Abstract. Living cells are extremely well-organized autonomous systems, consisting of discrete interacting components. Key to understanding and modeling their behavior is modeling their system organization. Four distinct chemical toolkits (classes of macromolecules) have been characterized, each combinatorial in nature. Each toolkit consists of a small number of simple components that are assembled (polymerized) into complex structures that interact in rich ways. Each toolkit abstracts away from chemistry; it embodies an abstract machine with its own instruction set and its own peculiar interaction model. These interaction models are highly effective, but are not ones commonly used in computing: proteins stick together, genes have fixed output, membranes carry activity on their surfaces. Biologists have invented a number of notations attempting to describe these abstract machines and the processes they implement. Moving up from molecular biology, systems biology aims to understand how these interaction models work, separately and together. 1

Abstract. One central issue in systems biology is the definition of formal languages for describing complex biochemical systems and their behavior at different levels. The biochemical abstract machine BIOCHAM is based on two formal languages, one rule-based language used for modeling biochemical networks, at three abstraction levels corresponding to three semantics: boolean, concentration and population; and one temporal logic language used for formalizing the biological properties of the system. In this paper, we show how the temporal logic language can be turned into a specification language. We describe two algorithms for inferring reaction rules and kinetic parameter values from a temporal specification formalizing the biological data. Then, with an example of the cell cycle control, we illustrate how these machine learning techniques may be useful to the modeler. 1

In this work we present Bio-PEPA, a process algebra for the modelling and the analysis of biochemical networks. It is a modification of PEPA, originally defined for the performance analysis of computer systems, in order to handle some features of biological models, such as stoichiometry and the use of general kinetic laws. The domain of application is the one of biochemical networks. Bio-PEPA may be seen as an intermediate, formal, compositional representation of biological systems, on which different kinds of analysis can be carried out. Bio-PEPA is enriched with some notions of equivalence. Specifically, the isomorphism and strong bisimulation for PEPA have been considered. Finally, we show the translation of three biological models into the new language and we report some analysis results.

Abstract interpretation is a theory of abstraction that has been introduced for the analysis of programs. In particular, it has proved useful for organizing the multiple semantics of a given programming language in a hierarchy corresponding to different detail levels, and for defining type systems for programming languages and program analyzers in software engineering. In this paper, we investigate the application of these concepts to systems biology formalisms. More specifically, we consider the Systems Biology Markup Language SBML, and the Biochemical Abstract Machine BIOCHAM with its differential, stochastic, discrete and boolean semantics. We first show how all of these different semantics, except the differential one, can be formally related by simple Galois connections. Then we define three type systems: one for checking or inferring the functions of proteins in a reaction model, one for checking or inferring the activation and inhibition effects of proteins in a reaction model, and another one for checking or inferring the topology of compartments or locations. We show that the framework of abstract interpretation elegantly applies to the formalization of these further abstractions, and to the implementation of linear or quadratic time type checking as well as type inference algorithms. Furthermore, we show a theorem of independence of the graph of activation and inhibition effects from the kinetic expressions in the reaction model, under general conditions. Through some examples, we show that the analysis of biochemical models by type inference provides accurate and useful information. Interestingly, such a mathematical formalization of the abstractions commonly used in systems biology already provides some guidelines for the extensions of biochemical reaction rule languages.

Beyond numerical simulation, the possibility of performing symbolic computation on biomolecular interaction networks opens the way to the design of new automated reasoning tools for biologists/modelers. The Biochemical Abstract machine BIOCHAM provides a precise semantics to biomolecular interaction maps as concurrent transition systems. Based on this formal semantics, BIOCHAM offers a compositional rule-based language for modeling biochemical systems, and an original query language based on temporal logic for expressing biological queries about reachability, checkpoints, oscillations or stability. Turning the temporal logic query language into a specification language for expressing the observed behavior of the system (in wild-life and mutated organisms) makes it possible to use machine learning techniques for completing or correcting biological models semi-automatically. Machine learning from temporal logic formulae is quite new however, both from the machine learning perspective and from the Systems Biology perspective. In this paper, we report on the machine learning system of BIOCHAM which allows to discover, on the one hand, interaction rules from a partial model with constraints on the system behavior expressed in temporal logic, and on the other hand, kinetic parameter values from a temporal logic specification with constraints on numerical concentrations.

