Session Y49: Evolutionary Systems Biology II

Bifurcations and critical transitions in cell population dynamics: Why it is so hard to control cancer?

It is increasingly recognized that development of drug resistance and recurrence in cancer is to some extent driven by treatment-induced cell state transitions, namely from a drug-sensitive to a resilient, stem-cell-like state, instead of solely a selection of mutant cells that ``happen'' to be drug resistant. We have previously postulated non-genetic, non-Darwinian (quasi-Lamarckian) evolution of drug resistance and now provide experimental support for our model for acquisition of resistance: In general, state transition of a cell from one stable phenotype --represented by a high-dimensional attractor state in gene expression space-- to another one requires the destabilization of the original attractor such that cells can, without overcoming an ``energy barrier'', enter the new attractor state (``alternative regime'') that encodes the gene expression profile conferring the resistant, stem-like phenotype. In response to cytotoxic treatment cells undergo such a transition which represents a bifurcation event --and is thus observable as a critical transition. Single-cell resolution gene expression profiles of entire cell populations undergoing such cell state transitions were consistent with two major predictions from the theory: appearance of the equivalent of ``Early Warning Signals'' and emergence of ``rebellious cells''. The latter have undergone a state change in the ``opposite direction''. Indeed, cancer therapy seeks a state transition of tumor cells to the apoptotic state but as predicted by theory, also generates stem-cell like cells, which are the source of recurrence. But experiments now expose a complication due to cell-cell interactions, giving rise to non-linear tumor behaviors which have serious implications for treatment of cancer. Theoretical and practical consequences of this cell-population level resilience will be discussed, including alternatives to cell-killing therapies and possible theoretical limits of ``curability'' of cancer.   

The Fitness Trade-offs of Predation: When to Scavenge and When to Steal

Predator foraging behavior can fall on a continuous spectrum between hunting and scavenging. Here, we study the behavior of a group of foragers that can actively hunt for prey, or scavenge from the foils of a fixed pool of predators either by eating leftovers (passive scavenging) or by stealing from a predator (active scavenging). To do this, we employ stochastic dynamic programming which enables us to construct a deterministic matrix of decisions and associated fitness values for a set of potential behaviors. This approach is centred around finding consumer behaviors that maximize fitness. Our results suggest that there are well-defined parameter regimes where each foraging strategy maximizes fitness, and that risky behaviour (active scavenging) becomes a viable choice for a small range of parameters when costs associated with hunting and scavenging are comparable or when the mortality associated with active scavenging is low. We then generalise this model in terms of organismal body mass so that it can be applied to real-life systems to determine the relationship between body-size classes and different predatory behaviors, and to better understand trade-offs in decision-making associated with body-size limitations.   

Statistical Mechanics of Large and Complex Ecosystems

Our intuition for ecological and evolutionary dynamics comes from simple models representing the interactions among two or three distinct kinds of organisms. But real ecosystems contain large numbers of distinct kinds of individuals, and the high dimensionality of the resulting state space can invalidate low-dimensional insights. The cavity method from spin glass physics has recently emerged as a powerful tool for exploring the opposite limit, with approximations that become more accurate as the dimensionality grows. I will present some results I have recently obtained using this approach, which shed new light on classic ecological observations and suggest intriguing avenues for further investigation.   

Invasion dynamics in generalized MacArthur's consumer resource models

A fundamental problem in community ecology is to identify the principles governing ecosystem evolution due to invasions by new species. By studying the MacArthur's consumer resource model (MCRM) with renewable resources, we show that a successful invasions (almost) always increases the total power consumption of an ecosystem. We show that this is generally true even when we include more complicated dynamics such as nonlinear response functions and cross feeding, suggesting there exists a maximum energy utilization efficiency principle underlying successful invasions in ecosystems with renewable resources. As a test of this idea, we show that this principle can be used to predict the success of an invasion with high probability. Furthermore in simulations where we repeatedly invade ecosystems, we show that ecosystems eventually reach an approximate steady-state dynamic where the probability of successful invasion drops dramatically. We argue that this is the analogue of a jamming transition in 'species packing' and can be naturally explained in terms of glass physics.   

Untangling the biological hairball: Network evolution and fitness based reduction

Complex mathematical models of interaction networks are routinely used for prediction in systems biology. However, it is difficult to reconcile network complexities with a formal understanding of their behavior. I will introduce several models of immune recognition by T cells and will show how a simple procedure can be used to reduce them to functional submodules, using statistical mechanics of complex systems combined with a fitness-based approach inspired by in silico evolution. Our procedure works by putting parameters or combination of parameters to some asymptotic limit, while keeping (or slightly improving) the model performance, and requires parameter symmetry breaking for more complex models. An intractable model of immune recognition with close to a hundred individual transition rates is reduced to a simple two-parameter model, and connected to the ``adaptive sorting" principle that we previously identified and experimentally validated. Our procedure extracts three different mechanisms for early immune recognition, and automatically discovers similar functional modules in different models of the same process allowing for model classification and comparison.   

