Inferring Chemical Reaction Patterns Using Rule Composition in Graph Grammars

Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tom odeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like merging, splitting, and isomerisation of molecules. It is often convenient, in particular in the analysis of larger systems, to summarize several subsequent reactions into a single composite chemical reaction. We use a generic approach for composing graph grammar rules to define a chemically useful rule compositions. We iteratively apply these rule compositions to elementary transformations in order to automatically infer complex transformation patterns. This is useful for instance to understand the net effect of complex catalytic cycles such as the Formose reaction. The automatically inferred graph grammar rule is a generic representative that also covers the overall reaction pattern of the Formose cycle, namely two carbonyl groups that can react with a bound glycolaldehyde to a second glycolaldehyde. Rule composition also can be used to study polymerization reactions as well as more complicated iterative reaction schemes. Terpenes and the polyketides, for instance, form two naturally occurring classes of compounds of utmost pharmaceutical interest that can be understood as "generalized polymers" consisting of five-carbon (isoprene) and two-carbon units, respectively

Generic Strategies for Chemical Space Exploration

Computational approaches to exploring "chemical universes", i.e., very large sets, potentially infinite sets of compounds that can be constructed by a prescribed collection of reaction mechanisms, in practice suffer from a combinatorial explosion. It quickly becomes impossible to test, for all pairs of compounds in a rapidly growing network, whether they can react with each other. More sophisticated and efficient strategies are therefore required to construct very large chemical reaction networks. Undirected labeled graphs and graph rewriting are natural models of chemical compounds and chemical reactions. Borrowing the idea of partial evaluation from functional programming, we introduce partial applications of rewrite rules. Binding substrate to rules increases the number of rules but drastically prunes the substrate sets to which it might match, resulting in dramatically reduced resource requirements. At the same time, exploration strategies can be guided, e.g. based on restrictions on the product molecules to avoid the explicit enumeration of very unlikely compounds. To this end we introduce here a generic framework for the specification of exploration strategies in graph-rewriting systems. Using key examples of complex chemical networks from sugar chemistry and the realm of metabolic networks we demonstrate the feasibility of a high-level strategy framework. The ideas presented here can not only be used for a strategy-based chemical space exploration that has close correspondence of experimental results, but are much more general. In particular, the framework can be used to emulate higher-level transformation models such as illustrated in a small puzzle game

Evolution of Metabolic Networks: A Computational Framework

Background: The metabolic architectures of extant organisms share many key pathways such as the citric acid cycle, glycolysis, or the biosynthesis of most amino acids. Several competing hypotheses for the evolutionary mechanisms that shape metabolic networks have been discussed in the literature, each of which finds support from comparative analysis of extant genomes. Alternatively, the principles of metabolic evolution can be studied by direct computer simulation. This requires, however, an explicit implementation of all pertinent components: a universe of chemical reaction upon which the metabolism is built, an explicit representation of the enzymes that implement the metabolism, of a genetic system that encodes these enzymes, and of a fitness function that can be selected for. Results: We describe here a simulation environment that implements all these components in a simplified ways so that large-scale evolutionary studies are feasible. We employ an artificial chemistry that views chemical reactions as graph rewriting operations and utilizes a toy-version of quantum chemistry to derive thermodynamic parameters. Minimalist organisms with simple string-encoded genomes produce model ribozymes whose catalytic activity is determined by an ad hoc mapping between their secondary structure and the transition state graphs that they stabilize. Fitness is computed utilizing the ideas of metabolic flux analysis. We present an implementation of the complete system and first simulation results. Conclusions: The simulation system presented here allows coherent investigations into the evolutionary mechanisms of the first steps of metabolic evolution using a self-consistent toy univers

