Session X20: Statistical Physics of Large Populations of Cells: from Microbes to Tissues

Statistical Physics of Noninteracting Bacterial Populations

Genetically identical bacterial cells in identical environments display significant variability in their phenotypic behavior; they grow at different rates, divide at different sizes, and have different generation times. With recent advances in single-cell technologies, now we can measure not only the distributions of these quantities but also the subtle correlations between these variables both within and across generations. These statistical descriptions have paved the way for the phenomenological models of cellular growth and division. In this talk, I will take these phenomenological models as the microscopic dynamics of individual cells to quantitatively predict the macroscopic properties of populations both in batch and chemostat settings. In particular, I derive the growth rate of the population, the rate at which a population approaches its steady state, and the rate of neutral genetic drift from the single-cell variables.   

Optimal segregation of key proteins in microbes

Asymmetric segregation of key proteins at cell division has been observed in various unicellular organisms, including E. coli and budding yeast. It is often assumed to enhance the fitness of the population. We study the population growth in the presence of asymmetric segregation and find, generically, a phase transition occurring between a regime where asymmetry is beneficial to one where it is detrimental. We investigate the nature of this phase transition in the presence of asymmetry in cell division, stochasticity and multiple key proteins, each of which can be beneficial or deleterious, segregating in different proportions.   

Understanding Cell Size Homeostasis and Phenotypic Switching Dynamics during Bacterial Filamentation

Colonies of bacteria undergoing filamentation present a noticeable phenotypic diversity in terms of their size and yet homeostasis is achieved. While the mechanism for achieving size homeostasis at a normal size scale is clear, the following questions remain in the context of filamentation. How do filamentous strains achieve size homeostasis? What is the dynamics underlying phenotypic switching? To answer these questions, we have modeled the bacterial growth and division processes during filamentation and performed analyses of experimental phenotypic lineage trees. Our model reveals how making compatible the observed adder-like correlations at the collective level and sizer properties at the individual cell level. We further show that size homeostasis is independent on the division pattern (i.e. what septa are eventually selected for cell cleavage in filamentous cells). Also, our analyses of lineage trees combined with mathematical models suggest that changes in the phenotypic composition of colonies mainly derive from a switch of the growth/division mode. Altogether, our work sheds light on the dynamics of filamentation and helps to understand the transition from a regular to a filamentous phenotype.   

Effect of non-genetic inheritance dynamics on the variation in cellular traits

Isogenic cell populations exhibit large phenotypic heterogeneity even when experiencing homogenous environmental conditions. The evolution of this heterogeneity is limited in part by the inheritance of cellular traits from one generation to the next. In this talk, we will introduce a new experimental technique based on trapping sister bacterial cells in microfluidic channels immediately after they separate from a single mother. Our new setup allows us to follow the sister cells growth and gene expression dynamics for up to ~100 generations while both cells experience identical environmental conditions. This in turn, provides a quantitative measurement of how identical cells become different over time, which reflects the non-genetic inheritance effects, and reveals their contribution to restraining the variability of cellular traits. Our results show that the inheritance dynamics vary significantly among different cellular traits, and its effects, can extend up to ~10 generations.
  

A large deviation principle linking lineage statistics to fitness

In exponentially proliferating populations of bacteria, a population may double at a rate greater than or less than the average doubling time of a single-cell, depending on the variability and heritability of generation times at the single-cell level. Previous studies have shown that the distribution of generation times obtained from an isolated lineage is, in general, insufficient to determine the population’s doubling time or growth rate, both of which are proxies for fitness. This poses a fundamental challenge for experimentalists who wish to probe the fitness effects of physiological perturbations using single-cell tracking data. Using a large deviation approach, we present a procedure for inferring a population’s fitness from lineage statistics that is independent of the model specifics. Interestingly, the Large deviation structure underlying the population dynamics imposes a fundamental constraint on the accuracy to which one can infer a population’s fitness from finite lineage data.   

A Sensitivity Analysis of Growth Rate to Perturbations in Essential Gene Expression

Cell growth is one of the most fundamental physiological processes that bacteria perform, yet the mechanisms by which cells achieve specific growth rates are unknown. To elucidate the genetic basis for cell growth, we performed an essential genome-wide stability analysis of single-cell growth rate upon CRISPRi-mediated perturbation in gene expression. We used mechanistic mathematical modeling to interpret our data. We found that acute transcriptional inhibition of expression of a ribosomal subunit resulted in a growth rate decay that could be predicted by the linear correlation between ribosome concentration and growth rate previously reported. While this confirms that ribosome concentration is rate-limiting with respect to growth, transcriptional inhibition of several other genes involved in various processes resulted in much more rapid growth decay. Overall, decay times were heterogeneous even among genes in the same metabolic pathway. Genes whose inhibition yields fast growth-rate decay times represent key regulators of cellular growth rate. We found that the proteolysis of these proteins is critical for their ability to efficiently mediate growth-rate kinetics in response to nutrient shifts.
  

Modeling and Optimizing Treatments of Bacterial Infections by Phage and Phage-Antibiotic Combinations

The spread of antibiotic-resistant pathogens is a global threat to public health. As such, there is growing interest in alternative antimicrobials including phage, or viruses that only infect bacteria. However, phage therapy has shown inconsistent efficacy in clinical trials, possibly due to heterogeneity in the host immune response. By combining nonlinear population models and animal experiments, we have shown that host immunity can work synergistically with phage to cure an acute respiratory infection. Nonetheless, phage therapy could still fail when phage resistance is high. In such cases, we consider two strategies proposed to enhance the robustness of phage therapy: combining phage with antibiotics and combining different strains of phage (phage cocktail). Our model predicts that host immunity is also required for the efficacy of phage-antibiotic combinations. Finally, we discuss applications of optimal control theory to optimize the dosing and composition of single phage and phage cocktail therapy, and opportunities to extend findings to application of phage therapy to complex spatial environments.   

New homeostatic principles in biology - how cells go back to their normal size without feedback

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and the field is currently enjoying its second Renaissance due to physicists. In this talk, I will focus on cell-size control and homeostasis, a fundmental problem that has been rapidly transforming just in the past few years. I will introduce some of the long-standing questions, and explain the answers that experimentalists and theorists have provided so far. Collectively, the emerging picture is likely to answer a general class of problmes in biology beyond bacteria, i.e., how individual cells can converge to their average state without invoking any apparent feedback mechanisms.