Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations

This work was supported in part by the French National Research Agency through the “ANR blanche” project Kibord [ANR-13-BS01-0004].Background: A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. Results: To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. Conclusions: Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the ‘maximum-tolerated-dose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.Publisher PDFPeer reviewe

Building a Morphogen Gradient without Diffusion in a Growing Tissue

In many developmental systems, spatial pattern arises from morphogen gradients, which provide positional information for cells to determine their fate. Typically, diffusion is thought to be the mechanism responsible for building a morphogen gradient. An alternative mechanism is investigated here. Using mathematical modeling, we demonstrate how a non-diffusive morphogen concentration gradient can develop in axially growing tissue systems, where growth is due to cell proliferation only. Two distinct cases are considered: in the first, all cell proliferation occurs in a localized zone where active transcription of a morphogen-producing gene occurs, and in the second, cell proliferation is uniformly distributed throughout the tissue, occurring in both the active transcription zone and beyond. A cell containing morphogen mRNA produces the morphogen protein, hence any gradient in mRNA transcripts translates into a corresponding morphogen protein gradient. Proliferation-driven growth gives rise to both advection (the transport term) and dilution (a reaction term). These two key mechanisms determine the resultant mRNA transcript distribution. Using the full range of uniform initial conditions, we show that advection and dilution due to cell proliferation are, in general, sufficient for morphogen gradient formation for both types of axially growing systems. In particular, mRNA transcript degradation is not necessary for gradient formation; it is only necessary with localized proliferation for one special value of the initial concentration. Furthermore, the morphogen concentration decreases with distance away from the transcription zone, except in the case of localized proliferation with the initial concentration sufficiently large, when the concentration can either increase with distance from the transcription zone or sustain a local minimum. In both localized and uniformly distributed proliferation, in order for a concentration gradient to form across the whole domain, transcription must occur in a zone equal to the initial domain size; otherwise, it will only form across part of the tissue

Dissecting the dynamics of epigenetic changes in phenotype-structured populations exposed to fluctuating environments

International audienceAn enduring puzzle in evolutionary biology is to understand how individuals and populations adapt to fluctuating environments. Here we present an integro-differential model of adaptive dynamics in a phenotype-structured population whose fitness landscape evolves in time due to periodic environmental oscillations. The analytical tractability of our model allows for a systematic investigation of the relative contributions of heritable variations in gene expression, environmental changes and natural selection as drivers of phenotypic adaptation. We show that environmental fluctuations can induce the population to enter an unstable and fluctuation-driven epigenetic state. We demonstrate that this can trigger the emergence of oscillations in the size of the population, and we establish a full characterisation of such oscillations. Moreover, the results of our analyses provide a formal basis for the claim that higher rates of epimutations can bring about higher levels of intrapopulation heterogeneity, whilst intense selection pressures can deplete variation in the phenotypic pool of asexual populations. Finally, our work illustrates how the dynamics of the population size is led by a strong synergism between the rate of phenotypic variation and the frequency of environmental oscillations, and identifies possible ecological conditions that promote the maximisation of the population size in fluctuating environments

Evolutionary dynamics of phenotype-structured populations : from individual-level mechanisms to population-level consequences

This research was supported in part by the Australian Research Council (DP140100339) and by the French National Research Agency through the ANR blanche project Kibord [ANR-13-BS01-0004] and the “ANR JC” project Modevol [ANR-13-JS01-0009]. TL was also supported in part by the Hadamard Mathematics Labex, backed by the Fondation Mathématique Jacques Hadamard, through a grant overseen by the French National Research Agency [ANR-11-LABX-0056-LMH]. LD was also supported in part by Université Sorbonne Paris Cité “Investissements d’Avenir”[ANR-11-IDEX-0005].Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.PostprintPeer reviewe

U SPOMEN - Dr.sc. Radmila Matejčić (1922. - 1990.) u povodu 25. obljetnice smrti

Background. Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. Scope of review. We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Major conclusions. Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. General significance. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.PostprintPeer reviewe

Growth patterns in Onychophora (velvet worms): lack of a localised posterior proliferation zone