A Domain-Specific Language and Editor for Parallel Particle Methods

Domain-specific languages (DSLs) are of increasing importance in scientific high-performance computing to reduce development costs, raise the level of abstraction and, thus, ease scientific programming. However, designing and implementing DSLs is not an easy task, as it requires knowledge of the application domain and experience in language engineering and compilers. Consequently, many DSLs follow a weak approach using macros or text generators, which lack many of the features that make a DSL a comfortable for programmers. Some of these features---e.g., syntax highlighting, type inference, error reporting, and code completion---are easily provided by language workbenches, which combine language engineering techniques and tools in a common ecosystem. In this paper, we present the Parallel Particle-Mesh Environment (PPME), a DSL and development environment for numerical simulations based on particle methods and hybrid particle-mesh methods. PPME uses the meta programming system (MPS), a projectional language workbench. PPME is the successor of the Parallel Particle-Mesh Language (PPML), a Fortran-based DSL that used conventional implementation strategies. We analyze and compare both languages and demonstrate how the programmer's experience can be improved using static analyses and projectional editing. Furthermore, we present an explicit domain model for particle abstractions and the first formal type system for particle methods.Comment: Submitted to ACM Transactions on Mathematical Software on Dec. 25, 201

Analysis of Generative Chemistries

For the modelling of chemistry we use undirected, labelled graphs as explicit models of molecules and graph transformation rules for modelling generalised chemical reactions. This is used to define artificial chemistries on the level of individual bonds and atoms, where formal graph grammars implicitly represent large spaces of chemical compounds. We use a graph rewriting formalism, rooted in category theory, called the Double Pushout approach, which directly expresses the transition state of chemical reactions. Using concurrency theory for transformation rules, we define algorithms for the composition of rewrite rules in a chemically intuitive manner that enable automatic abstraction of the level of detail in chemical pathways. Based on this rule composition we define an algorithmic framework for generation of vast reaction networks for specific spaces of a given chemistry, while still maintaining the level of detail of the model down to the atomic level. The framework also allows for computation with graphs and graph grammars, which is utilised to model non-trivial chemical systems. The graph generation relies on graph isomorphism testing, and we review the general individualisation-refinement paradigm used in the state-of-the-art algorithms for graph canonicalisation, isomorphism testing, and automorphism discovery. We present a model for chemical pathways based on a generalisation of network flows from ordinary directed graphs to directed hypergraphs. The model allows for reasoning about the flow of individual molecules in general pathways, and the introduction of chemically motivated routing constraints. It further provides the foundation for defining specialised pathway motifs, which is illustrated by defining necessary topological constraints for both catalytic and autocatalytic pathways. We also prove that central types of pathway questions are NP-complete, even for restricted classes of reaction networks. The complete pathway model, including constraints for catalytic and autocatalytic pathways, is implemented using integer linear programming. This implementation is used in a tree search method to enumerate both optimal and near-optimal pathway solutions. The formal methods are applied to multiple chemical systems: the enzyme catalysed beta-lactamase reaction, variations of the glycolysis pathway, and the formose process. In each of these systems we use rule composition to abstract pathways and calculate traces for isotope labelled carbon atoms. The pathway model is used to automatically enumerate alternative non-oxidative glycolysis pathways, and enumerate thousands of candidates for autocatalytic pathways in the formose process

Specification of Software Architecture Reconfiguration

In the past years, Software Architecture has attracted increased attention by academia and industry as the unifying concept to structure the design of complex systems. One particular research area deals with the possibility of reconfiguring architectures to adapt the systems they describe to new requirements. Reconfiguration amounts to adding and removing components and connections, and may have to occur without stopping the execution of the system being reconfigured. This work contributes to the formal description of such a process. Taking as a premise that a single formalism hardly ever satisfies all requirements in every situation, we present three approaches, each one with its own assumptions about the systems it can be applied to and with different advantages and disadvantages. Each approach is based on work of other researchers and has the aesthetic concern of changing as little as possible the original formalism, keeping its spirit. The first approach shows how a given reconfiguration can be specified in the same manner as the system it is applied to and in a way to be efficiently executed. The second approach explores the Chemical Abstract Machine, a formalism for rewriting multisets of terms, to describe architectures, computations, and reconfigurations in a uniform way. The last approach uses a UNITY-like parallel programming design language to describe computations, represents architectures by diagrams in the sense of Category Theory, and specifies reconfigurations by graph transformation rules