Motivated by an intricate mechanism to transport folded proteins across biological membranes, known as the Twin-arginine translocation (Tat) pathway, we construct lattice protein models in an attempt to study the aggregation of the membrane protein TatA, which plays an integral role during active Tat translocation. We develop force field that characterizes intra- and inter-residue interactions, as well as how each residue interacts with its environment. Although written with the Tat process in mind, this thesis is mainly devoted to developing efficient Monte Carlo schemes for biomolecular simulations, which are often challenged and impeded by complex energy landscapes. To tackle the local trap problem that is typical in Metropolis sampling, the idea of dynamic weighting is incorporated into the parallel tempering (PT) algorithm. Our results show that, when applied to the lattice-protein model, the modified PT algorithm is capable of locating the low energy state much more quickly, but does not produce reliable estimates for equilibrium expectations. A modern method for free energy calculation, called the multistate Bennett acceptance ratio (MBAR) estimator, is reviewed from a statistical perspective, reminiscent of the underlying statistical theory which the method is based upon. Instead of adopting the common practice of using MBAR as a post-simulation analysis tool, we propose a new approach that integrates MBAR into simulation, allowing the simulation to benefit from the statistical optimality of the MBAR estimator. We show that the MBAR-enhanced Monte Carlo improves simulation efficiency of the lattice-protein aggregation model and, since it can also be applied to continuous models, provides a promising alternative to the study of more realistic systems. The new method is then applied to our model of TatA, where the protein features both a transmembrane and an amphipathic helix. The effect of individual helices on dimerization was studied and problem with the move set was identified. In this thesis, we used pull move and translation move as our Monte Carlo trial moves. Implementation details of pull moves, which are often omitted by many researchers who use them for sampling configuration space, are given in Chapter 1. We show that, for our double-helix TatA model, pull moves are no longer efficient moves and therefore, for future study of more realistic systems, we point to several methods which all attempt to design efficient trial moves. Aggregation of more than two polymer chains was also considered in this thesis.

Mosquito-borne diseases cause substantial mortality and morbidity worldwide. These impacts are widely predicted to increase as temperatures warm, since mosquito biology and disease ecology are strongly linked to temperature. However, direct evidence linking environmental change to changes in mosquito-borne disease is rare, and the ecological mechanisms that may underpin such changes are poorly understood. Environmental drivers, can have non-linear, opposing impacts on the demographic rates of different mosquito life cycle stages and on disease transmission processes. As such, model frameworks that explicitly incorporate the effects of temperature are required to predict seasonal mosquito abundance and the intensity and persistence of disease transmission under environmental fluctuations. Chapter 2 develops a variable-delay delay differential equation (DDE) model to estimate seasonal abundance of each life stage of the West Nile virus (WNV) vector mosquito species, Cx. pipiens, given temperature and photoperiod conditions experienced. The model highlights that the timing and intensity of warm periods can be more influential in shaping abundance patterns than average temperatures. Chapter 3 presents an extensive body of fieldwork, which led to a high temporal resolution seasonal abundance dataset of each life stage of Cx. pipiens. Chapter 4 challenges assumptions of the DDE model from Chapter 2 in light of the seasonal abundance data collected in Chapter 3. The importance of using appropriate, high temporal resolution input temperature datasets is displayed. Chapter 5 extends the DDE model from Chapter 4 to explicitly model WNV transmission cycles between vectors and avian hosts. The disease model predicts that the current climate in the South of England is too cold to facilitate WNV outbreaks. However, given projected warming in the UK in coming decades it is predicted that WNV infection rates in mosquitoes will be consistent with the lower range of values observed during WNV outbreaks 2080 if virus introduction coincides with warm periods. The risk of these outbreaks is predicted to increase sharply with increases in human greenhouse gas emissions.

