State Estimation for Delayed Genetic Regulatory Networks With Reaction-Diffusion Terms.
IEEE Transactions on Neural Networks and Learning Systems
|January 24, 2017
Summary
This study develops a state observer for delayed genetic regulatory networks with reaction-diffusion terms. The proposed method ensures accurate estimation of mRNA and protein concentrations using linear matrix inequalities.
Area of Science:
- Systems Biology
- Control Theory
- Mathematical Biology
Background:
- Genetic regulatory networks (GRNs) are fundamental to cellular processes.
- Incorporating delays and spatial diffusion is crucial for realistic GRN modeling.
- State estimation in such complex systems presents significant challenges.
Purpose of the Study:
- To design a state observer for delayed genetic regulatory networks (DGRNs) with reaction-diffusion terms.
- To estimate the concentrations of mRNAs and proteins in DGRNs.
- To ensure the stability and feasibility of the state estimation process.
Main Methods:
- Utilizing the Hill function for nonlinear regulation.
- Developing a Lyapunov-Krasovskii functional with novel integral terms.
- Applying Wirtinger-type integral inequality, convex analysis, Green's identity, and Wirtinger's inequality.
- Establishing stability criteria via linear matrix inequalities (LMIs).
Main Results:
- An asymptotic stability criterion for the error system was derived.
- The criterion is dependent on delay bounds and their derivatives.
- Feasibility of the LMIs guarantees successful state estimation for DGRNs.
Conclusions:
- The proposed observer design enables accurate state estimation for DGRNs with delays and reaction-diffusion terms.
- The method is validated through numerical examples, demonstrating its effectiveness.
- This work contributes to the robust analysis and control of biological systems.
Related Concept Videos
01:29Reaction Mechanisms: Rate-limiting Step Approximation
37
The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
37
02:31Multi-Step Reactions
8.9K
Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
8.9K
01:14Pharmacodynamic Models: Link Model and Systems Pharmacodynamic Model
65
The link model is a fundamental pharmacokinetic-pharmacodynamic (PK–PD) approach to account for delayed drug responses when the observed effect does not immediately correlate with the drug's plasma concentration peak. This delay is mathematically addressed by introducing an effect compartment concentration, Ce, which is kinetically linked to the plasma concentration, Cp, via a first-order rate constant, ke0. The linkage allows for a more accurate prediction of drug effects over time. A...
65
01:28Global Regulatory Systems
812
Global regulatory systems in bacteria enable rapid and coordinated responses to environmental changes by integrating sensory inputs with gene expression, ensuring efficient adaptation to fluctuating conditions. Key global regulatory mechanisms include regulons, two-component systems, sigma factors, and secondary messengers.Regulons and Global RegulatorsA regulon is a collection of genes and operons controlled by a common global regulator. These regulators enable bacteria to prioritize resource...
812
01:25Modeling with Differential Equations
138
Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
138
01:09Pharmacodynamic Models: Additive and Proportional Drug Effect Model
50
Drug response models describe how pharmacological agents interact with biological systems to produce measurable effects. Baseline responses are inherent physiological activities without a drug significantly influencing the observed pharmacological outcomes. Depending on the drug response model employed, these baseline responses may combine with the drug's effect in either an additive or proportional manner.Additive Drug Response ModelIn the additive model, the drug effect is independent of the...
50