Models Of Biochemical Networks Research Articles

Cross-Domain Text Mining of Pathophysiological Processes Associated with Diabetic Kidney Disease.

Diabetic kidney disease (DKD) is the leading cause of end-stage renal disease worldwide. This study's goal was to identify the signaling drivers and pathways that modulate glomerular endothelial dysfunction in DKD via artificial intelligence-enabled literature-based discovery. Cross-domain text mining of 33+ million PubMed articles was performed with SemNet 2.0 to identify and rank multi-scalar and multi-factorial pathophysiological concepts related to DKD. A set of identified relevant genes and proteins that regulate different pathological events associated with DKD were analyzed and ranked using normalized mean HeteSim scores. High-ranking genes and proteins intersected three domains-DKD, the immune response, and glomerular endothelial cells. The top 10% of ranked concepts were mapped to the following biological functions: angiogenesis, apoptotic processes, cell adhesion, chemotaxis, growth factor signaling, vascular permeability, the nitric oxide response, oxidative stress, the cytokine response, macrophage signaling, NFκB factor activity, the TLR pathway, glucose metabolism, the inflammatory response, the ERK/MAPK signaling response, the JAK/STAT pathway, the T-cell-mediated response, the WNT/β-catenin pathway, the renin-angiotensin system, and NADPH oxidase activity. High-ranking genes and proteins were used to generate a protein-protein interaction network. The study results prioritized interactions or molecules involved in dysregulated signaling in DKD, which can be further assessed through biochemical network models or experiments.

Bayesian Regression Facilitates Quantitative Modeling of Cell Metabolism.

This paper presents Maud, a command-line application that implements Bayesian statistical inference for kinetic models of biochemical metabolic reaction networks. Maud takes into account quantitative information from omics experiments and background knowledge as well as structural information about kinetic mechanisms, regulatory interactions, and enzyme knockouts. Our paper reviews the existing options in this area, presents a case study illustrating how Maud can be used to analyze a metabolic network, and explains the biological, statistical, and computational design decisions underpinning Maud.

A mathematically rigorous algorithm to define, compute and assess relevance of the probable dissociation constants in characterizing a biochemical network

Metabolism results from enzymatic- and non-enzymatic interactions of several molecules, is easily parameterized with the dissociation constant and occurs via biochemical networks. The dissociation constant is an empirically determined parameter and cannot be used directly to investigate in silico models of biochemical networks. Here, we develop and present an algorithm to define, compute and assess the relevance of the probable dissociation constant for every reaction of a biochemical network. The reactants and reactions of this network are modelled by a stoichiometry number matrix. The algorithm computes the null space and then serially generates subspaces by combinatorially summing the spanning vectors that are non-trivial and unique. This is done until the terms of each row either monotonically diverge or form an alternating sequence whose terms can be partitioned into subsets with almost the same number of oppositely signed terms. For a selected null space-generated subspace the algorithm utilizes several statistical and mathematical descriptors to select and bin terms from each row into distinct outcome-specific subsets. The terms of each subset are summed, mapped to the real-valued open interval 0,∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(0,\\infty \\right)$$\\end{document} and used to populate a reaction-specific outcome vector. The p1-norm for this vector is then the probable dissociation constant for this reaction. These steps are continued until every reaction of a modelled network is unambiguously annotated. The assertions presented are complemented by computational studies of a biochemical network for aerobic glycolysis. The fundamental premise of this work is that every row of a null space-generated subspace is a valid reaction and can therefore, be modelled as a reaction-specific sequence vector with a dimension that corresponds to the cardinality of the subspace after excluding all trivial- and redundant-vectors. A major finding of this study is that the row-wise sum or the sum of the terms contained in each reaction-specific sequence vector is mapped unambiguously to a positive real number. This means that the probable dissociation constants, for all reactions, can be directly computed from the stoichiometry number matrix and are suitable indicators of outcome for every reaction of the modelled biochemical network. Additionally, we find that the unambiguous annotation for a biochemical network will require a minimum number of iterations and will determine computational complexity.

