Synthesis of Biological and Mathematical Methods for Gene Network Control

abstract: Synthetic biology is an emerging field which melds genetics, molecular biology, network theory, and mathematical systems to understand, build, and predict gene network behavior. As an engineering discipline, developing a mathematical understanding of the genetic circuits being studied is of fundamental importance. In this dissertation, mathematical concepts for understanding, predicting, and controlling gene transcriptional networks are presented and applied to two synthetic gene network contexts. First, this engineering approach is used to improve the function of the guide ribonucleic acid (gRNA)-targeted, dCas9-regulated transcriptional cascades through analysis and targeted modification of the RNA transcript. In so doing, a fluorescent guide RNA (fgRNA) is developed to more clearly observe gRNA dynamics and aid design. It is shown that through careful optimization, RNA Polymerase II (Pol II) driven gRNA transcripts can be strong enough to exhibit measurable cascading behavior, previously only shown in RNA Polymerase III (Pol III) circuits. Second, inherent gene expression noise is used to achieve precise fractional differentiation of a population. Mathematical methods are employed to predict and understand the observed behavior, and metrics for analyzing and quantifying similar differentiation kinetics are presented. Through careful mathematical analysis and simulation, coupled with experimental data, two methods for achieving ratio control are presented, with the optimal schema for any application being dependent on the noisiness of the system under study. Together, these studies push the boundaries of gene network control, with potential applications in stem cell differentiation, therapeutics, and bio-production.Dissertation/ThesisDoctoral Dissertation Biomedical Engineering 201

Forward and Reverse Engineering of Cellular Decision-Making

Cells reside in highly dynamic environments to which they must adapt. Throughout its lifetime, an individual cell receives numerous chemical and mechanical signals, communicated through dense molecular networks, and eliciting a diverse array of responses. A large number of these signals necessitate discrete, all-or-none responses. For instance, a cell receiving proliferation signals must respond by committing to the cell-cycle and dividing, or by not initiating the process at all; that is, the cell must not adopt an intermediate route. Analogously, a stem-cell receiving signals for different lineages must commit exclusively to one of these lineages. How individual cells integrate multiple, possibly conflicting, noisy inputs, and make discrete decisions is poorly understood. Detailed insight into cellular decision-making can enable cell-based therapies, shed light on diseases arising out of dysregulation of control, and suggest practical design strategies for implementing this behavior in synthetic systems for research and industrial use. In this thesis, we have employed both mathematical modeling and experiments to further elucidate the mechanistic underpinnings of decision-making in cells. First, we describe a computational study that assesses the entire space of minimal networks to identify topologies that can not only make decisions but can do so robustly in the dynamic and noisy cellular environment. Second, via model-driven, quantitative experiments in a megakaryocyte erythroid progenitor line, we demonstrate that a simple network with mutual antagonism and autoregulation captures the dynamics of the master transcription factors at the level of individual cells. Expansion of this model to account for extrinsic cues reconciles the competing stochastic and instructive theories of hematopoietic lineage commitment, and implicates cytokine receptors in broader regulatory roles. Third, to assess the impact of specific genetic perturbations on the distribution of the population, and on commitment trajectories of individual cells, we implemented the core mutual antagonism and autoregulation topology synthetically in yeast cells. Our approach of using orthogonal variants of a single core protein represents a general, modular design strategy for building synthetic circuits, and model-driven experiments elucidate how gene dosage, repression strength, and promoter architecture can modulate decision-making behavior

