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

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

Effects of thymic selection of the T cell repertoire on HLA-class I associated control of HIV infection

Without therapy, most people infected with human immunodeficiency virus (HIV) ultimately progress to AIDS. Rare individuals (‘elite controllers’) maintain very low levels of HIV RNA without therapy, thereby making disease progression and transmission unlikely. Certain HLA class I alleles are markedly enriched in elite controllers, with the highest association observed for HLA-B57 (ref. 1). Because HLA molecules present viral peptides that activate CD8+ T cells, an immune-mediated mechanism is probably responsible for superior control of HIV. Here we describe how the peptide-binding characteristics of HLA-B57 molecules affect thymic development such that, compared to other HLA-restricted T cells, a larger fraction of the naive repertoire of B57-restricted clones recognizes a viral epitope, and these T cells are more cross-reactive to mutants of targeted epitopes. Our calculations predict that such a T-cell repertoire imposes strong immune pressure on immunodominant HIV epitopes and emergent mutants, thereby promoting efficient control of the virus. Supporting these predictions, in a large cohort of HLA-typed individuals, our experiments show that the relative ability of HLA-B alleles to control HIV correlates with their peptide-binding characteristics that affect thymic development. Our results provide a conceptual framework that unifies diverse empirical observations, and have implications for vaccination strategies.Mark and Lisa Schwartz FoundationNational Institutes of Health (U.S.) (Director’s Pioneer award)Philip T. and Susan M. Ragon FoundationJane Coffin Childs Memorial Fund for Medical ResearchBill & Melinda Gates FoundationNational Institute of Allergy and Infectious Diseases (U.S.)National Institutes of Health (U.S.) (contract no. HHSN261200800001E)National Institutes of Health (U.S.). Intramural Research ProgramNational Cancer Institute (U.S.)Center for Cancer Research (National Cancer Institute (U.S.)

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

Lateral adhesion drives reintegration of misplaced cells into epithelial monolayers.

Cells in simple epithelia orient their mitotic spindles in the plane of the epithelium so that both daughter cells are born within the epithelial sheet. This is assumed to be important to maintain epithelial integrity and prevent hyperplasia, because misaligned divisions give rise to cells outside the epithelium. Here we test this assumption in three types of Drosophila epithelium; the cuboidal follicle epithelium, the columnar early embryonic ectoderm, and the pseudostratified neuroepithelium. Ectopic expression of Inscuteable in these tissues reorients mitotic spindles, resulting in one daughter cell being born outside the epithelial layer. Live imaging reveals that these misplaced cells reintegrate into the tissue. Reducing the levels of the lateral homophilic adhesion molecules Neuroglian or Fasciclin 2 disrupts reintegration, giving rise to extra-epithelial cells, whereas disruption of adherens junctions has no effect. Thus, the reinsertion of misplaced cells seems to be driven by lateral adhesion, which pulls cells born outside the epithelial layer back into it. Our findings reveal a robust mechanism that protects epithelia against the consequences of misoriented divisions.The authors are grateful to R. Nieuwburg, the St Johnston group, and other Gurdon Institute members for suggestions. We thank the Bloomington Stock Center, J. Knoblich, and the TRiP at Harvard Medical School (NIH/NIGMS R01-GM084947) for fly stocks. We thank N. Lowe for technical assistance. This work was supported by a Wellcome Trust Principal Fellowship to D.St.J. (080007), and by core support from the Wellcome Trust (092096) and Cancer Research UK (A14492). D.T.B. was supported by a Marie Curie Fellowship and the Wellcome Trust. H.E.L. was supported by a Herchel Smith Studentship.This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/ncb324

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

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

An apicobasal gradient of Rac activity determines protrusion form and position

Each cell within a polarised epithelial sheet must align and correctly position a wide range of subcellular structures, including actin-based dynamic protrusions. Using in vivo inducible transgenes that can sense or modify Rac activity, we demonstrate an apicobasal gradient of Rac activity that is required to correctly form and position distinct classes of dynamic protrusion along the apicobasal axis of the cell. We show that we can modify the Rac activity gradient in genetic mutants for specific polarity proteins, with consequent changes in protrusion form and position and additionally show, using photoactivatable Rac transgenes, that it is the level of Rac activity that determines protrusion form. Thus, we demonstrate a mechanism by which polarity proteins can spatially regulate Rac activity and the actin cytoskeleton to ensure correct epithelial cell shape and prevent epithelial-to-mesenchymal transitions

Optimal Drug Synergy in Antimicrobial Treatments

The rapid proliferation of antibiotic-resistant pathogens has spurred the use of drug combinations to maintain clinical efficacy and combat the evolution of resistance. Drug pairs can interact synergistically or antagonistically, yielding inhibitory effects larger or smaller than expected from the drugs' individual potencies. Clinical strategies often favor synergistic interactions because they maximize the rate at which the infection is cleared from an individual, but it is unclear how such interactions affect the evolution of multi-drug resistance. We used a mathematical model of in vivo infection dynamics to determine the optimal treatment strategy for preventing the evolution of multi-drug resistance. We found that synergy has two conflicting effects: it clears the infection faster and thereby decreases the time during which resistant mutants can arise, but increases the selective advantage of these mutants over wild-type cells. When competition for resources is weak, the former effect is dominant and greater synergy more effectively prevents multi-drug resistance. However, under conditions of strong resource competition, a tradeoff emerges in which greater synergy increases the rate of infection clearance, but also increases the risk of multi-drug resistance. This tradeoff breaks down at a critical level of drug interaction, above which greater synergy has no effect on infection clearance, but still increases the risk of multi-drug resistance. These results suggest that the optimal strategy for suppressing multi-drug resistance is not always to maximize synergy, and that in some cases drug antagonism, despite its weaker efficacy, may better suppress the evolution of multi-drug resistance.Molecular and Cellular Biolog

Bazooka/PAR3 is dispensable for polarity in Drosophila follicular epithelial cells

Apico-basal polarity is the defining characteristic of epithelial cells. In Drosophila, apical membrane identity is established and regulated through interactions between the highly conserved Par complex (Bazooka/Par3, atypical protein kinase C and Par6), and the Crumbs complex (Crumbs, Stardust and PATJ). It has been proposed that Bazooka operates at the top of a genetic hierarchy in the establishment and maintenance of apico-basal polarity. However, there is still ambiguity over the correct sequence of events and cross-talk with other pathways during this process. In this study, we reassess this issue by comparing the phenotypes of the commonly used baz4 and baz815-8 alleles with those of the so far uncharacterized bazXR11 and bazEH747 null alleles in different Drosophila epithelia. While all these baz alleles display identical phenotypes during embryonic epithelial development, we observe strong discrepancies in the severity and penetrance of polarity defects in the follicular epithelium: polarity is mostly normal in bazEH747 and bazXR11 while baz4 and baz815-8 show loss of polarity, severe multilayering and loss of epithelial integrity throughout the clones. Further analysis reveals that the chromosomes carrying the baz4 and baz815-8 alleles may contain additional mutations that enhance the true baz loss-of-function phenotype in the follicular epithelium. This study clearly shows that Baz is dispensable for the regulation of polarity in the follicular epithelium, and that the requirement for key regulators of cell polarity is highly dependent on developmental context and cell type