Abstract. With the advent of formal languages for modeling bio-molecular interaction systems, the design of automated reasoning tools to assist the biologist becomes possible. The biochemical abstract machine BIOCHAM software environment offers a rule-based language to model bio-molecular interactions and an original temporal logic based language to formalize the biological properties of the system. Building on these two formal languages, machine learning techniques can be used to infer new molecular interaction rules from temporal properties. In this context, the aim is to semi-automatically correct or complete models from observed biological properties of the system. Machine learning from temporal logic formulae is quite new however, both from the machine learning perspective and from the Systems Biology perspective. In this paper we present an ad hoc enumerative method for structural learning from temporal properties and report on the evaluation of this method on formal biological models of the literature. 1

Mathematical biology has for a long time investigated the dynamics of biomolecular systems by developing numerical models involving (highly non-linear) differential equations and using tools such as Bifurcation Theory for estimating parameters [1]. Mathematical biology provides a firm ground for the numerical analysis of biological systems. However, state-of-the-art quantitative models can hardly be re-used and composed with other models in a systematic fashion, and are limited to a few tenths of variables [2]. Qualitative models of bio-molecular interactions constitute the core of nowadays cell systems biology. Interaction diagrams are the first tool used by biologists to reason about complex systems. The accumulation of knowledge on gene interaction and pathways is currently entered in databases such as KEGG[3], EcoCyc [4], etc. in the form of annotated diagrams. Tools such as BioSpice, Gepasi, GON, E-cell, etc. have been developed for making simulations based on these databases when numerical data is present. Furthermore the interoperability between databases and simulation tools is now possible with standard exchange formats such as the Systems

Abstract. Recent progress in Biology and data-production technologies push research toward a new interdisciplinary field, named Systems Biology, where the challenge is to break the complexity walls for reasoning about large biomolecular interaction systems. Pioneered by Regev, Silverman and Shapiro, the application of process calculi to the description of biological processes has been a source of inspiration for many researchers coming from the programming language community. Machine (BIOCHAM), in which biochemical systems are modeled using a simple language of reaction rules, and the biological properties of the system, known from experiments, are formalized in temporal logic. In this setting, the biological validation of a model can be done by modelchecking, both qualitatively and quantitatively. Moreover, the temporal properties can be turned into specifications for learning modifications or refinements of the model, when incorporating new biological knowledge. 1

We present a method for generating a biochemical reaction network from a description of the interactions of components of biomolecules. The interactions are specified in the form of reaction rules, each of which defines a class of reaction associated with a type of interaction. Reactants within a class have shared properties, which are specified in the rule defining the class. A rule also provides a rate law, which governs each reaction in a class, and a template for transforming reactants into products. A set of reaction rules can be applied to a seed set of chemical species and, subsequently, any new species that are found as products of reactions to generate a list of reactions and a list of the chemical species that participate in these reactions, i.e., a reaction network, which can be translated into a mathematical model. © 2005 Wiley Periodicals, Inc. Complexity 10: 22–41, 2005 Key Words: local rules; automatic model generation; networks; signal transduction; combinatorial complexity; systems biology The cell is a complex adaptive system whose emergent behavior we understand only poorly. One reason for our lack of understanding is the complexity of cellular decision making, which is often mediated by a system of interacting proteins. Systems of interacting proteins are particularly prominent in signal transduction [1], 1 the focus Correspondence to: William S. Hlavacek,

Abstract. Temporal logics and model-checking techniques have proved successful to respectively express biological properties of complex biochemical systems, and automatically verify their satisfaction in both qualitative and quantitative models. In this paper, we propose a finite time horizon model-checking algorithm for the existential fragment of LTL with numerical constraints over the reals, with the ability to compute the range of values of the real variables occurring in a formula that makes it true in a model. We illustrate this approach for the analysis of biological data time series, provide a set of biologically relevant patterns of formulas, and evaluate them on models of the cell cycle control and MAPK signal transduction. 1