Steven D. Webb

Modelling aspects of cancer dynamics : a review

Cancer is a complex disease in which a variety of factors interact over a wide range of spatial and temporal scales with huge datasets relating to the different scales available. However, these data do not always reveal the mechanisms underpinning the observed phenomena. In this paper, we explain why mathematics is a powerful tool for interpreting such data by presenting case studies that illustrate the types of insight that realistic theoretical models of solid tumour growth may yield. These range from discriminating between competing hypotheses for the formation of collagenous capsules associated with benign tumours to predicting the most likely stimulus for protease production in early breast cancer. We will also illustrate the benefits that may result when experimentalists and theoreticians collaborate by considering a novel anti-cancer therapy.

Chemotaxis: A Feedback-Based Computational Model Robustly Predicts Multiple Aspects of Real Cell Behaviour

A simple feedback model of chemotaxis explains how new pseudopods are made and how eukaryotic cells steer toward chemical gradients.

Modeling Cell Movement and Chemotaxis Using Pseudopod-Based Feedback

A computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis. An empirical pattern formation model, based on a system of nonlinear reaction-diffusion equations, is approximated on an evolving cell boundary using an arbitrary Lagrangian Eulerian surface finite element method (ALE-SFEM). The solution state is used to drive a mechanical model of the protrusive and retractive forces exerted on the cell boundary. Movement of the cell is achieved using a level set method. Results are presented for cell migration with and without chemotaxis. The simulated behavior is compared with experimental results of migrating Dictyostelium discoideum cells.

Alterations in proteolytic activity at low pH and its association with invasion: A theoretical model

The extracellular pH (pHe) of solid tumours is often lower than in normal tissues, with median pH values of about 7.0 in tumours and 7.5 in normal tissue. Despite this more acidic tumour microenvironment, non-invasive measurements of intracellular pH (pHi) have shown that the pHi of solid tumours is neutral or slightly alkaline compared to normal tissue (pHi 7.0–7.4). This gives rise to a reversed cellular pH gradient between tumours and normal tissue, which has been implicated in many aspects of tumour progression. One such area is tumour invasion: the incubation of tumour cells at low pH has been shown to induce more aggressive invasive behaviour in vitro. In this paper the authors use mathematical models to investigate whether altered proteolytic activity at low pH is responsible for the stimulation of a more metastatic phenotype. The authors examined the effect of culture pH on the secretion and activity of two different classes of proteinases: the metalloproteinases (MMPs), and the cysteine proteinases (such as cathepsin B). The modelling suggests that changes in MMP activity at low pH do not have significant effects on invasive behaviour. However, the model predicts that the levels of active-cathepsin B are significantly altered by acidic pH. This result suggests a critical role for the cysteine proteinases in tumour progression.

Transport of gabapentin by LAT1 (SLC7A5).

Gabapentin is used in the treatment of epilepsy and neuropathic pain. Gabapentin has high and saturable permeability across the BBB, but no mechanistic studies underpinning this process have been reported. The aim of the current study was to investigate the transport of gabapentin in a model of the BBB, identify the important drug transporter(s) and to use mathematical modelling to quantify the processes involved. A human brain endothelial cell line (hCMEC/D3) was utilised as an in-vitro model of the BBB. Uptake of radiolabeled gabapentin into cells in the presence of chemical inhibitors, siRNA or overexpressed drug transporters of interest was investigated. Gabapentin was demonstrated to be a LAT1 substrate in brain endothelial cells (LAT1-process; Km=530μM and Vmax=7039pmoles/million cells/min versus other-processes; Km=923μM and Vmax=3656pmoles/million cells/min) and in transfected HEK 293 LAT1 cells (LAT1-process; Km=217μM and Vmax=5192pmoles/million cells/min versus otherprocesses; Km=1546μM and Vmax=3375pmoles/million cells/min). At physiological concentrations of gabapentin, LAT1 mediated transport was 3 or ~10-fold higher than the other transport processes in the two systems, respectively, demonstrating clear selectivity for gabapentin. In-silico structural homology modelling confirmed that LAT1 could have the LeuT conserved fold and functions by the alternative access mechanism. Mathematical modelling of this mechanism revealed revised significance of Vmax and Km so that a low Km may not necessarily imply a high affinity transport process. Gabapentin was negative for OCT like transport and LAT2 activity in the hCMEC/D3 and OCT1 transfected cells. Our data shows that gabapentin is a substrate for the influx transporter LAT1 at therapeutic concentrations.

A Flexible Mathematical Model Platform for Studying Branching Networks: Experimentally Validated Using the Model Actinomycete, Streptomyces coelicolor

Branching networks are ubiquitous in nature and their growth often responds to environmental cues dynamically. Using the antibiotic-producing soil bacterium Streptomyces as a model we have developed a flexible mathematical model platform for the study of branched biological networks. Streptomyces form large aggregates in liquid culture that can impair industrial antibiotic fermentations. Understanding the features of these could aid improvement of such processes. The model requires relatively few experimental values for parameterisation, yet delivers realistic simulations of Streptomyces pellet and is able to predict features, such as the density of hyphae, the number of growing tips and the location of antibiotic production within a pellet in response to pellet size and external nutrient supply. The model is scalable and will find utility in a range of branched biological networks such as angiogenesis, plant root growth and fungal hyphal networks.

