arXiv subjects

Christoph Flamm

Publications and source records attributed to Christoph Flamm.

At least 19 recordsLinked to original sources

arXiv2026

On the realizability of abstract reaction networks with real molecules and reactions

Abstract reaction networks appear not only as models of chemical reactions but also as models of complex systems, with applications in areas such as ecology and epidemiology, and as one of several alternative paradigms for non-standard computation. It is therefore of interest to determine whether an abstract reaction network can be realized by a concrete set of molecules and plausible chemical reaction mechanisms. It is known that a reaction network has a realization in terms of chemical graphs (i.e., Lewis structures) if and only if it is conservative. Here we consider the problem of assigning a set M of known molecules to a set X of abstract entities in a reaction network (X,R) such that each reaction satisfies mass balance and adheres to one of an allowed set of chemical reaction mechanisms. We show that this problem is NP-complete. Nevertheless, it can be solved in practice using a backtrack-and-prune algorithm inspired by the VF2 family of algorithms originally designed for the subgraph isomorphism problem.

q-bio.MN↗

arXiv2025

Rule-Based Gillespie Simulation of Chemical Systems

The M{\O}D computational framework implements rule-based generative chemistries as explicit transformations of graphs representing chemical structural formulae. Here, we expand M{\O}D by a stochastic simulation module that simulates the time evolution of species concentrations using Gillespie's well-known stochastic simulation algorithm (SSA). This module distinguishes itself among competing implementations of rule-based stochastic simulation engines by its flexible network expansion mechanism and its functionality for defining custom reaction rate functions. It enables direct sampling from actual reactions instead of rules. We present methodology and implementation details followed by examples which demonstrate the capabilities of the stochastic simulation engine.

q-bio.MN↗

arXiv2025

Thermodynamic ranking of pathways in reaction networks

One of the puzzles left open by energetic analyses of irreversible stochastic processes is that boundary conditions that prevent the performance of work or the dissipation of heat make no contribution to an entropy-production budget; yet we see ubiquitously in both engineered and living systems that both transient and persistent energy costs are paid to create and maintain such boundaries. We wish to know whether there are inherent limits for the costs of such phenomena, and common units in which those can be traded off against more familiar costs measured in terms of heat dissipation. We give this problem a concrete framing in the context of CRNs, for the problem of extracting a topologically restricted pathway from a larger distributed network, through activation of some reactions and selective elimination of others. We define a thermodynamic cost function for pathways derived from large-deviation theory of stochastic CRNs, which decomposes into two components: an ongoing maintenance cost to sustain a NESS, and a restriction cost, quantifying the ongoing improbability of neutralizing reactions outside the specified pathway. Applying this formalism to detailed-balanced CRNs in the linear response regime, we make use of their formal equivalence to electrical circuits. We prove that the resistance of a CRN decreases as reactions are added that support the throughput current, and that the maintenance cost, the restriction cost, and the thermodynamic cost of nested pathways are bounded below by those of their hosting network. For small CRNs, we show how catalytic and inhibitory mechanisms can drastically alter pathway costs, enabling unfavorable pathways to become favorable and approach the cost of the hosting pathway. Our results provide insights into the thermodynamic principles governing open CRNs and offer a foundation for understanding the evolution of metabolic networks.

q-bio.MN↗

arXiv2025

Assembly in Directed Hypergraphs

Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to generalize the notion of assembly to general chemical reaction systems and to make explicit the connection to rule based models of chemistry, in particular DPO graph rewriting. We observe, furthermore, that assembly theory is closely related to retrosynthetic analysis in chemistry. The assembly index fits seamlessly into a large family of cost measures for directed hyperpath problems that also encompasses cost functions used in computational synthesis planning. This allows to devise a generic approach to compute complexity measures derived from minimal hyperpaths in rule-derived directed hypergraphs using integer linear programming.

cs.DM↗

arXiv2024

Finding Thermodynamically Favorable Pathways in Chemical Reaction Networks Using Flows in Hypergraphs and Mixed-Integer Linear Programming

