The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel method of the graph transformation model construction, combining generative and dynamical viewpoints to give a fully automated data-driven model inference method. The method takes the input dynamical properties, given as a "snapshot" of the dynamics encoded by explicit transitions, and constructs a compatible model. The obtained model is guaranteed to be minimal, thus framing the approach as model compression (from a set of transitions into a set of rules). The compression is permissive to a lossy case, where the constructed model is allowed to exhibit behavior outside of the input transitions, thus suggesting a completion of the input dynamics. The task of graph transformation model inference is naturally highly challenging due to the combinatorics involved. We tackle the exponential explosion by proposing a heuristically minimal translation of the task into a well-established problem, set cover, for which highly optimized solutions exist. We further showcase how our results relate to Kolmogorov complexity expressed in terms of graph transformation.

RNA is a dynamic biomolecule crucial for cellular regulation, with its function largely determined by its folding into complex structures, while misfolding can lead to multifaceted biological sequelae. During the folding process, RNA traverses through a series of intermediate structural states, with each transition occurring at variable rates that collectively influence the time required to reach the functional form. Understanding these folding kinetics is vital for predicting RNA behavior and optimizing applications in synthetic biology and drug discovery. While in silico kinetic RNA folding simulators are often computationally intensive and time-consuming, accurate approximations of the folding times can already be very informative to assess the efficiency of the folding process. In this work, we present KinPFN, a novel approach that leverages prior-data fitted networks to directly model the posterior predictive distribution of RNA folding times. By training on synthetic data representing arbitrary prior folding times, KinPFN efficiently approximates the cumulative distribution function of RNA folding times in a single forward pass, given only a few initial folding time examples. Our method offers a modular extension to existing RNA kinetics algorithms, promising significant computational speed-ups orders of magnitude faster, while achieving comparable results. We showcase the effectiveness of KinPFN through extensive evaluations and real-world case studies, demonstrating its potential for RNA folding kinetics analysis, its practical relevance, and generalization to other biological data.

Many properties of molecules vary systematically with changes in the structural formula and can thus be estimated from regression models defined on small structural building blocks, usually functional groups. Typically, such approaches are limited to a particular class of compounds and requires hand-curated lists of chemically plausible groups. This limits their use in particular in the context of generative approaches to explore large chemical spaces. Here we overcome this limitation by proposing a generic group contribution method that iteratively identifies significant regressors of increasing size. To this end, LASSO regression is used and the context-dependent contributions are "anchored" around a reference edge to reduce ambiguities and prevent overcounting due to multiple embeddings. We benchmark our approach, which is available as "Context AwaRe Group cOntribution" ( CARGO), on artificial data, typical applications from chemical thermodynamics. As we shall see, this method yields stable results with accuracies comparable to other regression techniques. As a by-product, we obtain interpretable additive contributions for individual chemical bonds and correction terms depending on local contexts.

MOTIVATION: The design of enzymes is as challenging as it is consequential for making chemical synthesis in medical and industrial applications more efficient, cost-effective and environmentally friendly. While several aspects of this complex problem are computationally assisted, the drafting of catalytic mechanisms, i.e. the specification of the chemical steps-and hence intermediate states-that the enzyme is meant to implement, is largely left to human expertise. The ability to capture specific chemistries of multistep catalysis in a fashion that enables its computational construction and design is therefore highly desirable and would equally impact the elucidation of existing enzymatic reactions whose mechanisms are unknown. RESULTS: We use the mathematical framework of graph transformation to express the distinction between rules and reactions in chemistry. We derive about 1000 rules for amino acid side chain chemistry from the M-CSA database, a curated repository of enzymatic mechanisms. Using graph transformation, we are able to propose hundreds of hypothetical catalytic mechanisms for a large number of unrelated reactions in the Rhea database. We analyze these mechanisms to find that they combine in chemically sound fashion individual steps from a variety of known multistep mechanisms, showing that plausible novel mechanisms for catalysis can be constructed computationally. AVAILABILITY AND IMPLEMENTATION: The source code of the initial prototype of our approach is available at https://github.com/Nojgaard/mechsearch. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and hyperedges to reactions. Pathways are modelled as integer hyperflows and we expand the network model by detailed routing constraints. In contrast to the more traditional approaches like Flux Balance Analysis or Elementary Mode analysis we insist on integer-valued flows. While this choice makes it necessary to solve possibly hard integer linear programs, it has the advantage that more detailed mechanistic questions can be formulated. It is thus possible to query networks for general transformation motifs, and to automatically enumerate optimal and near-optimal pathways. Similarities and differences between our work and traditional approaches in metabolic network analysis are discussed in detail. To demonstrate the applicability of the mathematical framework to real-life problems we first explore the design space of possible non-oxidative glycolysis pathways and show that recent manually designed pathways can be further optimized. We then use a model of sugar chemistry to investigate pathways in the autocatalytic formose process. A graph transformation-based approach is used to automatically generate the reaction networks of interest.

