Rebecca H. Chisholm

Emergence of Drug Tolerance in Cancer Cell Populations: An Evolutionary Outcome of Selection, Nongenetic Instability, and Stress-Induced Adaptation

In recent experiments on isogenetic cancer cell lines, it was observed that exposure to high doses of anticancer drugs can induce the emergence of a subpopulation of weakly proliferative and drug-tolerant cells, which display markers associated with stem cell-like cancer cells. After a period of time, some of the surviving cells were observed to change their phenotype to resume normal proliferation and eventually repopulate the sample. Furthermore, the drug-tolerant cells could be drug resensitized following drug washout. Here, we propose a theoretical mechanism for the transient emergence of such drug tolerance. In this framework, we formulate an individual-based model and an integro-differential equation model of reversible phenotypic evolution in a cell population exposed to cytotoxic drugs. The outcomes of both models suggest that nongenetic instability, stress-induced adaptation, selection, and the interplay between these mechanisms can push an actively proliferating cell population to transition into a weakly proliferative and drug-tolerant state. Hence, the cell population experiences much less stress in the presence of the drugs and, in the long run, reacquires a proliferative phenotype, due to phenotypic fluctuations and selection pressure. These mechanisms can also reverse epigenetic drug tolerance following drug washout. Our study highlights how the transient appearance of the weakly proliferative and drug-tolerant cells is related to the use of high-dose therapy. Furthermore, we show how stem-like characteristics can act to stabilize the transient, weakly proliferative, and drug-tolerant subpopulation for a longer time window. Finally, using our models as in silico laboratories, we propose new testable hypotheses that could help uncover general principles underlying the emergence of cancer drug tolerance.

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.

Controlled fire use in early humans might have triggered the evolutionary emergence of tuberculosis

Significance Tuberculosis is an ancient human disease that continues to affect millions of people worldwide. A crucial component of the origins of the tuberculosis bacterium remains a mystery: What were the conditions that precipitated its emergence as an obligate transmissible human pathogen? Here, we identify a connection between the emergence of tuberculosis and another major event in human prehistory, namely the discovery of controlled fire use. Our results have serious and cautionary implications for the emergence of new infectious diseases—feedback between cultural innovation and alteration of living conditions can catalyze unexpected changes with potentially devastating consequences lasting thousands of years. Tuberculosis (TB) is caused by the Mycobacterium tuberculosis complex (MTBC), a wildly successful group of organisms and the leading cause of death resulting from a single bacterial pathogen worldwide. It is generally accepted that MTBC established itself in human populations in Africa and that animal-infecting strains diverged from human strains. However, the precise causal factors of TB emergence remain unknown. Here, we propose that the advent of controlled fire use in early humans created the ideal conditions for the emergence of TB as a transmissible disease. This hypothesis is supported by mathematical modeling together with a synthesis of evidence from epidemiology, evolutionary genetics, and paleoanthropology.

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

An 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.

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

BackgroundA 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.ResultsTo 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.ConclusionsOur 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.ReviewersThis article was reviewed by Angela Pisco, Sébastien Benzekry and Heiko Enderling.

Mathematical model reveals how regulating the three phases of T-cell response could counteract immune evasion

T cells are key players in immune action against the invasion of target cells expressing non‐self antigens. During an immune response, antigen‐specific T cells dynamically sculpt the antigenic distribution of target cells, and target cells concurrently shape the hosts repertoire of antigen‐specific T cells. The succession of these reciprocal selective sweeps can result in ‘chase‐and‐escape’ dynamics and lead to immune evasion. It has been proposed that immune evasion can be countered by immunotherapy strategies aimed at regulating the three phases of the immune response orchestrated by antigen‐specific T cells: expansion, contraction and memory. Here, we test this hypothesis with a mathematical model that considers the immune response as a selection contest between T cells and target cells. The outcomes of our model suggest that shortening the duration of the contraction phase and stabilizing as many T cells as possible inside the long‐lived memory reservoir, using dual immunotherapies based on the cytokines interleukin‐7 and/or interleukin‐15 in combination with molecular factors that can keep the immunomodulatory action of these interleukins under control, should be an important focus of future immunotherapy research.

