Phylogenetic models generally assume a homogeneous, time reversible, stationary process. These assumptions are often violated by the real, far more complex, evolutionary process. This thesis is centered on non-homogeneous, lineage-specific, properties of molecular sequences. It consist several related but independent studies. LineageSpecificSeqgen, an extension to the Seq-Gen program, which allows generation of sequences with changes in the proportion of variable sites, is introduced. This program is then used in a simulation study showing that changes in the proportion of variable sites can hinder tree estimation accuracy, and that tree reconstruction under the best-fit model chosen using a relative test can result in a wrong tree. In this case, the less commonly used absolute model-fit was a better predictor of tree estimation accuracy. This study found that increased taxon sampling of lineages that have undergone a change in the proportion of variable sites was critical for accurate tree reconstruction and that, in contrast to some earlier findings, the accuracy of maximum parsimony is adversely affected by such changes. This thesis also addresses the well-known long-branch attraction artifact. A nonparametric bootstrap test to identify changes in the substitution process is introduced, validated, and applied to the case of Microsporidia, a highly reduced intracellular parasite. Microsporidia was first thought to be an early branching eukaryote, but is now believed to be sister to, or included within, fungi. Its apparent basal eukaryote position is considered a result of long-branch attraction due to an elevated evolutionary rate in the microsporidian lineage. This study shows that long-branch estimates and basal positioning of Microsporidia both correlate with increased proportions of radical substitutions in the microsporidian lineage. In simulated data, such increased proportions of radical substitutions leads to erroneous long-branch estimates. These results suggest that the long microsporidian branch is likely to be a result of an increased proportion of radical substitutions on that branch, rather than increased evolutionary rate per se. The focus of the last study is the intriguing case of Mesostigma, a fresh water green alga for which contradicting phylogenetic relationships were inferred. While some studies placed Mesostigma within the Streptophyta lineage (which includes land plants), others placed it as the deepest green algae divergence. This basal positioning is regarded as a result of long-branch attraction due to poor taxon sampling. Reinvestigation of a 13- taxon mitochondrial amino acid dataset and a sub-dataset of 8 taxa reveals that site sampling, and in particular the treatment of missing data, is just as important a factor for accurate tree reconstruction as taxon sampling. This study identifies a difficulty in recreating the long-branch attraction observed for the 8-taxon dataset in simulated data. The cause is likely to be the smaller number of amino acid characters per site in simulated data compared to real data, highlighting the fact that there are properties of the evolutionary process that are yet to be accurately modeled.

This thesis addresses chemotherapy-induced peripheral neuropathy (CIPN)- a form of pain sensation and a prevalent dose-limiting side-effect of several chemotherapy agents such as vincristine, paclitaxel, and oxaliplatin. These agents are used for treating various cancers such as leukemia, brain tumor, lung cancer. Peripheral neuropathy is a numbing, tingling, and burning sensation felt in the palms and feet, which occurs due to damage to neurons (nerve cells). Prolonged CIPN can impact the quality of life of cancer patients. Occasionally, severe CIPN can result in termination of chemotherapy treatment altogether. Currently, there are no established strategies for treating CIPN due to a lack of understanding of its mechanisms. Moreover, different patients react differently to the same treatment; a subgroup of patient population may never experience CIPN, while another may experience severe CIPN for the same dose. In addition, there are no established strategies for predicting CIPN either. This thesis addresses both prediction and mechanisms of CIPN.<br><br>The following paragraphs reflect the organization of this thesis. Each paragraph introduces a research problem, the approaches taken to investigate it, and states the key results.<br><br>First, a metabolomics-based approach was used to investigate CIPN prediction. Blood samples of pediatric leukemic cancer patients who underwent treatment with a chemotherapy agent - vincristine were provided. These blood samples were analyzed at different treatment time points using mass spectrometry to obtain the metabolite profiles. Machine learning was then employed to identify specific metabolites that can predict overall susceptibility to peripheral neuropathy in those patients at specific treatment time points. Subsequently, selected metabolites were used to train machine learning models to predict neuropathy susceptibility. Finally, the models were deployed into an open-source interactive tool- <i>VIPNp</i>- that can be used by researchers to predict CIPN in new pediatric leukemic cancer patients.<br><br>Second, the focus was shifted to the pathophysiology of pain and the pain-sensing neuron; specifically: (i) investigating pain sensation mutations and the dynamics of the pain-sensing neuron, and (ii) exploring chemotherapy-induced peripheral neuropathy mechanisms. <br><br>While pain is a common experience, genetic mutations in individuals can alter their experience of pain, if any at all (certain mutations yield individuals insensitive to pain). Despite its ubiquity, we do not have a complete understanding of the onset and/or mechanisms of pain sensation. Pain sensation can be broadly classified into three types: (i) nociceptive, (ii) neuropathic, and (iii) inflammatory. Nociceptive pain arises due to a noxious external stimulus (e.g., upon touching a hot object). Neuropathic pain (which is felt as a side-effect of the aforementioned chemotherapy agents) is the numbing and tingling sensation due to nerve damage. Inflammatory pain occurs due to damage to internal tissues. Pain in any form can be characterized in terms of electrical signaling by the pain-sensing neuron. Signal transmission regarding pain occurs through generation of an electrical signal called the action potential- a peak in neuron membrane potential. Excessive firing of action potentials by a pain-sensing neuron indicates pain of a specific form and intensity. In order to investigate this electrical signaling, a mathematical modeling approach was employed. The neuron membrane was assumed to be an electrical circuit and the potential across the membrane was modeled in terms of the sodium and potassium ions flowing across it via