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Persistent activity in neural networks with dynamic synapses.

Barak O, Tsodyks M - PLoS Comput. Biol. (2007)

Bottom Line: One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections.Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks.This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.

View Article: PubMed Central - PubMed

Affiliation: Department of Neurobiology, The Weizmann Institute of Science, Rehovot, Israel.

ABSTRACT
Persistent activity states (attractors), observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.

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Related in: MedlinePlus

Fast DynamicsLeft and right columns use parameter sets A and C, respectively (see Methods, Table 2).(A,B) Steady state analysis similar to Figure 3, but with x,u frozen at their resting values (see Equation 4). The dashed line illustrates recurrent excitation after an external input is increased. Note that only in (A) does a steady state remain.(C,D) Steady state value of Jux as a function of R (solid blue line) overlaid with the condition for persistent activity Jux = 1 (dashed blue line) and the trajectory caused by current increase (green line).(E,F) Time course of the firing rate for both cases.
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pcbi-0030035-g004: Fast DynamicsLeft and right columns use parameter sets A and C, respectively (see Methods, Table 2).(A,B) Steady state analysis similar to Figure 3, but with x,u frozen at their resting values (see Equation 4). The dashed line illustrates recurrent excitation after an external input is increased. Note that only in (A) does a steady state remain.(C,D) Steady state value of Jux as a function of R (solid blue line) overlaid with the condition for persistent activity Jux = 1 (dashed blue line) and the trajectory caused by current increase (green line).(E,F) Time course of the firing rate for both cases.

Mentions: The firing rate of a network without recurrent excitation will decay once external input is removed. Recurrent excitation provides a positive feedback that, if powerful enough, can balance this decay even in the lack of external input and sustain persistent activity. The balancing condition is given by the steady state equation for the population firing rate obtained from Equation 1:where the steady state value of ux depends on R as stationary solutions of the second and third equations of Equation 1 (see Equation 15 in Methods). Figure 3 illustrates graphically the solutions of the steady state equation. Figure 3A and 3B shows the balance between the decay term and the recurrent excitation term for two input levels. For a small input, the system has three steady state solutions, the lowest representing a spontaneous low-activity state, and the highest representing a persistent state (Figure 3A). The intermediate solution is always unstable. The presence of the low-activity state is due to the facilitation that results in the initial increase in the effective connection strength Jux with R, until depression takes over for higher R (Figure 4C and 4D, solid blue lines; see also [17]). This initial facilitation leads to the corresponding increase in the slope of the effective excitation as the network activity increases (inset in Figure 3A). The minimal facilitation time constant tf that is needed for this regime to be observed can be computed (see Methods, after Equation 16):For smaller values of tf/tr, the facilitation effect is not observed, and the effective connection strength monotonically decreases with the activity rate R (Figure 4D).


Persistent activity in neural networks with dynamic synapses.

Barak O, Tsodyks M - PLoS Comput. Biol. (2007)

Fast DynamicsLeft and right columns use parameter sets A and C, respectively (see Methods, Table 2).(A,B) Steady state analysis similar to Figure 3, but with x,u frozen at their resting values (see Equation 4). The dashed line illustrates recurrent excitation after an external input is increased. Note that only in (A) does a steady state remain.(C,D) Steady state value of Jux as a function of R (solid blue line) overlaid with the condition for persistent activity Jux = 1 (dashed blue line) and the trajectory caused by current increase (green line).(E,F) Time course of the firing rate for both cases.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1808024&req=5

pcbi-0030035-g004: Fast DynamicsLeft and right columns use parameter sets A and C, respectively (see Methods, Table 2).(A,B) Steady state analysis similar to Figure 3, but with x,u frozen at their resting values (see Equation 4). The dashed line illustrates recurrent excitation after an external input is increased. Note that only in (A) does a steady state remain.(C,D) Steady state value of Jux as a function of R (solid blue line) overlaid with the condition for persistent activity Jux = 1 (dashed blue line) and the trajectory caused by current increase (green line).(E,F) Time course of the firing rate for both cases.
Mentions: The firing rate of a network without recurrent excitation will decay once external input is removed. Recurrent excitation provides a positive feedback that, if powerful enough, can balance this decay even in the lack of external input and sustain persistent activity. The balancing condition is given by the steady state equation for the population firing rate obtained from Equation 1:where the steady state value of ux depends on R as stationary solutions of the second and third equations of Equation 1 (see Equation 15 in Methods). Figure 3 illustrates graphically the solutions of the steady state equation. Figure 3A and 3B shows the balance between the decay term and the recurrent excitation term for two input levels. For a small input, the system has three steady state solutions, the lowest representing a spontaneous low-activity state, and the highest representing a persistent state (Figure 3A). The intermediate solution is always unstable. The presence of the low-activity state is due to the facilitation that results in the initial increase in the effective connection strength Jux with R, until depression takes over for higher R (Figure 4C and 4D, solid blue lines; see also [17]). This initial facilitation leads to the corresponding increase in the slope of the effective excitation as the network activity increases (inset in Figure 3A). The minimal facilitation time constant tf that is needed for this regime to be observed can be computed (see Methods, after Equation 16):For smaller values of tf/tr, the facilitation effect is not observed, and the effective connection strength monotonically decreases with the activity rate R (Figure 4D).

Bottom Line: One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections.Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks.This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.

View Article: PubMed Central - PubMed

Affiliation: Department of Neurobiology, The Weizmann Institute of Science, Rehovot, Israel.

ABSTRACT
Persistent activity states (attractors), observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.

Show MeSH
Related in: MedlinePlus