Robust Network Topologies for Generating Switch-Like Cellular Responses

Signaling networks that convert graded stimuli into binary, all-or-none cellular responses are critical in processes ranging from cell-cycle control to lineage commitment. To exhaustively enumerate topologies that exhibit this switch-like behavior, we simulated all possible two- and three-component networks on random parameter sets, and assessed the resulting response profiles for both steepness (ultrasensitivity) and extent of memory (bistability). Simulations were used to study purely enzymatic networks, purely transcriptional networks, and hybrid enzymatic/transcriptional networks, and the topologies in each class were rank ordered by parametric robustness (i.e., the percentage of applied parameter sets exhibiting ultrasensitivity or bistability). Results reveal that the distribution of network robustness is highly skewed, with the most robust topologies clustering into a small number of motifs. Hybrid networks are the most robust in generating ultrasensitivity (up to 28%) and bistability (up to 18%); strikingly, a purely transcriptional framework is the most fragile in generating either ultrasensitive (up to 3%) or bistable (up to 1%) responses. The disparity in robustness among the network classes is due in part to zero-order ultrasensitivity, an enzyme-specific phenomenon, which repeatedly emerges as a particularly robust mechanism for generating nonlinearity and can act as a building block for switch-like responses. We also highlight experimentally studied examples of topologies enabling switching behavior, in both native and synthetic systems, that rank highly in our simulations. This unbiased approach for identifying topologies capable of a given response may be useful in discovering new natural motifs and in designing robust synthetic gene networks

Perfect Sampling of the Master Equation for Gene Regulatory Networks

We present a Perfect Sampling algorithm that can be applied to the Master Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo methods and combines it with the Dominated Coupling From The Past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for GRNs have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system, and the repressilator, a six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa

Interplay of Extrinsic and Intrinsic Cues in Cell-Fate Decisions

A cell’s decision making process is coordinated by dynamic interplay between its extracellular environment and its intracellular milieu. For example, during stem cell differentiation, fate decisions are believed to be ultimately controlled by differential expression of lineage-specific transcription factors, but cytokine receptor signals also play a crucial instructive role in addition to providing permissive proliferation and survival cues. Here, we present a minimal computational framework that integrates the intrinsic and extrinsic regulatory elements implicated in the commitment of hematopoietic progenitor cells to mature red blood cells (Chapter 2). Our model highlights the importance of bidirectional interactions between cytokine receptors and transcription factors in conferring properties such as ultrasensitivity and bistability to differentiating cells. These system-level properties can induce a switch-like characteristic during differentiation and provide robustness to the mature state. We then experimentally test predictions from this lineage commitment model in a model system for studying erythropoiesis (Chapter 3). Our experiments show that hemoglobin synthesis is highly switch-like in response to cytokine and cells undergoing lineage commitment possess memory of earlier cytokine signals. We show that erythrocyte-specific receptor and transcription factor are indeed synchronously co-upregulated and the heterogeneity in their expression is positively correlated during differentiation, confirming the presence of autofeedback and receptor-mediated positive feedback loops. To evaluate the possibility of employing this minimal topology as a synthetic “memory module” for cell engineering applications, we constructed this topology synthetically in Saccharomyces cerevisiae by integrating Arabidopsis thaliana signaling components with an endogenous yeast pathway (Chapter 4). Our experiments show that any graded and unimodal signaling pathway can be rationally rewired to achieve our desired topology and the resulting network immediately attains high ultrasensitivity and bimodality without tweaking. We further show that this topology can be tuned to regulate system dynamics such as activation/deactivation kinetics, signal amplitude, switching threshold and sensitivity. We conclude with a computational study to explore the generality of this interplay between extrinsic and intrinsic cues in hematopoiesis. We extend our minimal model analysis in Chapter 2 to examine the more complex fate decisions in bipotent and multipotent progenitors, particularly how these cells can make robust decisions in the presence of multiple extrinsic cues and intrinsic noise (Chapter 5). Our model provides support to both the instructive and stochastic theories of commitment: cell fates are ultimately driven by lineage-specific transcription factors, but cytokine signaling can strongly bias lineage commitment by regulating these inherently noisy cell-fate decisions with complex, pertinent behaviors such as ligand-mediated ultrasensitivity and robust multistability. The simulations further suggest that the kinetics of differentiation to a mature cell state can depend on the starting progenitor state as well as on the route of commitment that is chosen. Lastly, our model shows good agreement with lineage-specific receptor expression kinetics from microarray experiments and provides a computational framework that can integrate both classical and alternative commitment paths in hematopoiesis that have been observed experimentally