voltage-gated sodium and potassium channels, respectively. Generation of a single action potential followed by a resting state corresponds to a normal state, whereas periodic firing of action potentials (an oscillatory state) corresponds to pain of some form and intensity <i>in vitro</i>. Therefore, an investigation into the switch from a resting state to an oscillatory state was proposed. A bifurcation theory approach (generally useful in exploring changes in qualitative behavior of a model) was used to explore possible bifurcations to explain this switch. Firstly, genetic mutations that can shift the pain sensation threshold in the pain-sensing neuron were explored. The detected bifurcation points were found to be sensitive to specific sodium channels’ model parameters, implying sodium channels’ sensitivity towards the pain sensation threshold. This was corroborated by experimental evidence in existing literature. Secondly, a theoretical analysis was performed to explore all possible bifurcations that can explain the dynamics of this pain-sensing neuron model. The mathematical modeling simulations revealed a mixture of small amplitude and large amplitude membrane potential oscillations (mixed-mode oscillations) for specific parameter values. The onset and disappearance of the oscillations were investigated. Model simulations further demonstrated that the mixed-mode oscillations solutions belonged to Farey sequences. Furthermore, regions of bistability- where stable steady state and periodic solutions coexisted- were explored. Additionally, chaotic behavior was observed for specific model parameters.<br><br>Finally, this thesis investigated the role of voltage-gated ion channels in inducing CIPN using the same mathematical model. Repetitive firing of action potentials in the absence of any external stimulus was used as an indicator of peripheral neuropathy. Bifurcation analysis revealed that specific sodium and potassium conductances can induce repetitive firing without any external stimulus. The findings were supplemented by recording the firing rate of a sensory neuron culture. Next, a chemotherapy agent - paclitaxel, was introduced in the model to investigate its potential effects on the firing behavior. It was seen that a medium dose of paclitaxel increased repetitive firing. This was supported by the firing rate recordings of the sensory neuron culture.<br><br>In summary, this thesis presents a prediction strategy for CIPN. Moreover, it presents a bifurcation theory-based framework that can be used to investigate pain sensation, in particular, genetic mutations related to pain sensation and chemotherapy-induced peripheral neuropathy. This framework can be used to find potential voltage-gated ion channels that can be targeted to control the pain sensation threshold in individuals, and can be extended to investigate various degeneracies in CIPN mechanisms to find therapeutic cures for it.

Living cells are made up of networks of interacting genes, proteins and other bio-molecules. Simple interactions between network components in forms of feedback regulations can lead to complex collective dynamics. A key task in cell biology is to gain a thorough understanding of the dynamics of intracellular systems and processes. In this thesis, a combined approach of mathematical modelling, computational simulation and analytical techniques, has been used to obtain a deeper insight into the dynamical aspects of a variety of feedback systems commonly encountered in cells. These systems range from model system with detailed available molecular knowledge to general regulatory motifs with varying network structures. Deterministic as well as stochastic modelling techniques have been employed, depending primarily on the specific questions asked. The first part of the thesis focuses on dissecting the principles behind the regulatory design of the Tryptophan Operon system in Escherichia coli. It has evolved three negative feedback loops, namely repression, attenuation and enzyme inhibition, as core regulator mechanisms to control the intracellular level of tryptophan amino acid, which is taken up for protein synthesis. Despite extensive experimental knowledge, the roles of these seemingly redundant loops remain unclear from a dynamical point of view. We aim to understand why three loops, rather than one, have evolved. Using a large-scale perturbation/response analysis through modelling and simulations and novel metrics for transient dynamics quantification, it has been revealed that the multiple negative feedback loops employed by the tryptophan operon are not redundant. In fact, they have evolved to concertedly give rise to a much more efficient, adaptive and stable system, than any single mechanism would provide. Since even the full topology of feedback interactions within a network is insufficient to determine its behavioural dynamics, other factors underlying feedback loops must be characterised to better predict system dynamics. In the second part of the thesis, we aim to derive these factors and explore how they shape system dynamics. We develop an analytical approach for stability and bifurcation analysis and apply it to class of feedback systems commonly encountered in cells. Our analysis showed that the strength and the Hill coefficient of a feedback loop play key role in determining the dynamics of the system carrying the loop. Not only that, the position of the loop was also found to be crucial in this decision. The analytical method we developed also facilitates parameter sensitivity analysis in which we investigate how the production and degradation rates affect system dynamics. We find that these rates are quite different in the way they shape up system behaviour, with the degradation rates exhibiting a more intricate manner. We demonstrated that coupled-loop systems display greater complexity and a richer repertoire of behaviours in comparison with single-loop ones. Different combinations of the feedback strengths of individual loops give rise to different dynamical regimes. The final part of the thesis aims to understand the effects of molecular noise on dynamics of specific systems, in this case the Tryptophan Operon. We developed two stochastic models for the system and compared their predictions to those given by the deterministic model. By means of simulations, we have shown that noise can induce oscillatory behaviour. On the other hand, incorporating noise in an oscillatory system can alter the characteristics of oscillation by shifting the bifurcation point of certain parameters by a substantial amount. Measurement of fluctuations reveals that that noise at the transcript level is most significant while noise at the enzyme level is smallest. This study highlights that noise should not be neglected if we want to obtain a complete understanding of the dynamic behaviour of cells.

