Mathematical models have been used to capture the behaviour of biological systems, from low-level biochemical reactions to multi-scale whole-organ models. Models are typically based on experimentally-derived data, attempting to reproduce the observed behaviour through mathematical constructs, e.g. using Ordinary Differential Equations (ODEs) for spatially-homogeneous systems. These models are developed and published as mathematical equations, yet are of such complexity that they necessitate computational simulation. This computational model development is often performed in an ad hoc fashion by modellers who lack extensive software engineering experience, resulting in brittle, inefficient model code that is hard to extend and reuse. Several Domain Specific Languages (DSLs) exist to aid capturing such biological models, including CellML and SBML; however these DSLs are designed to facilitate model curation rather than simplify model development. We present research into the application of techniques from software engineering to this domain; starting with the design, development and implementation of a DSL, termed Ode, to aid the creation of ODE-based biological models. This introduces features beneficial to model development, such as model verification and reproducible results. We compare and contrast model development to large-scale software development, focussing on extensibility and reuse. This work results in a module system that enables the independent construction and combination of model components. We further investigate the use of software engineering processes and patterns to develop complex modular cardiac models. Model simulation is increasingly computationally demanding, thus models are often created in complex low-level languages such as C/C++. We introduce a highly-efficient, optimising native-code compiler for Ode that generates custom, model-specific simulation code and allows use of our structured modelling features without degrading performance. Finally, in certain contexts the stochastic nature of biological systems becomes relevant. We introduce stochastic constructs to the Ode DSL that enable models to use Stochastic Differential Equations (SDEs), the Stochastic Simulation Algorithm (SSA), and hybrid methods. These use our native-code implementation and demonstrate highly-efficient stochastic simulation, beneficial as stochastic simulation is highly computationally intensive. We introduce a further DSL to model ion channels declaratively, demonstrating the benefits of DSLs in the biological domain. This thesis demonstrates the application of software engineering methodologies, and in particular DSLs, to facilitate the development of both deterministic and stochastic biological models. We demonstrate their benefits with several features that enable the construction of large-scale, reusable and extensible models. This is accomplished whilst providing efficient simulation, creating new opportunities for biological model development, investigation and experimentation.

Studies of avian navigation are making increasing use of miniature Global Positioning Satellite devices, to regularly record the position of birds in flight with high spatial and temporal resolution. I suggest a novel approach to analysing the data sets pro- duced in these experiments, focussing on studies of the domesticated homing pigeon (Columba Livia) in the local, familiar area. Using Gaussian processes and Bayesian inference as a mathematical foundation I develop and apply a statistical model to make quantitative predictions of homing pigeon flight paths. Using this model I show that pigeons, when released repeatedly from the same site, learn and follow a habitual route back to their home loft. The model reveals the rate of route learning and provides a quantitative estimate of the habitual route complete with associated spatio-temporal covariance. Furthermore I show that this habitual route is best described by a sequence of isolated waypoints rather than as a continuous path, and that these waypoints are preferentially found in certain terrain types, being especially rare within urban and forested environments. As a corollary I demonstrate an extension of the flight path model to simulate ex- periments where pigeons are released in pairs, and show that this can account for observed large scale patterns in such experiments based only on the individual birds’ previous behaviour in solo flights, making a successful quantitative prediction of the critical value associated with a non-linear behavioural transition.

This work concerns itself with understanding the organisation of cellular immune responses to three major human pathogens - HIV, CMV and Hepatitis C (HCV). Each was studied to form three projects, each undertaken with a different approach - arrived at independently - and largely owing their origins to opportunity and circumstance as much as design. Each project led to exploration of a particular aspect of T-cell phenotype (that is the expression of particular molecular markers on T-cells) and its’ broader biological significance. I found that T-cell phenotype was strongly linked to the magnitude of T-cell responses (CMV) and the ability of T-cells to control infection (HIV). Finally I explored the significance of expression of a molecule known as CD161 on the surface of HCV specific CD8+ T-cells, indicating a phenotype of T-cell that may not follow the ‘normal rules’ applicable to T-cells in general.

Capillaries in tumours are often severely buckled (in a plane perpendicular to the axis) and / or chaotic in their direction. We develop a model of these phenomena using nonlinear solid mechanics. Our model focusses on the immediate surrounding of a capillary. The vessel and surrounding tissue are modelled as concentric annulii. The growth is dependent on the concentration of a nutrient (oxygen) diffusing from the vessel into the tumour interstitium. The stress is modelled using a multiplicative decomposition of the deformation gradient F=F_e F_g. The stress is determined by substituting the elastic deformation gradient F_e (which gives the deformation gradient from the hypothetical configuration to the current configuration) into a hyperelastic constitutive model as per classical solid mechanics. We use a Blatz-Ko model, parameterised using uniaxial compression experiments. The entire system is in quasi-static equilibrium, with the divergence of the stress tensor equal to zero. We determine the onset of buckling using a linear stability analysis. We then investigate the postbuckling behaviour by introducing higher order perturbations in the deformation and growth before using the Fredholm Alternative to obtain the magnitude of the buckle. Our results demonstrate that the growth-induced stresses are sufficient for the capillary to buckle in the absence of external loading and / or constraints. Planar buckling usually occurs after 2-5 times the cellular proliferation timescale. Buckles with axial variation almost always go unstable after planar buckles. Buckles of fine wavelength are initially preferred by the system, but over time buckles of large wavelength become energetically more favourable. The tumoural hoop stress T_{ThetaTheta} is the most invariant (Eulerian) variable at the time of buckling: it is typically of the order of the tumoural Young's Modulus when this occurs.

