A mathematical approach to virus therapy of glioblastomas

Mathematical modelling of reoviruses in cancer cell cultures

Oncolytic virotherapy has emerged as a potential cancer therapy, utilizing viruses to selectively target and replicate within cancer cells while preserving normal cells. In this paper, we investigate the oncolytic potential of unmodified reovirus T3wt relative to a mutated variant SV5. In animal cancer cell monolayer experiments it was found that SV5 was more oncolytic relative to T3wt. SV5 forms larger sized plaques on cancer cell monolayers and spreads to farther distances from the initial site of infection as compared to T3wt. Paradoxically, SV5 attaches to cancer cells less efficiently than T3wt, which lead us to hypothesize that there might be an optimal binding affinity with maximal oncolytic activity. To understand the relationship between the binding process and virus spread for T3wt and SV5, we employ mathematical modelling. A reaction-diffusion model is applied, which is fit to the available data and then validated on data that were not used for the fit. Analysis of our model shows that there is an optimal binding rate that leads to maximum viral infection of the cancer monolayer, and we estimate this value for T3wt and SV5. Moreover, we find that the viral burst size is an important parameter for viral spread, and that a combination of efficient binding and large burst sizes is a promising direction to further develop anti-cancer viruses.

Oscillations in a Spatial Oncolytic Virus Model

Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator-prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods.

HSC Niche Dynamics in Regeneration, Pre-malignancy, and Cancer: Insights From Mathematical Modeling

The hematopoietic stem cell (HSC) niche is a crucial driver of regeneration and malignancy. Its interaction with hematopoietic and malignant stem cells is highly complex and direct experimental observations are challenging. We here develop a mathematical model which helps relate processes in the niche to measurable changes of stem and non-stem cell counts. HSC attached to the niche are assumed to be quiescent. After detachment HSC become activated and divide or differentiate. To maintain their stemness, the progeny originating from division must reattach to the niche. We use mouse data from literature to parametrize the model. By combining mathematical analysis and computer simulations, we systematically investigate the impact of stem cell proliferation, differentiation, niche attachment, and detachment on clinically relevant scenarios. These include bone marrow transplantation, clonal competition, and eradication of malignant cells. According to our model, sampling of blood or bulk marrow provides only limited information about cellular interactions in the niche and the clonal composition of the stem cell population. Furthermore, we investigate how interference with processes in the stem cell niche could help to increase the effect of low-dose chemotherapy or to improve the homing of genetically engineered cells.

Prevalent association with the bacterial cell envelope of prokaryotic expansins revealed by bioinformatics analysis

Expansins are a group of proteins from diverse organisms from bacteria to plants. Although expansins show structural conservation, their biological roles seem to differ among kingdoms. In plants, these proteins remodel the cell wall during plant growth and other processes. Contrarily, determination of bacterial expansin activity has proven difficult, although genetic evidence of bacterial mutants indicates that expansins participate in bacteria-plant interactions. Nevertheless, a large proportion of expansin genes are found in the genomes of free-living bacteria, suggesting roles that are independent of the interaction with living plants. Here, we analyzed all available sequences of prokaryotic expansins for correlations between surface electric charge, extra protein modules, and sequence motifs for association with the bacteria exterior after export. Additionally, information on the fate of protein after translocation across the membrane also points to bacterial cell association of expansins through six different mechanisms, such as attachment of a lipid molecule for membrane anchoring in diderm species or covalent linking to the peptidoglycan layer in monoderms such as the Bacilliales. Our results have implications for expansin function in the context of bacteria-plant interactions and also for free-living species in which expansins might affect cell-cell or cell-substrate interaction properties and indicate the need to re-examine the roles currently considered for these proteins.

Aspirin's effect on kinetic parameters of cells contributes to its role in reducing incidence of advanced colorectal adenomas, shown by a multiscale computational study

Aspirin intake has been shown to lead to significant protection against colorectal cancer, for example with an up to twofold reduction in colorectal adenoma incidence rates at higher doses. The mechanisms contributing to protection are not yet fully understood. While aspirin is an anti-inflammatory drug and can thus influence the tumor microenvironment, in vitro and in vivo experiments have recently shown that aspirin can also have a direct effect on cellular kinetics and fitness. It reduces the rate of tumor cell division and increases the rate of cell death. The question arises whether such changes in cellular fitness are sufficient to significantly contribute to the epidemiologically observed protection. To investigate this, we constructed a class of mathematical models of in vivo evolution of advanced adenomas, parameterized it with available estimates, and calculated population level incidence. Fitting the predictions to age incidence data revealed that only a model that included colonic crypt competition can account for the observed age-incidence curve. This model was then used to predict modified incidence patterns if cellular kinetics were altered as a result of aspirin treatment. We found that changes in cellular fitness that were within the experimentally observed ranges could reduce advanced adenoma incidence by a sufficient amount to account for age incidence data in aspirin-treated patient cohorts. While the mechanisms that contribute to the protective effect of aspirin are likely complex and multi-factorial, our study demonstrates that direct aspirin-induced changes of tumor cell fitness can significantly contribute to epidemiologically observed reduced incidence patterns.