<p>Abstract</p> <p>Background</p> <p>During embryonic development of segmented animals, body segments are thought to arise from the so-called "posterior growth zone" and the occurrence of this "zone" has been used to support the homology of segmentation between arthropods, annelids, and vertebrates. However, the term "posterior growth zone" is used ambiguously in the literature, mostly referring to a region of increased proliferation at the posterior end of the embryo. To determine whether such a localised posterior proliferation zone is an ancestral feature of Panarthropoda (Onychophora + Tardigrada + Arthropoda), we examined cell division patterns in embryos of Onychophora.</p> <p>Results</p> <p>Using in vivo incorporation of the DNA replication marker BrdU (5-bromo-2'-deoxyuridine) and anti-phospho-histone H3 immunolabelling, we found that a localised posterior region of proliferating cells does not occur at any developmental stage in onychophoran embryos. This contrasts with a localised pattern of cell divisions at the posterior end of annelid embryos, which we used as a positive control. Based on our data, we present a mathematical model, which challenges the paradigm that a localised posterior proliferation zone is necessary for segment patterning in short germ developing arthropods.</p> <p>Conclusions</p> <p>Our findings suggest that a posterior proliferation zone was absent in the last common ancestor of Onychophora and Arthropoda. By comparing our data from Onychophora with those from annelids, arthropods, and chordates, we suggest that the occurrence of a "posterior growth zone" currently cannot be used to support the homology of segmentation between these three animal groups.</p

Emergence of cytotoxic resistance in cancer cell populations: single-cell mechanisms and population-level consequences

International audienceWe formulate an individual-based model and a population model of phenotypic evolution, under cytotoxic drugs, in a cancer cell population structured by the expression levels of survival-potential and proliferation-potential. We apply these models to a recently studied experimental system. Our results suggest that mechanisms based on fundamental laws of biology can reversibly push an actively-proliferating, and drug-sensitive, cell population to transition into a weakly-proliferative and drug-tolerant state, which will eventually facilitate the emergence of more potent, proliferating and drug-tolerant cells

Systems Integration of Biodefense Omics Data for Analysis of Pathogen-Host Interactions and Identification of Potential Targets

The NIAID (National Institute for Allergy and Infectious Diseases) Biodefense Proteomics program aims to identify targets for potential vaccines, therapeutics, and diagnostics for agents of concern in bioterrorism, including bacterial, parasitic, and viral pathogens. The program includes seven Proteomics Research Centers, generating diverse types of pathogen-host data, including mass spectrometry, microarray transcriptional profiles, protein interactions, protein structures and biological reagents. The Biodefense Resource Center (www.proteomicsresource.org) has developed a bioinformatics framework, employing a protein-centric approach to integrate and support mining and analysis of the large and heterogeneous data. Underlying this approach is a data warehouse with comprehensive protein + gene identifier and name mappings and annotations extracted from over 100 molecular databases. Value-added annotations are provided for key proteins from experimental findings using controlled vocabulary. The availability of pathogen and host omics data in an integrated framework allows global analysis of the data and comparisons across different experiments and organisms, as illustrated in several case studies presented here. (1) The identification of a hypothetical protein with differential gene and protein expressions in two host systems (mouse macrophage and human HeLa cells) infected by different bacterial (Bacillus anthracis and Salmonella typhimurium) and viral (orthopox) pathogens suggesting that this protein can be prioritized for additional analysis and functional characterization. (2) The analysis of a vaccinia-human protein interaction network supplemented with protein accumulation levels led to the identification of human Keratin, type II cytoskeletal 4 protein as a potential therapeutic target. (3) Comparison of complete genomes from pathogenic variants coupled with experimental information on complete proteomes allowed the identification and prioritization of ten potential diagnostic targets from Bacillus anthracis. The integrative analysis across data sets from multiple centers can reveal potential functional significance and hidden relationships between pathogen and host proteins, thereby providing a systems approach to basic understanding of pathogenicity and target identification

Influenza vaccination for immunocompromised patients: systematic review and meta-analysis from a public health policy perspective.

Immunocompromised patients are vulnerable to severe or complicated influenza infection. Vaccination is widely recommended for this group. This systematic review and meta-analysis assesses influenza vaccination for immunocompromised patients in terms of preventing influenza-like illness and laboratory confirmed influenza, serological response and adverse events