Tumour-associated macrophages and oncolytic virotherapies:a mathematical investigation into a complex dynamics

Anti-cancer therapies based on oncolytic viruses are emerging as important approaches in cancer treatment. However, the effectiveness of these therapies depends significantly on the interactions between the oncolytic viruses and the host immune response. Macrophages are one of the most important cell types in the anti-viral immune responses, by acting as a first line of defence against infections. Here, we consider a mathematical approach to investigate the possible outcomes of the interactions between two extreme phenotypes of macrophages (M1 and M2 cells) and an oncolytic virus (VSV), in the context of B16F10 melanoma. We show that polarization towards either an M1 or M2 phenotype can enhance oncolytic virus therapy through either (i) anti-tumour immune activation, or (ii) enhanced oncolysis. Moreover, we show that tumour reduction and elimination does not depend only on the ratio of M1:M2 cells, but also on the number of tumour-infiltrating macrophages

Asymptotic behaviour of random tridiagonal Markov chains in biological applications

Discrete-time discrete-state random Markov chains with a tridiagonal generator are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors. The proof uses the Hilbert projection metric and the fact that the linear cocycle generated by the Markov chain is a uniformly contractive mapping of the positive cone into itself. The proof does not involve probabilistic properties of the sample path and is thus equally valid in the nonautonomous deterministic context of Markov chains with, say, periodically varying transitions probabilities, in which case the attractor is a periodic path.Comment: 13 pages, 22 bibliography references, submitted to DCDS-B, added references and minor correction

Towards Predictive Computational Models of Oncolytic Virus Therapy: Basis for Experimental Validation and Model Selection

Oncolytic viruses are viruses that specifically infect cancer cells and kill them, while leaving healthy cells largely intact. Their ability to spread through the tumor makes them an attractive therapy approach. While promising results have been observed in clinical trials, solid success remains elusive since we lack understanding of the basic principles that govern the dynamical interactions between the virus and the cancer. In this respect, computational models can help experimental research at optimizing treatment regimes. Although preliminary mathematical work has been performed, this suffers from the fact that individual models are largely arbitrary and based on biologically uncertain assumptions. Here, we present a general framework to study the dynamics of oncolytic viruses that is independent of uncertain and arbitrary mathematical formulations. We find two categories of dynamics, depending on the assumptions about spatial constraints that govern that spread of the virus from cell to cell. If infected cells are mixed among uninfected cells, there exists a viral replication rate threshold beyond which tumor control is the only outcome. On the other hand, if infected cells are clustered together (e.g. in a solid tumor), then we observe more complicated dynamics in which the outcome of therapy might go either way, depending on the initial number of cells and viruses. We fit our models to previously published experimental data and discuss aspects of model validation, selection, and experimental design. This framework can be used as a basis for model selection and validation in the context of future, more detailed experimental studies. It can further serve as the basis for future, more complex models that take into account other clinically relevant factors such as immune responses

A mathematical model for the onset of avascular tumor growth in response to the loss of p53 function

We present a mathematical model for the formation of an avascular tumor based on the loss by gene mutation of the tumor suppressor function of p53. The wild type p53 protein regulates apoptosis, cell expression of growth factor and matrix metalloproteinase, which are regulatory functions that many mutant p53 proteins do not possess. The focus is on a description of cell movement as the transport of cell population density rather than as the movement of individual cells. In contrast to earlier works on solid tumor growth, a model is proposed for the initiation of tumor growth. The central idea, taken from the mathematical theory of dynamical systems, is to view the loss of p53 function in a few cells as a small instability in a rest state for an appropriate system of differential equations describing cell movement. This instability is shown (numerically) to lead to a second, spatially inhomogeneous, solution that can be thought of as a solid tumor whose growth is nutrient diffusion limited. In this formulation, one is led to a system of nine partial differential equations. We show computationally that there can be tumor states that coexist with benign states and that are highly unstable in the sense that a slight increase in tumor size results in the tumor occupying the sample region while a slight decrease in tumor size results in its ultimate disappearance

Virus Replication Strategies and the Critical CTL Numbers Required for the Control of Infection

