Peter Dittrich

Finding pathways that optimize the formation of a particular target molecule in a chemical reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well-represented as hypergraphs, a 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 chemical reaction network representing the HCN-formamide chemistry. Alternative pathways to the one currently hypothesized in literature are queried and enumerated, including some that score better according to our chosen objective function.

Microbial communities typically consist of numerous species that coexist through intricate mutual dependencies. Understanding the structure of these communities and the interactions among their species is essential for explaining their functions and predicting their behavior. In this study, we follow the idea that a community organizes itself into a hierarchy of potentially persistent sub-communities. Previously, this hierarchy was described using Chemical Organization Theory (COT). However, that approach did not account for negative interactions. Here, we enhance the theory by incorporating negative interactions through an inhibitory resource called a toxin. For simplicity, we assume that a taxon sensitive to a toxin cannot coexist with a taxon that produces that toxin. Our results demonstrate that introducing a toxin reduces the number of organizations, with the extent of this reduction depending on various modeling parameters. Further, we show that the usage of essential resources leads to a computationally NP-hard transformation problem into direct taxa interactions. Additionally, we demonstrate that the number of measurements required to infer all persistent subspaces increases. We determine which groups of species are mutually excluded due to toxin interactions. Besides toxic interactions, it is also possible to infer cross-feeding aspects of the microbial community, for which a potential algorithm is outlined and illustrated by an example.

Measuring the dynamics of microbial communities results in high-dimensional measurements of taxa abundances over time and space, which is difficult to analyze due to complex changes in taxonomic compositions. This paper presents a new method to investigate and visualize the intrinsic hierarchical community structure implied by the measurements. The basic idea is to identify significant intersection sets, which can be seen as sub-communities making up the measured communities. Using the subset relationship, the intersection sets together with the measurements form a hierarchical structure visualized as a Hasse diagram. Chemical organization theory (COT) is used to relate the hierarchy of the sets of taxa to potential taxa interactions and to their potential dynamical persistence. The approach is demonstrated on a data set of community data obtained from bacterial 16S rRNA gene sequencing for samples collected monthly from four groundwater wells over a nearly 3-year period (n = 114) along a hillslope area. The significance of the hierarchies derived from the data is evaluated by showing that they significantly deviate from a random model. Furthermore, it is demonstrated how the hierarchy is related to temporal and spatial factors; and how the idea of a core microbiome can be extended to a set of interrelated core microbiomes. Together the results suggest that the approach can support developing models of taxa interactions in the future.

An algorithm is presented for computing a reaction-diffusion partial differential equation (PDE) system for all possible subspaces that can hold a persistent solution of the equation. For this, all possible sub-networks of the underlying reaction network that are distributed organizations (DOs) are identified. Recently it has been shown that a persistent subspace must be a DO. The algorithm computes the hierarchy of DOs starting from the largest by a linear programming approach using integer cuts. The underlying constraints use elementary reaction closures as minimal building blocks to guarantee local closedness and global self-maintenance, required for a DO. Additionally, the algorithm delivers for each subspace an affiliated set of organizational reactions and minimal compartmentalization that is necessary for this subspace to persist. It is proved that all sets of organizational reactions of a reaction network, as already DOs, form a lattice. This lattice contains all potentially persistent sets of reactions of all constrained solutions of reaction-diffusion PDEs. This provides a hierarchical structure of all persistent subspaces with regard to the species and also to the reactions of the reaction-diffusion PDE system. Here, the algorithm is described and the corresponding Python source code is provided. Furthermore, an analysis of its run time is performed and all models from the BioModels database as well as further examples are examined. Apart from the practical implications of the algorithm the results also give insights into the complexity of solving reaction-diffusion PDEs.

