Abstract
Motivated by experiments employing optogenetic stimulation of cortical regions, we consider spike control strategies for ensembles of uncoupled integrate and fire neurons with a common conductance input. We construct strategies for control of spike patterns, that is, multineuron trains of action potentials, up to some maximal spike rate determined by the neural biophysics. We emphasize a constructive role for parameter heterogeneity, and find a simple rule for controllability in pairs of neurons. In particular, we determine parameters for which common drive is not limited to inducing synchronous spiking. For large ensembles, we determine how the number of controllable neurons varies with the number of observed (recorded) neurons, and what collateral spiking occurs in the full ensemble during control of the subensemble. While complete control of spiking in every neuron is not possible with a single input, we find that a degree of subensemble control is made possible by exploiting dynamical heterogeneity. As most available technologies for neural stimulation are underactuated, in the sense that the number of target neurons far exceeds the number of independent channels of stimulation, these results suggest partial control strategies that may be important in the development of sensory neuroprosthetics and other neurocontrol applications.
Highlights
Neurocontrol underlies an expanding range of applications, especially in the development of neuroprosthetics (Shenoy et al, 2003)
An additional complication in experimental applications is that the spiking activity of only a fraction of neurons in a given area is directly observed, so control strategies for a large ensemble treats recorded neurons as proxies for the general network
Our goal has been to consider large ensemble properties in a “pessimistic” control regime we believe applies to many neurocontrol applications in chronically implanted animals
Summary
Neurocontrol underlies an expanding range of applications, especially in the development of neuroprosthetics (Shenoy et al, 2003). Neurocontrol, in principle, is the application of established control theory to the stimulation of neural tissue (Khalil, 2002; Danzl et al, 2009; Schiff, 2009; Liu et al, 2010; Ahmadian et al, 2011; Dasanayake and Li, 2011). Optogenetic stimulation (Zhang et al, 2009; Anikeeva et al, 2011; Deisseroth, 2011; Peron and Svoboda, 2011; Siegle et al, 2011; Yizhar et al, 2011) does not overcome the underactuation issue, but does provide some new opportunities in control design. A somewhat less appreciated aspect of optogenetic stimulation is that broader areas may be activated per input than with electrical microstimulation, due to the ability to illuminate larger tissue volumes. In the context of a single or small number of illumination sources, common in experiments using chronic implants in behaving animals, stimulation might be thought to produce only bulk, synchronous firing: a mass of action potentials induced with each stimulating pulse
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