Cell size homeostasis and optimal viral strategies for host exploitation

Singh, AbhyudaiZurakowski, Ryan M.The first part of this thesis address a question formulated more than 80 years ago (and still remains elusive): how does a cell control its size? Growth of a cell and its subsequent division into daughters is a fundamental aspect of all cellular living systems. During these processes, how do individual cells correct size aberrations so that they do not grow abnormally large or small? How do cells ensure that the concentration of essential gene products are maintained at desired levels, in spite of dynamic/stochastic changes in cell size during growth and division? ☐ In chapter 1, we introduce the reader to the field of cell size/content homeostasis. We review how advances in singe-cell technologies and measurements are providing unique insights into these questions across organisms from prokaryotes to human cells. More specifically, how diverse strategies based on timing of cell-cycle events, regulating growth, and number of daughters are employed to maintain cell size homeostasis. We further discuss how size-dependent expression or gene-replication timing can buffer concentration of a gene product from cell-to-cell size variations within a population. ☐ In chapter 2, we propose the use of stochastic hybrid systems as a framework for studying cell size homeostasis. We assume that cell grows exponentially in size (volume) over time and probabilistic division events are triggered at discrete time intervals. We first consider a scenario, where a timer (i.e., cell-cycle clock) that measures the time since the last division event regulates both the cellular growth and division rates. We also study size-dependent growth / division rate regulation mechanisms. We provide bounds on different statistical indicators (mean, variance, skewness, etc). Additionally, we assess the effect of different physiological parameters (growth rate, partition errors, etc) on cell size distribution. ☐ Chapter 3 introduces a mechanistic model that might explain the recently uncovered added principle, i.e., selected species add a fixed size (volume) from birth to division, irrespective of their size at birth. To explain this principle, we consider a timekeeper protein that begins to get stochastically expressed after cell birth at a rate proportional to the volume. Cell-division time is formulated as the first-passage time for protein copy numbers to hit a fixed threshold. Consistent with data, the model predicts that the noise in division timing increases with size at birth. We show that the distribution of the volume added between successive cell-division events is independent of the newborn cell size. This fact is corroborated through experimental data available. The model also suggest that the distribution of the added volume when scaled by its mean become invariant of the growth rate, a fact also veri ed through available experimental data. ☐ In part 2 of this thesis, we study which strategies are implemented by a viral species, ranging from bacteriophages to human immunodeficiency virus (HIV), in order to exploit host resources. In chapter 4, we review the classical theory of viral-host dynamics and describe the key knobs that viruses tweak to exploit a cell population. This theory suggest that viruses might evolved to have infinite infectivity and virulence. In the case of infectivity, chapter 5 gives an alternative to infinite infectivity: virus will evolve to moderate infectivity because of local interactions. As an example, we study a phage attacking a bacterial population. We include the effect of local interactions by assuming that the phage needs to scape from bacterial death remains (debris). ☐ Infinite virulence is also challenged as evolutionary alternative for viral propagation. In chapter 5 we study environments where availability of susceptible bacteria fluctuates across time. Under such scenarios bacteria behaves contrary to classical ecology theory: phages evolve to a moderate virulence (lysis time). We present this insights through the use of the stochastic hybrid system framework. ☐ In chapter 7, we present a mathematical model of HIV transmission including cell-free and cell-cell transmission pathways. A variation of this model is considered including two populations of virus. The first infects cells only by the cell-free virus pathway, and the second infects cells by either the cell-free or the cell-cell pathway (synapse-forming virus). Synapse-forming HIV is shown to provide an evolutionary advantage relative to non synapse-forming virus when the average number of virus transmitted across a synapse is a su ciently small fraction of the burst size. ☐ HIV disease is well-controlled by the use of combination antiviral therapy (cART), but lifelong adherence to the prescribed drug regimens is necessary to prevent viral rebound and treatment failure. Populations of quiescently infected cells form a "latent pool" which causes rapid recurrence of viremia whenever antiviral treatment is interrupted. A "cure" for HIV will require a method by which this latent pool may be eradicated. Current efforts are focused on the development of drugs that force the quiescent cells to become active. Previous research has shown that cell-fate decisions leading to latency are heavily in uenced by the concentration of the viral protein Tat. While Tat does not cause quiescent cells to become active, in high concentrations it prevents a newly infected cell from becoming quiescent. In chapter 8, we introduce a model of the effects of two drugs on the latent pool in a patient on background suppressive therapy. The first drug is a quiescent pool stimulator, which acts by causing quiescent cells to become active. The second is a Tat analog, which acts by preventing the creation of new quiescently infected cells. We apply optimal control techniques to explore which combination therapies are optimal for different parameter values of the model.University of Delaware, Department of Electrical and Computer EngineeringPh.D