"Minimal metabolism": A key concept to investigate the origins and nature of biological systems.

The systems view on life and its emergence from complex chemistry has remarkably increased the scientific attention on metabolism in the last two decades. However, during this time there has not been much theoretical discussion on what constitutes a metabolism and what role it actually played in biogenesis. A critical and updated review on the topic is here offered, including some references to classical models from last century, but focusing more on current and future research. Metabolism is considered as intrinsically related to the living but not necessarily equivalent to it. More precisely, the idea of "minimal metabolism", in contrast to previous, top-down conceptions, is formulated as a heuristic construct, halfway between chemistry and biology. Thus, rather than providing a complete or final characterization of metabolism, our aim is to encourage further investigations on it, particularly in the context of life's origin, for which some concrete methodological suggestions are provided. Also see the video abstract here: https://youtu.be/DP7VMKk2qpA.

Graph transformation for enzymatic mechanisms.

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.

Representing Catalytic Mechanisms with Rule Composition.

An "imaginary transition structure" overlays the molecular graphs of the educt and product sides of an elementary chemical reaction in a single graph to highlight the changes in bond structure. We generalize this idea to reactions with complex mechanisms in a formally rigorous approach based on composing arrow-pushing steps represented as graph-transformation rules to construct an overall composite rule and a derived transition structure. This transition structure retains information about transient bond changes that are invisible at the overall level and can be constructed automatically from an existing database of detailed enzymatic mechanisms. We use the construction to (i) illuminate the distribution of catalytic action across enzymes and substrates and (ii) to search in a large database for reactions of known or unknown mechanisms that are compatible with the mechanism captured by the constructed composite rule.

EHreact: Extended Hasse Diagrams for the Extraction and Scoring of Enzymatic Reaction Templates.

Data-driven computer-aided synthesis planning utilizing organic or biocatalyzed reactions from large databases has gained increasing interest in the last decade, sparking the development of numerous tools to extract, apply, and score general reaction templates. The generation of reaction rules for enzymatic reactions is especially challenging since substrate promiscuity varies between enzymes, causing the optimal levels of rule specificity and optimal number of included atoms to differ between enzymes. This complicates an automated extraction from databases and has promoted the creation of manually curated reaction rule sets. Here, we present EHreact, a purely data-driven open-source software tool, to extract and score reaction rules from sets of reactions known to be catalyzed by an enzyme at appropriate levels of specificity without expert knowledge. EHreact extracts and groups reaction rules into tree-like structures, Hasse diagrams, based on common substructures in the imaginary transition structures. Each diagram can be utilized to output a single or a set of reaction rules, as well as calculate the probability of a new substrate to be processed by the given enzyme by inferring information about the reactive site of the enzyme from the known reactions and their grouping in the template tree. EHreact heuristically predicts the activity of a given enzyme on a new substrate, outperforming current approaches in accuracy and functionality.

Efficient computation of co-transcriptional RNA-ligand interaction dynamics.

Riboswitches form an abundant class of cis-regulatory RNA elements that mediate gene expression by binding a small metabolite. For synthetic biology applications, they are becoming cheap and accessible systems for selectively triggering transcription or translation of downstream genes. Many riboswitches are kinetically controlled, hence knowledge of their co-transcriptional mechanisms is essential. We present here an efficient implementation for analyzing co-transcriptional RNA-ligand interaction dynamics. This approach allows for the first time to model concentration-dependent metabolite binding/unbinding kinetics. We exemplify this novel approach by means of the recently studied I-A 2'-deoxyguanosine (2'dG)-sensing riboswitch from Mesoplasma florum.

In silico design of ligand triggered RNA switches.