MOTIVATION: Realizing the value of synthetic biology in biotechnology and medicine requires the design of molecules with specialized functions. Due to its close structure to function relationship, and the availability of good structure prediction methods and energy models, RNA is perfectly suited to be synthetically engineered with predefined properties. However, currently available RNA design tools cannot be easily adapted to accommodate new design specifications. Furthermore, complicated sampling and optimization methods are often developed to suit a specific RNA design goal, adding to their inflexibility. RESULTS: We developed a C ++ library implementing a graph coloring approach to stochastically sample sequences compatible with structural and sequence constraints from the typically very large solution space. The approach allows to specify and explore the solution space in a well defined way. Our library also guarantees uniform sampling, which makes optimization runs performant by not only avoiding re-evaluation of already found solutions, but also by raising the probability of finding better solutions for long optimization runs. We show that our software can be combined with any other software package to allow diverse RNA design applications. Scripting interfaces allow the easy adaption of existing code to accommodate new scenarios, making the whole design process very flexible. We implemented example design approaches written in Python to demonstrate these advantages. AVAILABILITY AND IMPLEMENTATION: RNAblueprint , Python implementations and benchmark datasets are available at github: https://github.com/ViennaRNA . CONTACT: [email protected], [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

RNA molecules engineered to fold into predefined conformations have enabled the design of a multitude of functional RNA devices in the field of synthetic biology and nanotechnology. More complex designs require efficient computational methods, which need to consider not only equilibrium thermodynamics but also the kinetics of structure formation. Here we present a novel type of RNA design that mimics the behavior of prions, that is, sequences capable of interaction-triggered autocatalytic replication of conformations. Our design was computed with the ViennaRNA package and is based on circular RNA that embeds domains amenable to intermolecular kissing interactions.

Modeling gene regulatory networks (GRNs) is essential for conceptualizing how genes are expressed and how they influence each other. Typically, a reverse engineering approach is employed; this strategy is effective in reproducing possible fitting models of GRNs. To use this strategy, however, two daunting tasks must be undertaken: one task is to optimize the accuracy of inferred network behaviors; and the other task is to designate valid biological topologies for target networks. Although existing studies have addressed these two tasks for years, few of the studies can satisfy both of the requirements simultaneously. To address these difficulties, we propose an integrative modeling framework that combines knowledge-based and data-driven input sources to construct biological topologies with their corresponding network behaviors. To validate the proposed approach, a real dataset collected from the cell cycle of the yeast S. cerevisiae is used. The results show that the proposed framework can successfully infer solutions that meet the requirements of both the network behaviors and biological structures. Therefore, the outcomes are exploitable for future in vivo experimental design.

Andersen J, Flamm C, Hanczyc M, Merkle D. Towards an Optimal DNA-Templated Molecular Assembler. In: Artificial Life 14: Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems. The MIT Press; 2014: 557-564.

MOTIVATION: Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the landscape enable the study of larger systems; however, they are still restricted by huge memory requirements of exact approaches. RESULTS: We present a highly parallelizable local enumeration scheme that enables the computation of exact macro-state transition models with highly reduced memory requirements. The approach is evaluated on RNA secondary structure landscapes using a gradient basin definition for macro-states. Furthermore, we demonstrate the need for exact transition models by comparing two barrier-based approaches, and perform a detailed investigation of gradient basins in RNA energy landscapes. AVAILABILITY AND IMPLEMENTATION: Source code is part of the C++ Energy Landscape Library available at http://www.bioinf.uni-freiburg.de/Software/.

