14 research outputs found
Ergodicity, Output-Controllability, and Antithetic Integral Control of Uncertain Stochastic Reaction Networks
The ergodicity and the output-controllability of stochastic reaction networks
have been shown to be essential properties to fulfill to enable their control
using, for instance, antithetic integral control. We propose here to extend
those properties to the case of uncertain networks. To this aim, the notions of
interval, robust, sign, and structural ergodicity/output-controllability are
introduced. The obtained results lie in the same spirit as those obtained in
[Briat, Gupta & Khammash, Cell Systems, 2016] where those properties are
characterized in terms of control theoretic concepts, linear algebraic
conditions, linear programs, and graph-theoretic/algebraic conditions. An
important conclusion is that all those properties can be characterized by
linear programs. Two examples are given for illustration.Comment: 29 pages. arXiv admin note: text overlap with arXiv:1703.0031
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
Optimal and 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 control, and the
sampled-data 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 DNA controllers
Reliable biochemical implementations of linear controllers can provide a large set of tools for the design and analysis of control in Synthetic Biology. Theoretical frameworks are now available to represent feedback control systems as chemical reaction networks which can be readily translated into equivalent nucleic acid-based chemistry. However, the development of tools for constructing and analysing such controllers is still in its infancy.
Nucleic acid-based chemistry is a strong candidate framework for the construction of future synthetic biomolecular control circuits. The capacity of strand displacement reactions with Deoxyribonucleic Acid (DNA) to implement analogue signal processing in vitro and in vivo makes them a promising candidate to embed synthetic feedback control circuitry in biomolecular environments. However, little progress has so far been made in developing the requisite theoretical machinery to inform the systematic design of feedback controllers in this context.
Here, the potential complexity of such controllers is extended significantly by showing how time-delays, numerical differentiation (to allow proportional-integral-derivative control), and state feedback may be implemented via chemical reaction network-based designs.
This work also provides a number of foundational theoretical results on the equilibria, stability, and dynamics of nucleic acid controllers, and the analysis highlights the many interesting and unique characteristics of this important new class of feedback control systems. In particular, that the implementation of feedback controllers using DNA strand displacement reactions introduces additional nonlinear dynamics, even in the case of purely linear control designs, and a robust design of the linear system does not imply the robustness of its chemical implementation.
The robustness of the controllers to experimental uncertainty is analysed with the structured singular value (Β΅) analysis tool, which is extended with a model of how parametric uncertainty in the system affects the location of its equilibrium. This framework provides more reliable results than sampled based statistical methods, where analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by Β΅-analysis.
The implementations of the examples and controllers in nucleic acid-based chemistry are simulated and checked using the Visual DSD simulation package, a bespoke software tool for simulating nucleic acid-based circuits