Tissue engineering has great potential as a method for replacing or repairing lost or damaged tissue. However, progress in the field to date has been limited, with only a few clinical successes despite active research covering a wide range of cell types and experimental approaches. Mathematical modelling can complement experiments and help improve understanding of the inherently complex tissue engineering systems, providing an alternative perspective in a more cost- and time-efficient manner. This thesis focusses on one particular experimental setup, a hollow fibre membrane bioreactor (HFMB). We develop a suite of mathematical models which consider the fluid flow, solute transport, and cell yield and distribution within a HFMB, each relevant to a different setup which could be implemented experimentally. In each case, the governing equations are obtained by taking the appropriate limit of a generalised multiphase model, based on porous flow mixture theory. These equations are then reduced as far as possible, through exploitation of the small aspect ratio of the bioreactor and by considering suitable parameter limits in the subsequent asymptotic analysis. The reduced systems are then either solved numerically or, if possible, analytically. In this way we not only aim to illustrate typical behaviours of each system in turn, but also highlight the dependence of results on key experimentally controllable parameter values in an analytically tractable and transparent manner. Due to the flexibility of the modelling approach, the models we present can readily be adapted to specific experimental conditions given appropriate data and, once validated, be used to inform and direct future experiments.

A validated model of water transport in the cerebral environment is both an ambitious and timely task; many brain diseases relate to imbalances in water regulation. From tumours to strokes, chronic or acute, transport of fluid in the brain plays a crucial role. The importance and complexity of the brain, together with the range of unmet clinical needs that are connected with this organ,make the current research a high-priority. One of the most paradoxical cerebral conditions, hydrocephalus, serves as an excellent metric for judging the success of anymodel developed. In particular, normal pressure hydrocephalus (NPH) is a paradoxical condition with no known cure and existing treatments display unacceptably high failure rates. NPH is considered to be a disease of old age, and like many such diseases, it is related to a change in the transport of fluid in the cerebral environment. This complex system ranges from organ-level transport to cellular membrane channels such as aquaporins; through integrating it in a novel mathematical framework, we suggest that the underlying logic of treatment methods may be misleading. By modelling the transport of cerebrospinal fluid (CSF) between the ventricular system, cerebral tissue and blood networks, we find that changes to the biophysical properties of the brain (rather than structural changes such as aqueduct obstruction) are capable of producing clinically relevant ventriculomegaly in the absence of any obstruction to CSF flowthrough the ventricular system. Specifically, the combination of increased leakiness and compliance of the capillary bed leads to the development of enlarged ventricles with a normal ventricular pressure, replicating clinical features of the presentation of NPH. These results, while needing experimental validation, imply that treatment methods like shunting, that are focussed on structural manipulation, may continue to fail at unacceptably high rates.

The homologous recombination (HR) pathway contributes to genome integrity by mediating double strand break (DSB) repair using a homologous DNA sequence as a template. In mammals Rad51 and Brca2 are molecules central to this process. Little is known about HR repair in Dictyostelium. However, research previously conducted on DSB repair using this organism has shown that DSB repair pathways are highly conserved when compared to humans. This encouraged study of HR in this organism. In this study, through a bioinformatics search I have identified putative orthologues of most human HR proteins and most interestingly of BRCA2, which cannot be found in other lower eukaryotes used as models for DSB repair, such as the budding yeast S.cerevisiae. Brcp, the Dictyostelium BRCA2 ortholog, shows similar domain structure when compared to BRCA2-related proteins identified in other organisms. To verify the implication of HR proteins in DSB repair, I developed a method to monitor recruitment of DNA repair proteins on chromatin upon DSB induction. Findings of this study suggest that both Brcp and Rad51 get recruited to chromatin upon DSB induction and are therefore implicated in DSB repair in Dictyostelium. To further study Brcp function and based on findings suggesting that disruption of brcp might be lethal, I developed a novel system for specific and conditional depletion of endogenous Dictyostelium proteins. Utilizing this system, I conducted phenotypic studies in a strain depleted of Brcp to examine its role in DNA repair. Overall this study shows that the HR pathway in Dictyostelium shows great similarity to vertebrates, making Dictyostelium an appealing model for the study of DSB repair and specifically HR.