The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as hypergraphs, modeling that facilitates the search for pathways by computational means. We propose to enrich an existing search method for pathways by including thermodynamic principles. In more detail, we give a mixed-integer linear programming (mixed ILP) formulation of the search problem into which we integrate chemical potentials and concentrations for individual molecules, enabling us to constrain the search to return pathways containing only thermodynamically favorable reactions. Moreover, if multiple possible pathways are found, we can rank these by objective functions based on thermodynamics. As an example of use, we apply the framework to a reaction network representing the HCN-formamide chemistry. Alternative pathways to the one currently hypothesized in the literature are queried and enumerated, including some that score better according to our chosen objective function.

q-bio.MN↗

arXiv2024

Automated Inference of Graph Transformation Rules

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.

cs.DM↗

arXiv2023

Every atom-atom map can be explained by electron pushing diagrams

Chemical reactions can be understood as transformations of multigraphs (molecules) that preserve vertex labels (atoms) and degrees (sums of bonding and non-bonding electrons), thereby implying the atom-atom map of a reaction. The corresponding reaction mechanism is often described by an electron pushing diagram that explains the transformation by consecutive local relocations of invidudal edges (electron pairs). Here, we show that every degree-preserving map between multigraphs, and thus every atom-atom map, can be generated by cyclic electron pushing. Moreover, it is always possible to decompose such an explanation into electron pushing diagrams involving only four electron pairs. This in turn implies that every reaction can be decomposed into a sequence of elementary reactions that involve at most two educt molecules and two product molecules. Hence, the requirement of a mechanistic explantion in terms of electron pushing and small imaginary transition states does not impose a combinatorial constraint on the feasibility of hypothetical chemical reactions.

math.CO↗

arXiv2023

Pathway Realisability in Chemical Networks

The exploration of pathways and alternative pathways that have a specific function is of interest in numerous chemical contexts. A framework for specifying and searching for pathways has previously been developed, but a focus on which of the many pathway solutions are realisable, or can be made realisable, is missing. Realisable here means that there actually exists some sequencing of the reactions of the pathway that will execute the pathway. We present a method for analysing the realisability of pathways based on the reachability question in Petri nets. For realisable pathways, our method also provides a certificate encoding an order of the reactions which realises the pathway. We present two extended notions of realisability of pathways, one of which is related to the concept of network catalysts. We exemplify our findings on the pentose phosphate pathway. Furthermore, we discuss the relevance of our concepts for elucidating the choices often implicitly made when depicting pathways. Lastly, we lay the foundation for the mathematical theory of realisability.

q-bio.MN↗

arXiv2022

Representing catalytic mechanisms with rule composition

Reaction mechanisms are often presented as sequences of elementary steps, such as codified by arrow pushing. We propose an approach for representing such mechanisms using graph transformation. In this framework, each elementary step is a rule for modifying a molecular graph and a mechanism is a sequence of such rules. To generate a compact representation of a multi-step reaction, we compose the rules of individual steps into a composite rule, providing a rigorous and fully automated approach to coarse-graining. While the composite rule retains the graphical conditions necessary for the execution of a mechanism, it also records information about transient changes not visible by comparing educts and products. By projecting the rule onto a single "overlay graph", we generalize Fujita's idea of an Imaginary Transition Structure from elementary reactions to composite reactions. The utility of the overlay graph construct is exemplified in the context of enzyme-catalyzed reactions. In a first application, we exploit mechanistic information in the Mechanism and Catalytic Site Atlas to construct overlay graphs of hydrolase reactions listed in the database. These graphs point at a spectrum of catalytic entanglement of enzyme and substrate, de-emphasizing the notion of a singular catalyst in favor of a collection of catalytic sites that can be distributed across enzyme and substrate. In a second application, we deploy composite rules to search the Rhea database for reactions of known or unknown mechanism that are, in principle, compatible with the mechanisms implied by the composite rules. We believe this work adds to the utility of graph-transformation formalisms in representing and reasoning about chemistry in an automated yet insightful fashion.

cs.DM↗

arXiv2022

What makes a reaction network "chemical"?

Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$ of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$ into a multiset $Y'\subseteq X$ 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 $\mathbf{S} \in \mathbb{R}^{X\times\mathscr{R}}$ have been discussed extensively in the literature. Here, we provide sufficient conditions for $\mathbf{S}$ that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively. 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 $\mathbf{S}$. 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. Furthermore, it is 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 $\mathbf{S}$ 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.

q-bio.MN↗

arXiv2021

Defining Autocatalysis in Chemical Reaction Networks

Autocatalysis is a deceptively simple concept, referring to the situation that a chemical species $X$ catalyzes its own formation. From the perspective of chemical kinetics, autocatalysts show a regime of super-linear growth. Given a chemical reaction network, however, it is not at all straightforward to identify species that are autocatalytic in the sense that there is a sub-network that takes $X$ as input and produces more than one copy of $X$ as output. The difficulty arises from the need to distinguish autocatalysis e.g. from the superposition of a cycle that consumes and produces equal amounts of $X$ and a pathway that produces $X$. To deal with this issue, a number of competing notions, such as exclusive autocatalysis and autocatalytic cycles, have been introduced. A closer inspection of concepts and their usage by different authors shows, however, that subtle differences in the definitions often makes conceptually matching ideas difficult to bring together formally. In this contribution we make some of the available approaches comparable by translating them into a common formal framework that uses integer hyperflows as a basis to study autocatalysis in large chemical reaction networks. As an application we investigate the prevalence of autocatalysis in metabolic networks.

q-bio.MN↗

arXiv2021

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 multi-step 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 multi-step mechanisms, showing that plausible novel mechanisms for catalysis can be constructed computationally.

q-bio.MN↗

arXiv2017

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 optimised. 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.

q-bio.MN↗

arXiv2017

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, since 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 auto-catalysis, in large reaction networks using optimization techniques.

q-bio.MN↗

arXiv2016

A Software Package for Chemically Inspired Graph Transformation

Chemical reaction networks can be automatically generated from graph grammar descriptions, where rewrite rules model reaction patterns. Because a molecule graph is connected and reactions in general involve multiple molecules, the rewriting must be performed on multisets of graphs. We present a general software package for this type of graph rewriting system, which can be used for modelling chemical systems. The package contains a C++ library with algorithms for working with transformation rules in the Double Pushout formalism, e.g., composition of rules and a domain specific language for programming graph language generation. A Python interface makes these features easily accessible. The package also has extensive procedures for automatically visualising not only graphs and rewrite rules, but also Double Pushout diagrams and graph languages in form of directed hypergraphs. The software is available as an open source package, and interactive examples can be found on the accompanying webpage.

cs.FL↗

arXiv2016

Automatic Inference of Graph Transformation Rules Using the Cyclic Nature of Chemical Reactions

Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the computation of atom-atom mappings, i.e., the atom-wise correspondence between products and educts of all published chemical reactions. This can be phrased as a maximum common edge subgraph problem with the constraint that transition states must have cyclic structure. We describe a search tree method well suited for small edit distance and an integer linear program best suited for general instances and demonstrate that it is feasible to compute atom-atom maps at large scales using a manually curated database of biochemical reactions as an example. In this context we address the network completion problem.

cs.DM↗

arXiv2015

Support for Eschenmoser's Glyoxylate Scenario

A core topic of research in prebiotic chemistry is the search for plausible synthetic routes that connect the building blocks of modern life such as sugars, nucleotides, amino acids, and lipids to "molecular food sources" that have likely been abundant on Early Earth. In a recent contribution, Albert Eschenmoser emphasised the importance of catalytic and autocatalytic cycles in establishing such abiotic synthesis pathways. The accumulation of intermediate products furthermore provides additional catalysts that allow pathways to change over time. We show here that generative models of chemical spaces based on graph grammars make it possible to study such phenomena is a systematic manner. In addition to repro- ducing the key steps of Eschenmoser's hypothesis paper, we discovered previously unexplored potentially autocatalytic pathways from HCN to glyoxylate. A cascading of autocatalytic cycles could efficiently re-route matter, distributed over the combinatorial complex network of HCN hydrolysation chemistry, towards a potential primordial metabolism. The generative approach also has it intrinsic limitations: the unsupervised expansion of the chemical space remains infeasible due to the exponential growth of possible molecules and reactions between them. Here in particular the combinatorial complexity of the HCN polymerisation and hydrolysation networks forms the computational bottleneck. As a consequence, guidance of the computational exploration by chemical experience is indispensable.

q-bio.MN↗

arXiv2014

Memory efficient RNA energy landscape exploration

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. 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 appoaches and perform a detailed investigation of gradient basins in RNA energy landscapes. Source code is part of the C++ Energy Landscape Library available at http://www.bioinf.uni-freiburg.de/Software/.

q-bio.BM↗