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New conditions for pattern solutions of a Brusselator model
This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions...
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Biomolecular Topology: Modelling and Analysis
With the great advancement of experimental tools, a tremendous amount of biomolecular data has been generated and accumulated in various databases....
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Fractional-Order Susceptible-Infected Model: Definition and Applications to the Study of COVID-19 Main Protease
We propose a model for the transmission of perturbations across the amino acids of a protein represented as an interaction network. The dynamics...
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Existence and Uniqueness of the Positive Steady State Solution for a Lotka-Volterra Predator-Prey Model with a Crowding Term
This paper deals with a Lotka-Volterra predator-prey model with a crowding term in the predator equation. We obtain a critical value λ
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Stability for a diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes
A diffusive delayed predator-prey model with modified Leslie-Gower and Holling-type II schemes is considered. Local stability for each constant...
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Mathematical Models for Blood Coagulation
This chapter presents an overview and introduction to blood coagulation models. The historical exposure of the development of classical coagulation...
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The mean and noise of protein numbers in stochastic gene expression
Gene expression is the central process in cells, and is stochastic in nature. In this work, we study the mean expression level of, and the expression...
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Knot theory in understanding proteins
This paper aims to enthuse mathematicians, especially topologists, knot theorists and geometers to examine problems in the study of proteins. We have...
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Model Reduction of Chemical Reaction Systems using Elimination
There exist different schemes of model reduction for parametric ordinary differential systems arising from chemical reaction systems. In this paper,...
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Multiscale stochastic modelling of gene expression
Stochastic phenomena in gene regulatory networks can be modelled by the chemical master equation for gene products such as mRNA and proteins. If some...
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Stability Analysis of Diffusive Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes
The stability of a diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemes is investigated. A threshold property of the...
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Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression
Gene expression at the single-cell level incorporates reaction mechanisms which are intrinsically stochastic as they involve molecular species...
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Graph Representations and Algorithms in Computational Biology of RNA Secondary Structure
The analysis of RNA structures is an important problem in computational biology. In this chapter we review various algorithms to predict and compare...
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Modulation of gene transcription noise by competing transcription factors
Sequence specific transcription factors (TFs) are critical to ensuring that genes are transcribed in the right cell at the right time. Often, the...
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Model of cell signal transduction in a three-dimensional domain
Intracellular signalling molecules form pathways inside the cell. These pathways carry a signal to target proteins which results in cellular...
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Design of regulation and dynamics in simple biochemical pathways
Complex regulation of biochemical pathways in a cell is brought about by the interaction of simpler regulatory structures. Among the basic regulatory...
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Graph-theoretic characterizations of monotonicity of chemical networks in reaction coordinates
This paper derives new results for certain classes of chemical reaction networks, linking structural to dynamical properties. In particular, it...
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An age-dependent feedback control model of calcium dynamics in yeast cells
The functional decline of selected proteins or organelles leads to aging at the intracellular level. Identification of these proteins or organelles...
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Introducing total substrates simplifies theoretical analysis at non-negligible enzyme concentrations: pseudo first-order kinetics and the loss of zero-order ultrasensitivity
The Briggs–Haldane standard quasi-steady state approximation and the resulting rate expressions for enzyme driven biochemical reactions provide...