Revealing the hierarchical structure of microbial communities.

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.

Computing all persistent subspaces of a reaction-diffusion system.

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.

The Concilium of Information Processing Networks of Chemical Oscillators for Determining Drug Response in Patients With Multiple Myeloma.

It can be expected that medical treatments in the future will be individually tailored for each patient. Here we present a step towards personally addressed drug therapy. We consider multiple myeloma treatment with drugs: bortezomib and dexamethasone. It has been observed that these drugs are effective for some patients and do not help others. We describe a network of chemical oscillators that can help to differentiate between non-responsive and responsive patients. In our numerical simulations, we consider a network of 3 interacting oscillators described with the Oregonator model. The input information is the gene expression value for one of 15 genes measured for patients with multiple myeloma. The single-gene networks optimized on a training set containing outcomes of 239 therapies, 169 using bortezomib and 70 using dexamethasone, show up to 71% accuracy in differentiating between non-responsive and responsive patients. If the results of single-gene networks are combined into the concilium with the majority voting strategy, then the accuracy of predicting the patient's response to the therapy increases to ∼ 85%.

Structure and Hierarchy of SARS-CoV-2 Infection Dynamics Models Revealed by Reaction Network Analysis.

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.

Epidemiology of age-dependent prevalence of Bovine Herpes Virus Type 1 (BoHV-1) in dairy herds with and without vaccination.

Many studies report age as a risk factor for BoHV-1 infection or seropositivity. However, it is unclear whether this pattern reflects true epidemiological causation or is a consequence of study design and other issues. Here, we seek to understand the age-related dynamics of BoHV-1 seroprevalence in seasonal calving Irish dairy herds and provide decision support for the design and implementation of effective BoHV-1 testing strategies. We analysed seroprevalence data from dairy herds taken during two Irish seroprevalence surveys conducted between 2010 and 2017. Age-dependent seroprevalence profiles were constructed for herds that were seropositive and unvaccinated. Some of these profiles revealed a sudden increase in seroprevalence between adjacent age-cohorts, from absent or low to close to 100% of seropositive animals. By coupling the outcome of our data analysis with simulation output of an individual-based model at the herd scale, we have shown that these sudden increases are related to extensive virus circulation within a herd for a limited time, which may then subsequently remain latent over the following years. BoHV-1 outbreaks in dairy cattle herds affect animals independent of age and lead to almost 100% seroconversion in all age groups, or at least in all animals within a single epidemiological unit. In the absence of circulating infection, there is a year-on-year increase in the age-cohort at which seroprevalence changes from low to high. The findings of this study inform recommendations regarding testing regimes in the context of contingency planning or an eradication programme in seasonal calving dairy herds.

Combining evolution and self-organization to find natural Boolean representations in unconventional computational media.

Designing novel unconventional computing systems often requires the selection of the computational structure as well as choosing the right symbol encoding. Several approaches apply heuristic search and evolutionary algorithms to find both computational structure and symbol encoding, which is time consuming because they depend on each other. Here, we present a novel approach that combines evolution with self-organization, in particular we evolve the computational structure but let the symbol encoding emerge through self-organization. This should not only be more efficient but should also lead to a more "natural" symbol encoding. We successfully demonstrate the potential of the technique, using an evolutionary algorithm to optimize the parameters of two non-linear media to perform as NAND-gates: a continuous-time recurrent neural network (CTRNN) and a computational model of BZ-droplet-based computing (DropSim). In both cases, the technique identified representations for TRUE and FALSE, and system configurations that performed successfully as NAND-gates. The effectiveness of the evolved NAND gates was further evaluated by their performance in half-adder networks, where again, both evolved systems performed correctly, producing the correct output for all possible inputs and for all possible transitions between inputs. We conclude that beyond the specific applications demonstrated here, combining evolution with self-organization could be a promising strategy widely applicable.

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis.

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.

Spatial Rule-Based Simulations: The SRSim Software.

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.

Multi-scale stochastic organization-oriented coarse-graining exemplified on the human mitotic checkpoint.

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.

Cefuroxime plasma and tissue concentrations in patients undergoing elective cardiac surgery: Continuous vs bolus application. A pilot study.