Cardiovascular disease is the primary cause of death globally. Although this group encompasses a heterogeneous range of conditions, many of these diseases are associated with abnormalities in the cardiac electrical propagation. In these conditions, structural abnormalities in the form of scars and fibrotic tissue are known to play an important role, leading to a high individual variability in the exact disease mechanisms. Because of this, clinical interventions such as ablation therapy and CRT that work by modifying the electrical propagation should ideally be optimized on a patient specific basis. As a tool for optimizing these interventions, computational modelling and simulation of the heart have become increasingly important. However, in order to construct these models, a crucial step is the estimation of tissue conduction properties, which have a profound impact on the cardiac activation sequence predicted by simulations. Information about the conduction properties of the cardiac tissue can be gained from electrophysiological data, obtained using electroanatomical mapping systems. However, as in other clinical modalities, electrophysiological data are often sparse and noisy, and this results in high levels of uncertainty in the estimated quantities. In this dissertation, we develop a methodology based on Bayesian inference, together with a computationally efficient model of electrical propagation to achieve two main aims: 1) to quantify values and associated uncertainty for different tissue conduction properties inferred from electroanatomical data, and 2) to design strategies to optimise the location and number of measurements required to maximise information and reduce uncertainty. The methodology is validated in several studies performed using simulated data obtained from image-based ventricular models, including realistic fibre orientation and conduction heterogeneities. Subsequently, by using the developed methodology to investigate how the uncertainty decreases in response to added measurements, we derive an a priori index for placing electrophysiological measurements in order to optimise the information content of the collected data. Results show that the derived index has a clear benefit in minimising the uncertainty of inferred conduction properties compared to a random distribution of measurements, suggesting that the methodology presented in this dissertation provides an important step towards improving the quality of the spatiotemporal information obtained using electroanatomical mapping.

I develop social evolution theory to study the evolution of cooperation as follows: (1) Many organisms undergo a dispersal phase prior to breeding; I demonstrate that knowing ones dispersal status aids the evolution of helping (by non-dispersers) and harming (by dispersers). (2) Policing driven by group-benefits may be selected to enforce cooperation in human and animal societies. I extend existing theory to show that policing may be harder to evolve that previously thought, but that it is maintained more readily than it evolves. (3) Archeological and anthropological evidence suggests that warfare was prevalent during our evolution. I show that, contrary to previous suggestions, between-group competition can favour any social behaviour (pro-social or anti-social) so long as it helps the group compete, and that such traits can be altruistic or mutually beneficial. (4) Reproductive leveling is analogous to policing; in the human literature there is doubt as to whether it can evolve. I extend my previous work to consider the coevolution of culturally and genetically inherited traits for reproductive leveling and selfishness. I find that cooperation can evolve between non-kin if they share the same culture. (5) Monogamy is thought to favour the evolution of cooperative breeding. I show that in the simplest case, because of the cost of competition between non-dispersing siblings, the level of promiscuity has little or no effect on the evolution of cooperation. (6) Spatial structure (limited dispersal) is thought to favour the evolution of inter-specific mutualisms as it aligns the partners’ interests. I consider the case of plant-fungi mutualisms and show that spatial structure can disfavour cooperation if it limits the potential fungal partners available to the plant.

Novel infectious diseases in humans are of great concern to public health authorities and researchers in epidemiology. Zoonotic pathogens in particular have the potential to cause epidemics without any or little warning. In this thesis, I investigate evolutionary and environmental conditions, and the interactions between both, which facilitate the zoonotic emergence of novel pathogens. I start with a list of the mechanisms and processes which might influence a zoonotic emergence, and identify some unsolved problems. I address these with multiple, theoretical models. First, I use a village-city model with different adaptation scenarios to examine the influence of spatial heterogeneity on the emergence process. I derive general analytical results for the statistical properties of emergence events, including the probability distribution of outbreak sizes. My results suggest that, for typical connection strengths between communities, spatial heterogeneity has only a weak effect on outbreak size distributions, and on the risk of emergence per introduction. Next, I extend the research on environmental conditions by looking at pathogen specialisation in multi-host systems. I derive threshold connectivities for which generalist pathogens, which infect multiple species and might therefore be more dangerous to cross into the human species, can sustain transmission and are not dominated by specialists, which can only cause sustained transmission chains in a single host species, but are able to cause emergences with little warning. My third research chapter is interested in the effect of the loss of biodiversity. I analytically derive expected prevalences for fast growing and slow growing species. If fast growing species tend to perform better in degraded environments, my analytical results suggest that the overall prevalence level of infectious diseases will rise as environments degrade, which facilitates the chance of zoonotic jumps. In my last research chapter, I examine the actual impact of a novel, emerging infectious disease. I use data from the recent `Swine flu' epidemic in England to estimate epidemiological parameters of the infectious agent. My results suggest that the majority of infected cases showed no or only mild symptoms. This reveals that more data than just the estimated number of cases are necessary to fully evaluate the danger of a possible zoonotic, emerging infectious disease. I conclude by discussing my results and the implications which these might have.