On Robustness Computation and Optimization in BIOCHAM-4

Long version with appendicesInternational audienceBIOCHAM-4 is a tool for modeling, analyzing and synthesizing biochemical reaction networks with respect to some formal, yet possibly imprecise, specification of their behavior. We focus here on one new capability of this tool to optimize the robustness of a parametric model with respect to a specification of its dynamics in quantitative temporal logic. More precisely, we present two complementary notions of robustness: the statistical notion of model robustness to parameter perturbations, defined as its mean functionality, and a metric notion of formula satisfaction robustness, defined as the penetration depth in the validity domain of the temporal logic constraints. We show how the formula robustness can be used in BIOCHAM-4 with no extra cost as an objective function in the parameter optimization procedure, to actually improve the model robustness. We illustrate these unique features with a classical example of the hybrid systems community and provide some performance figures on a model of MAPK signalling with 37 parameters

A Taxonomy of Causality-Based Biological Properties

We formally characterize a set of causality-based properties of metabolic networks. This set of properties aims at making precise several notions on the production of metabolites, which are familiar in the biologists' terminology. From a theoretical point of view, biochemical reactions are abstractly represented as causal implications and the produced metabolites as causal consequences of the implication representing the corresponding reaction. The fact that a reactant is produced is represented by means of the chain of reactions that have made it exist. Such representation abstracts away from quantities, stoichiometric and thermodynamic parameters and constitutes the basis for the characterization of our properties. Moreover, we propose an effective method for verifying our properties based on an abstract model of system dynamics. This consists of a new abstract semantics for the system seen as a concurrent network and expressed using the Chemical Ground Form calculus. We illustrate an application of this framework to a portion of a real metabolic pathway

A general computational method for robustness analysis with applications to synthetic gene networks

Motivation: Robustness is the capacity of a system to maintain a function in the face of perturbations. It is essential for the correct functioning of natural and engineered biological systems. Robustness is generally defined in an ad hoc, problem-dependent manner, thus hampering the fruitful development of a theory of biological robustness, recently advocated by Kitano

A Skin Microbiome Model with AMP interactions and Analysis of Quasi-Stability vs Stability in Population Dynamics

The skin microbiome plays an important role in the maintenance of a healthy skin. It is an ecosystem, composed of several species, competing for resources and interacting with the skin cells. Imbalance in the cutaneous microbiome, also called dysbiosis, has been correlated with several skin conditions, including acne and atopic dermatitis. Generally, dysbiosis is linked to colonization of the skin by a population of opportunistic pathogenic bacteria. Treatments consisting in non-specific elimination of cutaneous microflora have shown conflicting results. In this article, we introduce a mathematical model based on ordinary differential equations, with 2 types of bacteria populations (skin commensals and opportunistic pathogens) and including the production of antimicrobial peptides to study the mechanisms driving the dominance of one population over the other. By using published experimental data, assumed to correspond to the observation of stable states in our model, we reduce the number of parameters of the model from 13 to 5. We then use a formal specification in quantitative temporal logic to calibrate our model by global parameter optimization and perform sensitivity analyses. On the time scale of 2 days of the experiments, the model predicts that certain changes of the environment, like the elevation of skin surface pH, create favorable conditions for the emergence and colonization of the skin by the opportunistic pathogen population, while the production of human AMPs has non-linear effect on the balance between pathogens and commensals. Surprisingly, simulations on longer time scales reveal that the equilibrium reached around 2 days can in fact be a quasi-stable state followed by the reaching of a reversed stable state after 12 days or more. We analyse the conditions of quasi-stability observed in this model using tropical algebraic methods, and show their non-generic character in contrast to slow-fast systems. These conditions are then generalized to a large class of population dynamics models over any number of species.Comment: arXiv admin note: substantial text overlap with arXiv:2206.1022

Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures

International audienceFinding mathematical models satisfying a specification built from the formalization of biological experiments, is a common task of the modeler that techniques like model-checking help solving, in the qualitative but also in the quantitative case. In this article we go one step further by defining a continuous degree of satisfaction of temporal logic formulae with constraints. We show how such a satisfaction measure can be used as a fitness function with state-of-the-art evolutionary optimization methods in order to find biochemical kinetic parameter values satisfying a set of biological properties formalized in temporal logic. We also show how it can be used to define a measure of robustness of a biological model with respect to some temporal specification. These methods are evaluated on models of the cell cycle and of the MAPK signalling cascade

Computational Modeling, Formal Analysis, and Tools for Systems Biology.

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science

Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE. This algorithm is used as a front-end transformation to compile any elementary mathematical function, either of time or of some input species, into a finite CRN. We illustrate the performance of our compiler on a benchmark of elementary functions relevant to CRN design problems in synthetic biology specified by mathematical functions. In particular, the abstract CRN obtained by compilation of the Hill function of order 5 is compared to the natural CRN structure of MAPK signalling networks

An overview of existing modeling tools making use of model checking in the analysis of biochemical networks

Model checking is a well-established technique for automaticallyverifying complex systems. Recently, model checkers have appearedin computer tools for the analysis of biochemical (and generegulatory) networks. We survey several such tools to assess thepotential of model checking in computational biology. Next, our overviewfocuses on direct applications of existing model checkers, as well ason algorithms for biochemical network analysis influenced by modelchecking, such as those using binary decision diagrams or Booleansatisfiability solvers. We conclude with advantages and drawbacks ofmodel checking for the analysis of biochemical networks

Robustness Analysis for Value-Freezing Signal Temporal Logic

In our previous work we have introduced the logic STL*, an extension of Signal Temporal Logic (STL) that allows value freezing. In this paper, we define robustness measures for STL* by adapting the robustness measures previously introduced for Metric Temporal Logic (MTL). Furthermore, we present an algorithm for STL* robustness computation, which is implemented in the tool Parasim. Application of STL* robustness analysis is demonstrated on case studies.Comment: In Proceedings HSB 2013, arXiv:1308.572

On Chemical Reaction Network Design by a Nested Evolution Algorithm

International audienceOne goal of synthetic biology is to implement useful functions with biochemical reactions, either by reprogramming living cells or programming artificial vesicles. In this perspective, we consider Chemical Reaction Networks (CRN) as a programming language, and investigate the CRN program synthesis problem. Recent work has shown that CRN interpreted by differential equations are Turing-complete and can be seen as analog computers where the molecular concentrations play the role of information carriers. Any real function that is computable by a Turing machine in arbitrary precision can thus be computed by a CRN over a finite set of molecular species. The proof of this result gives a numerical method to generate a finite CRN for implementing a real function presented as the solution of a Polynomial Initial Values Problem (PIVP). In this paper, we study an alternative method based on artificial evolution to build a CRN that approximates a real function given on finite sets of input values. We present a nested search algorithm that evolves the structure of the CRN and optimizes the kinetic parameters at each generation. We evaluate this algorithm on the Heaviside and Cosine functions both as functions of time and functions of input molecular species. We then compare the CRN obtained by artificial evolution both to the CRN generated by the numerical method from a PIVP definition of the function, and to the natural CRN found in the BioModels repository for switches and oscillators