Formal executable descriptions of biological systems

The similarities between systems of living entities and systems of concurrent processes may support biological experiments in silico. Process calculi offer a formal framework to describe biological systems, as well as to analyse their behaviour, both from a qualitative and a quantitative point of view. A couple of little examples help us in showing how this can be done. We mainly focus our attention on the qualitative and quantitative aspects of the considered biological systems, and briefly illustrate which kinds of analysis are possible. We use a known stochastic calculus for the first example. We then present some statistics collected by repeatedly running the specification, that turn out to agree with those obtained by experiments in vivo. Our second example motivates a richer calculus. Its stochastic extension requires a non trivial machinery to faithfully reflect the real dynamic behaviour of biological systems

In silico estimation of annealing specificity of query searches in DNA databases

We consider DNA implementations of databases for digital signals with retrieval and mining capabilities. Digital signals are encoded in DNA sequences and retrieved through annealing between query DNA primers and data carrying DNA target sequences. The hybridization between query and target can be non-specific containing multiple mismatches thus implementing similarity-based searches. In this paper we examine theoretically and by simulation the efficiency of such a system by estimating the concentrations of query-target duplex formations at equilibrium. A coupled kinetic model is used to estimate the concentrations. We offer a derivation that results in an equation that is guaranteed to have a solution and can be easily and accurately solved computationally with bi-section root-finding methods. Finally, we also provide an approximate solution at dilute query concentrations that results in a closed form expression. This expression is used to improve the speed of the bi-section algorithm and also to find a closed form expression for the specificity ratios

Gene Regulation in the Pi Calculus: Simulating Cooperativity at the Lambda Switch

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4230).Also part of the Lecture Notes in Bioinformatics book sub series (volume 4230).International audienceWe propose to model the dynamics of gene regulatory networks as concurrent processes in the stochastic pi calculus. As a first case study, we show how to express the control of transcription initiation at the lambda switch, a prototypical example where cooperative enhancement is crucial. This requires concurrent programming techniques that are new to systems biology, and necessitates stochastic parameters that we derive from the literature. We test all components of our model by exhaustive stochastic simulations. A comparison with previous results reported in the literature, experimental and simulation based, confirms the appropriateness of our modeling approach

Deciphering noise amplification and reduction in open chemical reaction networks

The impact of random fluctuations on the dynamical behavior a complex biological systems is a longstanding issue, whose understanding would shed light on the evolutionary pressure that nature imposes on the intrinsic noise levels and would allow rationally designing synthetic networks with controlled noise. Using the It\=o stochastic differential equation formalism, we performed both analytic and numerical analyses of several model systems containing different molecular species in contact with the environment and interacting with each other through mass-action kinetics. These systems represent for example biomolecular oligomerization processes, complex-breakage reactions, signaling cascades or metabolic networks. For chemical reaction networks with zero deficiency values, which admit a detailed- or complex-balanced steady state, all molecular species are uncorrelated. The number of molecules of each species follow a Poisson distribution and their Fano factors, which measure the intrinsic noise, are equal to one. Systems with deficiency one have an unbalanced non-equilibrium steady state and a non-zero S-flux, defined as the flux flowing between the complexes multiplied by an adequate stoichiometric coefficient. In this case, the noise on each species is reduced if the flux flows from the species of lowest to highest complexity, and is amplified is the flux goes in the opposite direction. These results are generalized to systems of deficiency two, which possess two independent non-vanishing S-fluxes, and we conjecture that a similar relation holds for higher deficiency systems

Cellular signaling networks function as generalized Wiener-Kolmogorov filters to suppress noise

Cellular signaling involves the transmission of environmental information through cascades of stochastic biochemical reactions, inevitably introducing noise that compromises signal fidelity. Each stage of the cascade often takes the form of a kinase-phosphatase push-pull network, a basic unit of signaling pathways whose malfunction is linked with a host of cancers. We show this ubiquitous enzymatic network motif effectively behaves as a Wiener-Kolmogorov (WK) optimal noise filter. Using concepts from umbral calculus, we generalize the linear WK theory, originally introduced in the context of communication and control engineering, to take nonlinear signal transduction and discrete molecule populations into account. This allows us to derive rigorous constraints for efficient noise reduction in this biochemical system. Our mathematical formalism yields bounds on filter performance in cases important to cellular function---like ultrasensitive response to stimuli. We highlight features of the system relevant for optimizing filter efficiency, encoded in a single, measurable, dimensionless parameter. Our theory, which describes noise control in a large class of signal transduction networks, is also useful both for the design of synthetic biochemical signaling pathways, and the manipulation of pathways through experimental probes like oscillatory input.Comment: 15 pages, 5 figures; to appear in Phys. Rev.