Adaptation to acetaminophen exposure elicits major changes in expression and distribution of the hepatic proteome

Acetaminophen overdose is the leading cause of acute liver failure. One dose of 10–15 g causes severe liver damage in humans, whereas repeated exposure to acetaminophen in humans and animal models results in autoprotection. Insight of this process is limited to select proteins implicated in acetaminophen toxicity and cellular defence. Here we investigate hepatic adaptation to acetaminophen toxicity from a whole proteome perspective, using quantitative mass spectrometry. In a rat model, we show the response to acetaminophen involves the expression of 30% of all proteins detected in the liver. Genetic ablation of a master regulator of cellular defence, NFE2L2, has little effect, suggesting redundancy in the regulation of adaptation. We show that adaptation to acetaminophen has a spatial component, involving a shift in regionalisation of CYP2E1, which may prevent toxicity thresholds being reached. These data reveal unexpected complexity and dynamic behaviour in the biological response to drug-induced liver injury.

Combined mathematical modelling and experimentation to predict polymersome uptake by oral cancer cells

UNLABELLED This study is motivated by understanding and controlling the key physical properties underlying internalisation of nano drug delivery. We consider the internalisation of specific nanometre size delivery vehicles, comprised of self-assembling amphiphilic block copolymers, called polymersomes that have the potential to specifically deliver anticancer therapeutics to tumour cells. The possible benefits of targeted polymersome drug delivery include reduced off-target toxic effects in healthy tissue and increased drug uptake by diseased tissue. Through a combination of in vitro experimentation and mathematical modelling, we develop a validated model of nanoparticle uptake by cells via the clathrin-mediated endocytotic pathway, incorporating receptor binding, clustering and recycling. The model predicts how the characteristics of receptor targeting, and the size and concentration of polymersomes alter uptake by tumour cells. The number of receptors per cell was identified as being the dominant mechanism accounting for the difference between cell types in polymersome uptake rate. FROM THE CLINICAL EDITOR This article reports on a validated model developed through a combination of in vitro experimentation and mathematical modeling of nanoparticle uptake by cells via the clathrin-mediated endocytotic pathway. The model incorporates receptor binding, clustering, and recycling and predicts how the characteristics of receptor targeting, the size and concentration alter polymersome uptake by cancer cells.

The role of spatial population structure on the evolution of parasites with acquired immunity and demography.

It is clear that the evolution of infectious disease may be influenced by population spatial structure and transmission networks but we lack an understanding of the role of acquired immunity. Here we examine theoretically the role of spatial structure in the evolution of infectious disease described by the classic Susceptible, Infected, Recovered (SIR) model focusing on the impact of host demographics. We find that, for the classic assumption of a trade-off between transmission and virulence, localised transmission does favor, as predicted from other models, chronic pathogens with low transmission and virulence, but that this effect reduces as the recovery rate increases. However, under the assumption that pathogens reproduce rapidly within the host are harder to clear but result in higher virulence local interactions favor more virulent parasites and, depending on the nature of the disease interaction, can increase or decrease the chance of evolutionary bistabilities that may lead to sudden persistent changes in virulence. Therefore, our work further emphasizes the importance of spatial structure to parasite evolution. This spatial evolutionary theory is important because it predicts how different pathogens may respond to changes in patterns of mixing.

The effect of landscape heterogeneity and host movement on a tick-borne pathogen

Landscape heterogeneity can be instrumental in determining local disease risk, pathogen persistence and spread. This is because different landscape features such as habitat type determine the abundance and spatial distributions of hosts and pathogen vectors. Therefore, disease prevalence and distribution are intrinsically linked to the hosts and vectors that utilise the different habitats. Here, we develop a simplified reaction diffusion model of the louping-ill virus and red grouse (Lagopus lagopus scoticus) system to investigate the occurrence of a tick-borne pathogen and the effect of host movement and landscape structure. Ticks (Ixodes ricinus), the virus-vector, are dispersed by a virally incompetent tick host, red deer (Cervus elephus), between different habitats, whilst the virus infects only red grouse. We investigated how deer movement between different habitats (forest and moorland) affected tick distribution and hence prevalence of infected ticks and grouse and hence, the effect of habitat size ratio and fragmentation on infection. When habitat type has a role in the survival of the pathogen vector, we demonstrated that habitat fragmentation can have a considerable effect on infection. These results highlight the importance of landscape heterogeneity and the proximity and size of adjacent habitats when predicting disease risk in a particular location. In addition, this model could be useful for other pathogen systems with generalist vectors and may inform policy on possible disease management strategies that incorporate host movements.