| Molecular Biology is the study of structure and function of biological systems at the molecular level, aiming to reveal the nature of life. It is a fundamental research frontier field in contemporary life science. In molecular biology, gene expression is the basic process in living systems and it describes the process of genetic information transfer from DNA to protein. If gene mutation happens in the process of genetic information transfer, it may lead to some changes of genetic information along the polypeptide chain, which results in the variation of biological characters or biochemical functions. Recently, understanding and description of this process is mainly based on the traditional textual representation model. Although this model is able to clearly and completely describe the entire process of genetic information transfer, the lack of system-based model has become the bottleneck of system science, information science, molecular biology and their discipline-crossing research. In view of the process of gene expression and its relevant processes have the typical characteristics of discrete event system, so incorporate them into the framework of the discrete event dynamic systems theory is an innovative research direction. As a mature mathematical theory tools used in the process analysis, Petri net has been widely used in modeling and analysis of discrete event dynamic systems, which provides a new and effective theoretical methods for studying the basic processes in living systems, such as the process of gene expression.Gene regulatory networks are types of complex biological systems, governed by a series of complicated control structures and regulation mechanisms. Oftentimes metabolic control is focused on maintaining homeostasis, by balancing a variety of internal and external factors. Recently, the quantitative models of gene regulatory networks provide favorable conditions for studying the regulation of gene expression from the view of system. Particularly, differential equation models are established based on the biochemical experimental data, which provide necessary premise for researchers applying control theory to the control of gene regulatory networks. However, biological systems in nature are nonlinear systems, and thus control of cellular systems should be better implemented through nonlinear control. Therefore, apply nonlinear control methods to study the gene regulatory networks, is an effective application attempt of nonlinear control for biological systems at the molecular level. It has become a fast emerging research area in control theory, systems biology, synthetic biology, and cell/molecular engineering.This dissertation focuses on the modeling of gene expression and nonlinear control of gene regulatory networks, the main contents and results are summarized as follows:(1) Aiming at the lack of a systematic mathematical model to describe the process of gene expression, a Colored Petri Net model is built to describe the process of genetic information transfer, based on the Central Dogma of molecular biology. The model’s places and token colors are defined according to the status of the various stages of the process of gene expression. The fire rules and guard functions of model’s transitions are defined based on the state changes and regulation methods during the genetic information transfer. The operation of this model can be divided into five stages:initialization, transcription, determination of the start codon, determination of the stop codons, and translation. It successfully characterized the processes of genetic information transfer, i.e., from DNA transcribes to mRNA and then translates to protein. This model is conducive to understand and analysis the micro-biological processes intuitively. Furthermore, it establishes a theoretical foundation for modeling other life processes by using Colored Petri Nets.(2) Gene mutation has important effects on protein synthesis and biological characters of organism. To solve the problem of the lack of the mathematical model to determine the mutation type, a Colored Petri Nets model is constructed to classify the type of gene mutation, according to the essence of gene mutation and its classification principle. Furthermore, a determining principle of gene mutation classification is proposed. The original DNA strand and its mutated strand have been read into the model respectively. Based on the proposed determining principle, the position, number and type of mutations can be obtained via contrasting the bases of DNA strands and the codons of amino acids along the polypeptide chain, thereby determining whether the mutated gene changes the sequence of amino acids along the polypeptide chain. The validity and accuracy of the presented model are illustrated by the biological examples. This work provides model basis for the study of whether gene mutation changes the structure and function of the protein synthesis.(3) In view of the low accuracy of biochemical tests for determining the type of20amino acids, the classification rule of the amino acid is proposed and a Colored Petri Net model of amino acid type determination is built, which based on the classification principle of20amino acids and the codons triplet representation. This model can determine the type of amino acids, encoded by codon, through judging the bases of the codon. The classification principle of amino acids is summarized based on the genetic code table, and then the determining functions are given, finally the amino acid type determination theorem is obtained by the model operation and calculation rules. Example analysis shows that this model is able to determine the type of amino acid accurately. The model can be extended to determine the distribution of the different types of amino acids along the polypeptide chain, and has important significance for the study and prediction of protein spatial structures and types.(4) According to the differential equation models of the gene regulatory networks are complicated nonlinear systems, the problem of state observer and controller design for multi-input multi-output nonlinear systems that can describe the gene regulatory networks is investigated. Aiming at the defects of some state variables in biological systems is difficult to detect or impossible to be measured in real time, a nonlinear observer-based output feedback controller is designed, which can guarantee the asymptotical stabilization of the nonlinear system under the designed controller. This control strategy provides a feasible and practicable design approach for the nonlinear dynamic biological systems under closed-loop feedback control, particularly for the molecular-level cellular systems control. Using this method, only the output variables need to be monitored to realize the feedback control, which effectively avoid the problem that some gene regulatory networks whose states information is often difficult or impossible to obtain in real-time.(5) The galactose metabolism network (GAL nework) in S. cerevisiae yeast is chosen as a case study to verify the correctness and effectiveness of the proposed nonlinear control strategy for gene regulation. Based on the established mathematical model of the GAL network, we organize the GAL network model into a nonlinear affine form by defining the appropriate input and output, and then apply the observer-based output feedback nonlinear control to the regulation of the GAL network. Simulation results demonstrate that the proposed control approach not only allows the GAL network to reach a steady state within a desired timeframe, but also shortens the convergence time of various state variables in the system, i.e., the system can rapidly achieve the desired equilibrium under the designed nonlinear controller. The successful application of nonlinear control strategy in the GAL network, can be regarded as the breakthrough point of the nonlinear control applied to molecular biological systems, which lays the theoretical foundation for more control strategy applied to micro and nano bio-systems. |
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