Rondoni, N. (AM) – Inverse Problems and Control of Nonlinear Systems with Applications in Biology
Steering living systems toward a desired behavior is a central goal in synthetic and quantitative biology. Levers of control range from electric fields and optogenetic stimulation to engineered gene circuits, chemical dosing, and tuning the adhesive attraction and repulsion between cells. Biology makes it hard to know how much each lever should be pulled, or even to discern the current state of the system. Dynamics are nonlinear, and observations are noisy and indirect. Models are often incomplete, as exact replication of dynamics requires an immense number of parameters. This dissertation solves inverse problems and develops control methods within this setting across three biological testbeds. Here we take steps toward more reliably engineering tissues to form patterns on demand, cells to manufacture therapeutics to desired specifications, and neural experiments to respond to activity in real time.
In the first chapter, we invert the forward mapping between the firing of a neuron and the noisy calcium indicator traces actually recordable in high throughput imaging. This work utilizes model predictive control on a novel mechanistic set of ODEs, competes with the state of the art, and is the first of its kind to our knowledge able to provide real time inference of this type with no variable backtracking. While other methods may edit their answers based on future information, ours operates with 60ms of lag, then leaves predictions fixed.
In the second chapter, we suppose direct control of the forward mapping, a nonlinear model representing production of thyroxine by engineered cellular factories, and ensure the measured output tracks a desired value even when the plant and observations are confounded by stochasticity. We use a radial basis function neural network for online function approximation, and introduce numerous modifications to this classic architecture to empirically track setpoints stably even in the presence of immense delays in the forward model’s output. We show the median steady state error in terms of normalized root mean square error to be 12.5% or less across setpoints in a Monte Carlo study.
In the final chapter, we again solve an inverse problem, this time in spatial cellular patterning. Treating a black box agent based model as the forward map, we recover attraction and repulsion rates that reproduce a target pattern up to rotation, using an objective defined only on summary entropies of the pattern, rather than on target cell positions or the true parameters. We show convergence from 100 initial layouts, for two different target patterns. For a layout where convergence is marginal, we show that converging and nonconverging initial rates have statistically distinct centroids, then build a classifier that predicts which initializations are likely to succeed under this iterative intervention strategy.
Applications such as engineered spatial patterns, bioelectronic interventions, and closed loop neural experiments each depend on three tasks. The first is deriving a forward model, potentially black box or explicit in equations. The second task is computing the input that drives the biological system to a target, while the third is recovering hidden inputs from what observations are actually available. More broadly, this dissertation advances control of living systems that are only partially observed and partially understood.
Event Host: Nicholas Rondoni, PhD Candidate, Applied Mathematics
Advisor: Marcella Gomez
Zoom: https://ucsc.zoom.us/j/97002422471?pwd=BarPJkyaLcJ6OUA1a2Za74GyrAb274.1
Passcode: 970 0242 2471