Ever wondered what neurons do to each other? How does a signal generated in one neuron cause a reaction in another neuron? Neurons behavior is fairly complex (see this post), but with some simplification we can begin to understand, and model, how neurons affect each other and ultimately determine information processing in the brain.
The software presented in this post does just that. As part of the software repository of the CNS Technology Lab, Bret Fortenberry has put together a very nice demo that describes the effect that a spike, the event universally accepted as the alphabet that neurons use to communicate with each other, causes on other neurons.
Bret presents a model that demonstrate the effect of Excitatory Postsynaptic Potentials (EPSP) and Inhibitory Postsynaptic Potentials (IPSP) on a neuron. The model is based on synaptic conductance equations from (Kohn and Worgotter 1998) and a fast resonate-and-fire neuron spiking equation from (Izhikevich 2001). The citations are below.
The model shows the properties of EPSPs and IPSPs in the postsynaptic cell. The model, which is an oper source MATLAB code, allows the user to adjust the number of EPSP and IPSP inputs, the rise and fall times and the weighted effect on the postsynaptic cell. The model displays the current of the EPSP and the IPSP and the spiking output of the postsynaptic cell.
An excitatory postsynaptic potentials (EPSP) is a temporary depolarization of postsynaptic membrane caused by the flow of positively charged ions into the postsynaptic cell as a result of opening of ligand-sensitive channels. An EPSP is received when an excitatory presynaptic cell, connected to the dendrite, fires an action potential. The EPSP signal is propagated down the dendrite and is summed with other inputs at the axon hilllock. The EPSP increases the neurons membrane potential. When the membrane potential reaches threshold the cell will produce an action potential and send the information down the axon to communicate with postsynaptic cells. The strength of the EPSP depends on the distance from the soma. The signal degrades across the dendrite such that the more proximal connections have more of an influence.
An inhibitory postsynaptic potentials (IPSP) is a temporary hyperpolarization of postsynaptic membrane caused by the flow of negatively charged ions into the postsynaptic cell. An IPSP is received when an inhibitory presynaptic cell, connected to the dendrite, fires an action potential. The IPSP signal is propagated down the dendrite and is summed with other inputs at the axon hilllock. The IPSP decreases the neurons membrane potential and makes more unlikely for an action potential to occur. A postsynaptic cell typically has less inhibitory connections but the connections are closer to the soma. The proximity of the inhibitory connections produces a stronger signal such that fewer IPSPs are needed to cancel out the effect of EPSPs.
The membrane potential and spiking rate are dependent on a cells biophysical mechanism and the interaction of the cells internal and external voltage. Hodgkin and Huxley (1952) have introduced a standard model to describe the dynamics of cell's membrane potential. That model, described in terms of differential equations, tends to be computationally slow. Over the years, several other simplified spiking models have been designed. Although the later models are faster, they are less accurate than the Hodgkin and Huxley model. In this demonstration the Izhikevich resonate-and-fire model is used. This spiking model is used because it is faster than quadratic firing models and more biologically accurate than integrate and fire models.
You can download the software here.
Enjoy!
Izhikevich, EM (2001). Resonate-and-fire neurons. Neural Networks 14: 883-894.
Kohn, J and Worgotter, F (1998). Employing the Z-transform to Optimize the calculation of the synaptic conductance of NMDA and other synaptic channels in network simulations. Neural Computation 10: 1639-1651.
