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

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

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

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

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

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

Clonal Interference in the Evolution of Influenza

The seasonal influenza A virus undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic epitopes, the antibody-binding domains of the viral hemagglutinin. This process involves recurrent selective sweeps, in which clusters of simultaneous nucleotide fixations in the hemagglutinin coding sequence are observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference. This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal interference explains and quantifies the observed sweep pattern: we find an average of at least one strongly beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations on average. The inference of selection and clonal interference is based on frequency time series of single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39 years. Our results imply that mode and speed of influenza evolution are governed not only by positive selection within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be particularly brittle. We conclude that a quantitative understanding of influenza's evolutionary and epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference

Toggling a genetic switch using reinforcement learning

peer reviewedIn 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

A phase I study of volasertib combined with afatinib, in advanced solid tumors

PURPOSE: To determine the maximum tolerated dose (MTD) of volasertib, a Polo-like kinase inhibitor, combined with afatinib, an oral irreversible ErbB family blocker, in patients with advanced solid tumors (NCT01206816; Study 1230.20). METHODS: Patients with advanced non-resectable and/or metastatic disease following failure of conventional treatment received intravenous volasertib 150-300 mg on day 1 every 21 days, combined with oral afatinib 30-40 mg on days 2-21 of a 3-week cycle (Schedule A), or 50-90 mg on days 2-6 of a 3-week cycle (Schedule B). The primary objective was to determine the MTD of volasertib in combination with afatinib. RESULTS: Fifty-seven patients (Schedule A, N = 29; Schedule B, N = 28) were treated. The MTDs were volasertib 300 mg plus afatinib 30 mg days 2-21 and 70 mg days 2-6 of a 3-week cycle for Schedules A and B, respectively. The most common Grade 3/4 adverse events were neutropenia (31.0 %), diarrhea (13.8 %), and thrombocytopenia (10.3 %) in Schedule A; neutropenia (39.3 %), thrombocytopenia (35.7 %), hypokalemia (14.3 %), febrile neutropenia, and nausea (each 10.7 %) in Schedule B. The best overall response was two partial responses (6.9 %; both in Schedule A); eight patients in each schedule achieved stable disease. Volasertib showed multi-exponential pharmacokinetic (PK) behavior; co-administration of volasertib and afatinib had no significant effects on the PK profile of either drug. CONCLUSIONS: Volasertib combined with afatinib had manageable adverse effects and limited antitumor activity in this heavily pretreated population