models/chapter11

Chapter 11 - Modeling of large scale networks.

The simple examples presented here provide an overview of some basic components of large scale network simulations. Most of these examples show an integrate and fire simulation, introducing how such models represent the membrane potential and spiking properties of individual neurons, excitatory afferent input and intrinsic connectivity, feedforward and feedback inhibition, and the modification of excitatory synapses which can mediate encoding and retrieval of sequences. In addition, the final examples illustrate some properties of continuous firing rate networks.

example1	Chapter 11. Example 1. - Integrate and fire model - Principal cell. TOP LEFT: In this example, a single integrate and fire neuron (labelled G_0) receives a current injection from a stimulus node (labelled S_0). The injection is provided via a direct electrical connection (yellow line). TOP RIGHT: The iafcalc window shows the membrane potential plotted as a grey scale representing the amount of depolarization. Click on the find button in the upper right corner of the graph if nothing is visible. Time is plotted horizontally and the output of different neurons is plotted vertically (in different rows). When the neuron is very depolarized during spiking, this appears as a vertical white line (at low resolutions, this line may not be visible). When the neuron is moderately depolarized, this appears as different shades of grey. The strength of the current injection can be altered by clicking on the yellow line in the network diagram on the left and then changing the conductance G_0. This should change the number of spikes generated by the neuron. BOTTOM LEFT: The current injection waveform provides input to the stimulus node. You can raise or lower the magnitude of the current injection by clicking on the upper left hand node of the square wave and moving it up and down. This should cause the neuron to generate different numbers of spikes. This is a the waveform window entitled current injection. BOTTOM MIDDLE: To activate the middle panel, click on the two icons in the green panel on the right (a white square containing a grey circle and a green square containing a grey circle). Clicking these makes labels G_0_1 and TT(S_0_0) appear in the middle panel. Then click the find button to see lines plotting the membrane potential of selected neurons over time. This is the netview-results window. BOTTOM RIGHT: This panel controls which membrane potential lines will be plotted in the middle panel. This is the netview window. Close the simulation by clicking the X button in the upper right hand corner.
example2	Example 2 - Excitatory synaptic connection. TOP LEFT: This second example extends example 1 by including a synaptic connection between neuron G_0 and a new neuron, neuron G_1. TOP RIGHT: The graph now shows a grey scale representation of the membrane potentials of all three units in the network. Time is plotted horizontally, and the membrane potentials of different cells are plotted in different rows. BOTTOM LEFT: The waveform for input to G_0. Changes in the amplitude or duration will cause the network to be rerun with the new values, with the results displayed in the windows above. BOTTOM MIDDLE: This window shows the membrane potentials of the units in the network, when they have been selected in the window in the lower right. BOTTOM RIGHT: Units in the network can be selected by clicking on the colored squares in this window (e.g. S_0=red, G_0=green, G_1=blue). The size of the synaptic potential elicited by synaptic input from G_0 can be changed by going to the TOP LEFT and clicking on the connecting link (pink line with green circle) between G_0 and G_1. This reveals sliders for the connection type labelled IaFLinkSC. The synaptic conductance strength can be altered by changing G_0, and the rise and decay time constants of the potential can be altered by moving the sliders for Trise and Tfall.
