Multiscale modeling of microbial communities

Although bacteria are single-celled organisms, they exist in nature primarily in the form of complex communities, participating in a vast array of social interactions through regulatory gene networks. The social interactions between individual cells drive the emergence of community structures, resulting in an intricate relationship across multiple spatiotemporal scales. Here, I present my work towards developing and applying the tools necessary to model the complex dynamics of bacterial communities. In Chapter 2, I utilize a reaction–diffusion model to determine the population dynamics for a population with two species. One species (CDI+) utilizes contact dependent inhibition to kill the other sensitive species (CDI-). The competition can produce diverse patterns, including extinction, coexistence, and localized aggregation. The emergence, relative abundance, and characteristic features of these patterns are collectively determined by the competitive benefit of CDI and its growth disadvantage for a given rate of population diffusion. The results provide a systematic and statistical view of CDI-based bacterial population competition, expanding the spectrum of our knowledge about CDI systems and possibly facilitating new experimental tests for a deeper understanding of bacterial interactions. In the following chapter, I present a systematic computational survey on the relationship between social interaction types and population structures for two-species communities by developing and utilizing a hybrid computational framework that combines discrete element techniques with reaction-diffusion equations. The impact of deleterious and beneficial interactions on the community are quantified. Deleterious interactions generate an increased variance in relative abundance, a drastic decrease in surviving lineages, and a rough expanding front. In contrast, beneficial interactions contribute to a reduced variance in relative abundance, an enhancement in lineage number, and a smooth expanding front. More specifically, mutualism promotes spatial homogeneity and population robustness while competition increases spatial segregation and population fluctuations. To examine the generality of these findings, a large set of initial conditions with varying density and species abundance was tested and analyzed. The results and the computational framework presented provide the basis for further explorations of individual based simulations of bacterial communities. For Chapter 4, I consider the role of gene regulation in shaping the outcome of competition between a bacteriocin (i.e. toxin) producing and sensitive strain. In natural systems, bacteriocin production is often conditional, governed by underlying quorum sensing regulatory circuitry. By developing an ordinary differential equation (ODE) model integrating population dynamics with molecular regulation, we find that the ecological contribution of bacteriocin production can be positive or negative, determined by the tradeoff between the benefit of bacteriocins in mediating competition and the fitness cost due to metabolic load. Interestingly, under the naturally occurring scenario where bacteriocin production has a high cost, density-dependent synthesis is more advantageous than constitutive synthesis, which offers a quantitative interpretation for the wide prevalence of density-related bacteriocin production in nature. By incorporating the modeling framework presented in Chapter 3, the results of the ODE model were extended to the spatial setting, providing ecological insights into the costs and benefits of bacteriocin synthesis in competitive environments. For the final research chapter, I consider the impact of growth coupling on protein production at both the single cell and population scales. The same machinery (e.g. ribosomes) and resources (e.g. amino acids and ATP) are used within cells to produce both endogenous (host) and exogenous (circuit) proteins. Thus, the introduction of a gene circuit generates a metabolic burden on the cell which can slow its growth rate relative to the wild type. Building off of the computational framework introduced in Chapter 3 with single cell resolution, I utilize deterministic and stochastic simulations to characterize the changes in protein production due to host-circuit coupling for a simple gene regulatory architecture. Analytical arguments and simulation results show that incorporating growth can lead to drastic changes in both the steady state and time scales for protein production at the single cell and population level. Furthermore, host-circuit coupling can induce bimodality at the population level well outside the bistable region for single cell dynamics

