In-Silico Proportional-Integral Moment Control of Stochastic Gene Expression

The problem of controlling the mean and the variance of a species of interest in a simple gene expression is addressed. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies certain sufficient conditions. Controlling both the mean and variance however requires an additional control input, e.g. the mRNA degradation rate, and local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the system. Even more importantly, it is shown that there exist PI controllers that locally, robustly and simultaneously stabilize all the equilibrium points inside the admissible region. The results are then extended to the mean control of a gene expression with protein dimerization. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and convergence of the average dimer population to any desired reference value is ensured using a pure integral control law. Explicit bounds on the controller gain are provided and shown to be valid for any reference value. As a byproduct, an explicit upper-bound of the variance of the monomer species, acting on the system as unknown input due to the moment openness, is obtained. The results are illustrated by simulation.Comment: 28 pages; 9 Figures. arXiv admin note: substantial text overlap with arXiv:1207.4766, arXiv:1307.644

PID Control of Biochemical Reaction Networks

Principles of feedback control have been shown to naturally arise in biological systems and successfully applied to build synthetic circuits. In this work we consider Biochemical Reaction Networks (CRNs) as a paradigm for modelling biochemical systems and provide the first implementation of a derivative component in CRNs. That is, given an input signal represented by the concentration level of some species, we build a CRN that produces as output the concentration of two species whose difference is the derivative of the input signal. By relying on this component, we present a CRN implementation of a feedback control loop with Proportional-Integral-Derivative (PID) controller and apply the resulting control architecture to regulate the protein expression in a microRNA regulated gene expression model.Comment: 8 Pages, 4 figures, Submitted to CDC 201

Optimal and H∞H_\infty Control of Stochastic Reaction Networks

Stochastic reaction networks is a powerful class of models for the representation a wide variety of population models including biochemistry. The control of such networks has been recently considered due to their important implications for the control of biological systems. Their optimal control, however, has been relatively few studied until now. The continuous-time finite-horizon optimal control problem is formulated first and explicitly solved in the case of unimolecular reaction networks. The problems of the optimal sampled-data control, the continuous $H_\infty$ control, and the sampled-data $H_\infty$ control of such networks are addressed next. The results in the unimolecular case take the form of nonstandard Riccati differential equations or differential Lyapunov equations coupled with difference Riccati equations, which can all be solved numerically by backward-in-time integration.Comment: 39 page

Design and analysis of genetic feedback architectures for synthetic biology

Synthetic Biology seeks to design and assemble novel biological systems with favourable properties. It allows us to comprehend and modify the fundamental mechanisms of life and holds significant promise in revolutionizing current technologies ranging from medicine and biomanufacturing to energy and environmental protection. Biological processes constitute remarkably complex dynamical systems operating impeccably well in messy and constantly changing environments. Their ability to do so is rooted in sophisticated molecular control architectures crafted by natural evolutionary innovation over billions of years. Such control architectures, often blended with human-engineering approaches, are the key to realizing efficient and reliable synthetic biological systems. Aiming to accelerate the development of the latter, the present thesis addresses some fundamental challenges in biomolecular systems and control design. We begin by elucidating biological mechanisms of temporal gradient computation, enabling cells to adjust their behaviour in response to anticipated environmental changes. Specifically, we introduce biomolecular motifs capable of functioning as highly tunable and accurate signal differentiators to input molecular signals around their nominal operation. We investigate strategies to deal with high-frequency input signal components which can be detrimental to the performance of most differentiators. We ascertain the occurrence of such motifs in natural regulatory networks and demonstrate the potential of synthetic experimental realizations. Our motifs can serve as reliable speed biosensors and can form the basis for derivative feedback control. Motivated by the pervasiveness of Proportional-Integral-Derivative (PID) controllers in modern technological applications, we present the realization of a PID controller via biomolecular reactions employing, among others, our differentiator motifs. This biomolecular architecture represents a PID control law with set point weighting and filtered derivative action, offering robust regulation of a single-output biological process with enhanced dynamic performance and low levels of stochastic noise. It is characterized by significant ease of tuning and can be of particular experimental interest in molecular programming applications. Finally, we investigate efficient regulation strategies for multi-output biological processes with internal coupling interactions, expanding previously established single-output control approaches. More specifically, we propose control schemes allowing for robust manipulation of the outputs in various ways, namely manipulation of their product/ratio, linear combinations of them as well as manipulation of each of the outputs independently. Our analysis is centered around two-output biological processes, yet the scalability of the proposed regulation strategies to processes with a higher number of outputs is highlighted. In parallel, their experimental implementability is explored in both in vivo and in vitro settings

An Efficient Quadrature Sequence and Sparsifying Methodology for Mean-Field Variational Inference

This work proposes a quasirandom sequence of quadratures for high-dimensional mean-field variational inference and a related sparsifying methodology. Each iterate of the sequence contains two evaluations points that combine to correctly integrate all univariate quadratic functions, as well as univariate cubics if the mean-field factors are symmetric. More importantly, averaging results over short subsequences achieves periodic exactness on a much larger space of multivariate polynomials of quadratic total degree. This framework is devised by first considering stochastic blocked mean-field quadratures, which may be useful in other contexts. By replacing pseudorandom sequences with quasirandom sequences, over half of all multivariate quadratic basis functions integrate exactly with only 4 function evaluations, and the exactness dimension increases for longer subsequences. Analysis shows how these efficient integrals characterize the dominant log-posterior contributions to mean-field variational approximations, including diagonal Hessian approximations, to support a robust sparsifying methodology in deep learning algorithms. A numerical demonstration of this approach on a simple Convolutional Neural Network for MNIST retains high test accuracy, 96.9%, while training over 98.9% of parameters to zero in only 10 epochs, bearing potential to reduce both storage and energy requirements for deep learning models