Why Biological Systems Suddenly Change State: An Intuitive Guide to Freidlin–Wentzell Theory

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  Stochasticity is ubiquitous in biology and neuroscience, manifesting in various forms, including ion channel noise, synaptic variability, gene regulatory fluctuations, noisy population dynamics, and more. Many biological systems spend long periods in a stable “state” and only rarely transition to another state due to noise. For instance, a neuron typically remains inactive but may occasionally trigger a spontaneous spike. Similarly, a gene can switch from the OFF state to the ON state due to rare bursts of transcription factors. Cells can also transition out of metabolic or epigenetic states, populations might shift between different ecological equilibria, and a viral infection can fluctuate between phases of control and uncontrollability. Freidlin–Wentzell theory provides a mathematically rigorous framework to study these phenomena when noise is small but nonzero . It tells you, firstly, h ow likely rare transitions are,    secondly,   h ow fast they occ...
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NEUROBIOLOGY OF DECISIONAL PROCESSES

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The exploration of the neurobiological bases of the cognitive processes that underlie the decision-making (DM) have been recently the object of many studies in neurophysiology and computational neuroscience. By tracing the neuronal circuits that are involved in the DM it is possible to get biophysically reliable models linking the dynamics of the neuronal activities to decisional behavior.  The present section recalls the major findings regarding this issue. Firstly, it is focused the role of the basal ganglia and the related model of reinforcement learning is described. Afterward, the neuronal circuits involving the dynamics of the lateral intraparietal area (LIP) and the superior colliculus (SC) are considered. They provide the theoretical bases for the development and implementation of  the models of DM that are set up as a two-fold circuitry of valuation and choice, by which the accumulation and the processing of information (evidence) take place. A mathematical reasoning have been argued here to assess that both the phases of valuation and choice are exposed to the noise effects. This lays the foundations for the Bayesian brain conception (noisy-information-and-bayesian-brain.html).

It is known that DM is a process that involves different areas of the brain. These regions include the cortical areas that are supposed to integrate evidence supporting alternative actions, and the basal ganglia (BG), that are hypothesized to act as a central switch in gating behavioral requests [1-7]. In natural environments several sensory stimuli produce different alternatives and hence demand the evaluation of different possible responses, i.e. a variety of behaviors. In other terms, it arises also a selection question [4] by which the (probability) distribution of the correct response has to take control of the individual’s motor plant [8]. The action selection then would resolve a conflict among decisional centers throughout the brain. A central switch that considers the urgency and opportunity of specific response to the stimuli result an optimal solution in computational terms and physiologically reliable by taking the BG as the neural base for that switch. Accordingly, BG gather input from all over the brain and, by sending tonic inhibition to midbrain and brain stem targets involved in motor actions, block the cortical control over these actions [1,2,9]. Therefore, the inhibition of the neurons in the output nuclei, caused by BG activity, determines the disinhibition of their targets and the actions would be consequently selected.
This model, ultimately explains that in the DM among alternative options, the cortical areas associated with the alternatives integrate their corresponding evidence, whilst the BG by acting as a central switch evaluates the evidence and facilitates the best supported responses (behaviors) [8].
Many studies have also reported a significant increase in the firing rate of the neurons of cortical areas representing the alternative choices during DM in visual tasks. The increase of the firing rates then would provide accumulation of evidence (i.e., information) related to the alternatives [5,6]. Reliable models of DM based on the neurophysiology, consider connections from neurons representing stimuli to the appropriate cortical neurons representing decisions (e.g., motor actions). This functional relationship provides the stimulus-to-response mapping [6,10]. 
  1. Chevalier, G., Vacher, S., Deniau, J. M., Desban, M. (1985). Disinhibition as a basic process in the expression of striatal functions. I. The striato-nigral influence on tectospinal/tecto-diencephalic neurons. Brain Res, 334(2), 215-226.
  2. Deniau, J. M., Chevalier, G. (1985). Disinhibition as a basic process in the expression of striatal functions. II. The striato-nigral influence on thalamocortical cells of the ventromedial thalamic nucleus. Brain Res, 334(2), 227-233.
  3. Medina, L., Reiner, A. (1995). Neurotransmitter organization and connectivity of the basal ganglia in vertebrates: implications for the evolution of basal ganglia. Brain Behav Evol, 46(4-5), 235-258.
  4. Redgrave, P., Prescott, T. J., Gurney, K. (1999). The basal ganglia: a vertebrate solution to the selection problem? Neurosci 89(4), 1009-1023.
  5. Schall, J. D. (2001). Neural basis of deciding, choosing and acting. Nat Rev Neurosci, 2(1), 33-42.
  6. Shadlen, M. N., Newsome, W. T. (2001). Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. J Neurophysiol, 86(4), 1916-1936.
  7. Smith, Y., Bevan, M. D., Shink, E., Bolam, J. P. (1998). Microcircuitry of the direct and indirect pathways of the basal ganglia. Neurosci, 86(2), 353-387.
  8. Bogacz, R., Gurney, K. (2007). The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Comput 19(2):442-477.
  9. Parent, A., Hazrati, L. N. (1995). Functional anatomy of the basal ganglia. I. The cortico-basal ganglia thalamocortical loop. Brain Res Brain Res Rev, 20(1), 91-127.
  10. Wang, X. J. (2002). Probabilistic decision making by slow reverberation in cortical circuits. Neuron, 36(5), 955-968.

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