Cholinergic Control of Chaos and Evidence Sensitivity in a Neocortical Model
93
Cortical models have been widely used to study how the brain makes decisions about
incoming perceptual evidence (e.g., discrimination between two similar stimuli). In particular, it is assumed that competing populations of pyramidal cells tuned to certain
stimuli generate attractor dynamics that drive the network into a perceptual decision.
However, the contribution of perceptual evidence during the decision process is not uniform and changes through time [1]. Hence, a basic question that remains unanswered
is how the sensitivity to perceptual evidence can be modulated in neocortical circuits
during perceptual decision-making. To clarify this issue, we developed a spiking neural
network (Fig. 1; based on [2]) under cholinergic modulation. Two populations of excitatory neurons with sparse recurrent connections were stimulated following a Gaussian
distribution, with the mean representing the amount of perceptual evidence. The competition between the two populations was implemented as mutual inhibition (Parvalbuminpositive interneurons) and global inhibition (Somatostatin-positive interneurons). Neurons were modeled as leaky integrate-and-fire units, with the parameters being grounded
in physiology [3]. Excitatory and inhibitory synapses were modeled as single decaying
exponentials, with the time constants reproducing slow NMDA and fast GABAergic
kinematics, respectively. The differential effect of ACh on the subtypes of GABAergic
interneurons [4] was modeled so that high ACh decreased the synaptic efficacies of
global inhibition and increased the synaptic efficacies of mutual inhibition and recurrent excitation (Fig. 1). Two task conditions were studied: one in which both stimuli
had equal evidence strengths, and another in which one stimulus had stronger evidence.
For both conditions, the network dynamics were compared between low and high ACh
levels. The state of the network was defined by the combined compound potentials of
both excitatory populations. Pseudo phase space trajectories of independent 2-second
trials were then plotted, along with their corresponding convergent points. Based on
the convergence, thresholds determined by a simple clustering algorithm classified the
trials to extract the decision statistics. Additionally, attractor dynamics were studied, and
chaos was detected by computing the Lyapunov exponents [5]. The phase trajectories
and the corresponding convergent points (Fig. 2A, B) showed the stable formation of two
limit-cycle attractors corresponding to one of the populations winning over the other.
We observed that the attractors’ center of mass was pushed to the extremes of the phase
space in the high ACh condition, suggesting a deepening of the attractors. Interestingly,
only in the low ACh condition we saw the emergence of a chaotic attractor (Lyapunov
exponent of 0.358) in-between the phase space of the two stable attractors. Moreover,
decision statistics (Fig. 2C) clearly showed that convergence into the weakest attractor
was more preserved under low ACh, hence mitigating the effects of the biased evidence
towards one of the stimuli. Contrarily, the network was more likely to converge into
the strongest attractor under high ACh, despite the high levels of noise and stimulation
overlap. Our results are in line with previous proposals suggesting that chaos is part of
a default state of cortical circuits [6] caused by a particular balance between excitation
and inhibition [7]. Moreover, it complements previous studies that show how the error
landscape can be chaotically bootstrapped across trials to improve the learning performance [8]. In this regard, high ACh levels would (1) disinhibit the circuits, thus reducing
chaos at the single-trial level during decisions and enhancing stimulus discriminability;
and (2) enhance synaptic plasticity, thus increasing chaos across trials during learning
93
Cortical models have been widely used to study how the brain makes decisions about
incoming perceptual evidence (e.g., discrimination between two similar stimuli). In particular, it is assumed that competing populations of pyramidal cells tuned to certain
stimuli generate attractor dynamics that drive the network into a perceptual decision.
However, the contribution of perceptual evidence during the decision process is not uniform and changes through time [1]. Hence, a basic question that remains unanswered
is how the sensitivity to perceptual evidence can be modulated in neocortical circuits
during perceptual decision-making. To clarify this issue, we developed a spiking neural
network (Fig. 1; based on [2]) under cholinergic modulation. Two populations of excitatory neurons with sparse recurrent connections were stimulated following a Gaussian
distribution, with the mean representing the amount of perceptual evidence. The competition between the two populations was implemented as mutual inhibition (Parvalbuminpositive interneurons) and global inhibition (Somatostatin-positive interneurons). Neurons were modeled as leaky integrate-and-fire units, with the parameters being grounded
in physiology [3]. Excitatory and inhibitory synapses were modeled as single decaying
exponentials, with the time constants reproducing slow NMDA and fast GABAergic
kinematics, respectively. The differential effect of ACh on the subtypes of GABAergic
interneurons [4] was modeled so that high ACh decreased the synaptic efficacies of
global inhibition and increased the synaptic efficacies of mutual inhibition and recurrent excitation (Fig. 1). Two task conditions were studied: one in which both stimuli
had equal evidence strengths, and another in which one stimulus had stronger evidence.
For both conditions, the network dynamics were compared between low and high ACh
levels. The state of the network was defined by the combined compound potentials of
both excitatory populations. Pseudo phase space trajectories of independent 2-second
trials were then plotted, along with their corresponding convergent points. Based on
the convergence, thresholds determined by a simple clustering algorithm classified the
trials to extract the decision statistics. Additionally, attractor dynamics were studied, and
chaos was detected by computing the Lyapunov exponents [5]. The phase trajectories
and the corresponding convergent points (Fig. 2A, B) showed the stable formation of two
limit-cycle attractors corresponding to one of the populations winning over the other.
We observed that the attractors’ center of mass was pushed to the extremes of the phase
space in the high ACh condition, suggesting a deepening of the attractors. Interestingly,
only in the low ACh condition we saw the emergence of a chaotic attractor (Lyapunov
exponent of 0.358) in-between the phase space of the two stable attractors. Moreover,
decision statistics (Fig. 2C) clearly showed that convergence into the weakest attractor
was more preserved under low ACh, hence mitigating the effects of the biased evidence
towards one of the stimuli. Contrarily, the network was more likely to converge into
the strongest attractor under high ACh, despite the high levels of noise and stimulation
overlap. Our results are in line with previous proposals suggesting that chaos is part of
a default state of cortical circuits [6] caused by a particular balance between excitation
and inhibition [7]. Moreover, it complements previous studies that show how the error
landscape can be chaotically bootstrapped across trials to improve the learning performance [8]. In this regard, high ACh levels would (1) disinhibit the circuits, thus reducing
chaos at the single-trial level during decisions and enhancing stimulus discriminability;
and (2) enhance synaptic plasticity, thus increasing chaos across trials during learning