<p>Interleukin-15 (IL-15) is a cytokine that promotes maintenance and activation of cytotoxic immune cells. Therapeutic IL-15 stimulates these cells to fight cancer and chronic infections, such as Human Immunodeficiency Virus (HIV). Animal models of HIV have demonstrated that IL-15 agonists can suppress the virus, but this was transient and was not observed in all cohorts. We developed a mechanistic mathematical model of IL-15 therapy of HIV to explain these differences in efficacy and to explore solutions. First, the model was applied to evaluate mitigating factors, including immune regulation, viral escape, and drug tolerance, using Akaike Information Criterion.  We found that immune regulatory mechanisms could explain the viral rebound observed with continued IL-15 therapy. Next, the model was expanded to allow it to simultaneously explain both the transient viral suppression noted above and the lack of viral suppression observed in another animal cohort.  In this cohort, the model suggested that higher pre-treatment viral load came with higher activation of immune cells and a balancing regulatory inhibition of cytotoxicity. Finally, we conducted stability analysis at a range of IL-15 therapeutic strengths. While there was an ideal IL-15 strength, monotherapy could not maintain viral levels below what would clinically be considered to be safely controlled. Stable viral control in the model required the combination of IL-15 with blockade of key regulatory pathways. Immune therapy of complex diseases will likely require combinations of medicines that boost the immune response at multiple key points. Mathematical models like this can expedite development of these treatments.</p>

A metapopulation is defined as a set of potential local populations among which dispersal may occur. Metapopulation theory has grown rapidly in recent years, but much has focused on the mathematical properties of metapopulations rather than their relevance to real systems. Indeed, barring some notable exceptions, metapopulation theory remains largely untested in the field. This thesis investigates the importance of metapopulation structure in the ‘real world’, firstly by building additional realism into metapopulation models, and secondly through a 3-year field study of a real metapopulation system. The modelling analyses include discrete-and continuous-time models, and cover single species, host-parasitoid, and disease-host systems, with and without stochasticity. In all cases, metapopulation structure enhanced species persistence in time, and often allowed long-term continuance of otherwise non-persistent interactions. Spatial heterogeneity and patterning was evident whenever local populations were stochastic or deterministically unstable in isolation. In metapopulations, the latter case often gave rise to self-organising spatial patterns. These were composed of spiral wave fronts (or ‘arcs of infection’ in disease models) of different sizes, and were related to the stability characteristics of local populations as well as the dispersal rates. There was no evidence for self-organising spatial patterns in the host-parasitoid system studied in the field (the weevil Sitona discoideus and its braconid parasitoid Microctonus aethiopoides), and a new model for the interaction suggested that this is probably due to the strong host density-dependence and stabilising parasitism acting on local populations. Dispersal may be important because of very high mortality in dispersing weevils, which may be related to the scarcity of their host plant in the landscape. If this is the case, the model suggested that local weevil density may be sensitive to the area of crop grown. Stochastic models showed that species in suitably large metapopulations may persist for very long times at relatively low overall density and with very low incidence of density-dependence. This suggests that metapopulation processes may explain a general inability to detect density-dependence in many real populations, and may also play an important part in the persistence of rare species. For host-parasitoid metapopulation models, persistence often depended on the way in which they were initialised. Initial conditions corresponding to a biological control release were the least likely to persist, and the maximum host suppression observed in this case was 84%, as compared with 60% for the corresponding non-spatial models and >90% often observed in the field. Metapopulation structure also allowed persistence of ‘boom-bust’ disease models, although the dynamics of these were particularly dependent on assumptions about what happens to disease classes at very low densities. Models assuming infinitely divisible units of density, models incorporating a non-zero extinction threshold, and individual-based models all gave differing results in terms of disease persistence and rate of spatial spread. Fitting models to overall metapopulation dynamics often gave misleading results in terms of underlying local dynamics, emphasising the need to sample real populations at an appropriate scale when seeking to understand their behaviour.