example3	Example3 - Network with recurrent excitation. TOP LEFT: Summary of the network connectivity. A population of 10 excitatory principal neurons G_0 receives a binary input pattern (P_0). The excitatory neurons G_0 act as afferent input to a second population of excitatory neurons G_1. For this example, the synaptic connections from G_0 to G_1 are set to 1-1 connectivity under the connect option. This allows the activity of each neuron in G_0 to induce synaptic potentials in the corresponding neuron in G_1. In addition, the neurons in region G_1 send excitatory intrinsic connections (recurrent connections) to all other neurons in region G_1 (connect = any). TOP RIGHT: The binaryControl window shows the pattern of depolarizing inputs being presented to individual neurons in the population G_0. This causes spiking in the individual units in the network. The pattern can be altered by clicking the select button and then clicking on each individual line. After changing the input pattern, one must click the rerun button in the lower right corner of the TOP LEFT window showing network connectivity. The strength of the binary input can be manipulated by clicking on P_0 in the iafNetwork window and altering the slider for input conductance G. BOTTOM: The iafCalc-results window shows the pattern of spiking activity in the 10 neurons of region G_0 and the 10 neurons in region G_1 (starting from the botton, each horizontal strip between 0 and 10 represents the membrane potential of a single neuron in region G_0, while strips between 10 and 20 represent region G_1. Each spike appears as a white rectangle, but some neurons do not receive input. Click on the recurrent loop and then change the slider for the parameter G_0 from 0.001 (1.00e-3) to higher values (note that despite similar names this parameter is not related to population G_0). For values near zero, there is no excitatory spread within region G_1. For larger values, excitatory feedback rapidly causes spiking throughout the entire G_1 region.
example4	Example4 - Feedforward inhibition. TOP LEFT: The iafNetwork window includes the network from Example 3 (with G_0 providing afferent input to G_1). In addition, G_0 provides excitatory input to a population of inhibitory interneurons G_2. These interneurons provide inhibitory synaptic input to population G_1 (click on the connection from G_2 to G_1 and you can see that the reversal potential Erev for this connection is -70 mV, corresponding to GABAA type inhibition). TOP RIGHT: The binaryControl window shows the binary input pattern being presented to the network. Different rates of input are presented as input to different neuron. BOTTOM LEFT: Membrane potential of all neurons in the network (G_0 at bottom, G_1 population in center, G_2 at top). In particular, notice that in the middle rows (region G_1), the feedforward inhibition allows only neurons receiving a higher rate of afferent input to show spiking responses (neuron 11 and neuron 14). The feedforward inhibition blocks spiking activity in the other neurons receiving lower rates of afferent input (neurons 10, 12 and 13). You can see this more clearly if you click to the lower left of the activity in the middle rows, then move the slider down to the left, then back up to the right. This will create a red box which you can then move around this region of activity, giving you a closer view of the spiking activity in neurons 11 and 14. BOTTOM MIDDLE: All units in the network are shown in the middle. Click one of the cells in the lowest block, corresponding to region G_1, to show its membrane potential on the bottom right (use the find button if necessary to recenter the display).
example5	Example 5 - Feedback Inhibition The iafNetwork window shows the network layout for feedback inhibition. Binary input P_0 activates units in the afferent region G_0. G_0 provides excitatory afferent input to region G_1. G_1 provides excitatory input to the inhibitory interneurons G_2. These interneurons provide feedback inhibitory synaptic input to G_1. This feedback inhibition uses reversal potential Erev = -70 mV. Note that slower time constants are used for the inhibitory potentials, corresponding to the slower time constants of GABAA inhibition relative to excitatory AMPA currents. The binaryControl window shows the binary input pattern. The binaryControl window shows the binary input pattern being presented to the network. In this example, patterns with three neurons each are activated at 20 msec intervals, with additional spikes presented at tmes between these patterns.