Spatial-temporal patterns in evolutionary ecology and fluid turbulence

This thesis explores the turbulence of ecosystems, and the ecology of turbulence. Ecosystems and turbulent fluids are both highly non-equilibrium and exhibit spatio-temporal complexity during the course of their evolution. It might seem that they are too complicated to extract universal properties, even if there are any. Surprisingly, it turns out that each of them can shed light on the other, enabling them both to be solved. In particular, the techniques used to explore ecosystem dynamics turn out to be exactly what is needed to solve the problem of the laminar-turbulent transition in pipes. Accordingly, this thesis is organized into two parts. Part 1 discusses what governs the rate of evolution and what are the consequences of the interplay between ecology and evolution at different scales. Three different aspects of these underlying questions are included in this part: (1) We first study the phenomenon of anomalous population dynamics known as "rapid evolution", in which a fast evolutionary time scale emerges from intense ecological interactions between species. Specific examples are rotifer-algae and bacteria-phage, where the ecosystem is composed of a predator and its prey. However, a sub-population of mutant prey arises from strong environmental pressure, and the trade-off between selection from reproduction and predation is manifested in the patterns of eco-evolutionary dynamics. We discuss how to solve such system with inherent stochasticity by a generic and systematic analytical approach in the spirit of statistical mechanics, using a stochastic individual-level model. We show that this method can naturally capture the universal behavior of the stochastic dynamics from demographic noise without any additional and more biologically detailed assumptions. (2) Second, we address the question of the role of selection in evolution and its relationship with phenotypic fluctuations. Phenotypic fluctuations have been conjectured to be beneficial characteristics to protect against fluctuating selection from environmental changes. But it is not well-understood how phenotypic fluctuations shape the evolutionary trajectories of organisms. We address these questions in the context of directed evolution experiments on bacterial chemotactic phenotypes. Our stochastic modeling and experiments on the evolution of chemotactic fronts suggest that the strength of selection can determine whether or not phenotypic fluctuations grow or shrink during successive rounds of selection and growth. (3) The third aspect of the first part focuses on the paradox of coexistent stability in microbial ecosystems that display especially intricate evolutionary phenomena. We propose that horizontal gene transfer, an important evolutionary driving force, is also the driving force that can stabilize microbe-virus ecosystems. The particular biological system for our model is that of the marine cyanobacteria Prochlorococcus spp., one of the most abundant organisms on the planet, and its phage predator. Phylogenetic analysis reveals compelling evidence for horizontal gene transfer of photosynthesis genes between the bacteria and phage. We test our hypothesis by building a spatially-extended stochastic individual-level model and show that the presence of viral-mediated horizontal gene transfer can induce collective coevolution and ecosystem stability, leading to a large pan-genome, an accelerated evolutionary timescale, and the emergence of ecotypes that are adapted to the stratified levels of light transmission as a function of ocean depth. The goal of Part 2 is to understand the nature of the transition to turbulence in fluids, which has been a puzzle for more than a century. The novelty of our approach is that we consider transitional turbulence as a non-equilibrium phase transition. Accordingly we attempt to approach this problem by looking for an appropriate long-wavelength effective theory. We report evidence of candidate long-wavelength collective modes in direct numerical simulations of the Navier-Stokes equations in a pipe geometry, where we uncover unexpected spatio-temporal patterns reminiscent of ecological predator-prey dynamics. This finding allows us to construct a minimal Landau theory for transitional turbulence, which resembles a stochastic predator-prey model. This in turn can be mapped into the generic universality class of directed percolation. Stochastic simulations of this spatial-extended individual-level predator-prey model are able to recapitulate the experimentally observed super-exponential dependence of the lifetime of turbulent regions on Reynolds number near the onset of turbulence. We argue that these remarkable scaling phenomena reflect the presence of finite-size effects as the correlation length becomes of order the pipe diameter, leading to a universal finite-size scaling distribution for the velocity fluctuations.Ope

Spatial organisation of expanding bacterial colonies is affected by contact-dependent growth inhibition