The emergence of latent infection in the early evolution of Mycobacterium tuberculosis

Mycobacterium tuberculosis has an unusual natural history in that the vast majority of its human hosts enter a latent state that is both non-infectious and devoid of any symptoms of disease. From the pathogen perspective, it seems counterproductive to relinquish reproductive opportunities to achieve a détente with the host immune response. However, a small fraction of latent infections reactivate to the disease state. Thus, latency has been argued to provide a safe harbour for future infections which optimizes the persistence of M. tuberculosis in human populations. Yet, if a pathogen begins interactions with humans as an active disease without latency, how could it begin to evolve latency properties without incurring an immediate reproductive disadvantage? We address this question with a mathematical model. Results suggest that the emergence of tuberculosis latency may have been enabled by a mechanism akin to cryptic genetic variation in that detrimental latency properties were hidden from natural selection until their expression became evolutionarily favoured.

When are cellular oscillators sufficient for sequential segmentation

Sequential segmentation during embryogenesis involves the generation of a repeated pattern along the embryo, which is concurrently undergoing axial elongation by cell division. Most mathematical models of sequential segmentation involve inherent cellular oscillators, acting as a segmentation clock. The cellular oscillation is assumed to be governed by the cells physiological age or by its interaction with an external morphogen gradient. Here, we address the issue of when cellular oscillators alone are sufficient for predicting segmentation, and when a morphogen gradient is required. The key to resolving this issue lies in how cells determine positional information in the model--this is directly related to the distribution of cell divisions responsible for axial elongation. Mathematical models demonstrate that if axial elongation occurs through cell divisions restricted to the posterior end of the unsegmented region, a cell can obtain its positional information from its physiological age, and therefore cellular oscillators will suffice. Alternatively, if axial elongation occurs through cell divisions distributed throughout the unsegmented region, then positional information can be obtained through another mechanism, such as a morphogen gradient. Two alternative ways to establish a morphogen gradient in tissue with distributed cell divisions are presented--one with diffusion and the other without diffusion. Our model produces segment polarity and a distribution of segment size from the anterior-to-posterior ends, as observed in some systems. Furthermore, the model predicts segment deletions when there is an interruption in cell division, just as seen in heat shock experiments, as well as the growth and final shrinkage of the presomitic mesoderm during somitogenesis.

Analytic Study of Three-Dimensional Single Cell Migration with and without Proteolytic Enzymes

Cell motility is a fundamental physiological process that regulates cellular fate in healthy and diseased systems. Cells cultured in 3D environments often exhibit biphasic dependence of migration speed with cell adhesion. Much is not understood about this very common behavior. A phenomenological model for 3D single-cell migration that exhibits biphasic behavior and highlights the important role of steric hindrance is developed and studied analytically. Changes in the biphasic behavior in the presence of proteolytic enzymes are investigated. Our methods produce a framework to determine analytic formulae for the mean cell speed, allowing general statements in terms of parameters to be explored, which will be useful when interpreting future experimental results. Our formula for mean cell speed as a function of ligand concentration generalizes and extends previous computational models that have shown good agreement with in vitro experiments.

The Role of Pleiotropy in the Evolutionary Maintenance of Positive Niche Construction

Organisms often modify their environments to their advantage through a process of niche construction. Environments that are improved through positive niche construction can be viewed as a public good. If free riders appear that do not contribute to the shared resource and therefore do not incur any associated costs, the constructed niche may become degraded, resulting in a tragedy of the commons and the extinction of niche constructors. Niche construction can persist if free riders are excluded, for example, if niche constructors monopolize the resource they produce to a sufficient degree. We suggest, however, that the problem of free riders remains because it is possible that nonniche constructors with an enhanced ability to access the resource appear and invade a population of constructors. Using mathematical models we show that positive niche construction can be maintained if it is inextricably linked to a mechanism that makes free riding costly, such as a trait that confers a benefit to only niche constructors. We discuss this finding in terms of genetic interactions and illustrate the principle with a two-locus model. We conclude that positive niche construction can both evolve and be maintained when it has other beneficial effects via pleiotropy. This situation may apply generally to the evolutionary maintenance of cooperation.