Stochastic analysis of nonlinear dynamics and feedback control for gene regulatory networks with applications to synthetic biology

The focus of the thesis is the investigation of the generalized repressilator model (repressing genes ordered in a ring structure). Using nonlinear bifurcation analysis stable and quasi-stable periodic orbits in this genetic network are characterized and a design for a switchable and controllable genetic oscillator is proposed. The oscillator operates around a quasi-stable periodic orbit using the classical engineering idea of read-out based control. Previous genetic oscillators have been designed around stable periodic orbits, however we explore the possibility of quasi-stable periodic orbit expecting better controllability. The ring topology of the generalized repressilator model has spatio-temporal symmetries that can be understood as propagating perturbations in discrete lattices. Network topology is a universal cross-discipline transferable concept and based on it analytical conditions for the emergence of stable and quasi-stable periodic orbits are derived. Also the length and distribution of quasi-stable oscillations are obtained. The findings suggest that long-lived transient dynamics due to feedback loops can dominate gene network dynamics. Taking the stochastic nature of gene expression into account a master equation for the generalized repressilator is derived. The stochasticity is shown to influence the onset of bifurcations and quality of oscillations. Internal noise is shown to have an overall stabilizing effect on the oscillating transients emerging from the quasi-stable periodic orbits. The insights from the read-out based control scheme for the genetic oscillator lead us to the idea to implement an algorithmic controller, which would direct any genetic circuit to a desired state. The algorithm operates model-free, i.e. in principle it is applicable to any genetic network and the input information is a data matrix of measured time series from the network dynamics. The application areas for readout-based control in genetic networks range from classical tissue engineering to stem cells specification, whenever a quantitatively and temporarily targeted intervention is required

Transient dynamics around unstable periodic orbits in the generalized repressilator model.

We study the spatio-temporal dynamics of the generalized repressilator, a system of coupled repressing genes arranged in a directed ring topology, and give analytical conditions for the emergence of a cascade of unstable periodic orbits (UPOs) that lead to reachable long-lived oscillating transients. Such transients dominate the finite time horizon dynamics that is relevant in confined, noisy environments such as bacterial cells (see our previous work [Strelkowa and Barahona, 2010]) and are therefore of interest for bioengineering and synthetic biology. We show that the family of unstable orbits possesses spatial symmetries and can also be understood in terms of traveling wave solutions of kink-like topological defects. The long-lived oscillatory transients correspond to the propagation of quasistable two-kink configurations that unravel over a long time. We also assess the similarities between the generalized repressilator model and other unidirectionally coupled electronic systems, such as magnetic flux gates, which have been implemented experimentally.Comment: 24 pages, 8 figure

Switchable Genetic Oscillator Operating in Quasi-Stable Mode

Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in transient and stochastic environments such as the cell. We show here that even repressilators possess quasi-stable, travelling-wave periodic solutions that are reachable, long-lived and robust to parameter changes. These solutions underlie the sustained oscillations observed in even rings in the stochastic regime, even if these circuits are expected to behave as switches. The existence of such solutions can also be exploited for control purposes: operation of the system around the quasi-stable orbit allows us to turn on and off the oscillations reliably and on demand. We illustrate these ideas with a simple protocol based on optical interference that can induce oscillations robustly both in the stochastic and deterministic regimes.Comment: 24 pages, 5 main figure

Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

Approximate Bayesian computation methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper we discuss and apply an approximate Bayesian computation (ABC) method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC gives information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.Comment: 26 pages, 9 figure

Toggling a Genetic Switch Using Reinforcement Learning

In this paper, we consider the problem of optimal exogenous control of gene regulatory networks. Our approach consists in adapting an established reinforcement learning algorithm called the fitted Q iteration. This algorithm infers the control law directly from the measurements of the system's response to external control inputs without the use of a mathematical model of the system. The measurement data set can either be collected from wet-lab experiments or artificially created by computer simulations of dynamical models of the system. The algorithm is applicable to a wide range of biological systems due to its ability to deal with nonlinear and stochastic system dynamics. To illustrate the application of the algorithm to a gene regulatory network, the regulation of the toggle switch system is considered. The control objective of this problem is to drive the concentrations of two specific proteins to a target region in the state space.Comment: 12 pages, presented at the 9th French Meeting on Planning, Decision Making and Learning, Li\`ege (Belgium), May 12-13, 201

Engineering and ethical perspectives in synthetic biology: Rigorous, robust and predictable designs, public engagement and a modern ethical framework are vital to the continued success of synthetic biology

The applications of synthetic biology will involve the release of artificial life forms into the environment. These organisms will present unique safety challenges that need to be addressed by researchers and regulators to win public engagement and support

Hopf bifurcation in the full repressilator equations

Agraïments: The first author is supported by FAPESP-BRAZIL grant 2007/06896-5, CAPES-PROCAD-BRAZIL grant 035/2007 and CNPQ-BRAZIL grant 472787/2009-8. Both authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC.In this paper we prove that the full repressilator equations, in dimension six undergo a supercritical Hopf bifurcation

A large effective population size for established within-host influenza virus infection

Strains of the influenza virus form coherent global populations, yet exist at the level of single infections in individual hosts. The relationship between these scales is a critical topic for understanding viral evolution. Here we investigate the within-host relationship between selection and the stochastic effects of genetic drift, estimating an effective population size of infection N-e for influenza infection. Examining whole-genome sequence data describing a chronic case of influenza B in a severely immunocompromised child we infer an N-e of 2.5 x 10(7) (95% confidence range 1.0 x 10(7) to 9.0 x 10(7)) suggesting that genetic drift is of minimal importance during an established influenza infection. Our result, supported by data from influenza A infection, suggests that positive selection during within-host infection is primarily limited by the typically short period of infection. Atypically long infections may have a disproportionate influence upon global patterns of viral evolution.Peer reviewe

Two first-in-human studies of xentuzumab, a humanised insulin-like growth factor (IGF)-neutralising antibody, in patients with advanced solid tumours

BACKGROUND: Xentuzumab, an insulin-like growth factor (IGF)-1/IGF-2-neutralising antibody, binds IGF-1 and IGF-2, inhibiting their growth-promoting signalling. Two first-in-human trials assessed the maximum-tolerated/relevant biological dose (MTD/RBD), safety, pharmacokinetics, pharmacodynamics, and activity of xentuzumab in advanced/metastatic solid cancers. METHODS: These phase 1, open-label trials comprised dose-finding (part I; 3 + 3 design) and expansion cohorts (part II; selected tumours; RBD [weekly dosing]). Primary endpoints were MTD/RBD. RESULTS: Study 1280.1 involved 61 patients (part I: xentuzumab 10–1800 mg weekly, n = 48; part II: 1000 mg weekly, n = 13); study 1280.2, 64 patients (part I: 10–3600 mg three-weekly, n = 33; part II: 1000 mg weekly, n = 31). One dose-limiting toxicity occurred; the MTD was not reached for either schedule. Adverse events were generally grade 1/2, mostly gastrointestinal. Xentuzumab showed dose-proportional pharmacokinetics. Total plasma IGF-1 increased dose dependently, plateauing at ~1000 mg/week; at ≥450 mg/week, IGF bioactivity was almost undetectable. Two partial responses occurred (poorly differentiated nasopharyngeal carcinoma and peripheral primitive neuroectodermal tumour). Integration of biomarker and response data by Bayesian Logistic Regression Modeling (BLRM) confirmed the RBD. CONCLUSIONS: Xentuzumab was well tolerated; MTD was not reached. RBD was 1000 mg weekly, confirmed by BLRM. Xentuzumab showed preliminary anti-tumour activity