CRNs Exposed: A Method for the Systematic Exploration of Chemical Reaction Networks

Formal methods have enabled breakthroughs in many fields, such as in hardware verification, machine learning and biological systems. The key object of interest in systems biology, synthetic biology, and molecular programming is chemical reaction networks (CRNs) which formalizes coupled chemical reactions in a well-mixed solution. CRNs are pivotal for our understanding of biological regulatory and metabolic networks, as well as for programming engineered molecular behavior. Although it is clear that small CRNs are capable of complex dynamics and computational behavior, it remains difficult to explore the space of CRNs in search for desired functionality. We use Alloy, a tool for expressing structural constraints and behavior in software systems, to enumerate CRNs with declaratively specified properties. We show how this framework can enumerate CRNs with a variety of structural constraints including biologically motivated catalytic networks and metabolic networks, and seesaw networks motivated by DNA nanotechnology. We also use the framework to explore analog function computation in rate-independent CRNs. By computing the desired output value with stoichiometry rather than with reaction rates (in the sense that X ? Y+Y computes multiplication by 2), such CRNs are completely robust to the choice of reaction rates or rate law. We find the smallest CRNs computing the max, minmax, abs and ReLU (rectified linear unit) functions in a natural subclass of rate-independent CRNs where rate-independence follows from structural network properties

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

A Modelling and Simulation Tool for DNA Strand Displacement Systems

DNA is the hereditary material in almost all organisms, and the sequence of its monomers efficiently conveys essential biological information. Although DNA is well known for its biological functions, the unique material properties of DNA also motivate scientists to design and manufacture DNA complexes for technological purposes. This research field is termed DNA nanotechnology, and it aims to construct arbitrary biomolecular structures using DNA molecules as building blocks. DNA nanotechnology initially focused on programmable static structures, but it has further inspired the designs of engineering systems with dynamic properties such as logic circuits and catalytic systems. This dynamic variant of DNA nanotechnology is enabled by the DNA strand displacement (DSD) mechanism. The design of a DSD system involves discreetly designed initial species that can execute expected sequential reactions. However, such task is hard to be accomplished by hand as the complete reaction network of a large-scaled DSD system can be intractable. In this thesis, we study the problem of modelling DSD systems, i.e., enumerating combinatorially the full space of molecular complexes reachable from the initial species and transferring the resulting chemical reaction network to a simulation engine. We present a rule-based modelling pipeline RuleDSD for generating and simulating reaction networks of DSD systems. RuleDSD is implemented as a software package DSDPy, a tool that automatically generates a complete reaction network for a described DSD system and integrates with the PySB framework for further simulations using the BioNetGen engine. The reaction networks produced by DSDPy show that it is suitable for modelling various DSD systems from existing literature

Graph embedding in SYNCHEM2, an expert system for organic synthesis discovery

AbstractGraph embedding (subgraph isomorphism) is an NP-complete problem of great theoretical and practical importance in the sciences, especially chemistry and computer science. This paper presents positive test results for techniques to speed embedding by modeling graphs with subroutines, precalculating edge tables, turning recursion into iteration, and using search-ordering heuristics.The expert system synchem2 searches for synthesis routes of organic molecules without the online guidance of a user, and this paper examines how embedding information helps to implement the central operations of synchem2: selection, application, and evaluation of chemical reactions. The paper also outlines the architecture of synchem2, analyzes the computational time complexity of embedding and related problems in graph isomorphism and canonical chemical naming, and suggests topics and techniques for further research

Functional stoichiometric analysis of metabolic networks

Motivation: An important tool in Systems Biology is the stoichiometric modeling of metabolic networks, where the stationary states of the network are described by a high-dimensional polyhedral cone, the so-called flux cone. Exhaustive descriptions of the metabolism can be obtained by computing the elementary vectors of this cone but, owing to a combinatorial explosion of the number of elementary vectors, this approach becomes computationally intractable for genome scale networks. Result: Hence, we propose to instead focus on the conversion cone, a projection of the flux cone, which describes the interaction of the metabolism with its external chemical environment. We present a direct method for calculating the elementary vectors of this cone and, by studying the metabolism of Saccharomyces cerevisiae, we demonstrate that such an analysis is computationally feasible even for genome scale networks. Contact: [email protected]

Computational Methods in Systems Biology. 17th International Conference, CMSB 2019, Trieste, Italy, September 18\u201320, 2019, Proceedings

This volume contains the papers presented at CMSB 2019, the 17th Conference on Computational Methods in Systems Biology, held during September 18\u201320, 2019, at the University of Trieste, Italy. The CMSB annual conference series, initiated in 2003, provides a unique discussion forum for computer scientists, biologists, mathematicians, engineers, and physicists interested in a system-level understanding of biological processes. Topics covered by the CMSB proceedings include: formalisms for modeling biological processes; models and their biological applications; frameworks for model verification, validation, anal- ysis, and simulation of biological systems; high-performance computational systems biology and parallel implementations; model inference from experimental data; model integration from biological databases; multi-scale modeling and analysis methods; computational approaches for synthetic biology; and case studies in systems and synthetic biology. This year there were 53 submissions in total for the 4 conference tracks. Each regular submission and tool paper submission were reviewed by at least three Program Committee members. Additionally, tools were subjected to an additional review by members of the Tool Evaluation Committee, testing the usability of the software and the reproducibility of the results. For the proceedings, the Program Committee decided to accept 14 regular papers, 7 tool papers, and 11 short papers. This rich program of talks was complemented by a poster session, providing an opportunity for informal discussion of preliminary results and results in related fields. In view of the broad scope of the CMSB conference series, we selected the fol- lowing five high-profile invited speakers: Kobi Benenson (ETH Zurich, Switzerland), Trevor Graham (Barts Cancer Hospital, London, UK), Gaspar Tkacik (IST, Austria), Adelinde Uhrmacher (Rostock University, Germany), and Manuel Zimmer (University of Vienna, Austria). Their invited talks covered a broad area within the technical and applicative domains of the conference, and stimulated fruitful discussions among the conference attendees. Further details on CMSB 2019 are available on the following website: https://cmsb2019.units.it. Finally, as the program co-chairs, we are extremely grateful to the members of the Program Committee and the external reviewers for their peer reviews and the valuable feedback they provided to the authors. Our special thanks go to Laura Nenzi as local organization co-chair, Dimitrios Milios as chair of the Tool Evaluation Committee, and to Fran\ue7ois Fages and all the members of the CMSB Steering Committee, for their advice on organizing and running the conference. We acknowledge the support of the EasyChair conference system during the reviewing process and the production of these proceedings. We also thank Springer for publishing the CMSB proceedings in its Lecture Notes in Computer Science series. Additionally, we would like to thank the Department of Mathematics and Geo- sciences of the University of Trieste, for sponsoring and hosting this event, and Confindustria Venezia Giulia, for supporting this event and providing administrative help. Finally, we would like to thank all the participants of the conference. It was the quality of their presentations and their contribution to the discussions that made the meeting a scientific success