This work provides a mathematical technique for analyzing and comparing infection dynamics models with respect to their potential long-term behavior, resulting in a hierarchy integrating all models. We apply our technique to coupled ordinary and partial differential equation models of SARS-CoV-2 infection dynamics operating on different scales, that is, within a single organism and between several hosts. The structure of a model is assessed by the theory of chemical organizations, not requiring quantitative kinetic information. We present the Hasse diagrams of organizations for the twelve virus models analyzed within this study. For comparing models, each organization is characterized by the types of species it contains. For this, each species is mapped to one out of four types, representing uninfected, infected, immune system, and bacterial species, respectively. Subsequently, we can integrate these results with those of our former work on Influenza-A virus resulting in a single joint hierarchy of 24 models. It appears that the SARS-CoV-2 models are simpler with respect to their long term behavior and thus display a simpler hierarchy with little dependencies compared to the Influenza-A models. Our results can support further development towards more complex SARS-CoV-2 models targeting the higher levels of the hierarchy.

Influenza A virus is recognized today as one of the most challenging viruses that threatens both human and animal health worldwide. Understanding the control mechanisms of influenza infection and dynamics is crucial and could result in effective future treatment strategies. Many kinetic models based on differential equations have been developed in recent decades to capture viral dynamics within a host. These models differ in their complexity in terms of number of species elements and number of reactions. Here, we present a new approach to understanding the overall structure of twelve influenza A virus infection models and their relationship to each other. To this end, we apply chemical organization theory to obtain a hierarchical decomposition of the models into chemical organizations. The decomposition is based on the model structure (reaction rules) but is independent of kinetic details such as rate constants. We found different types of model structures ranging from two to eight organizations. Furthermore, the model’s organizations imply a partial order among models entailing a hierarchy of model, revealing a high model diversity with respect to their long-term behavior. Our methods and results can be helpful in model development and model integration, also beyond the influenza area.

SRSim combines rule-based reaction network models with spatial particle simulations allowing to simulate the dynamics of large molecular complexes changing according to a set of chemical reaction rules. As the rule can contain patterns of molecular complexes and specific states of certain binding sites, a combinatorially complex or even infinitely sized reaction network can be defined. Particles move in a three-dimensional space according to molecular dynamics implemented by LAMMPS, while the BioNetGen language is used to formulate reaction rules. Geometric information is added in a specific XML format. The simulation protocol is exemplified by two different variants of polymerization as well as a toy model of DNA helix formation. SRSim is open source and available for download.

The complexity of biological models makes methods for their analysis and understanding highly desirable. Here, we demonstrate the orchestration of various novel coarse-graining methods by applying them to the mitotic spindle assembly checkpoint. We begin with a detailed fine-grained spatial model in which individual molecules are simulated moving and reacting in a three-dimensional space. A sequence of manual and automatic coarse-grainings finally leads to the coarsest deterministic and stochastic models containing only four molecular species and four states for each kinetochore, respectively. We are able to relate each more coarse-grained level to a finer one, which allows us to relate model parameters between coarse-grainings and which provides a more precise meaning for the elements of the more abstract models. Furthermore, we discuss how organizational coarse-graining can be applied to spatial dynamics by showing spatial organizations during mitotic checkpoint inactivation. We demonstrate how these models lead to insights if the model has different “meaningful” behaviors that differ in the set of (molecular) species. We conclude that understanding, modeling and analyzing complex bio-molecular systems can greatly benefit from a set of coarse-graining methods that, ideally, can be automatically applied and that allow the different levels of abstraction to be related.

Chemical organisation theory is a framework developed to simplify the analysis of long-term behaviour of chemical systems. In this work, we build on these ideas to develop novel techniques for formal quantitative analysis of chemical reaction networks, using discrete stochastic models represented as continuous-time Markov chains. We propose methods to identify organisations, and to study quantitative properties regarding movements between these organisations. We then construct and formalise a coarse-grained Markov chain model of hierarchic organisations for a given reaction network, which can be used to approximate the behaviour of the original reaction network. As an application of the coarse-grained model, we predict the behaviour of the reaction network systems over time via the master equation. Experiments show that our predictions can mimic the main pattern of the concrete behaviour in the long run, but the precision varies for different models and reaction rule rates. Finally, we propose an algorithm to selectively refine the coarse-grained models and show experiments demonstrating that the precision of the prediction has been improved.