Model Building and Model Checking for Biochemical Processes

Abstract

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto- Voit-Sorribas-Cascante's purine metabolism reaction model.

Abstract Machines of Systems Biology

“…Temporal modelchecking asks qualitative questions such as whether the systems can reach a certain state (and how), or whether a state is a necessary checkpoint for reaching another state [9] [20]. Quantitative modelchecking asks quantitative questions about, e.g., whether a certain concentration can eventually equal or double some other concentration in some state [4] [6]. Stochastic modelchecking, based, e.g., on discrete or continuous-time Markov chain models, can ask questions about the probability of reaching a given state [31].…”

Formal Cell Biology in Biocham

“…A version of LTL with constraints over the reals, called Constraint-LTL, is used in Biocham [14] to express temporal properties about molecular concentrations. A similar approach is used in the DARPA BioSpice project [43]. Constraint-LTL considers first-order atomic formulae with equality, inequality and arithmetic operators ranging over real values of concentrations and of their derivatives.…”

“…[14,43] In particular, given an ODE model and a temporal property φ to verify within a finite time horizon, the computation of a finite simulation trace by numerical integration provides a linear Kripke structure where the terminal state is completed with a loop. Note that the notion of next state (operator X) refers to the state of the following time point in a discretized trace, and thus does not necessarily imply real time neighborhood.…”

Trace Simplifications Preserving Temporal Logic Formulae with Case Study in a Coupled Model of the Cell Cycle and the Circadian Clock

“…In the early days of systems biology, propositional temporal logic was proposed by computer scientists to formalize the Boolean properties of the behavior of biochemical reaction systems [11,5] or gene regulatory networks [4,3]. Generalizing these techniques to quantitative models can be done in two ways: either by discretizing the different regimes of the dynamics in piece-wise linear or affine models [8,2], or by relying on numerical simulations and taking a first-order version of temporal logic with constraints on concentrations, as query language for the numerical traces [1,13,14]. Such language can be used not only to extract information from numerical traces coming from either experimental data or model simulations, but also to specify the expected behaviors as constraints for model calibration and robustness measure [20,21,9].…”