A computational method for the investigation of multistable systems and its application to genetic switches

BACKGROUND: Genetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology. RESULTS: Here we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour. CONCLUSIONS: Our results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks

State switching in multi-stable systems: control and optimisation.

This thesis studies state-switching in multistable systems, so that they can switch from inefficient operating states to a more efficient one, in order to achieve performance enhancement in real-life engineering systems. Multistable systems have more than one stable state under a set of parameters and the process of switching from an undesired state to a desired state is achieved by the proposed PD-like controller. It exploits the difference of the displacement and velocity between the undesired and the desired stable conditions for feedback in state switching. Three test systems are used for investigating the performance of this PD-like controller, namely: the Duffing oscillator, which is a typical smooth multistable system; the non-smooth soft-impact oscillator; and the soft-impact oscillator with a drift. A randomised triangular subdivision algorithm is proposed to reconstruct the basins of attraction of the target multistable systems, in order to identify the desired state for switching. Due to the limited capacity of physical actuators, behaviours of the constrained PD-like controller are investigated using extensive simulation on the test systems. Moreover, optimisation of the controller (based on multiple performance objectives) can further improve system performance. Two performance objectives - maximum peak of control input and switching duration - are adopted in optimising the proposed PD-like controller. The first objective is minimised in order to avoid output limit and reduce energy consumption in the actuator, while the second objective is minimised in order to shorten the time required for state switching. These two performance objectives are considered independently in performance optimisation, using particle swarm optimisation (PSO). Since these two objectives are in conflict with each other, both objectives are minimised simultaneously in multiobjective optimisation of the performance of the PD-like controller using Non-Dominated Sorting Genetic Algorithms-II (NSGA-II). A trade-off in performance enhancement is achieved through selecting control parameters from the Pareto optimal set

Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches

During tissue development, patterns of gene expression determine the spatial arrangement of cell types. In many cases, gradients of secreted signaling molecules - morphogens - guide this process. The continuous positional information provided by the gradient is converted into discrete cell types by the downstream transcriptional network that responds to the morphogen. A mechanism commonly used to implement a sharp transition between two adjacent cell fates is the genetic toggle switch, composed of cross-repressing transcriptional determinants. Previous analyses emphasize the steady state output of these mechanisms. Here, we explore the dynamics of the toggle switch and use exact numerical simulations of the kinetic reactions, the Chemical Langevin Equation, and Minimum Action Path theory to establish a framework for studying the effect of gene expression noise on patterning time and boundary position. This provides insight into the time scale, gene expression trajectories and directionality of stochastic switching events between cell states. Taking gene expression noise into account predicts that the final boundary position of a morphogen-induced toggle switch, although robust to changes in the details of the noise, is distinct from that of the deterministic system. Moreover, stochastic switching introduces differences in patterning time along the morphogen gradient that result in a patterning wave propagating away from the morphogen source. The velocity of this wave is influenced by noise; the wave sharpens and slows as it advances and may never reach steady state in a biologically relevant time. This could explain experimentally observed dynamics of pattern formation. Together the analysis reveals the importance of dynamical transients for understanding morphogen-driven transcriptional networks and indicates that gene expression noise can qualitatively alter developmental patterning

Linking Bistable Dynamics to Metabolic P Systems

Bistability, or more generally multistability, is an important recurring theme in biological systems. In particular, the discovery of bistability in signal pathways of genetic networks, prompts strong interest in understanding both the design and function of these networks. Therefore, modelling these systems is crucial to understand their behaviors, and also to analyze and identify characteristics that would otherwise be di cult to realize. Although di erent classes of models have been used to study bistable dynamics, there is a lag in the development of models for bistable systems starting from experimental data. This is due to the lack of detailed knowledge of biochemical reactions and kinetic rates. In this work, we propose a procedure to develop, starting from observed dynamics, Metabolic P models for multistable processes. As a case study, a mathematical model of the Schl ogel's dynamics, which represents an example of a chemical reaction system that exhibits bistability, is inferred starting from observed stochastic bistable dynamics. Since, recent experiments indicate that noise plays an important role in the switching of bistable systems, the success of this work suggests that this approach is a very promising one for studying dynamics and role of noise in biological systems, such as, for example, genetic regulatory networks

Synthetic multistability in mammalian cells

In multicellular organisms, gene regulatory circuits generate thousands of molecularly distinct, mitotically heritable states, through the property of multistability. Designing synthetic multistable circuits would provide insight into natural cell fate control circuit architectures and allow engineering of multicellular programs that require interactions among cells in distinct states. Here we introduce MultiFate, a naturally-inspired, synthetic circuit that supports long-term, controllable, and expandable multistability in mammalian cells. MultiFate uses engineered zinc finger transcription factors that transcriptionally self-activate as homodimers and mutually inhibit one another through heterodimerization. Using model-based design, we engineered MultiFate circuits that generate up to seven states, each stable for at least 18 days. MultiFate permits controlled state-switching and modulation of state stability through external inputs, and can be easily expanded with additional transcription factors. Together, these results provide a foundation for engineering multicellular behaviors in mammalian cells

Engineering of a synthetic quadrastable gene network to approach Waddington landscape and cell fate determination

abstract: The process of cell fate determination has been depicted intuitively as cells travelling and resting on a rugged landscape, which has been probed by various theoretical studies. However, few studies have experimentally demonstrated how underlying gene regulatory networks shape the landscape and hence orchestrate cellular decision-making in the presence of both signal and noise. Here we tested different topologies and verified a synthetic gene circuit with mutual inhibition and auto-activations to be quadrastable, which enables direct study of quadruple cell fate determination on an engineered landscape. We show that cells indeed gravitate towards local minima and signal inductions dictate cell fates through modulating the shape of the multistable landscape. Experiments, guided by model predictions, reveal that sequential inductions generate distinct cell fates by changing landscape in sequence and hence navigating cells to different final states. This work provides a synthetic biology framework to approach cell fate determination and suggests a landscape-based explanation of fixed induction sequences for targeted differentiation

Automated design of gene circuits with optimal mushroom-bifurcation behavior

Recent advances in synthetic biology are enabling exciting technologies, including the next generation of biosensors, the rational design of cell memory, modulated synthetic cell differentiation, and generic multifunctional biocircuits. These novel applications require the design of gene circuits leading to sophisticated behaviors and functionalities. At the same time, designs need to be kept minimal to avoid compromising cell viability. Bifurcation theory addresses such challenges by associating circuit dynamical properties with molecular details of its design. Nevertheless, incorporating bifurcation analysis into automated design processes has not been accomplished yet. This work presents an optimization-based method for the automated design of synthetic gene circuits with specified bifurcation diagrams that employ minimal network topologies. Using this approach, we designed circuits exhibiting the mushroom bifurcation, distilled the most robust topologies, and explored its multifunctional behavior. We then outline potential applications in biosensors, memory devices, and synthetic cell differentiation

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