A query-response causal analysis of reaction events in biochemical reaction networks

The stochastic kinetics of biochemical reaction networks is described by a chemical master equation (CME) and the underlying laws of mass action. Assuming network-free simulations of the rule-based models of biochemical reaction networks (BRNs), this paper departs from the usual analysis of network dynamics as the time-dependent distributions of chemical species counts, and instead considers statistically evaluating the sequences of reaction events generated from the stochastic simulations. The reaction event-time series can be used for reaction clustering, identifying rare events, and recognizing the periods of increased or steady-state activity. However, the main aim of this paper is to device an effective method for identifying causally and anti-causally related sub-sequences of reaction events using their empirical probabilities. This allows discovering some of the causal dynamics of BRNs as well as uncovering their short-term deterministic behaviors. In particular, it is proposed that the reaction sub-sequences that are conditionally nearly certain or nearly uncertain can be considered as being causally related. Moreover, since the time-ordering of reaction events is locally irrelevant, the reaction sub-sequences can be transformed into the reaction sets or multi-sets. The distance metrics can be then used to define the equivalences among the reaction events. The proposed method for identifying the causally related reaction sub-sequences has been implemented as a computationally efficient query-response mechanism. The method was evaluated for five models of genetic networks in seven defined numerical experiments. The models were simulated in BioNetGen using the open-source network-free simulator NFsim. This simulator had to be modified first to allow recording the traces of reaction events, and it is available in the Github repository, ploskot/nfsim_1.20. The generated event time-series were analyzed with Python and Matlab scripts. The whole process of data generation, analysis and visualization has been nearly fully automated using shell scripts. This demonstrates the opportunities for substantially increasing the research productivity by creating automated data generation and processing pipelines.

ReDirection: an R-package to compute the probable dissociation constant for every reaction of a user-defined biochemical network.

Biochemical networks integrate enzyme-mediated substrate conversions with non-enzymatic complex formation and disassembly to accomplish complex biochemical and physiological functions. The choice of parameters and constraints used in most of these studies is numerically motivated and network-specific. Although sound in theory, the outcomes that result depart significantly from the intracellular milieu and are less likely to retain relevance in a clinical setting. There is a need for a computational tool which is biochemically relevant, mathematically rigorous, and unbiased, and can ascribe functionality to and generate potentially testable hypotheses for a user-defined biochemical network. Here, we present "ReDirection," an R-package which computes the probable dissociation constant for every reaction of a biochemical network directly from a null space-generated subspace of the stoichiometry number matrix of the modeled network. "ReDirection" delineates this subspace by excluding all trivial and redundant or duplicate occurrences of non-trivial vectors, combinatorially summing the vectors that remain and verifying that the upper or lower bounds of the sequence of terms formed by each row of this subspace belong to the open real-valued intervals or or whether the number of terms that are differently signed are almost equal. "ReDirection" iterates these steps until these bounds are consistent and unambiguous for all reactions of the modeled biochemical network. Thereafter, "ReDirection" filters the terms from each row of this subspace, bins them to outcome-specific subsets, sums and maps this to an outcome-specific reaction vector, and computes the p1-norm, which is the probable dissociation constant for a reaction. "ReDirection" works on first principles, does not discriminate between enzymatic and non-enzymatic reactions, offers a biochemically relevant and mathematically rigorous environment to explore user-defined biochemical networks under baseline and perturbed conditions, and can be used to address empirically intractable biochemical problems. The utility and relevance of "ReDirection" are highlighted by numerical studies on stoichiometric number models of biochemical networks of galactose metabolism and heme and cholesterol biosynthesis. "ReDirection" is freely available and accessible from the comprehensive R archive network (CRAN) with the URL (https://cran.r-project.org/package=ReDirection).

Semigroup models for biochemical reaction networks

The catalytic reaction system (CRS) formalism by Hordijk and Steel is a versatile method to model autocatalytic biochemical reaction networks. It is particularly suited, and has been widely used, to study self-sustainment and self-generation properties. Its distinguishing feature is the explicit assignment of a catalytic function to chemicals that are part of the system. In this work, it is shown that the subsequent and simultaneous catalytic functions give rise to an algebraic structure of a semigroup with the additional compatible operation of idempotent addition and a partial order. The aim of this article is to demonstrate that such semigroup models are a natural setup to describe and analyze self-sustaining CRS. The basic algebraic properties of the models are established and the notion of the function of any set of chemicals on the whole CRS is made precise. This leads to a natural discrete dynamical system on the power set of chemicals, which is obtained by iteratively considering the self-action on a set of chemicals by its own function. The fixed points of this dynamical system are proven to correspond to self-sustaining sets of chemicals, which are functionally closed. Finally, as the main application, a theorem on the maximal self-sustaining set and a structure theorem on the set of functionally closed self-sustaining sets of chemicals are proven.

Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks.

Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However, computing gradients becomes increasingly costly for larger models, which are required for capturing the complex interactions of multiple biochemical pathways. Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available. We propose a new adjoint method for computing gradients, which is applicable if the experimental data include steady-state measurements. The method is based on a reformulation of the backward integration problem to a system of linear algebraic equations. The evaluation of the proposed method using real-world problems shows a speedup of total simulation time by a factor of up to 4.4. Our results demonstrate that the proposed approach can achieve a substantial improvement in computation time, in particular for large-scale models, where computational efficiency is critical.

A Practical Guide to Reproducible Modeling for Biochemical Networks.

While scientific disciplines revere reproducibility, many studies - experimental and computational alike - fall short of this ideal and cannot be reproduced or even repeated when the model is shared. For computational modeling of biochemical networks, there is a dearth of formal training and resources available describing how to practically implement reproducible methods, despite a wealth of existing tools and formats which could be used to support reproducibility. This chapter points the reader to useful software tools and standardized formats that support reproducible modeling of biochemical networks and provides suggestions on how to implement reproducible methods in practice. Many of the suggestions encourage readers to use best practices from the software development community in order to automate, test, and version control their model components. A Jupyter Notebook demonstrating several of the key steps in building a reproducible biochemical network model is included to supplement the recommendations in the text.

Formal verification confirms the role of p53 protein in cell fate decision mechanism

The bio-cell cycle is controlled by a complex biochemical network of signaling pathways. Modeling such challenging networks accurately is imperative for the understanding of their detailed dynamical behavior. In this paper, we construct, analyze, and verify a hybrid Petri net (HPN) model of a complex biochemical network that captures the role of an important protein (namely p53) in deciding the fate of the cell. We model the behavior of the cell nucleus and cytoplasm as two stochastic and continuous Petri nets, respectively, combined together into a single HPN. We use simulative model checking to verify three different properties that capture the dynamical behavior of p53 protein with respect to the intensity of the ionizing radiation (IR) to which the cell is exposed. For each IR dose, 1000 simulation runs are carried out to verify each property. Our verification results showed that the fluctuations in p53, which relies on IR intensity, are compatible with the findings of the preceding simulation studies that have previously examined the role of p53 in cell fate decision.

The chemical Langevin equation for biochemical systems in dynamic environments.

Modeling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other-and mostly unknown-fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here, we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation (CLE)-a physically motivated extension of the CLE-to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the chemical master equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and it can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient, and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Dynamic publication media with the COPASI R Connector (CoRC)

In this article we show how dynamic publication media and the COPASI R Connector (CoRC) can be combined in a natural and synergistic way to communicate (biochemical) models. Dynamic publication media are becoming a popular tool for authors to effectively compose and publish their work. They are built from templates and the final documents are created dynamically. In addition, they can also be interactive. Working with dynamic publication media is made easy with the programming environment R via its integration with tools such as R Markdown, Jupyter and Shiny. Additionally, the COmplex PAthway SImulator COPASI (http://www.copasi.org), a widely used biochemical modelling toolkit, is available in R through the use of the COPASI R Connector (CoRC, https://jpahle.github.io/CoRC). Models are a common tool in the mathematical biosciences, in particular kinetic models of biochemical networks in (computational) systems biology.We focus on three application areas of dynamic publication media and CoRC: Documentation (reproducible workflows), Teaching (creating self-paced lessons) and Science Communication (immersive and engaging presentation). To illustrate these, we created six dynamic document examples in the form of R Markdown and Jupyter notebooks, hosted on the platforms GitHub, shinyapps.io, Google Colaboratory.Having code and output in one place, creating documents in template-form and the option of interactivity make the combination of dynamic documents and CoRC a versatile tool.All our example documents are freely available at https://jpahle.github.io/DynamiCoRC under the Creative Commons BY 4.0 licence.