This contribution sketches a work flow to design an RNA switch that is able to adapt two structural conformations in a ligand-dependent way. A well characterized RNA aptamer, i.e., knowing its Kd and adaptive structural features, is an essential ingredient of the described design process. We exemplify the principles using the well-known theophylline aptamer throughout this work. The aptamer in its ligand-binding competent structure represents one structural conformation of the switch while an alternative fold that disrupts the binding-competent structure forms the other conformation. To keep it simple we do not incorporate any regulatory mechanism to control transcription or translation. We elucidate a commonly used design process by explicitly dissecting and explaining the necessary steps in detail. We developed a novel objective function which specifies the mechanistics of this simple, ligand-triggered riboswitch and describe an extensive in silico analysis pipeline to evaluate important kinetic properties of the designed sequences. This protocol and the developed software can be easily extended or adapted to fit novel design scenarios and thus can serve as a template for future needs.

RNAblueprint: flexible multiple target nucleic acid sequence design.

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: s.hammer@univie.ac.at, ivo@tbi.univie.ac.at or sven@tbi.univie.ac.at. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Sequence-controlled RNA self-processing: computational design, biochemical analysis, and visualization by AFM.

Reversible chemistry allowing for assembly and disassembly of molecular entities is important for biological self-organization. Thus, ribozymes that support both cleavage and formation of phosphodiester bonds may have contributed to the emergence of functional diversity and increasing complexity of regulatory RNAs in early life. We have previously engineered a variant of the hairpin ribozyme that shows how ribozymes may have circularized or extended their own length by forming concatemers. Using the Vienna RNA package, we now optimized this hairpin ribozyme variant and selected four different RNA sequences that were expected to circularize more efficiently or form longer concatemers upon transcription. (Two-dimensional) PAGE analysis confirms that (i) all four selected ribozymes are catalytically active and (ii) high yields of cyclic species are obtained. AFM imaging in combination with RNA structure prediction enabled us to calculate the distributions of monomers and self-concatenated dimers and trimers. Our results show that computationally optimized molecules do form reasonable amounts of trimers, which has not been observed for the original system so far, and we demonstrate that the combination of theoretical prediction, biochemical and physical analysis is a promising approach toward accurate prediction of ribozyme behavior and design of ribozymes with predefined functions.

An intermediate level of abstraction for computational systems chemistry.

Computational techniques are required for narrowing down the vast space of possibilities to plausible prebiotic scenarios, because precise information on the molecular composition, the dominant reaction chemistry and the conditions for that era are scarce. The exploration of large chemical reaction networks is a central aspect in this endeavour. While quantum chemical methods can accurately predict the structures and reactivities of small molecules, they are not efficient enough to cope with large-scale reaction systems. The formalization of chemical reactions as graph grammars provides a generative system, well grounded in category theory, at the right level of abstraction for the analysis of large and complex reaction networks. An extension of the basic formalism into the realm of integer hyperflows allows for the identification of complex reaction patterns, such as autocatalysis, in large reaction networks using optimization techniques.This article is part of the themed issue 'Reconceptualizing the origins of life'.

Memory-efficient RNA energy landscape exploration.

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/.

Computational design of RNAs with complex energy landscapes.

RNA has become an integral building material in synthetic biology. Dominated by their secondary structures, which can be computed efficiently, RNA molecules are amenable not only to in vitro and in vivo selection, but also to rational, computation-based design. While the inverse folding problem of constructing an RNA sequence with a prescribed ground-state structure has received considerable attention for nearly two decades, there have been few efforts to design RNAs that can switch between distinct prescribed conformations. We introduce a user-friendly tool for designing RNA sequences that fold into multiple target structures. The underlying algorithm makes use of a combination of graph coloring and heuristic local optimization to find sequences whose energy landscapes are dominated by the prescribed conformations. A flexible interface allows the specification of a wide range of design goals. We demonstrate that bi- and tri-stable "switches" can be designed easily with moderate computational effort for the vast majority of compatible combinations of desired target structures. RNAdesign is freely available under the GPL-v3 license.

Statistical mechanics of biomolecular condensates via cavity methods.

