Mathematical modelling of carbohydrate and protein metabolism in muscle.

We propose a mathematical model based on coupled ordinary differential equations (ODEs) for metabolite concentrations with the aim of investigating how modifications to the rates affects outputs from a regulatory network. Our aim is to model the relationships between energy metabolism and the biosynthesis of non-essential amino acids, such as serine. We consider a network of cytosolic glycolysis, the mitochondrial TCA cycle, and the associated serine synthesis pathway, with the aim of modelling the role of metabolic reprogramming as a mechanism to enhance protein synthesis and growth, particularly in skeletal muscle.

Mathematical Models of Chiral Symmetry-breaking - A Review of General Theories, and Adiabatic Approximations of the APED System.

We review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedma's crystal grinding systems and the APED model. We include a few new results based on asymptotic analysis of the APED system.

Analysis of phenotype-genotype associations using genomic informational field theory (GIFT).

We show how field- and information theory can be used to quantify the relationship between genotype and phenotype in cases where phenotype is a continuous variable. Given a sample population of phenotype measurements, from various known genotypes, we show how the ordering of phenotype data can lead to quantification of the effect of genotype. This method does not assume that the data has a Gaussian distribution, it is particularly effective at extracting weak and unusual dependencies of genotype on phenotype.

Breather modes of fully nonlinear mass-in-mass chains.

We propose a model for a chain of particles coupled by nonlinear springs in which each mass has an internal mass and all interactions are assumed to be nonlinear. We show how to construct an asymptotic solution of this system using multiple timescales, the systematic solution of coupled equations by repeated application of a consistency condition. Our results show that for some combinations of nonlinearity the dynamics are governed by the NLS as in the more usual mass-in-mass chains with linear interactions between inner and outer masses.

Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana.

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of the world, the impact on the local health service is still significant. Compartmental models are a useful framework for investigating transmission of diseases in societies.

Stochastic fractal and Noether's theorem.

We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability p or disappears with probability 1-p. It describes a stochastic dyadic Cantor set that evolves in time, and eventually becomes a fractal. We investigate this phenomenon, through analytical methods and Monte Carlo simulation, for a generic class of models, where segment breakup points follow a symmetric beta distribution with shape parameter α, which also determines the fragmentation rate.

Mathematical modelling of telomere length dynamics.

Telomeres are repetitive DNA sequences located at the ends of chromosomes. During cell division, an incomplete copy of each chromosome's DNA is made, causing telomeres to shorten on successive generations. When a threshold length is reached replication ceases and the cell becomes 'senescent'.

Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains.

We study random sequential adsorption of particles from a pool onto a one-dimensional substrate following ballistic deposition rules with separate nucleation and growth processes occurring simultaneously. Nucleation describes the formation of point-sized seeds, and after a seed is sown, it acts as an attractor and grows in size by the addition of grains of a fixed size. At each time step either an already-nucleated seed can increase in size, or a new seed may be nucleated.

The Effects of Insulin Resistance on Individual Tissues: An Application of a Mathematical Model of Metabolism in Humans.

Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for both carbohydrates and fats, around all tissues of the body. Insulin-resistant states such as type 2 diabetes and obesity are characterised by reduced efficiency of these mechanisms.

Mathematical modelling of hepatic lipid metabolism.

The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model validation is carried out using experimental data for the ingestion of three mixed composition meals over a 24-h period. Comparison with experimental data suggests the model predicts key plasma lipids accurately given a prescribed insulin profile.

Stochastic simulations of normal aging and Werner's syndrome.

Human cells typically consist of 23 pairs of chromosomes. Telomeres are repetitive sequences of DNA located at the ends of chromosomes. During cell replication, a number of basepairs are lost from the end of the chromosome and this shortening restricts the number of divisions that a cell can complete before it becomes senescent, or non-replicative.

Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs.

Telomeres are guanine-rich sequences at the end of chromosomes which shorten during each replication event and trigger cell cycle arrest and/or controlled death (apoptosis) when reaching a threshold length. The enzyme telomerase replenishes the ends of telomeres and thus prolongs the life span of cells, but also causes cellular immortalisation in human cancer. G-quadruplex (G4) stabilising drugs are a potential anticancer treatment which work by changing the molecular structure of telomeres to inhibit the activity of telomerase.

Theory, modelling and simulation in origins of life studies.

