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

Tracking system for photon-counting laser radar

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 107).The purpose of this thesis is to build the tracking system for a photon-counting laser radar specifically a laser radar that has the ability to perform direct and coherent detection measurement at low signal levels with common laser, optics and detector hardware. The heart of the tracking algorithm is a Kalman filter, and optimal Kalman filter parameters are determined using software simulations. The tracking algorithm was tested against various simulated (software only) and emulated (with actual hardware) trajectories. We also built and tested the real-time tracking system hardware. The algorithms and methods proposed in this thesis achieve the objective of tracking a target at 1,500 km range to within 1-cm accuracy.by Joshua TsuKang Chang.M.Eng

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: (1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and (2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue

Optimal stimulus waveforms for eliciting a spike: How close is the spike-triggered average

Computing the average input stimulus preceding a spike, the spike-triggered average (STA), has been a powerful tool for discovering a neuron\u27s \u27preferred\u27 stimulus feature that enables efficient encoding of sensory information. Recent work in the squid giant axon has shown that STA waveforms can be remarkably similar to the energetically optimal stimulus waveforms for eliciting a spike. In the present study, we show using the Hodgkin-Huxley model that the STA can deviate from the global optimal solution if there is averaging of multiple solutions across different time scales and of multiple modes of spike induction. These findings inform attempts to develop model-free stochastic algorithms for finding energy-optimal stimuli, which is relevant to the efficient delivery of exogenous therapeutic stimuli in neurological diseases