The interaction between hosts and parasites in bird populations has been studied extensively. I use game theoretic methods to model this interaction. This has been done previously but has not been studied taking into account the detailed sequential nature of this game. I introduce models allowing the host and parasite to make a number of decisions which will depend on a number of natural factors. A sequence of events follows, which is broken down into two key stages; firstly the interaction between the host and the parasite adult, and secondly that between the host and the parasite chick. The final decision involves the host choosing whether to raise or abandon the chicks that are in the nest. There are certain natural parameters and probabilities which are central to these various decisions; in particular the host is generally uncertain whether parasitism has taken place, but can assess the likelihood of parasitism based upon certain cues (e.g. how many eggs remain in its nest). I have taken elements of games which have been previously created and constructed my own models to fully describe this interaction. These parasites have different methods of parasitizing the nests of their hosts, and the hosts can in turn have different reactions to these parasites. This is later built into a model where there is more than one host nesting over a breeding season. We have a number of nesting sites and different time points in which the host can begin to nest. In the previous models the host was given the opportunity to abandon the nest. In this game the host is allowed to abandon and then restart the nesting process. The probability that the host is parasitized can be decided using a number of factors including the number of hosts laying during a given time period, the nesting site or the number of parasites during the course of the season. Using these models we are able to find situations which match those which we have seen in nature. Also the models are able to predict what natural changes such as parasitism rate or mimicry will do to the interaction. Overall I believe these models to give as good an indication of the key elements of the interaction and how they can change over time.

Quorum sensing is a cell communication mechanism used to coordinate group behaviour based on population density. A mathematical model of quorum sensing in bacterial biofilms is developed, consisting of a nonlinear diffusion reaction system describing the effects of a growing biofilm on bacterial quorum sensing behaviour. In numerical experiments, the influence of the hydrodynamic environment and nutrient conditions on biofilm growth and quorum sensing behaviour are studied, and flow-facilitated inter-colony communication and spatiotemporal quorum sensing induction patterns are observed. The model is extended to include an impact of quorum sensing on biofilm growth, through the explicit description of EPS, the protective biomass layer surrounding bacterial biofilm cells. The circumstances under which quorum sensing-regulated EPS production is a beneficial strategy for cells are identified. Biofilm colonies that use this strategy have lower cell populations than non-quorum sensing colonies, but may secure nutrients in a space-limited environment and outcompete neighbouring colonies.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 0745. Adviser: German Bollero. Includes bibliographical references (leaves 172-181) Available on microfilm from Pro Quest Information and Learning.

The work presented in this thesis is concerned with modelling the growth of tissue constructs, with particular focus on the effects the local micro environment has on the cell cycle and metabolism. We consider two cases; multicellular tumour spheroids and orthopaedic tissue constructs. This thesis is divided into two parts. In the first part we will present a multispecies model of an avascular tumour that studies how a cell’s metabolism affects the cell cycle, spheroid growth and the mechanical forces that arise during growth. The second part consists of a study of the growth of an engineered cartilaginous tissue layer. Experimental observations will be compared to a model of the distribution of cells and extracellular matrix. The efficiency of cancer treatments such as radiotherapy and chemotherapy are sensitive to the local environment of a cell. Therefore an essential task in tumour biology is to understand the microenvironment within a tumour. Many mathematical models study the effects of nutrients and waste products, usually assuming growth is limited by the diffusion of a single nutrient. We will look in detail at the metabolic pathways from which cells obtain energy (ATP). A multispecies model is presented that considers the transition from aerobic to anaerobic respi- ration and includes relevant chemical and ionic buffering reactions and transport mechanisms. Results show that potential ATP production affects the cell cycle and consequently the rate of growth. This model is simplified using mathematical analysis and is integrated with a morphoelastic model to study the development of mechanical forces. The model shows that mechanical effects are particularly important during necrosis, where large tensile forces are shown to develop. A review of the equations governing nutrient conservation is given, by developing alternative macroscopic equations based on the microscopic features of a tumour using homogenization techniques. The second part of this thesis studies the growth of cartilaginous tissue. Bio-materials are being engineered in an attempt to replace dysfunctional tissue in the human body using cells extracted from living organisms. We model the growth of a cartilaginous tissue construct that has been grown from expanded chondrocytes seeded onto collagen coated filters. A model is developed to explain the distribution of cells and the concentration and distribution of collagen and GAGs. This is achieved by studying the local environment of the cells. Model predictions are compared to a range of experimental data and show most of the growth takes place in the upper region of the construct.

