This subdirectory contains several simulations that illustrate the capacity of SNNAP to simulate networks containing both Hodgkin-Huxley-type neurons and integrate-and-fire type cells. In addition, the simulations illustrate the different ‘learning rules’ that govern the weights of ‘synapses’ among integrate-and-fire cells.
The goal of the present simulation is to illustrate how to implement a hybrid neural network that contains both Hodgkin-Huxley (HH) type neurons and Integrate-and-Fire (gi) cells. In addition, this simulation illustrates the function of *.ws equation 1.
The structure of the network is illustrated in ws1_ntw.jpg. Note that HH and gi types of cells are depicted using different symbols. In addition, weighted synapses (ws) are depicted as open boxes. (Note, modulatory synapses are depicted a filled boxes and chemical synapses as open triangles.)
Initially, a stimulus is applied to the gi-type cell ‘gi_6’, elicits firing. The rate of firing is control by several factors including the “membrane capacitance” of the gi- type cell, the noise level (see \examples\integrate_fire\ws7), the threshold. gi_6, in turn, makes a synaptic connection with gi_7.cell. The gi_6 to gi_7 weighted synapse uses equation 1 of the *.ws file. This equation has no plasticity and the synaptic weight is a constant. The HH-type cell makes a synaptic connection with gi_6 and a treatment that elicits activity in the HH cell ultimately leds to some activity in gi_6 and gi_7.
The results of this simulation are illustrated in ws1_ous.gif
The goals of the present simulation are to illustrate two aspects of neural networks with integrate-and-fire cells and weighted synapses:
- Any network must contain at least one HH-type neuron and this neuron must contain at least voltage-dependent conductance with activation and inactivation functions. (see w2_ntw.jpg). SNNAP was originally designed to simulation HH-type neurons and synaptic connections. The present version of SNNAP must ‘see’ at least one HH-type cell. As the integrate-and-fire features of SNNAP are refined, this requirement maybe relaxed.
- Equation 2, in *.ws. Equation 2 in the *.ws file is referred as ‘associative’ because the voltages of both the pre- and postsynaptic cells are consider in calculating dw/dt (i.e., the change in synaptic weight).
The results of this simulation are illustrated in w2_ous.gif. In this simulation, cell gi_6.cell makes a weighted synaptic connection to gi_7.cell (see w2_ntw.jpg). Two identical stimuli are applied to gi_6.cell, which elicited 2 ‘spikes’ in gi_6.cell. Because the synaptic weight between i_6.cell and gi_7.cell (i.e., weight[gi_7.<-.gi_6..]) this initial activity in gi_6.cell does not elicit a response in gi_7.cell. Before the second stimulus to gi_6.cell, however, a stimulus is applied to gi_7.cell, which elicited activity in gi_7.cell. This activity initiated facilitation of the synaptic connection from gi_6.cell to gi_7.cell (i.e., weight[gi_7.<-.gi_6..]). As a result of this synaptic facilitation, the second stimulus to gi_6.cell elicited a ‘spike’ in the postsynaptic cell.
The goal of the present simulation is to illustrate equation 3 of the *.ws file.
Equations 2 and 3 are similar in that both use the ‘voltage’ of the pre- and postsynaptic cells in calculating changes in synaptic weight. The methods used to calculate the rate of change (i.e., dw/dt) are slightly different, however (see User’s Manual or *.ws file). The results of the present simulation are illustrated in w3_ous.gif.
The goal of the present simulation is to illustrate equation 4 of the *.ws file.
Equation 4 (and 5) of the *.ws file are referred to as ‘nonassociative’ in that only the ‘voltage’ of the presynaptic cell is used to determine changes in synaptic weight. Equation 4 induces a long-term potentiation of the synaptic connection, whereas, equation 5 induces synaptic depression.
In this simulation, an initial stimulus is given to the postsynaptic cell (gi_7.cell). This stimulus evokes activity in gi_7.cell, but does not alter the weight of the gi_6 to gi_7 synapse. Subsequently, two stimuli are given to gi6_6.cell (i.e., the presynaptic cell). The first stimulus failed to elicit activity in the postsynaptic cell (i.e., gi_7.cell), but did initiate a nonassociative increase in the synaptic weight. Thus, the second stimulus to the presynaptic cell, which occurred in the presence of enhanced synaptic weight, was able to elicit a postsynaptic response (i.e., a ‘spike’ in gi_7.cell).
Note that the change in synaptic weight reaches an asymptote (i.e., the Wmax parameter in the *.ws file.).
The goal of the present simulation is to illustrate equation 5 of the *.ws file.
Equation 5 is a ‘nonassociative’ learning rule that changes in synaptic weight (i.e., weight[gi_7.<-.gi_6..]) depend only on the ‘voltage’ of the presynaptic cell. Eq. 5 implements long-term depression of a synaptic connection.
As in a previous simulation (\examples\integrate_file\ws4\ws4.smu), an initial stimulus was delivered to the postsynaptic cell (i.e., gi_7.cell). This initial stimulus elicited activity in gi_7.cell, but did not alter the synaptic weight. In addition, two stimuli were given to the presynaptic cell (i.e., gi_6.cell). The first of these presynaptic stimuli evoked a response (i.e., a ‘spike’) in the postsynaptic cell and initiated a depression of the synaptic weight. Thus, a second stimulus to the presynaptic failed to evoke a postsynaptic ‘spike’. The results of this simulation are illustrated in ws5_ous.gif.
The goal of this simulation is to illustrate how to incorporate noise in the firing pattern of Integrate-and-Fire cells.
For Hodgkin-Huxley type neurons and synaptic connections, noise is introduced via the *.R file. In the Integrate-and-Fire cells, however, noise is incorporated directly into the *.cell file and alter the threshold for firing.
In this example, two identical cells (gi_6.cell and gi_7.cell) receive identical stimuli (a depolarizing current injected between 0.5 and 6.5 seconds). The only difference between the two cells is that noise was incorporated in the threshold of gi_6.cell. Note that the firing pattern of gi_7.cell is very constant, whereas there is variability in the firing pattern of gi_6.cell (see w7_ous.gif). Moreover, as the user runs the simulation over and over again, the pattern of activity in gi_6.cell will vary with each simulation.