Physical mechanisms of phase separation in living systems play key physiological roles and have recently been the focus of intensive studies. The strongly heterogeneous nature of such phenomena poses difficult modeling challenges that require going beyond mean-field approaches based on postulating a free energy landscape. The pathway we take here is to calculate the partition function starting from microscopic interactions by means of cavity methods, based on a tree approximation for the interaction graph. We illustrate them on the binary case and then apply them successfully to ternary systems, in which simpler one-factor approximations are proved inadequate. We demonstrate the agreement with lattice simulations and contrast our theory with coacervation experiments of associative de-mixing of nucleotides and poly-lysine. Different types of evidence are provided to support cavity methods as ideal tools for modeling biomolecular condensation, giving an optimal balance between the consideration of spatial aspects and fast computational results.

BarMap: RNA folding on dynamic energy landscapes.

Dynamical changes of RNA secondary structures play an important role in the function of many regulatory RNAs. Such kinetic effects, especially in time-variable and externally triggered systems, are usually investigated by means of extensive and expensive simulations of large sets of individual folding trajectories. Here we describe the theoretical foundations of a generic approach that not only allows the direct computation of approximate population densities but also reduces the efforts required to analyze the folding energy landscapes to a one-time preprocessing step. The basic idea is to consider the kinetics on individual landscapes and to model external triggers and environmental changes as small but discrete changes in the landscapes. A "barmap" links macrostates of temporally adjacent landscapes and defines the transfer of population densities from one "snapshot" to the next. Implemented in the BarMap software, this approach makes it feasible to study folding processes at the level of basins, saddle points, and barriers for many nonstationary scenarios, including temperature changes, cotranscriptional folding, refolding in consequence to degradation, and mechanically constrained kinetics, as in the case of the translocation of a polymer through a pore.

Modelling translation initiation under the influence of sRNA.

Bacterial small non-coding RNA (sRNA) plays an important role in post-transcriptional gene regulation. Although the number of annotated sRNA is steadily increasing, their functional characterization is still lagging behind. Various computational strategies for finding sRNA−mRNA interactions, and thus putative sRNA targets, were developed. Most of them suffer from a high false positive rate. Here, we present a qualitative model to simulate the effect of an sRNA on the translation initiation of a potential target. Information about the ribosome−mRNA interaction, sRNA−mRNA interaction and expression information from deep sequencing experiments is integrated to calculate the change in translation initiation complex formation, as a proxy for translational activity. This model can be used to post-evaluate predicted targets, hence condensing the list of potential targets. We show that our translation initiation model, under the influence of an sRNA, can successfully simulate thirteen out of fifteen tested sRNA−mRNA interactions in a qualitative manner. To show the gain in specificity, we applied our method to a target search for the Escherichia coli sRNA RyhB. Compared with simple target prediction without post-evaluation, we reduce the number of targets to less than one fourth potential targets, considerably reducing the burden of experimental validation.

What makes a reaction network "chemical"?

BACKGROUND: Reaction networks (RNs) comprise a set X of species and a set [Formula: see text] of reactions [Formula: see text], each converting a multiset of educts [Formula: see text] into a multiset [Formula: see text] of products. RNs are equivalent to directed hypergraphs. However, not all RNs necessarily admit a chemical interpretation. Instead, they might contradict fundamental principles of physics such as the conservation of energy and mass or the reversibility of chemical reactions. The consequences of these necessary conditions for the stoichiometric matrix [Formula: see text] have been discussed extensively in the chemical literature. Here, we provide sufficient conditions for [Formula: see text] that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively. RESULTS: Chemically plausible RNs allow neither a perpetuum mobile, i.e., a "futile cycle" of reactions with non-vanishing energy production, nor the creation or annihilation of mass. Such RNs are said to be thermodynamically sound and conservative. For finite RNs, both conditions can be expressed equivalently as properties of the stoichiometric matrix [Formula: see text]. The first condition is vacuous for reversible networks, but it excludes irreversible futile cycles and-in a stricter sense-futile cycles that even contain an irreversible reaction. The second condition is equivalent to the existence of a strictly positive reaction invariant. It is also sufficient for the existence of a realization in terms of sum formulas, obeying conservation of "atoms". In particular, these realizations can be chosen such that any two species have distinct sum formulas, unless [Formula: see text] implies that they are "obligatory isomers". In terms of structural formulas, every compound is a labeled multigraph, in essence a Lewis formula, and reactions comprise only a rearrangement of bonds such that the total bond order is preserved. In particular, for every conservative RN, there exists a Lewis realization, in which any two compounds are realized by pairwisely distinct multigraphs. Finally, we show that, in general, there are infinitely many realizations for a given conservative RN. CONCLUSIONS: "Chemical" RNs are directed hypergraphs with a stoichiometric matrix [Formula: see text] whose left kernel contains a strictly positive vector and whose right kernel does not contain a futile cycle involving an irreversible reaction. This simple characterization also provides a concise specification of random models for chemical RNs that additionally constrain [Formula: see text] by rank, sparsity, or distribution of the non-zero entries. Furthermore, it suggests several interesting avenues for future research, in particular, concerning alternative representations of reaction networks and infinite chemical universes.