We developed a simulation tool for investigating the evolution of early metabolism, allowing us to speculate on the formation of metabolic pathways from catalyzed chemical reactions and on the development of their characteristic properties. Our model consists of a protocellular entity with a simple RNA-based genetic system and an evolving metabolism of catalytically active ribozymes that manipulate a rich underlying chemistry. Ensuring an almost open-ended and fairly realistic simulation is crucial for understanding the first steps in metabolic evolution. We show here how our simulation tool can be helpful in arguing for or against hypotheses on the evolution of metabolic pathways. We demonstrate that seemingly mutually exclusive hypotheses may well be compatible when we take into account that different processes dominate different phases in the evolution of a metabolic system. Our results suggest that forward evolution shapes metabolic network in the very early steps of evolution. In later and more complex stages, enzyme recruitment supersedes forward evolution, keeping a core set of pathways from the early phase.

Large chemical reaction networks often exhibit distinctive features that can be interpreted as higher-level structures. Prime examples are metabolic pathways in a biochemical context. We review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of set-valued set functions that encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organization-theoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggests the exploration of the chemical meaning of well-established topological concepts. As an example, we consider connectedness in some detail.

Analysis of the spatial structure of proteins including folding processes is a challenge for modern bioinformatics. Due to limited experimental access to folding processes, computer simulations are a standard approach. Since realistic continuous (all-atom) simulations are far too expensive, lattice based protein folding simulations are a common coarse-graining. In this paper, we present a visualization tool for lattice based protein folding simulations. The system is based on Shneiderman’s mantra "Overview first, zoom and filter, details on demand" and uses a collection of information visualization techniques including multiple views, focus+context and table lenses which have been tailored towards our data. We demonstrate the potential of information visualization techniques for providing insight into such simulations.

The SBML ODE Solver Library (SOSlib) is a programming library for symbolic and numerical analysis of chemical reaction network models encoded in the Systems Biology Markup Language (SBML). It is written in ISO C and distributed under the open source LGPL license. The package employs libSBML structures for formula representation and associated functions to construct a system of ordinary differential equations, their Jacobian matrix and other derivatives. SUNDIALS' CVODES is incorporated for numerical integration and sensitivity analysis. Preliminary benchmarking results give a rough overview on the behavior of different tools and are discussed in the Supplementary Material. The native application program interface provides fine-grained interfaces to all internal data structures, symbolic operations and numerical routines, enabling the construction of very efficient analytic applications and hybrid or multi-scale solvers with interfaces to SBML and non SBML data sources. Optional modules based on XMGrace and Graphviz allow quick inspection of structure and dynamics.

BACKGROUND: Comparison of metabolic networks is typically performed based on the organisms' enzyme contents. This approach disregards functional replacements as well as orthologies that are misannotated. Direct comparison of the structure of metabolic networks can circumvent these problems. RESULTS: Metabolic networks are naturally represented as directed hypergraphs in such a way that metabolites are nodes and enzyme-catalyzed reactions form (hyper)edges. The familiar operations from set algebra (union, intersection, and difference) form a natural basis for both the pairwise comparison of networks and identification of distinct metabolic features of a set of algorithms. We report here on an implementation of this approach and its application to the procaryotes. CONCLUSION: We demonstrate that metabolic networks contain valuable phylogenetic information by comparing phylogenies obtained from network comparisons with 16S RNA phylogenies. The algebraic approach to metabolic networks is suitable to study metabolic innovations in two sets of organisms, free living microbes and Pyrococci, as well as obligate intracellular pathogens.

Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods that help to analyze the validity of these models. Here, we focus on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; thus they are huge and high dimensional. Their most salient features, however, are encapsulated by their so-called barrier tree that reflects the local minima and their connecting saddle points. For each length of the growing RNA chain there exists a folding landscape. We visualize the sequence of folding landscapes by an animation of the corresponding barrier trees. To generate the animation, we adapt the foresight layout with tolerance algorithm for general dynamic graph layout problems. Since it is very general, we give a detailed description of each phase: constructing a supergraph for the trees, layout of that supergraph using a modified DoT algorithm, and presentation techniques for the final animation.