Section: New Results
Other results
Chemical Programming
Participants : Pascal Fradet [contact person] , Marnes Hoff.
Chemical programming describes computation in terms of a chemical solution in which molecules (representing data) interact freely according to reaction rules (representing the program). Solutions are represented by multisets of elements and reactions by rewrite rules which consume and produce new elements according to conditions. This paradigm makes it possible to express programs without artificial sequentiality in a very abstract way. It bridges the gap between specification and implementation languages.
A drawback of chemical languages is that their very highlevel nature usually leads to very inefficient programs. We have proposed an approach [20] where the basic functionality is expressed as a chemical program whereas efficiency is achieved separately by:

structuring the multiset with a data type defining neighborhood relations;

describing the selection of elements according to their neighborhood;

specifying the evaluation strategy (i.e., the application of rules and termination).
Using these three implementation aspects (data structure, selection, and strategy), the chemical program can then be refined automatically into an efficient lowlevel program. The crucial methodological advantage is that logical issues are decoupled from efficiency issues.
This research, that takes place within the AutoChem project (see Section 8.2.1 ), is the subject matter of Marnes Hoff's PhD thesis.
Efficient Parameter Search for Qualitative Models of Regulatory Networks using Symbolic Model Checking
Participant : Gregor Gössler.
A central problem in the analysis of biological regulatory networks concerns the relation between their structure and dynamics. This problem can be narrowed down to the following two questions: (a) Is a hypothesized structure of the network consistent with the observed behavior? (b) Can a proposed structure generate a desired behavior?
Qualitative models of regulatory networks, such as (synchronous or asynchronous) Boolean models and piecewiseaffine differential equation (PADE) models, have been proven useful for addressing the above questions. The models are coarsegrained, in the sense that they do not explicitly specify the biochemical mechanisms. However, they include the logic of gene regulation and allow different expression levels of the genes to be distinguished.
Qualitative models bring specific advantages when studying the relation between structure and dynamics. In order to answer questions (a) and (b), one has to search the parameter space to check if for some parameter values the network is consistent with the data or can attain a desired control objective. In qualitative models, the number of different parametrizations is finite and the number of possible values for each parameter is usually rather low. This makes parameter search easier to handle than in quantitative models, where exhaustive search of the continuous parameter space is in general not feasible. Moreover, qualitative models are concerned with trends rather than with precise quantitative values, which corresponds to the nature of much of the available biological data.
Nevertheless, the parametrization of qualitative models remains a complex problem. For most models of networks of biological interest the state and parameter spaces are too large to exhaustively test all combinations of parameter values. The aim of this work was to address this search problem for PADE models by treating it in the context of formal verification and symbolic model checking.
Our contributions in [8] are twofold. On the methodological side, we have developed a method that makes it possible to efficiently analyze large and possibly incompletely parametrized PADE models. This is achieved by a symbolic encoding of the model structure, constraints on parameter values, and transition rules describing the qualitative dynamics of the system. We can thus take full advantage of symbolic model checkers for testing the consistency of the network structure with dynamic properties expressed in temporal logics. In comparison with related work, our method applies to incompletely instead of fully parametrized models, provides more precise results, and the encoding is efficient without (strongly) simplifying the PADE dynamics.
On the application side, we show that the method performs well on real problems, by means of the IRMA synthetic network and benchmark experimental datasets. More precisely, we are able to find parameter values for which the network satisfies temporallogic properties describing observed expression profiles. Analysis of these parameter values reveals that biologically relevant constraints have been identified. Moreover, we make suggestions to improve the robustness of the external control of the IRMA behavior by proposing a rewiring of the network.