Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Sequential antibiotic therapy in the laboratory and in the patient

Laboratory experiments suggest that rapid cycling of antibiotics during the course of treatment could successfully counter resistance evolution. Drugs involving collateral sensitivity could be particularly suitable for such therapies. However, the environmental conditions in vivo differ from those in vitro. One key difference is that drugs can be switched abruptly in the laboratory, while in the patient, pharmacokinetic processes lead to changing antibiotic concentrations including periods of dose overlaps from consecutive administrations. During such overlap phases, drug–drug interactions may affect the evolutionary dynamics. To address the gap between the laboratory and potential clinical applications, we set up two models for comparison—a ‘laboratory model’ and a pharmacokinetic-pharmacodynamic ‘patient model’. The analysis shows that in the laboratory, the most rapid cycling suppresses the bacterial population always at least as well as other regimens. For patient treatment, however, a little slower cycling can sometimes be preferable if the pharmacodynamic curve is steep or if drugs interact antagonistically. When resistance is absent prior to treatment, collateral sensitivity brings no substantial benefit unless the cell division rate is low and drug cycling slow. By contrast, drug–drug interactions strongly influence the treatment efficiency of rapid regimens, demonstrating their importance for the optimal choice of drug pairs

Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis:A Brief Review

Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases, mortality. Understanding the biological mechanisms behind the progression of the disease, as well as developing new methods for quantitative predictions of disease progression in the presence/absence of various therapies is important for the success of therapeutic approaches. The aim of this study is to review various quantitative predictive modelling approaches for understanding rheumatoid arthritis. To this end, we start by briefly discussing the biology of this disease and some current treatment approaches, as well as emphasising some of the open problems in the field. Then, we review various mathematical mechanistic models derived to address some of these open problems. We discuss models that investigate the biological mechanisms behind the progression of the disease, as well as pharmacokinetic and pharmacodynamic models for various drug therapies. Furthermore, we highlight models aimed at optimising the costs of the treatments while taking into consideration the evolution of the disease and potential complications.Publisher PDFPeer reviewe

Stochastic modelling of eukaryotic cell cycle

Stochastic models are developed to capture the inherent stochasticity of the biochemical networks associated to many biological processes. The objective of the present thesis is to present a detailed picture of stochastic approach for the mathematical modeling of eukaryotic cell cycle, to demonstrate an important application of such model in chemotherapy and to present a methodology for selecting the model parameters. The stochastic cell cycle model, developed using stochastic chemical kinetics approach, leads to the formation of an infinite dimensional differential equation in probabilities of system being in a specific state. Using Monte Carlo simulations of this model, dynamics of populations of eukaryotic cells such as yeasts or mammalian cells are obtained. Simulations are stochastic in nature and therefore exhibit variability among cells that is similar to the variability observed in natural populations. The model’s capability to predict heterogeneities in cell populations is used as a basis to implement it in a chemotherapic modeling framework to demonstrate how the model can be used to assist in the drug development stage by investigating drug administration strategies that can have different killing effect on cancer cells and healthy cells. Finally, basic cell cycle model is refined in a systematic way to make it more suitable for describing the population characteristics of budding yeast. Selection of model parameters using an evolutionary optimization strategy referred to as insilico evolution is described. The benefits of this approach lie in the fact that it generates an initial guess of reasonable set of parameters which in turn can be used in the least squares fitting of model to the steady state distributions obtained from flow cytometry measurements. The Insilco evolution algorithm serves as a tool for sensitivity analysis of the model parameters and leads to a synergistic approach of model and experiments guiding each other. To conclude, the stochastic model based on single cell kinetics will be useful for predicting the population distribution on whole organism level. Such models find applications in wide areas of biological and biomedical applications. Evolutionary optimization strategies can be used in parameter estimation methods based on steady state distributions

Pharmacokinetics and Pharmacodynamics of the Reverse Transcriptase Inhibitor Tenofovir and Prophylactic Efficacy against HIV-1 Infection

Antiviral pre-exposure prophylaxis (PrEP) through daily drug administration can protect healthy individuals from HIV-1 infection. While PrEP was recently approved by the FDA, the potential long-term consequences of PrEP implementation remain entirely unclear. The aim of this study is to predict the efficacy of different prophylactic strategies with the pro-drug tenofovir- disoproxil-fumarate (TDF) and to assess the sensitivity towards timing- and mode of TDF administration (daily- vs. single dose), adherence and the number of transmitted viruses. We developed a pharmacokinetic model for TDF and its active anabolite tenofovir-diphosphate (TFV-DP) and validated it with data from 4 different trials, including 4 distinct dosing regimes. Pharmacokinetics were coupled to an HIV model and viral decay following TDF mono-therapy was predicted, consistent with available data. Subsequently, a stochastic approach was used to estimate the % infections prevented by (i) daily TDF-based PrEP, (ii) one week TDF started either shortly before, or -after viral exposure and (iii) a single dose oral TDF before viral challenge (sd-PrEP). Analytical solutions were derived to assess the relation between intracellular TFV-DP concentrations and prophylactic efficacy. The predicted efficacy of TDF was limited by a slow accumulation of active compound (TFV-DP) and variable TFV-DP half-life and decreased with increasing numbers of transmitted viruses. Once daily TDF-based PrEP yielded 80% protection, if at least 40% of pills were taken. Sd-PrEP with 300 mg or 600 mg TDF could prevent 50% infections, when given at least before virus exposure. The efficacy dropped to 10%, when given 1 h before 24 h exposure. Efficacy could not be increased with increasing dosage or prolonged administration. Post-exposure prophylaxis poorly prevented infection. The use of drugs that accumulate more rapidly, or local application of tenofovir gel may overcome the need for drug administration long before virus exposure

