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.

Cerebrospinal fluid (CSF) fills a system of cavities at the centre of the brain, known as ventricles, and the subarachnoid space surrounding the brain and the spinal cord. In addition, CSF is in free communication with the interstitial fluid of the brain tissue. Disturbances in CSF dynamics can lead to diseases that cause severe brain damage or even death. So-called infusion tests are frequently performed in the diagnosis of such diseases. In this type of test, changes in average CSF pressure are related to changes in CSF volume through infusion of known volumes of additional fluid. Traditionally, infusion tests are analysed with single compartment models, which treat all CSF as part of one compartment and balance fluid inflow, outflow and storage through a single ordinary differential equation. Poroelastic models of the brain, on the other hand, have been used to simulate spatial changes with disease, particularly of the ventricle size, on larger time scales of days, weeks or months. Wirth and Sobey (2008) developed a two-fluid poroelastic model of the brain in which CSF pressure pulsations are linked to arterial blood pressure pulsations. In this thesis, this model is developed further and simulation results are compared to clinical data. At first, the functional form of the compliance, which governs the storage of CSF in single compartment models, is examined by comparison of two different compliance models with clinical data. The derivations of a single-fluid and a two-fluid poroelastic model of the brain in spherical symmetry are laid out in detail and some of the parameters are related to the compliance functions considered earlier. The finite element implementation of the two-fluid model is described and finally simulation results of the average CSF pressure response and the pressure pulsations are compared to clinical data.

Multiscale mathematical modelling is one of the major driving forces behind the systems biology revolution. The inherently interdisciplinary nature of its study and the multiple spatial and temporal scales which characterise its dynamics make cell migration an ideal candidate for a systems biology approach. Due to its ease of analysis and its compatibility with the type of data available, phenomenological continuum modelling has long been the default framework adopted by the cell migration modelling community. However, in recent years, with increased computational power, complex, discrete, cell-level models, able to capture the detailed dynamics of experimental systems, have become more prevalent. These two modelling paradigms have complementary advantages and disadvantages. The challenge now is to combine these two seemingly disparate modelling regimes in order to exploit the benefits offered by each in a comprehensive, multiscale equivalence framework for modelling cell migration. The main aim of this thesis is to begin with an on-lattice, individual-based model and derive a continuum, population-based model which is equivalent to it in certain limits. For simple models this is relatively easy to achieve: beginning with a one-dimensional, discrete model of cell migration on a regular lattice we derive a partial differential equation for the evolution of cell density on the same domain. We are also able to simply incorporate various signal sensing dynamics into our fledgling equivalence framework. However, as we begin to incorporate more complex model attributes such as cell proliferation/death, signalling dynamics and domain growth we find that deriving an equivalent continuum model requires some innovative mathematics. The same is true when considering a non-uniform domain discretisation in the one-dimensional model and when determining appropriate domain discretisations in higher dimensions. Higher-dimensional simulations of individual-based models bring with them their own computational challenges. Increased lattice sites in order to maintain spatial resolution and increased cell numbers in order to maintain consistent densities lead to dramatic reductions in simulation speeds. We consider a variety of methods to increase the efficiency of our simulations and derive novel acceleration techniques which can be applied to general reaction systems but are especially useful for our spatially extended cell migration algorithms. The incorporation of domain growth in higher dimensions is the final hurdle we clear on our way to constructing a complex discrete-continuum modelling framework capable of representing signal-mediated cell migration on growing (possibly non-standard) domains in multiple dimensions.