example6	Example 6 - Sequence learning. TOP LEFT: This window shows a binary input pattern P_0 being presented directly to a network of 25 neurons (G_0) with excitatory intrinsic (recurrent) connections. In this example, synaptic modification of the recurrent connections allows the network to encode the sequence and respond to the first pattern of the sequence with retrieval of the remaining patterns in the sequence. TOP RIGHT: The binaryControl window shows the afferent input being presented to the network. This consists of a sequence of 5 patterns, with 5 active input lines in each pattern. After the sequence is presented for learning, the first pattern consisting of five active neurons is presented to the network as a retrieval cue. BOTTOM LEFT: This window shows the LTP time course waveform. The zero point in this graph corresponds to the time of a spike in the presynaptic neuron, and the shape of the graph determines what happens in when a spike occurs in a postsynaptic neuron at that time. Click on the upper left corner of the waveform to lower the amplitude. This decreases modification and results in failure of sequence retrieval in the window to the right. Click on the top right of the waveform and expand the duration. This causes synaptic modification with later spikes, which results in a build-up of undesired retrieval causing excessive multiple spiking in the network. BOTTOM MIDDLE: This window shows the spiking response of the network to the binary input. The network spikes in response to the full sequence, and then responds to the first sequence in the pattern with readout of the full sequence, due to prior strengthening of synapses between coactivated neurons. Note that the timing of the retrieval depends on the maximum strength of the recurrent connections. The maximum strength attained can be altered in the sliders in the BOTTOM RIGHT. BOTTOM RIGHT: The iafSynPars window provides the parameters for changes in the properties of the intrinsic (recurrent) synapses. Changing the Gmax slider alters the maximum strength to which synapses can grow during synaptic modification. Note that as this slider is moved to lower values, the retrieval of the sequence becomes weaker, whereas moving it to higher values causes repetitive spiking during sequence retrieval. Exercise: Change in sparseness of connectivity. The ability of this small network to perform sequence retrieval varies with the sparseness of connectivity. In the TOP LEFT window change the Fconn slider from 1.0 to lower values. The retrieval in the BOTTOM MIDDLE window will immediately show impairments, even with decreases in Fconn to 0.8. These can be offset by increasing the Gmax slider in the IaFSynPars window. But for lower values of Fconn (0.1) even the increase in Gmax cannot offset the retrieval impairment.
example7	example7 Continuous firing rate network - Fixed point attractor. TOP LEFT: The CFNetwork window illustrates the basic connectivity necessary for fixed point attractor dynamics with interactions of an excitatory unit (E) and an inhibitory unit (I). This is the basic fixed point attractor circuit described in Hasselmo et al., 1995. The excitatory unit receives afferent input from a stimulus node (Input). The excitatory unit makes excitatory connections with itself (W). Click on the recurrent connection to see its weight (0.160). The excitatory unit also makes connections to the inhibitory unit (with weight W=0.042). The inhibitory unit makes connections to the excitatory unit (with weight H=-0.6). Each unit has threshold 8.0 and T_dec =10. These parameters can be viewed by clicking on the units. Note that these connections have action absolute, meaning that they do not depend upon a reversal potential (though this is possible in CFNet). TOP RIGHT: This graph will display the activation value of the different units. To activate the graph, click on the three units in the BOTTOM RIGHT window, then click the find button to the upper right in the TOP RIGHT window. BOTTOM LEFT: The runtime and timestep of the network can be altered in the cfcalc window. BOTTOM MIDDLE: This display shows the activity of all units, one unit per row as a function of time, color coded according to the scale on the right. For a line graph of individual units, open the next window at the same time. BOTTOM RIGHT: This window allows selection of neurons for which membrane potential will be displayed in the TOP RIGHT. Note that the units attain a steady state (fixed point attractor value) during the square wave afferent input (time 50 to 1000). When afferent input is removed, the network maintains self-sustained activity -- oscillating into a slightly lower fixed point attractor. The phase plane representation can be seen by clicking on the X button in this window and selecting I, then click find -- this plots the activation value for each unit against the activation for the I unit. The activation of the E unit spirals into the fixed point attractor. Test the stability of the attractor by clicking on each individual connection in the TOP LEFT window and changing the weight values to see which parameters allow self-sustained activity after the removal of afferent input. For values that explode to infinity, the network will cease to compute the value and will print an error message: ERROR -failed to converge. Explore connections within the following range of parameters: W (E to E) min = 0.0, max = 0.3 W' (E to I) min = 0.0, max = 1.0 H (I to E) min = -5.0, max = 0.