Vaccines that elicit protective cytotoxic T lymphocytes (CTL) may improve on or augment those designed primarily to elicit antibody responses. However, we have little basis for estimating the numbers of CTL required for sterilising immunity at an infection site. To address this we begin with a theoretical estimate obtained from measurements of CTL surveillance rates and the growth rate of a virus. We show how this estimate needs to be modified to account for (i) the dynamics of CTL-infected cell conjugates, and (ii) features of the virus lifecycle in infected cells. We show that provided the inoculum size of the virus is low, the dynamics of CTL-infected cell conjugates can be ignored, but knowledge of virus life-histories is required for estimating critical thresholds of CTL densities. We show that accounting for virus replication strategies increases estimates of the minimum density of CTL required for immunity over those obtained with the canonical model of virus dynamics, and demonstrate that this modeling framework allows us to predict and compare the ability of CTL to control viruses with different life history strategies. As an example we predict that lytic viruses are more difficult to control than budding viruses when net reproduction rates and infected cell lifetimes are controlled for. Further, we use data from acute SIV infection in rhesus macaques to calculate a lower bound on the density of CTL that a vaccine must generate to control infection at the entry site. We propose that critical CTL densities can be better estimated either using quantitative models incorporating virus life histories or with in vivo assays using virus-infected cells rather than peptide-pulsed targets

Live Imaging at the Onset of Cortical Neurogenesis Reveals Differential Appearance of the Neuronal Phenotype in Apical versus Basal Progenitor Progeny

The neurons of the mammalian brain are generated by progenitors dividing either at the apical surface of the ventricular zone (neuroepithelial and radial glial cells, collectively referred to as apical progenitors) or at its basal side (basal progenitors, also called intermediate progenitors). For apical progenitors, the orientation of the cleavage plane relative to their apical-basal axis is thought to be of critical importance for the fate of the daughter cells. For basal progenitors, the relationship between cell polarity, cleavage plane orientation and the fate of daughter cells is unknown. Here, we have investigated these issues at the very onset of cortical neurogenesis. To directly observe the generation of neurons from apical and basal progenitors, we established a novel transgenic mouse line in which membrane GFP is expressed from the beta-III-tubulin promoter, an early pan-neuronal marker, and crossed this line with a previously described knock-in line in which nuclear GFP is expressed from the Tis21 promoter, a pan-neurogenic progenitor marker. Mitotic Tis21-positive basal progenitors nearly always divided symmetrically, generating two neurons, but, in contrast to symmetrically dividing apical progenitors, lacked apical-basal polarity and showed a nearly randomized cleavage plane orientation. Moreover, the appearance of beta-III-tubulin–driven GFP fluorescence in basal progenitor-derived neurons, in contrast to that in apical progenitor-derived neurons, was so rapid that it suggested the initiation of the neuronal phenotype already in the progenitor. Our observations imply that (i) the loss of apical-basal polarity restricts neuronal progenitors to the symmetric mode of cell division, and that (ii) basal progenitors initiate the expression of neuronal phenotype already before mitosis, in contrast to apical progenitors

