The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises

Accelerating the Gillespie τ-Leaping Method Using Graphics Processing Units

The Gillespie τ-Leaping Method is an approximate algorithm that is faster than the exact Direct Method (DM) due to the progression of the simulation with larger time steps. However, the procedure to compute the time leap τ is quite expensive. In this paper, we explore the acceleration of the τ-Leaping Method using Graphics Processing Unit (GPUs) for ultra-large networks ( reaction channels). We have developed data structures and algorithms that take advantage of the unique hardware architecture and available libraries. Our results show that we obtain a performance gain of over 60x when compared with the best conventional implementations

Confidence from uncertainty - A multi-target drug screening method from robust control theory

<p>Abstract</p> <p>Background</p> <p>Robustness is a recognized feature of biological systems that evolved as a defence to environmental variability. Complex diseases such as diabetes, cancer, bacterial and viral infections, exploit the same mechanisms that allow for robust behaviour in healthy conditions to ensure their own continuance. Single drug therapies, while generally potent regulators of their specific protein/gene targets, often fail to counter the robustness of the disease in question. Multi-drug therapies offer a powerful means to restore disrupted biological networks, by targeting the subsystem of interest while preventing the diseased network from reconciling through available, redundant mechanisms. Modelling techniques are needed to manage the high number of combinatorial possibilities arising in multi-drug therapeutic design, and identify synergistic targets that are robust to system uncertainty.</p> <p>Results</p> <p>We present the application of a method from robust control theory, Structured Singular Value or μ- analysis, to identify highly effective multi-drug therapies by using robustness in the face of uncertainty as a new means of target discrimination. We illustrate the method by means of a case study of a negative feedback network motif subject to parametric uncertainty.</p> <p>Conclusions</p> <p>The paper contributes to the development of effective methods for drug screening in the context of network modelling affected by parametric uncertainty. The results have wide applicability for the analysis of different sources of uncertainty like noise experienced in the data, neglected dynamics, or intrinsic biological variability.</p

A Complete Pathway Model for Lipid A Biosynthesis in Escherichia coli.

Lipid A is a highly conserved component of lipopolysaccharide (LPS), itself a major component of the outer membrane of Gram-negative bacteria. Lipid A is essential to cells and elicits a strong immune response from humans and other animals. We developed a quantitative model of the nine enzyme-catalyzed steps of Escherichia coli lipid A biosynthesis, drawing parameters from the experimental literature. This model accounts for biosynthesis regulation, which occurs through regulated degradation of the LpxC and WaaA (also called KdtA) enzymes. The LpxC degradation signal appears to arise from the lipid A disaccharide concentration, which we deduced from prior results, model results, and new LpxK overexpression results. The model agrees reasonably well with many experimental findings, including the lipid A production rate, the behaviors of mutants with defective LpxA enzymes, correlations between LpxC half-lives and cell generation times, and the effects of LpxK overexpression on LpxC concentrations. Its predictions also differ from some experimental results, which suggest modifications to the current understanding of the lipid A pathway, such as the possibility that LpxD can replace LpxA and that there may be metabolic channeling between LpxH and LpxB. The model shows that WaaA regulation may serve to regulate the lipid A production rate when the 3-deoxy-D-manno-oct-2-ulosonic acid (KDO) concentration is low and/or to control the number of KDO residues that get attached to lipid A. Computation of flux control coefficients showed that LpxC is the rate-limiting enzyme if pathway regulation is ignored, but that LpxK is the rate-limiting enzyme if pathway regulation is present, as it is in real cells. Control also shifts to other enzymes if the pathway substrate concentrations are not in excess. Based on these results, we suggest that LpxK may be a much better drug target than LpxC, which has been pursued most often

A geometric analysis of fast-slow models for stochastic gene expression

Stochastic models for gene expression frequently exhibit dynamics on several different scales. One potential time-scale separation is caused by significant differences in the lifetimes of mRNA and protein; the ratio of the two degradation rates gives a natural small parameter in the resulting chemical master equation, allowing for the application of perturbation techniques. Here, we develop a framework for the analysis of a family of &lsquo;fast-slow&rsquo; models for gene expression that is based on geometric singular perturbation theory. We illustrate our approach by giving a complete characterisation of a standard two-stage model which assumes transcription, translation, and degradation to be first-order reactions. In particular, we present a systematic expansion procedure for the probability-generating function that can in principle be taken to any order in the perturbation parameter, allowing for an approximation of the corresponding propagator probabilities to that same order. For illustrative purposes, we perform this expansion explicitly to first order, both on the fast and the slow time-scales; then, we combine the resulting asymptotics into a composite fast-slow expansion that is uniformly valid in time. In the process, we extend, and prove rigorously, results previously obtained by Shahrezaei and Swain (Proc Natl Acad Sci USA 105(45):17256&ndash;17261, 2008) and Bokes et al. (J Math Biol 64(5):829&ndash;854, 2012; J Math Biol 65(3):493&ndash;520, 2012). We verify our asymptotics by numerical simulation, and we explore its practical applicability and the effects of a variation in the system parameters and the time-scale separation. Focussing on biologically relevant parameter regimes that induce translational bursting, as well as those in which mRNA is frequently transcribed, we find that the first-order correction can significantly improve the steady-state probability distribution. Similarly, in the time-dependent scenario, inclusion of the first-order fast asymptotics results in a uniform approximation for the propagator probabilities that is superior to the slow dynamics alone. Finally, we discuss the generalisation of our geometric framework to models for regulated gene expression that involve additional stages

Hypothetical biomolecular probe based on a genetic switch with tunable symmetry and stability

Background: Genetic switches are ubiquitous in nature, frequently associated with the control of cellular functions and developmental programs. In the realm of synthetic biology, it is of great interest to engineer genetic circuits that can change their mode of operation from monostable to bistable, or even to multistable, based on the experimental fine-tuning of readily accessible parameters. In order to successfully design robust, bistable synthetic circuits to be used as biomolecular probes, or understand modes of operation of such naturally occurring circuits, we must identify parameters that are key in determining their characteristics. Results: Here, we analyze the bistability properties of a general, asymmetric genetic toggle switch based on a chemical-reaction kinetic description. By making appropriate approximations, we are able to reduce the system to two coupled differential equations. Their deterministic stability analysis and stochastic numerical simulations are in excellent agreement. Drawing upon this general framework, we develop a model of an experimentally realized asymmetric bistable genetic switch based on the LacI and TetR repressors. By varying the concentrations of two synthetic inducers, doxycycline and isopropyl ??-D-1-thiogalactopyranoside, we predict that it will be possible to repeatedly fine-tune the mode of operation of this genetic switch from monostable to bistable, as well as the switching rates over many orders of magnitude, in an experimental setting. Furthermore, we find that the shape and size of the bistability region is closely connected with plasmid copy number. Conclusions: Based on our numerical calculations of the LacI-TetR asymmetric bistable switch phase diagram, we propose a generic work-flow for developing and applying biomolecular probes: Their initial state of operation should be specified by controlling inducer concentrations, and dilution due to cellular division would turn the probes into memory devices in which information could be preserved over multiple generations. Additionally, insights from our analysis of the LacI-TetR system suggest that this particular system is readily available to be employed in this kind of probe.clos