Homogenization of a reaction diffusion equation can explain influenza A virus load data

We study the influence of spatial heterogeneity on the antiviral activity of mouse embryonic fibroblasts (MEF) infected with influenza A. MEF of type Ube1L^-/- are composed of two distinct sub-populations, the strong type that sustains a strong viral infection and the weak type, sustaining a weak viral load. We present new data on the virus load infection of Ube1L^-/-, which have been micro-printed in a checker board pattern of different sizes of the inner squares. Surprisingly, the total viral load at one day after inoculation significantly depends on the sizes of the inner squares. We explain this observation by using a reaction diffusion model and we show that mathematical homogenization can explain the observed inhomogeneities. If the individual patches are large, then the growth rate and the carrying capacity will be the arithmetic means of the patches. For finer and finer patches the average growth rate is still the arithmetic mean, however, the carrying capacity uses the harmonic mean. While fitting the PDE to the experimental data, we also predict that a discrepancy in virus load would be unobservable after only half a day. Furthermore, we predict the viral load in different inner squares that had not been measured in our experiment and the travelling distance the virions can reach after one day.

A Mechanistic Investigation into Ischemia-Driven Distal Recurrence of Glioblastoma

Glioblastoma (GBM) is the most aggressive primary brain tumor with a short median survival. Tumor recurrence is a clinical expectation of this disease and usually occurs along the resection cavity wall. However, previous clinical observations have suggested that in cases of ischemia following surgery, tumors are more likely to recur distally. Through the use of a previously established mechanistic model of GBM, the Proliferation Invasion Hypoxia Necrosis Angiogenesis (PIHNA) model, we explore the phenotypic drivers of this observed behavior. We have extended the PIHNA model to include a new nutrient-based vascular efficiency term that encodes the ability of local vasculature to provide nutrients to the simulated tumor. The extended model suggests sensitivity to a hypoxic microenvironment and the inherent migration and proliferation rates of the tumor cells are key factors that drive distal recurrence.

Biased dispersal can explain fast human range expansions

Some human fronts spread faster than expected by models based on dispersal and reproduction. The only explanation proposed so far assumes that some autochthonous individuals are incorporated by the expanding populations, leading to faster front speeds. Here we show that simple models without this effect are also consistent with the observed speeds of two fronts (a Khoi-khoi expansion of herders and a Bantu expansion of farmers), provided that the dispersal of individuals is biased (i.e., more probable) in directions closer to the front propagation direction. The physical models presented may also be applied to other kinds of social phenomena, including innovation diffusion, rumor propagation, linguistic fronts, epidemic spread, diffusion in economic space and the evolution of cooperation in spatial systems. They can be also adapted to non-human systems with biased dispersal, including biological invasions, cancer tumors and virus treatment of tumors.

Recent advances in vesicular stomatitis virus-based oncolytic virotherapy: a 5-year update

Oncolytic virus (OV) therapy is an anti-cancer approach that uses viruses that preferentially infect, replicate in and kill cancer cells. Vesicular stomatitis virus (VSV, a rhabdovirus) is an OV that is currently being tested in the USA in several phase I clinical trials against different malignancies. Several factors make VSV a promising OV: lack of pre-existing human immunity against VSV, a small and easy to manipulate genome, cytoplasmic replication without risk of host cell transformation, independence of cell cycle and rapid growth to high titres in a broad range of cell lines facilitating large-scale virus production. While significant advances have been made in VSV-based OV therapy, room for improvement remains. Here we review recent studies (published in the last 5 years) that address 'old' and 'new' challenges of VSV-based OV therapy. These studies focused on improving VSV safety, oncoselectivity and oncotoxicity; breaking resistance of some cancers to VSV; preventing premature clearance of VSV; and stimulating tumour-specific immunity. Many of these approaches were based on combining VSV with other therapeutics. This review also discusses another rhabdovirus closely related to VSV, Maraba virus, which is currently being tested in Canada in phase I/II clinical trials.

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies.

Computational analysis of nascent peptides that induce ribosome stalling and their proteomic distribution in Saccharomyces cerevisiae

Interactions between the ribosomal exit tunnel and the nascent peptide can affect translation elongation rates. While previous studies have already demonstrated the feasibility of such interactions, little is known about the nature of the stalling peptide sequences and their distribution in the proteome. Here we ask which peptide sequences tend to occupy the tunnel of stalled ribosomes and how they are distributed in the proteome. Using computational analysis of ribosome profiling data from S. cerevisiae, we identified for the first time dozens of short stalling peptide sequences and studied their statistical properties. We found that short peptide sequences associated with ribosome stalling tend significantly to be either over- or underrepresented in the proteome. We then showed that the stalling interactions may occur at different positions along the length of the tunnel, prominently close to the P-site. Our findings throw light on the determinants of nascent peptide-mediated ribosome stalling during translation elongation and support the novel conjecture that mRNA translation affects the proteomic distribution of short peptide sequences.

Predictive biophysical modeling and understanding of the dynamics of mRNA translation and its evolution

mRNA translation is the fundamental process of decoding the information encoded in mRNA molecules by the ribosome for the synthesis of proteins. The centrality of this process in various biomedical disciplines such as cell biology, evolution and biotechnology, encouraged the development of dozens of mathematical and computational models of translation in recent years. These models aimed at capturing various biophysical aspects of the process. The objective of this review is to survey these models, focusing on those based and/or validated on real large-scale genomic data. We consider aspects such as the complexity of the models, the biophysical aspects they regard and the predictions they may provide. Furthermore, we survey the central systems biology discoveries reported on their basis. This review demonstrates the fundamental advantages of employing computational biophysical translation models in general, and discusses the relative advantages of the different approaches and the challenges in the field.