Genetic risk prediction and neurobiological understanding of alcoholism

We have used a translational Convergent Functional Genomics (CFG) approach to discover genes involved in alcoholism, by gene-level integration of genome-wide association study (GWAS) data from a German alcohol dependence cohort with other genetic and gene expression data, from human and animal model studies, similar to our previous work in bipolar disorder and schizophrenia. A panel of all the nominally significant P-value single-nucleotide length polymorphisms (SNPs) in the top candidate genes discovered by CFG (n = 135 genes, 713 SNPs) was used to generate a genetic risk prediction score (GRPS), which showed a trend towards significance (P = 0.053) in separating alcohol dependent individuals from controls in an independent German test cohort. We then validated and prioritized our top findings from this discovery work, and subsequently tested them in three independent cohorts, from two continents. In order to validate and prioritize the key genes that drive behavior without some of the pleiotropic environmental confounds present in humans, we used a stress-reactive animal model of alcoholism developed by our group, the D-box binding protein (DBP) knockout mouse, consistent with the surfeit of stress theory of addiction proposed by Koob and colleagues. A much smaller panel (n = 11 genes, 66 SNPs) of the top CFG-discovered genes for alcoholism, cross-validated and prioritized by this stress-reactive animal model showed better predictive ability in the independent German test cohort (P = 0.041). The top CFG scoring gene for alcoholism from the initial discovery step, synuclein alpha (SNCA) remained the top gene after the stress-reactive animal model cross-validation. We also tested this small panel of genes in two other independent test cohorts from the United States, one with alcohol dependence (P = 0.00012) and one with alcohol abuse (a less severe form of alcoholism; P = 0.0094). SNCA by itself was able to separate alcoholics from controls in the alcohol-dependent cohort (P = 0.000013) and the alcohol abuse cohort (P = 0.023). So did eight other genes from the panel of 11 genes taken individually, albeit to a lesser extent and/or less broadly across cohorts. SNCA, GRM3 and MBP survived strict Bonferroni correction for multiple comparisons. Taken together, these results suggest that our stress-reactive DBP animal model helped to validate and prioritize from the CFG-discovered genes some of the key behaviorally relevant genes for alcoholism. These genes fall into a series of biological pathways involved in signal transduction, transmission of nerve impulse (including myelination) and cocaine addiction. Overall, our work provides leads towards a better understanding of illness, diagnostics and therapeutics, including treatment with omega-3 fatty acids. We also examined the overlap between the top candidate genes for alcoholism from this work and the top candidate genes for bipolar disorder, schizophrenia, anxiety from previous CFG analyses conducted by us, as well as cross-tested genetic risk predictions. This revealed the significant genetic overlap with other major psychiatric disorder domains, providing a basis for comorbidity and dual diagnosis, and placing alcohol use in the broader context of modulating the mental landscape

Modelling the Influence of Foot-and-Mouth Disease Vaccine Antigen Stability and Dose on the Bovine Immune Response

Foot and mouth disease virus causes a livestock disease of significant global socio-economic importance. Advances in its control and eradication depend critically on improvements in vaccine efficacy, which can be best achieved by better understanding the complex within-host immunodynamic response to inoculation. We present a detailed and empirically parametrised dynamical mathematical model of the hypothesised immune response in cattle, and explore its behaviour with reference to a variety of experimental observations relating to foot and mouth immunology. The model system is able to qualitatively account for the observed responses during in-vivo experiments, and we use it to gain insight into the incompletely understood effect of single and repeat inoculations of differing dosage using vaccine formulations of different structural stability

Gain in cellular organization of inflammatory breast cancer: A 3D in vitro model that mimics the in vivo metastasis

<p>Abstract</p> <p>Background</p> <p>The initial step of metastasis in carcinomas, often referred to as the epithelial-mesenchymal transition (EMT), occurs via the loss of adherens junctions (e.g. cadherins) by the tumor embolus. This leads to a subsequent loss of cell polarity and cellular differentiation and organization, enabling cells of the embolus to become motile and invasive. However highly malignant inflammatory breast cancer (IBC) over-expresses E-cadherin. The human xenograft model of IBC (MARY-X), like IBC, displays the signature phenotype of an exaggerated degree of lymphovascular invasion (LVI) <it>in situ </it>by tumor emboli. An intact E-cadherin/α, β-catenin axis mediates the tight, compact clump of cells found both <it>in vitro </it>and <it>in vivo </it>as spheroids and tumor emboli, respectively.</p> <p>Methods</p> <p>Using electron microscopy and focused ion beam milling to acquire <it>in situ </it>sections, we performed ultrastructural analysis of both an IBC and non-IBC, E-cadherin positive cell line to determine if retention of this adhesion molecule contributed to cellular organization.</p> <p>Results</p> <p>Here we report through ultrastructural analysis that IBC exhibits a high degree of cellular organization with polar elements such as apical/lateral positioning of E-cadherin, apical surface microvilli, and tortuous lumen-like (canalis) structures. In contrast, agarose-induced spheroids of MCF-7, a weakly invasive E-cadherin positive breast carcinoma cell line, do not exhibit ultrastructural polar features.</p> <p>Conclusions</p> <p>This study has determined that the highly metastatic IBC with an exaggerated malignant phenotype challenges conventional wisdom in that instead of displaying a loss of cellular organization, IBC acquires a highly structured architecture.</p> <p>These findings suggest that the metastatic efficiency might be linked to the formation and maintenance of these architectural features. The comparative architectural features of both the spheroid and embolus of MARY-X provide an <it>in vitro </it>model with tractable <it>in vivo </it>applications.</p