AIMS: Surgical site infections contribute to morbidity and mortality after surgery. The authors hypothesized that higher antibiotic tissue concentrations can be reached for a prolonged time span by continuous administration of prophylactic cefuroxime compared to bolus administration. METHODS: Twelve patients undergoing elective cardiac surgery were investigated. Group A received 1.5 g cefuroxime as bolus infusions before surgery, and 12 and 24 hours thereafter. In group B, a continuous infusion of 3.0 g cefuroxime was started after a bolus of 1.5 g. Cefuroxim levels were determined in blood and tissue (microdialysis). T-test, Wilcoxon signed rank test and χ2 test were used for statistical analysis. RESULTS: The area under the curve (AUC) of plasma cefuroxime concentrations was greater in group B (399 [333-518]) as compared to group A (257 [177-297] h mg L-1 , [median and interquartile range], P = .026). Furthermore, a significantly longer percentage of time > minimal inhibitory concentrations of 2 mg L-1 (100% vs 50%), 4 mg L-1 (100% vs 42%), 8 mg L-1 (100% vs 17%) and 16 mg L-1 (83% vs 8%) was found for free plasma cefuroxime in group B. In group B, area under the curve in subcutaneous tissue (78 [61-113] h mg L-1 ) and median peak concentration (33 [26-38] mg L-1 ) were markedly higher compared to group A (P = 0.041 and P = .026, respectively). CONCLUSIONS: Higher cefuroxime concentrations were measured in plasma and subcutaneously over a prolonged period of time when cefuroxime was administered continuously. The clinical implication of this finding still has to be elucidated.

Organisation-Oriented Coarse Graining and Refinement of Stochastic Reaction Networks.

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.

Towards measuring the semantic capacity of a physical medium demonstrated with elementary cellular automata.

The organic code concept and its operationalization by molecular codes have been introduced to study the semiotic nature of living systems. This contribution develops further the idea that the semantic capacity of a physical medium can be measured by assessing its ability to implement a code as a contingent mapping. For demonstration and evaluation, the approach is applied to a formal medium: elementary cellular automata (ECA). The semantic capacity is measured by counting the number of ways codes can be implemented. Additionally, a link to information theory is established by taking multivariate mutual information for quantifying contingency. It is shown how ECAs differ in their semantic capacities, how this is related to various ECA classifications, and how this depends on how a meaning is defined. Interestingly, if the meaning should persist for a certain while, the highest semantic capacity is found in CAs with apparently simple behavior, i.e., the fixed-point and two-cycle class. Synergy as a predictor for a CA's ability to implement codes can only be used if context implementing codes are common. For large context spaces with sparse coding contexts synergy is a weak predictor. Concluding, the approach presented here can distinguish CA-like systems with respect to their ability to implement contingent mappings. Applying this to physical systems appears straight forward and might lead to a novel physical property indicating how suitable a physical medium is to implement a semiotic system.

A Dynamical Model for Activating and Silencing the Mitotic Checkpoint.

The spindle assembly checkpoint (SAC) is an evolutionarily conserved mechanism, exclusively sensitive to the states of kinetochores attached to microtubules. During metaphase, the anaphase-promoting complex/cyclosome (APC/C) is inhibited by the SAC but it rapidly switches to its active form following proper attachment of the final spindle. It had been thought that APC/C activity is an all-or-nothing response, but recent findings have demonstrated that it switches steadily. In this study, we develop a detailed mathematical model that considers all 92 human kinetochores and all major proteins involved in SAC activation and silencing. We perform deterministic and spatially-stochastic simulations and find that certain spatial properties do not play significant roles. Furthermore, we show that our model is consistent with in-vitro mutation experiments of crucial proteins as well as the recently-suggested rheostat switch behavior, measured by Securin or CyclinB concentration. Considering an autocatalytic feedback loop leads to an all-or-nothing toggle switch in the underlying core components, while the output signal of the SAC still behaves like a rheostat switch. The results of this study support the hypothesis that the SAC signal varies with increasing number of attached kinetochores, even though it might still contain toggle switches in some of its components.

Evolutionary Design of Classifiers Made of Droplets Containing a Nonlinear Chemical Medium.

