each time step, as some fraction of parameter MaxG. To maximize the flexibility and extensibility of the library, we use a rather long chain of subclasses, each adding functionality and providing a point to derive your own functionality. Most users will jump directly to the ChanStd class, which implements a standard voltage-gated ion channel using equations of a form originally used by Hodgkin & Huxley in their pioneering work on the squid giant axon.

Synapses

Another type of active channel is the synapse. The conductance of a synapse depends on the concentration of neurotransmitter in the synaptic cleft, which in turn depends on the membrane potential of the presynaptic neuron compartment. Two common synapse models are built into CONICAL. The first, AlphaSyn, is a stereotyped change in G which is initiated whenever the presynaptic voltage crosses a threshold. A more sophisticated model is provided in MarkovSyn, which uses a Markov kinetic model to simulate actual state transitions in the channel proteins. A MarkovSyn can act as simply a more accurate substitute for an AlphaSyn, or can be extended to model channels with desensitized states, etc.

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Last Updated: 11/01/95 Joe Strout.