Robust Genetic Circuit Design: A Mixed H∞ and IQC Analysis

Ruijuan Chen,Dongfei Fu,Wei Pan,Xin He

doi:10.1155/2017/5757943

Abstract

This paper considers the problem of designing a genetic circuit which is robust to noise effect. To achieve this goal, a mixed H∞ and Integral Quadratic Constraints (IQC) approach is proposed. In order to minimize the effects of external noise on the genetic regulatory network in terms of H∞ norm, a design procedure of Hill coefficients in the promoters is presented. The IQC approach is introduced to analyze and guarantee the stability of the designed circuit.

Highlights

Genetic regulatory network (GRN) is subjected to noise disturbances that may occur at transcription, translation, transport, chromatin remodeling, and pathway specific regulation
Β (x + k)n kn + (x + k)n and there exist real scalars α1 ≥ α2 ≥ 0, such that h(x) satisfies the Integral Quadratic Constraints (IQC) defined by π1
Since the linear matrix inequality (28) has to be solved simultaneously for all frequencies in the frequency domain, the basic strategy is to start with a small set of points and check whether the solution satisfies all ω

Summary

Introduction

Genetic regulatory network (GRN) is subjected to noise disturbances that may occur at transcription, translation, transport, chromatin remodeling, and pathway specific regulation. Mathematical and computational tools have been utilized to develop the genetic circuits and systems using biotechnological design principles of synthetic GRN, which involves new kinds of integrated circuits like neurochips inspired by the biological neural networks [2]. This method leads to a largescale system composed of several interconnected subsystems. The previous work [3] performs a hierarchical analysis by propagating the IQC characterization of each uncertain subsystem through their interaction channels Both plant states and the IQC dynamic states are used as feedback information in the closed-loop system model, and the robust l2 stability analysis is performed via dynamic IQCs. Thereby, the synthesis conditions for the proposed fullinformation feedback controller are derived for the linear matrix inequality (LMI) systems [4].

Problem Formulation

Analysis and Design

Biologically Inspired Example

Conclusion