Unconventional computing devices operating on nonlinear chemical media offer an interesting alternative to standard, semiconductor-based computers. In this work we study in-silico a chemical medium composed of communicating droplets that functions as a database classifier. The droplet network can be "programmed" by an externally provided illumination pattern. The complex relationship between the illumination pattern and the droplet behavior makes manual programming hard. We introduce an evolutionary algorithm that automatically finds the optimal illumination pattern for a given classification problem. Notably, our approach does not require us to prespecify the signals that represent the output classes of the classification problem, which is achieved by using a fitness function that measures the mutual information between chemical oscillation patterns and desired output classes. We illustrate the feasibility of our approach in computer simulations by evolving droplet classifiers for three machine learning datasets. We demonstrate that the same medium composed of 25 droplets located on a square lattice can be successfully used for different classification tasks by applying different illumination patterns as its externally supplied program.

Compressing molecular dynamics trajectories: Breaking the one-bit-per-sample barrier.

Molecular dynamics simulations yield large amounts of trajectory data. For their durable storage and accessibility an efficient compression algorithm is paramount. State of the art domain-specific algorithms combine quantization, Huffman encoding and occasionally domain knowledge. We propose the high resolution trajectory compression scheme (HRTC) that relies on piecewise linear functions to approximate quantized trajectories. By splitting the error budget between quantization and approximation, our approach beats the current state of the art by several orders of magnitude given the same error tolerance. It allows storing samples at far less than one bit per sample. It is simple and fast enough to be integrated into the inner simulation loop, store every time step, and become the primary representation of trajectory data. © 2016 Wiley Periodicals, Inc.

Towards rule-based metabolic databases: a requirement analysis based on KEGG.

Knowledge of metabolic processes is collected in easily accessable online databases which are increasing rapidly in content and detail. Using these databases for the automatic construction of metabolic network models requires high accuracy and consistency. In this bipartite study we evaluate current accuracy and consistency problems using the KEGG database as a prominent example and propose design principles for dealing with such problems. In the first half, we present our computational approach for classifying inconsistencies and provide an overview of the classes of inconsistencies we identified. We detected inconsistencies both for database entries referring to substances and entries referring to reactions. In the second part, we present strategies to deal with the detected problem classes. We especially propose a rule-based database approach which allows for the inclusion of parameterised molecular species and parameterised reactions. Detailed case-studies and a comparison of explicit networks from KEGG with their anticipated rule-based representation underline the applicability and scalability of this approach.

About the Therapy of Laryngotracheitis (Croup): Significance of Rectal Dosage Forms.

Glucocorticoids are drugs of choice for treatment of laryngotracheitis (croup). They may be administered orally as tablets or juice, locally as inhalation or rectally as suppository or capsule. If doctors decide to use a rectal administration for practical reasons, it is obvious from a pharmacokinetic and pharmacodynamic point of view that prednisolone capsules have an earlier and stronger anti-inflammatory effect than a prednisone suppository.

Thermodynamics of random reaction networks.

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdos-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Structural analysis of in silico mutant experiments of human inner-kinetochore structure.

Large multi-molecular complexes like the kinetochore are lacking of suitable methods to determine their spatial structure. Here, we use and evaluate a novel modeling approach that combines rule-bases reaction network models with spatial molecular geometries. In particular, we introduce a method that allows to study in silico the influence of single interactions (e.g. bonds) on the spatial organization of large multi-molecular complexes and apply this method to an extended model of the human inner-kinetochore. Our computational analysis method encompasses determination of bond frequency, geometrical distances, statistical moments, and inter-dependencies between bonds using mutual information. For the analysis we have extend our previously reported human inner-kinetochore model by adding 13 new protein interactions and three protein geometry details. The model is validated by comparing the results of in silico with reported in vitro single protein deletion experiments. Our studies revealed that most simulations mimic the in vitro behavior of the kinetochore complex as expected. To identify the most important bonds in this model, we have created 39 mutants in silico by selectively disabling single protein interactions. In a total of 11,800 simulation runs we have compared the resulting structures to the wild-type. In particular, this allowed us to identify the interaction Cenp-W-H3 and Cenp-S-Cenp-X as having the strongest influence on the inner-kinetochore's structure. We conclude that our approach can become a useful tool for the in silico dynamical study of large, multi-molecular complexes.