Trajectories of reaching for (a) critical noise amplitude, <i>D</i> = 3.3, (b) subcritical noise amplitude, <i>D</i> = 2.0, and (c) supercritical noise amplitude, <i>D</i> = 7.0.

<p>Solid line, which denotes hand position, depicts the transition from the resting position (<i>x</i> = −1) to the target position (<i>x</i> = 1). Dashed line denotes the stimulus – the sinusoidal “kick” with amplitude <i>A</i>₀ = 0.25.</p

Do Basal Ganglia Amplify Willed Action by Stochastic Resonance? A Model

<div><p>Basal ganglia are usually attributed a role in facilitating willed action, which is found to be impaired in Parkinson's disease, a pathology of basal ganglia. We hypothesize that basal ganglia possess the machinery to amplify will signals, presumably weak, by stochastic resonance. Recently we proposed a computational model of Parkinsonian reaching, in which the contributions from basal ganglia aid the motor cortex in learning to reach. The model was cast in reinforcement learning framework. We now show that the above basal ganglia computational model has all the ingredients of stochastic resonance process. In the proposed computational model, we consider the problem of moving an arm from a rest position to a target position: the two positions correspond to two extrema of the value function. A single kick (a half-wave of sinusoid, of sufficiently low amplitude) given to the system in resting position, succeeds in taking the system to the target position, with high probability, only at a critical noise level. But for suboptimal noise levels, the model arm's movements resemble Parkinsonian movement symptoms like akinetic rigidity (low noise) and dyskinesias (high noise).</p></div

A model of reaching involving basal ganglia (redrawn based on [24]).

<p>A model of reaching involving basal ganglia (redrawn based on <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075657#pone.0075657-Magdoom1" target="_blank">[24]</a>).</p

The Go, Explore and NoGo regimes of BG.

<p>The Go, Explore and NoGo regimes of BG.</p

Probability of Reach, <i>P</i>, as a function of noise amplitude, <i>D</i>, for various values of stimulus duration, <i>T</i>.

<p><i>P</i> is zero for very low values of <i>D</i>: since the stimulus amplitude, <i>A</i>₀, is subthreshold, a minimum level of noise is necessary for a successful reach. Beyond <i>D</i> = 4, <i>P</i> decreases slowly with increasing <i>D</i>. Corresponding to each value of <i>T</i>, there is a thin solid line and a thick dashed line. The solid line represents the original simulation result, and the dashed line is the smoother version of the same.</p

Reaching with colored noise.

<p>(a) Plots of probability of reach (<i>P</i>) vs. noise amplitude (<i>D</i>) for colored noise for various values of <i>T</i> ( = 100, 250, 500, 750, 1000). Corresponding to each value of <i>T</i>, there is a thin solid line and a thick dashed line. The solid line represents the original simulation result, and the dashed line is the smoother version of the same. <i>A</i>₀ = 0.25. <i>λ</i> = 0.001. (b) An instance of reaching under colored noise conditions. <i>λ</i> = 0.001, <i>D</i> = 3.3, <i>A</i>₀ = 0.25, <i>T</i> = 1000.</p

A block -diagram depicting the proposed neurobiological substrates of SR dynamics of eqn. (2.2.2).

<p>A block -diagram depicting the proposed neurobiological substrates of SR dynamics of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0075657#pone.0075657.e013" target="_blank">eqn. (2.2.2)</a>.</p

Simulation results depicting variation of (a) Neuronal <i>Ca²</i>

<p> ^<b>+</b><b> concentration along with (b) as reported in </b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048802#pone.0048802-Lee1" target="_blank">[<b>25</b>]</a><b>.</b></p

Regimes obtained for various combinations of stimulation current (I_S) and initial [ATP].

<p>(1) Bursting, (2)Transition phase from bursting to firing with initial pause, (3) Firing with initial pause and (4) Continuous firing.</p

(a) Neuronal membrane potential bound by reversal potential of sodium and potassium channel along with (b) corresponding change in extracellular [EET] and the vessel radius.

<p>(a) Neuronal membrane potential bound by reversal potential of sodium and potassium channel along with (b) corresponding change in extracellular [EET] and the vessel radius.</p