Controllability analysis and design for underactuated stochastic neurocontrol

Neuroengineering has advanced tremendously over the past decade, but for sensory prosthetics and similar applications, it remains an extraordinary challenge to access neurons at the single cell resolution of most sensory encoding theories. In particular, if each neuron is “tuned” to particular stimulus features, then eliciting a target percept requires activating only neurons tuned to that percept and not others. However, most available technology is underactuated, with orders of magnitude fewer independent control inputs than neural degrees of freedom, possibly limiting its effectiveness given the inherent trade-off of resolution with network size. Here I analyze controllability for pairs of neurons receiving a common input. In particular, I extend previous work on the deterministic control problem to include stochastic membrane dynamics, treating both cases as a bifurcation problem in the noise parameter. I determine controllable regions in parameter space using a combination of mathematical analysis and numerical solution of stochastic differential and Fokker-Planck equations. I explain how boundaries between these regions change with noise level, and connect to the dynamical mechanisms by which controllability is lost. I show that in stochastic systems, in contrast to deterministic systems, expanding the allowable input space to include exponential ramps expands the parameter range over which neuron pairs are controllable. I also describe an alternative controllability definition using only mean spike times, as compared to the probability distribution of spiking within prespecified time intervals. These results could guide future control strategies in the development of sensory neuroprosthetics and other neurocontrol application

Flipping Biological Switches: Solving for Optimal Control: A Dissertation

Switches play an important regulatory role at all levels of biology, from molecular switches triggering signaling cascades to cellular switches regulating cell maturation and apoptosis. Medical therapies are often designed to toggle a system from one state to another, achieving a specified health outcome. For instance, small doses of subpathologic viruses activate the immune system’s production of antibodies. Electrical stimulation revert cardiac arrhythmias back to normal sinus rhythm. In all of these examples, a major challenge is finding the optimal stimulus waveform necessary to cause the switch to flip. This thesis develops, validates, and applies a novel model-independent stochastic algorithm, the Extrema Distortion Algorithm (EDA), towards finding the optimal stimulus. We validate the EDA’s performance for the Hodgkin-Huxley model (an empirically validated ionic model of neuronal excitability), the FitzHugh-Nagumo model (an abstract model applied to a wide range of biological systems that that exhibit an oscillatory state and a quiescent state), and the genetic toggle switch (a model of bistable gene expression). We show that the EDA is able to not only find the optimal solution, but also in some cases excel beyond the traditional analytic approaches. Finally, we have computed novel optimal stimulus waveforms for aborting epileptic seizures using the EDA in cellular and network models of epilepsy. This work represents a first step in developing a new class of adaptive algorithms and devices that flip biological switches, revealing basic mechanistic insights and therapeutic applications for a broad range of disorders

Extrinsic and Intrinsic Control of Integrative Processes in Neural Systems

At the simplest dynamical level, neurons can be understood as integrators. That is, neurons accumulate excitation from afferent neurons until, eventually, a threshold is reached and they produce a spike. Here, we consider the control of integrative processes in neural circuits in two contexts. First, we consider the problem of extrinsic neurocontrol, or modulating the spiking activity of neural circuits using stimulation, as is desired in a wide range of neural engineering applications. From a control-theoretic standpoint, such a problem presents several interesting nuances, including discontinuity in the dynamics due to the spiking process, and the technological limitations associated with underactuation (i.e., many neurons controlled by the same stimulation input). We consider these factors in a canonical problem of selective spiking, wherein a particular integrative neuron is controlled to a spike, while other neurons remain below threshold. This problem is solved in an optimal control framework, wherein several new geometric phenomena associated with the aforementioned nuances are revealed. Further, in an effort to enable scaling to large populations, we develop relaxations and alternative approaches, including the use of statistical models within the control design framework. Following this treatment of extrinsic control, we turn attention to a scientifically-driven question pertaining to intrinsic control, i.e., how neurons in the brain may themselves be controlling higher-level perceptual processes. We specifically postulate that neural activity is decoded, or “read-out” in terms of a drift-diffusion process, so that spiking activity drives a latent state towards a detection/perception threshold. Under this premise, we optimize the neural spiking trajectories according to several empirical cost functions and show that the optimal responses are physiologically plausible. In this vein, we also examine the nature of \u27optimal evidence\u27 for the general class of threshold-based integrative decision problems