Deterministic characterization of stochastic genetic circuits

For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of deterministic rate equation models. Unfortunately, there are few analytic methods for examining the qualitative behavior of stochastic systems. Here we describe such a method that extends deterministic analysis to include leading-order corrections due to the molecular noise. The method allows the steady-state behavior of the stochastic model to be easily computed, facilitates the mapping of stability phase diagrams that include stochastic effects and reveals how model parameters affect noise susceptibility, in a manner not accessible to numerical simulation. By way of illustration we consider two genetic circuits: a bistable positive-feedback loop and a negative-feedback oscillator. We find in the positive feedback circuit that translational activation leads to a far more stable system than transcriptional control. Conversely, in a negative-feedback loop triggered by a positive-feedback switch, the stochasticity of transcriptional control is harnessed to generate reproducible oscillations.Comment: 6 pages (Supplementary Information is appended

Collective oscillation period of inter-coupled biological negative cyclic feedback oscillators

A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from that of an autonomous oscillator. Based on cyclic feedback oscillators, we analyze the collective oscillation pattern of coupled cellular oscillators. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior. Then we estimate the collective oscillation period based on a novel multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design.Comment: arXiv admin note: substantial text overlap with arXiv:1203.125

Synthetic in vitro transcriptional oscillators

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells

Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations

We study the effects of multiple binding sites in the promoter of a genetic oscillator. We evaluate the regulatory function of a promoter with multiple binding sites in the absence of cooperative binding, and consider different hypotheses for how the number of bound repressors affects transcription rate. Effective Hill exponents of the resulting regulatory functions reveal an increase in the nonlinearity of the feedback with the number of binding sites. We identify optimal configurations that maximize the nonlinearity of the feedback. We use a generic model of a biochemical oscillator to show that this increased nonlinearity is reflected in enhanced oscillations, with larger amplitudes over wider oscillatory ranges. Although the study is motivated by genetic oscillations in the zebrafish segmentation clock, our findings may reveal a general principle for gene regulation.Comment: 11 pages, 8 figure

Elucidating the genotype-phenotype map by automatic enumeration and analysis of the phenotypic repertoire.

BackgroundThe gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process.MethodsThe strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters.ResultsOur strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed.ConclusionsStarting with a system's relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy

Designer Gene Networks: Towards Fundamental Cellular Control

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics.Comment: 35 pages, 8 figure

Bifurcation discovery tool

Motivation: Biochemical networks often yield interesting behavior such as switching, oscillation and chaotic dynamics. This article describes a tool that is capable of searching for bifurcation points in arbitrary ODE-based reaction networks by directing the user to regions in the parameter space, where such interesting dynamical behavior can be observed. Results: We have implemented a genetic algorithm that searches for Hopf bifurcations, turning points and bistable switches. The software is implemented as a Systems Biology Workbench (SBW) enabled module and accepts the standard SBML model format. The interface permits a user to choose the parameters to be searched, admissible parameter ranges, and the nature of the bifurcation to be sought. The tool will return the parameter values for the model for which the particular behavior is observed. Availability: The software, tutorial manual and test models are available for download at the following website: http:/www.sys-bio.org/ under the bifurcation link. The software is an open source and licensed under BSD

Structural investigation of the Arabidopsis thaliana circadian clock

Plants, like most organisms, have developed elaborate mechanisms for anticipating periodic environmental changes. The circadian clock allows an organism to adapt its metabolic, developmental and physiological processes to coincide with favourable environmental conditions. At the centre of the Arabidopsis thaliana clock, linking environmental inputs and driving the overt biological rhythm is a central oscillator that consists of multiple interlocked transcriptional/translational negative feedback loops. What is known about the structure of the central oscillator comes primarily from genetic analysis. Less clear, is how putative oscillator proteins perform their perceived functions in circadian rhythm maintenance. Described are the cloning, expression and purification of clock-associated proteins; TOCI-PRR, ELF4, LUX and LIPl. Purified ELF4 was subjected to unsuccessful crystallisation trials, probably due to its intrinsically unstructured nature. A truncated form of LIP 1 was shown to be an active OTPase, representing the first example of an active OTPase in the plant clock. In addition, a protocol for the production of ssDNA aptamers has been developed (against SRRl), which can be used to replace antibody-based experimentation. The work presented discusses the difficulty in obtaining the novel, plant-specific proteins in quantities required for crystallisation, and suggests alternative methods for structural and biochemical analysis of these proteins. Moreover, this thesis combines experimental data with a range of Bioinformatic tools to aid design for subsequent biochemical expression, purification and crystallisation trials