Identifying how microbes are able to manipulate, survive and thrive in complex multispecies communities has expanded our understanding of how microbial ecosystems impact human health and the environment. The ability of bacteria to negatively affect neighbours, through explicit toxin delivery systems, provides them with an opportunity to manipulate the composition of growing microbial communities. Contact-dependent inhibition (CDI) systems (a Type Vb secretion system) are a distinct subset of competition systems whose contribution to shaping the development of spatially-structured bacterial communities are yet to be fully understood. Here we compare the impact of different CDI systems, at both the single cell and population level, to determine the key drivers of CDI-mediated competition within spatially-structured bacterial populations. Through an iterative approach using both an Escherichia coli experimental system and computational modelling, we show that CDI systems have subtle and system-specific effects at the single cell level, generating single cell wide boundaries between CDI-expressing inhibitor cells and their neighbouring targets. Despite the subtle effects of CDI at a single cell level, CDI systems greatly diminished the ability of susceptible targets to expand their range during colony growth. The inoculum density of the population, together with the CDI system-specific variables of the speed of inhibition after contact and biological cost of CDI, strongly affects CDI-mediated competition. In contrast, the magnitude of the toxin-induced growth retardation of target cells only weakly impacts the composition of the population. Our work reveals how distinct CDI systems can differentially affect the composition and spatial arrangement of bacterial populations

Differential Equations arising from Organising Principles in Biology

This workshop brought together experts in modeling and analysis of organising principles of multiscale biological systems such as cell assemblies, tissues and populations. We focused on questions arising in systems biology and medicine which are related to emergence, function and control of spatial and inter-individual heterogeneity in population dynamics. There were three main areas represented of differential equation models in mathematical biology. The first area involved the mathematical description of structured populations. The second area concerned invasion, pattern formation and collective dynamics. The third area treated the evolution and adaptation of populations, following the Darwinian paradigm. These problems led to differential equations, which frequently are non-trivial extensions of classical problems. The examples included but were not limited to transport-type equations with nonlocal boundary conditions, mixed ODE-reaction-diffusion models, nonlocal diffusion and cross-diffusion problems or kinetic equations

Putting ecological theories to the test : individual-based simulations of synthetic microbial community dynamics

Microbial communities are critical for the proper functioning of each and every ecosystem on Earth. The ability to understand the structure and functioning of these complex communities is crucial to manage and protect natural communities, as well as to rationally design engineered microbial communities for important applications ranging from medical and pharmaceutical uses to various bioindustrial processes. In recent years, synthetic microbial communities have gained increasing interest from microbiologists due to their reduced complexity and increased controllability, which favours them over more complex natural systems for examining ecological theories. In this thesis, the in silico counterpart of this approach was used to test ecological theories relating to biodiversity and functionality through the use of mathematical models. Models are abstractions of reality which allow for the testing of hypotheses in a controlled way. In this thesis, individual-based models of synthetic microbial communities were developed and used in simulation studies to answer research questions relating to community diversity, stability, productivity and functionality. The models are spatially explicit and track through time the characteristics, interactions and activities of every individual in the community. The modelling framework is flexible and thus also extendable to other avenues of research

The evolutionary ecology of CRISPR-Cas adaptive immunity

Microbial communities play a vital role in shaping their local environment and provide many important ecosystem services. The structure and function of microbial communities is dependent on interactions with prokaryote-specific viruses and other mobile genetic elements (MGEs), but we know relatively little about these interactions in nature. The prokaryotic adaptive immune system CRISPR-Cas provides resistance to phage and other MGEs by inserting phage-derived sequences into CRISPR loci on the host genome to allow sequence specific immunological memory against re-infection. Compared to the specific mechanism of CRISPR-Cas, phage resistance via surface modification provides general defense against a range of phage by physically modifying the cell surface to prevent phage infection. CRISPR-Cas and surface modification have been shown to be the most common mechanisms for rapid evolution of de novo phage resistance and therefore likely play important roles in shaping microbial communities. It has been suggested that we may be able to manipulate CRISPR-Cas evolution to our advantage, but very little research has been done investigating the evolutionary outcome of such manipulation. In this thesis I investigate the importance of different ecological drivers on when CRISPR-Cas is favoured over phage resistance via surface modification. I find that increasing CRISPR allele diversity within a host population increases phage immunity at the population level. However, increasing genetic diversity within the phage population increases selection for generalist phage defence via surface modification over specific CRISPR-Cas resistance. I also attempt to investigate the importance of cell-cell communication in the evolution of bacterial resistance; however these experiments were hampered by secondary effects of inhibiting cell-cell communication. These results are discussed in context with recent findings with the aim of expanding our knowledge of CRISPR-Cas evolution and ecology and suggesting where further research would be beneficial