Modelling heterogeneous intracellular networks at the cellular scale

Cell function relies on the coordinated action of heterogeneous interconnected networks of biomolecules. Mathematical models help us explore the dynamics and behaviour of these intracellular networks in greater detail. Models of increasing scale and complexity are being developed to probe cellular processes, often necessitating the use of several types of mathematical representation in hybrid models. Here we review recent efforts to incorporate the influences of stochasticity and spatial heterogeneity into cellular level models, ranging from abstract coarse-grained representations to large-scale hybrid models comprising thousands of biological components. We discuss the key challenges involved in, and recent mathematical advances enabling the development and analysis of mathematical models of complex intracellular processes

An Analysis of Genetic Diversity and Inbreeding in Wuchereria bancrofti: Implications for the Spread and Detection of Drug Resistance

Estimates of genetic diversity in helminth infections of humans often have to rely on genotyping (immature) parasite transmission stages instead of adult worms. Here we analyse the results of one such study investigating a single polymorphic locus (a change at position 200 of the β-tubulin gene) in microfilariae of the lymphatic filarial parasite Wuchereria bancrofti. The presence of this genetic change has been implicated in benzimidazole resistance in parasitic nematodes of farmed ruminants. Microfilariae were obtained from patients of three West African villages, two of which were sampled prior to the introduction of mass drug administration. An individual-based stochastic model was developed showing that a wide range of allele frequencies in the adult worm populations could have generated the observed microfilarial genetic diversity. This suggests that appropriate theoretical null models are required in order to interpret studies that genotype transmission stages. Wright's hierarchical F-statistic was used to investigate the population structure in W. bancrofti microfilariae and showed significant deficiency of heterozygotes compared to the Hardy-Weinberg equilibrium; this may be partially caused by a high degree of parasite genetic differentiation between hosts. Studies seeking to quantify accurately the genetic diversity of helminth populations by analysing transmission stages should increase their sample size to account for the variability in allele frequency between different parasite life-stages. Helminth genetic differentiation between hosts and non-random mating will also increase the number of hosts (and the number of samples per host) that need to be genotyped, and could enhance the rate of spread of anthelmintic resistance

Mathematical Modeling of Malaria: Theories of Malaria Elimination

This dissertation describes the development and application of a new mathematical model for simulating the progression of Plasmodium falciparum infections in individuals with no malarial acquired immunity. The model allows for stochastic simulation of asexual and sexual parasitemias as well as the onset of fever and human to mosquito infectivity on a daily time scale. The model components for the asexual and sexual stages were developed elsewhere but are here extended to allow for simulation of the full range of dynamics observed in a subset of malaria therapy patients. As a first application of the model, I calculate the human component of malarial R0, the basic reproductive number. I then compare this value to those from three other models and describe how this quantity can be used to model malaria transmission. The second application of the model incorporates the effects of drug treatment on progression of infection by utilizing modeled pharmacokinetic and pharmacodynamic properties of a variety of antimalarials. I utilize a stage specific proportional killing model for sexual stages, informed from recent in vitro data. The relationship of effect sizes to treatment coverage and type of treatment in both early and late treatment seeking settings is calculated. In the third chapter, I consider the economic and epidemiological ramifications of antimalarial and rapid diagnostic subsidization for malaria control. For the epidemiological modeling I utilize a semi-mechanistic model of the spread of drug resistance parameterized from historical malaria mortality data; for the economic model I consider the effect of rapid diagnostics on the intensive and extensive margins of antibiotics and antimalarials, as well as the benefits to improved targeting of both. I find that rapid diagnostic testing is justified given our baseline assumptions for areas with low proportions of malarious individuals among all treatment-seekers, but that caution is necessary before deployment worldwide. For antimalarial subsidization, we find that this is a cost-effective method for reducing mortality in developing countries, though efforts to delay the onset and slow the spread of resistance are urgently needed

Recipes for calibration and validation of agent-based models in cancer biomedicine

Computational models and simulations are not just appealing because of their intrinsic characteristics across spatiotemporal scales, scalability, and predictive power, but also because the set of problems in cancer biomedicine that can be addressed computationally exceeds the set of those amenable to analytical solutions. Agent-based models and simulations are especially interesting candidates among computational modelling strategies in cancer research due to their capabilities to replicate realistic local and global interaction dynamics at a convenient and relevant scale. Yet, the absence of methods to validate the consistency of the results across scales can hinder adoption by turning fine-tuned models into black boxes. This review compiles relevant literature to explore strategies to leverage high-fidelity simulations of multi-scale, or multi-level, cancer models with a focus on validation approached as simulation calibration. We argue that simulation calibration goes beyond parameter optimization by embedding informative priors to generate plausible parameter configurations across multiple dimensions