Limits...
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.

Show MeSH

Related in: MedlinePlus

Slow Dynamics on the x–u Phase PlaneThe x cline, the u cline, and the forbidden line (Jux = 1) are depicted in blue, red, and black, respectively. Simulated trajectories (performed in 3-D and projected onto 2-D) are in green. The attractive part of the forbidden line is shown as a dashed line, and the repulsive part as a solid line.(A) For a small input (I = 0.85 Hz), the network has three steady states; circles indicate the stable steady states, and crosses indicate the unstable ones.(B) For a high input (I = 8 Hz), the network has only one steady state.(C,D) Shaded area is the forbidden line's basin of attraction. Insets show R(t) for displayed trajectories. J is below and above J* for (C) and (D), respectively, leading to a smooth transition in (C) and a population spike in (D).In all plots, parameter set A is used (see Methods, Table 2), except for J = 6 in (C) and J = 7 in (D).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC1808024&req=5

pcbi-0030035-g005: Slow Dynamics on the x–u Phase PlaneThe x cline, the u cline, and the forbidden line (Jux = 1) are depicted in blue, red, and black, respectively. Simulated trajectories (performed in 3-D and projected onto 2-D) are in green. The attractive part of the forbidden line is shown as a dashed line, and the repulsive part as a solid line.(A) For a small input (I = 0.85 Hz), the network has three steady states; circles indicate the stable steady states, and crosses indicate the unstable ones.(B) For a high input (I = 8 Hz), the network has only one steady state.(C,D) Shaded area is the forbidden line's basin of attraction. Insets show R(t) for displayed trajectories. J is below and above J* for (C) and (D), respectively, leading to a smooth transition in (C) and a population spike in (D).In all plots, parameter set A is used (see Methods, Table 2), except for J = 6 in (C) and J = 7 in (D).

Mentions: Dealing with a 2-D system instead of a 3-D one greatly simplifies the analysis. Figure 5 shows the phase space for this system in the case of strong facilitation: the x and u clines are depicted in blue and red, respectively, and the “forbidden” line (Jux = 1) is drawn in black. We consider the bistable regime (Jlow < J < Jhigh), such that there are three fixed points for small values of I (A). When the input increases, the clines change their configuration such that only one, high-activity fixed point remains (B), and the system begins to move toward it. If the input falls back to its baseline in a short time, the system is still in the basin of attraction of the low-activity steady state and therefore quickly returns to its original state. If the input stays on for a longer time, however, the system will cross the border between the two basins of attraction and continue its ascent to the high-activity persistent state after the removal of the stimulus. Thus, the requirement for a minimal input duration for reaching the persistent state in a facilitating population observed above (Figure 2A) is explained.


Persistent activity in neural networks with dynamic synapses.

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

Slow Dynamics on the x–u Phase PlaneThe x cline, the u cline, and the forbidden line (Jux = 1) are depicted in blue, red, and black, respectively. Simulated trajectories (performed in 3-D and projected onto 2-D) are in green. The attractive part of the forbidden line is shown as a dashed line, and the repulsive part as a solid line.(A) For a small input (I = 0.85 Hz), the network has three steady states; circles indicate the stable steady states, and crosses indicate the unstable ones.(B) For a high input (I = 8 Hz), the network has only one steady state.(C,D) Shaded area is the forbidden line's basin of attraction. Insets show R(t) for displayed trajectories. J is below and above J* for (C) and (D), respectively, leading to a smooth transition in (C) and a population spike in (D).In all plots, parameter set A is used (see Methods, Table 2), except for J = 6 in (C) and J = 7 in (D).
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0030035-g005: Slow Dynamics on the x–u Phase PlaneThe x cline, the u cline, and the forbidden line (Jux = 1) are depicted in blue, red, and black, respectively. Simulated trajectories (performed in 3-D and projected onto 2-D) are in green. The attractive part of the forbidden line is shown as a dashed line, and the repulsive part as a solid line.(A) For a small input (I = 0.85 Hz), the network has three steady states; circles indicate the stable steady states, and crosses indicate the unstable ones.(B) For a high input (I = 8 Hz), the network has only one steady state.(C,D) Shaded area is the forbidden line's basin of attraction. Insets show R(t) for displayed trajectories. J is below and above J* for (C) and (D), respectively, leading to a smooth transition in (C) and a population spike in (D).In all plots, parameter set A is used (see Methods, Table 2), except for J = 6 in (C) and J = 7 in (D).
Mentions: Dealing with a 2-D system instead of a 3-D one greatly simplifies the analysis. Figure 5 shows the phase space for this system in the case of strong facilitation: the x and u clines are depicted in blue and red, respectively, and the “forbidden” line (Jux = 1) is drawn in black. We consider the bistable regime (Jlow < J < Jhigh), such that there are three fixed points for small values of I (A). When the input increases, the clines change their configuration such that only one, high-activity fixed point remains (B), and the system begins to move toward it. If the input falls back to its baseline in a short time, the system is still in the basin of attraction of the low-activity steady state and therefore quickly returns to its original state. If the input stays on for a longer time, however, the system will cross the border between the two basins of attraction and continue its ascent to the high-activity persistent state after the removal of the stimulus. Thus, the requirement for a minimal input duration for reaching the persistent state in a facilitating population observed above (Figure 2A) is explained.

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