Hopfield Brody synchronization (sync) model
How it works
Beyond the GUI -- Saving and displaying spikes
Synchronization measures
Procedure interval2() in ocomm.hoc sets cell periods randomly
Rewiring the network
Assessing connectivity
Graphing connectivity
Animate
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Hopfield Brody synchronization (sync) model

The exercises below are intended primarily to familiarize the student with techniques and tools useful for the implementation of networks in Neuron. We have chosen a relatively simple network in order to minimize distractions due to the complexities of channel kinetics, dendritic trees, detailed network architecture, etc. The following network uses an artificial integrate-and-fire cell without channels or compartments. There is only one kind of cell, so no issues of organizing interactions between cell populations. There is only one kind of synapse. Additionally, suggested algorithms were chosen for ease of implementation rather than quality of results.

Although this is a minimal model, learning the ropes is still difficult. Therefore, we suggest that you go through the entire lesson relatively quickly before returning to delve more deeply into the exercises. Some of the exercises are really more homework projects (eg design a new synchronization measure). These are marked with asterisks.

As you know, Neuron is optimized to handle the complex channel and compartment simulations that have been omitted from this exercise. The interested student might wish to convert this network into a network of spiking cells with realistic inhibitory interactions or a hybrid network with both realistic and artificial cells. Such an extended exercise would more clearly demonstrate Neuron's advantages for performing network simulations.

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How it works

The synchronization mechanism requires that all of the cells fire spontaneously at similar frequencies. It is obvious that if all cells are started at the same time, they will still be roughly synchronous after one cycle (since they have similar intrinsic cycle periods). After two cycles, they will have drifted further apart. After many cycles, differences in period will be magnified, leading to no temporal relationship of firing.

The key observation utilized here is that firing is fairly synchronized one cycle after onset. The trick is to reset the cells after each cycle so that they start together again. They then fire with temporal differences equal to the differences in their intrinsic periods. This resetting can be provided by an inhibitory input which pushes state variable m down far from threshold (hyperpolarized, as it were). This could be accomplished through an external pacemaker that reset all the cells, thereby imposing an external frequency onto the network. The interesting observation in this network is that pacemaking can also be imposed from within, though an intrinsic connectivity that enslaves all members to the will of the masses.

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Beyond the GUI -- Saving and displaying spikes

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Synchronization measures

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Procedure interval2() in ocomm.hoc sets cell periods randomly

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Rewiring the network

All of the programs discussed in the lecture are available in ocomm.hoc. The student may wish to use or rewrite any of these procedures. Below we suggest a different approach to wiring the network.

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Assessing connectivity

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Graphing connectivity

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Animate