Diversity, Stability, and Reproducibility in Stochastically Assembled Microbial Ecosystems

Microbial ecosystems are remarkably diverse, stable, and often consist of a balanced mixture of core and peripheral species. Here we propose a conceptual model exhibiting all these emergent properties in quantitative agreement with real ecosystem data, specifically species' abundance and prevalence distributions. Resource competition and metabolic commensalism drive stochastic ecosystem assembly in our model. We demonstrate that even when supplied with just one resource, ecosystems can exhibit high diversity, increasing stability, and partial reproducibility between samples.   

Eco-evolutionary Dynamics at High Diversity

Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining “fitness”. It is not always clear to what extent the intuition derived from low-dimensional models applies to the complex, high-dimensional reality. For instance, most naturally occurring microbial communities harbor a strikingly large number of coexisting species, and understanding the eco-evolutionary interplay in these systems is an exciting new domain for statistical physics. Recent work demonstrated that the high-diversity limit of classic consumer-resource models is analytically tractable, offering a promising new platform for investigating ecology in this regime. Here, we describe how the same analytical framework can be extended to also study evolutionary questions. Our analysis shows how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness can become misleading. Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to properties of high-dimensional geometry as manifested in our model.   

Evolution of Modularity and Hierarchy in CRISPR-Cas Target Recognition

Clustered, regularly interspaced, short, palindromic repeats (CRISPR) constitute a genetic adaptive immune system unique to prokaryotic cells used to combat phage threats. The host cell incorporates DNA sequences from invading phages into its CRISPR locus as spacers. These spacers are expressed as guide RNAs that direct CRISPR-associated (Cas) proteins to protect against subsequent attack by the same phages. The guide RNA and Cas protein complex recognize three distinct sequence modules: (1) a protospacer associated motif (PAM), (2) a short seed region, and (3) the residual spacer basepairs. There is a hierarchical significance to these three elements, as mismatches between the CRISPR machinery and target sequence are most sensitive in the PAM region, followed by those in the seed. Here we show that the CRISPR-Cas machinery evolved with this selection for modularity and hierarchy in order to efficiently and effectively recognize invaders.   

Host-pathogen coevolution and the corresponding phase diagram

Predicting the possible outcomes in a coevolutionary arms race between the predator and prey is the key to developing strategies that mitigate the risk of extinction of a species. For instance, in microbial systems the host will maintain resistance to the pathogen as long as the benefits outweigh the costs. Predicting this cost-benefit ratio in systems that coevolve is an open problem in the field. Here we present a simple three-dimensional model of host-pathogen interactions where the population dynamics can be analytically determined. In this system we describe the coevolution in terms of bifurcation theory, where changes in host/pathogen parameters lead to changes in population dynamics, from stable fixed points where resistance is maintained to periodic solutions to pathogen extinction. We recast these long-term outcomes in a phase diagram; trajectories in this diagram correspond to different coevolutionary pathways. This simple model can give insights into the evolutionary dynamics at a general level, extending to general host-pathogen and host-parasite systems, with possible applications in cancer biology.   

Metabolic Trade-Offs in Serial Dilution Culture

Microbial communities in nature typically exhibit a vast diversity of organisms. These observations clash with the predictions of resource-competition models, which allow only as many species as resources to coexist at steady state. One possible solution to this paradox is the idea that organisms are subject to trade-offs, which ensure no species has an absolute advantage over others. This concept was explored in the framework of a chemostat model by Posfai et al. (2017), who found that large regions of the nutrient supply space can support unlimited diversity if all organisms have the same fixed enzyme budget. However, while the chemostat provides a useful conceptual model, nutrient supply rates in nature are seldom steady. The other extreme corresponds to serial dilution or "seasonal" variation where nutrients are supplied periodically or even randomly in discrete packets. Here, we analyze how metabolic trade-offs influence diversity in such a serial dilution model. We characterize the effects of varying supply on the population dynamics, finding relationships that still permit unlimited diversity but differ qualitatively from those found in the chemostat case. We also examine connections between the chemostat and serial dilution models.   

How a Well-adapting Immune System Remembers

The adaptive immune system uses its past experience of pathogens to prepare for future infections. How much can the adaptive immune system learn about the statistics of changing pathogenic environments given its sampling of the antigenic universe? And how should it best adapt its repertoire of lymphocyte receptor specificities based on its experience? Here, to answer these questions we propose a view of adaptive immunity as a dynamic Bayesian machinery that predicts optimal repertoires based on past pathogen encounters and knowledge about typical pathogen dynamics. Two key experimentally observed characteristics of adaptive immunity emerge naturally from this model: (1) a negative correlation between fold change of protection upon a challenge and preexisting immune levels and (2) differential regulation of memory and naive cells. We argue that to explain the benefits of immune memory, antigenic environments need to be highly sparse. We derive experimentally testable predictions about the diversity of the memory repertoire over time in such sparse antigenic environments. The Bayesian perspective on immunological memory provides a unifying conceptual framework for a number of features of adaptive immunity and suggests further experiments