Generic Context-Aware Group Contributions.

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.

Caveats to Deep Learning Approaches to RNA Secondary Structure Prediction.

Machine learning (ML) and in particular deep learning techniques have gained popularity for predicting structures from biopolymer sequences. An interesting case is the prediction of RNA secondary structures, where well established biophysics based methods exist. The accuracy of these classical methods is limited due to lack of experimental parameters and certain simplifying assumptions and has seen little improvement over the last decade. This makes RNA folding an attractive target for machine learning and consequently several deep learning models have been proposed in recent years. However, for ML approaches to be competitive for de-novo structure prediction, the models must not just demonstrate good phenomenological fits, but be able to learn a (complex) biophysical model. In this contribution we discuss limitations of current approaches, in particular due to biases in the training data. Furthermore, we propose to study capabilities and limitations of ML models by first applying them on synthetic data (obtained from a simplified biophysical model) that can be generated in arbitrary amounts and where all biases can be controlled. We assume that a deep learning model that performs well on these synthetic, would also perform well on real data, and vice versa. We apply this idea by testing several ML models of varying complexity. Finally, we show that the best models are capable of capturing many, but not all, properties of RNA secondary structures. Most severely, the number of predicted base pairs scales quadratically with sequence length, even though a secondary structure can only accommodate a linear number of pairs.

Chemical Transformation Motifs-Modelling Pathways as Integer Hyperflows.

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.

Finding the K best synthesis plans.

In synthesis planning, the goal is to synthesize a target molecule from available starting materials, possibly optimizing costs such as price or environmental impact of the process. Current algorithmic approaches to synthesis planning are usually based on selecting a bond set and finding a single good plan among those induced by it. We demonstrate that synthesis planning can be phrased as a combinatorial optimization problem on hypergraphs by modeling individual synthesis plans as directed hyperpaths embedded in a hypergraph of reactions (HoR) representing the chemistry of interest. As a consequence, a polynomial time algorithm to find the K shortest hyperpaths can be used to compute the K best synthesis plans for a given target molecule. Having K good plans to choose from has many benefits: it makes the synthesis planning process much more robust when in later stages adding further chemical detail, it allows one to combine several notions of cost, and it provides a way to deal with imprecise yield estimates. A bond set gives rise to a HoR in a natural way. However, our modeling is not restricted to bond set based approaches-any set of known reactions and starting materials can be used to define a HoR. We also discuss classical quality measures for synthesis plans, such as overall yield and convergency, and demonstrate that convergency has a built-in inconsistency which could render its use in synthesis planning questionable. Decalin is used as an illustrative example of the use and implications of our results.

RNA structure prediction: from 2D to 3D.

We summarize different levels of RNA structure prediction, from classical 2D structure to extended secondary structure and motif-based research toward 3D structure prediction of RNA. We outline the importance of classical secondary structure during all those levels of structure prediction.