<p> Stochastic models of biochemical interactions elucidate essential properties of the network which are not accessible to deterministic modeling. In this thesis it is described how a network motif, the proportional-reversibility interaction with active intermediate states, gives rise to the ability for the variance of biochemical signals to be controlled without changing the mean, a property designated as mean-independent noise control (MINC). This noise control is demonstrated to be essential for macro-scale biological processes via spatial models of the zebrafish hindbrain boundary sharpening. Additionally, the ability to deduce noise origin from the aggregate noise properties is shown. </p><p> However, these large-scale stochastic models of developmental processes required significant advances in the methodology and tooling for solving stochastic differential equations. Two improvements to stochastic integration methods, an efficient method for time stepping adaptivity on high order stochastic Runge-Kutta methods termed Rejection Sampling with Memory (RSwM) and optimal-stability stochastic Runge-Kutta methods, are combined to give over 1000 times speedups on biological models over previously used methodologies. In addition, a new software for solving differential equations in the Julia programming language is detailed. Its unique features for handling complex biological models, along with its high performance (routinely benchmarking as faster than classic C++ and Fortran integrators of similar implementations) and new methods, give rise to an accessible tool for simulation of large-scale stochastic biological models.</p><p>

Although death due to lethal cardiac arrhythmias is the leading cause of mortality in Western Society, many of the fundamental mechanisms underlying their onset, maintenance and termination, still remain poorly understood. In recent years, experimental techniques such as optical mapping have provided useful high-resolution recordings of cardiac electrical dynamics during complex arrhythmias and defibrillation episodes, which have been combined with detailed computer simulations to further our understanding of these phenomena. However, mechanistic enquiry is severely restricted as the optical mapping technique suffers from a number of distortion effects which compromise the fidelity of the experimental measurements, presenting difficulties in the comparison of experimental data with computational simulations. This Thesis presents a thorough investigation into the distortion effects encountered in optical mapping experiments, guided by the development of a coherent series of computational models. The models presented successfully characterise the specific mechanisms of fluorescent signal distortion due to photon scattering. Photon transport in cardiac tissue is modelled using both continuous (reaction-diffusion) and discrete stochastic (Monte Carlo) approaches to simulate the effects of photon scattering within the myocardium upon the recorded fluorescent signal, which include differing levels of detail and associated computational complexity. Specifically, these models are used to investigate the important role played by the complex ventricular structural anatomy, as well as the specifics of the experimental set-up itself. In addition, a tightly coupled electromechanical model of a contracting cardiac fibre is developed which provides an important first-step towards the development of a model to quantitatively assess the distortion observed when recording from a freely contracting cardiac preparation. Simulation of these distortion effects using the models allows discrimination to be made between those parts of the experimental signal which are due to underlying tissue electrophysiology and those due to artifact, facilitating a more accurate interpretation of experimentally-obtained data. The models presented succeed in two main respects. Firstly, they provide a ‘post-processing’ tool which can be added on to computational simulations of electrical activation, allowing for a more accurate and faithful comparison between simulations and experiments, helping to validate predictions made by electrical models. Secondly, they provide a higher degree of mechanistic insight into the fundemental ways in which optical signals are distorted, showing how this distortion can be maximised or controlled. The understanding and quantification of the fundemental mechanisms of optical mapping signal distortion, provided by this Thesis, therefore fulfils an important role in the study of arrhythmia mechanisms.