Origins of life studies represent an exciting and highly multidisciplinary research field. In this review we focus on the contributions made by theory, modelling and simulation to addressing fundamental issues in the domain and the advances these approaches have helped to make in the field. Theoretical approaches will continue to make a major impact at the "systems chemistry" level based on the analysis of the remarkable properties of nonlinear catalytic chemical reaction networks, which arise due to the auto-catalytic and cross-catalytic nature of so many of the putative processes associated with self-replication and self-reproduction.

The effects of a telomere destabilizing agent on cancer cell-cycle dynamics--integrated modelling and experiments.

The pentacyclic acridinium salt RHPS4 displays anti-tumour properties in vitro as well as in vivo and is potentially cell-cycle specific. We have collected experimental data and formulated a compartmental model using ordinary differential equations to investigate how the compound affects cells in each stage of the cell cycle. In addition to a control case in which no drug was used, we treated colorectal cancer cells with three different concentrations of the drug and fitted simulations from our models to experimental observations.

Evidence that ACN1 (acetate non-utilizing 1) prevents carbon leakage from peroxisomes during lipid mobilization in Arabidopsis seedlings.

ACN1 (acetate non-utilizing 1) is a short-chain acyl-CoA synthetase which recycles free acetate to acetyl-CoA in peroxisomes of Arabidopsis. Pulse-chase [2-(13)C]acetate feeding of the mutant acn1-2 revealed that acetate accumulation and assimilation were no different to that of wild-type, Col-7. However, the lack of acn1-2 led to a decrease of nearly 50% in (13)C-labelling of glutamine, a major carbon sink in seedlings, and large decreases in primary metabolite levels.

Modelling the peroxisomal carbon leak during lipid mobilization in Arabidopsis.

Mutation of the ACN1 (acetate non-utilizing 1) locus of Arabidopsis results in altered acetate assimilation into gluconeogenic sugars and anapleurotic amino acids and leads to an overall depression in primary metabolite levels by approx. 50% during seedling development. Levels of acetyl-CoA were higher in acn1 compared with wild-type, which is counterintuitive to the activity of ACN1 as a peroxisomal acetyl-CoA synthetase.

Mathematical models of the homochiralisation of crystals by grinding.

We review the existing mathematical models which describe physicochemical mechanisms capable of producing a symmetry-breaking transition to a state in which one chirality dominates the other. A new model is proposed, with the aim of elucidating the fundamental processes at work in the crystal grinding systems of Viedma (Phys Rev Lett 94:065504, 2005) and Noorduin (J Am Chem Soc 130:1158-1159, 2008). We simplify the model as far as possible to uncover the fundamental competitive process which causes the symmetry-breaking, and analyse other simplifications which might be expected to show symmetry-breaking.

Nonlinear breathing modes at a defect site in DNA.

Molecular-dynamics simulations of a normal DNA duplex show that breathing events typically occur on the microsecond time scale. This paper analyzes a 12 base pairs DNA duplex containing the "rogue" base difluorotoluene (F) in place of a thymine base (T), for which the breathing events occur on the nanosecond time scale. Starting from a nonlinear Klein-Gordon lattice model and adding noise and damping, we obtain a mesoscopic model of the DNA duplex close to that observed in experiments and all-atom molecular dynamics simulations.

Sequence selection during copolymerization.

We analyze a simple model for the copolymerization of two chemically distinct monomers that displays a wide variety of product sequence compositions depending on the rate coefficients for the stepwise addition of each monomer to a growing polymer chain. We show that in certain regions of parameter space the copolymer sequence composition depends sensitively on these parameter values, and we compute the information content of the resultant sequences. Finally, we show how the model may be used to interpret experimental data on copolymerization reactions.

Symmetry-breaking in chiral polymerisation.

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to 'poisoning' by the opposite-handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor.

Nonlinear breathing modes due to a defect in a DNA chain.

Recent molecular-dynamics simulations of a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a thymine (T) base show that breathing events can occur on the nanosecond time-scale, whereas breathing events in a normal DNA duplex take place on the microsecond time-scale. The main aim of this paper is to analyse a nonlinear Klein-Gordon lattice model of the DNA duplex, including both nonlinear interactions between opposing bases and a defect in the interaction at one lattice site, each of which can cause localization of energy. Solutions for a breather mode either side of the defect are derived using multiple-scales asymptotics and are pieced together across the defect to form a solution which includes the effects of the nonlinearity and the defect.