This thesis considers aspects of modelling solid tumours. We begin by considering the common assumption that nutrient or drug concentrations in avascular tumour spheroids are radially symmetric. We derive a simple Poisson equation for biomolecular diffusion into an avascular tumour, but with highly oscillatory boundary conditions due to the surrounding capillary network. We find that the assumption of radial symmetry is legitimate for biomolecules that are taken up in sufficient quantities by proliferating cancer cells; however radially symmetric profiles need not be observed otherwise. We then investigate how the gap between an avascular tumour and the neighbouring vasculature varies as the tumour grows. This is explored by (i) using scaling arguments based on ordinary differential equations, (ii) coupling the rate of oxygen flux from the vasculature to oxygen evolution within the tumour, and (iii) deriving a system of six coupled non-linear partial differential equations modelling the tumour evolution. It is found that as the tumour grows any initial gap between the tumour and neighbouring vasculature closes since there is no mechanism which would sufficiently up-regulate non-cancerous cell proliferation. This is in contrast to the intra-cornea implantation observations, upon which several mathematical models are based. Finally, we study the growth and treatment of a vascular tumour subjected to chemotherapies, particularly when the therapies can exhibit an anti-angiogenic effect and resistance to the therapy is incorporated. A multi-compartment model is derived for the evolution of a tumour undergoing treatment and parameters are estimated, with extensions to incorporate numerous different therapy protocols in the literature. We find that anti-angiogens can be effective, though the appropriate scheduling is counter-intuative and contradicts many standard therapy rules. We conclude that chemotherapy protocol design is very sensitive to the mode of action of the drug and simple general strategies will, in many cases, not be the most effective.

In this thesis, I focus on methodological concepts of studying infectious disease transmission between agricultural premises. I used different disease systems as exemplars for spatial and network methods to investigate transmission patterns. Infectious diseases cause tangible economic threat to the farming industry worldwide by damaging livestock populations, reducing farm productivity and causing trade restriction. This implies the importance of veterinary epidemiological studies in control and eradication of pathogens. Recent increase in availability of data and computational power allowed for more opportunities to study mechanisms of pathogenic transmission. Nowadays, the bottleneck is primarily associated with efficient methods that can analyse vast amounts of high-resolution data. Here I address two livestock pathogens that differ in their epidemiology: bacteria Streptococcus agalactiae and foot-and-mouth disease (FMD) virus. Streptococcus agalactiae is a contagious pathogen that causes mastitis in cattle, and thus possesses a substantial economic burden to the dairy industry. Known transmission routes between cattle are restricted to those via milking machines, milkers’ hands and fomites during milking process. Additionally, recent studies suggested potential introductions from other host species: primarily, humans. However, strain typing data showed discrepancies in strain compositions of bacteria isolated from humans and bovines. In this thesis, strain-specific features of between-herd transmission of Streptococcus agalactiae within dairy cattle population in Denmark are investigated. Foot-and-mouth disease (FMD) is a viral infection that affects cloven-hoofed animals and is of big importance mainly because of the trade restrictions against infected regions and countries. Control programmes against FMD usually include vaccination and culling of animals. However, the debate on the optimal control for FMD is still ongoing. In this thesis, I address questions on identification of the routes of infection and on requirements for movement recording systems to be used for efficient contact tracing during an FMD outbreak. This thesis reveals several interesting findings. Firstly, the increased understanding of strain-specific transmission characteristics of Streptococcus agalactiae. One of the observed strains (ST103) showed significant and consistent spatial clustering of its cases among Danish dairy cattle herds in 2009–2011. Secondly, the network analysis of cattle movements and affiliations with veterinary practices showed that veterinary practices were exclusively associated with transmission of ST103 of Streptococcus agalactiae. Contrastingly, movement networks appeared to be important for all the three predominant bacterial strains (ST1, ST23 and ST103). Fourthly, the new extended approach that allows estimation of the whole transmission tree at once was proposed and tested for the Darlington cluster within the 2001 FMD UK epidemic. Finally, in chapter 6, it was shown that mathematical modelling did not suggest any advantages of ensuring smaller delays in the post-silent control of FMD-like pathogens.