SMGen: A Generator of Synthetic Models of Biochemical Reaction Networks

Several software tools for the simulation and analysis of biochemical reaction networks have been developed in the last decades; however, assessing and comparing their computational performance in executing the typical tasks of computational systems biology can be limited by the lack of a standardized benchmarking approach. To overcome these limitations, we propose here a novel tool, named SMGen, designed to automatically generate synthetic models of reaction networks that, by construction, are characterized by relevant features (e.g., system connectivity and reaction discreteness) and non-trivial emergent dynamics of real biochemical networks. The generation of synthetic models in SMGen is based on the definition of an undirected graph consisting of a single connected component that, generally, results in a computationally demanding task; to speed up the overall process, SMGen exploits a main–worker paradigm. SMGen is also provided with a user-friendly graphical user interface, which allows the user to easily set up all the parameters required to generate a set of synthetic models with any number of reactions and species. We analysed the computational performance of SMGen by generating batches of symmetric and asymmetric reaction-based models (RBMs) of increasing size, showing how a different number of reactions and/or species affects the generation time. Our results show that when the number of reactions is higher than the number of species, SMGen has to identify and correct a large number of errors during the creation process of the RBMs, a circumstance that increases the running time. Still, SMGen can generate synthetic models with hundreds of species and reactions in less than 7 s.

An inverse transformation algorithm to infer parameter distributions from population snapshot data

Population snapshot data can be used to study heterogeneity in cell populations. Various approaches to integrating such data into computational models have been published, which enable new treatment strategies for cancer therapy, by exploiting the intra-tumor heterogeneity. A precision medicine approach for the cure of cancer could benefit from the combination of single-cell data and respective analytical methods. Here, we introduce the inverse transformation algorithm, which transforms population snapshot data to parameter distributions that are consistent with the underlying data given a dynamic model with distributed parameters. Therefore, it enables the assessment of the heterogeneity in and behavior of the whole underlying cell population. In contrast to the frequently used Approximate Bayesian Computation methods for population matching, our algorithm is a non-parametric likelihood-free approach. It directly computes a density function value for a single parameter based on density transformation methods. If the model can be described as a one-to-one map that invertibly maps parameters to measurable outputs, the inverse transformation algorithm asymptotically returns the true underlying parameter distribution.The inverse transformation algorithm is applied to snapshot data simulated via standard differential equation models for biochemical reaction networks. In particular, we evaluate our algorithm on two small test-bed models and discuss advantages and limitations in comparison to other existing approaches.

FiCoS: A fine-grained and coarse-grained GPU-powered deterministic simulator for biochemical networks.

Mathematical models of biochemical networks can largely facilitate the comprehension of the mechanisms at the basis of cellular processes, as well as the formulation of hypotheses that can be tested by means of targeted laboratory experiments. However, two issues might hamper the achievement of fruitful outcomes. On the one hand, detailed mechanistic models can involve hundreds or thousands of molecular species and their intermediate complexes, as well as hundreds or thousands of chemical reactions, a situation generally occurring in rule-based modeling. On the other hand, the computational analysis of a model typically requires the execution of a large number of simulations for its calibration, or to test the effect of perturbations. As a consequence, the computational capabilities of modern Central Processing Units can be easily overtaken, possibly making the modeling of biochemical networks a worthless or ineffective effort. To the aim of overcoming the limitations of the current state-of-the-art simulation approaches, we present in this paper FiCoS, a novel "black-box" deterministic simulator that effectively realizes both a fine-grained and a coarse-grained parallelization on Graphics Processing Units. In particular, FiCoS exploits two different integration methods, namely, the Dormand-Prince and the Radau IIA, to efficiently solve both non-stiff and stiff systems of coupled Ordinary Differential Equations. We tested the performance of FiCoS against different deterministic simulators, by considering models of increasing size and by running analyses with increasing computational demands. FiCoS was able to dramatically speedup the computations up to 855×, showing to be a promising solution for the simulation and analysis of large-scale models of complex biological processes.

Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter.

Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.

The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling

The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization-the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.

Reducing Stochastic Discrete Models of Biochemical Networks

Biochemical systems have numerous practical applications, in particular to the study of critical intracellular processes. Frequently, biochemical kinetic models depict cellular processes as systems of chemical reactions. Many biological processes in a cell are inherently stochastic, due to the existence of some low molecular amounts. These stochastic fluctuations may have a great effect on the biochemical system’s behaviour. In such cases, stochastic models are necessary to accurately describe the system’s dynamics. Biochemical systems at the cellular level may entail many species or reactions and their mathematical models may be non-linear and with multiple scales in time. In this work, we provide a numerical technique for simplifying stochastic discrete models of well-stirred biochemical systems, which ensures that the main properties of the original system are preserved. The proposed technique employs sensitivity analysis and requires solving an optimization problem. The numerical tests on several models of practical interest show that our model reduction strategy performs very well.

An automatic adaptive method to combine summary statistics in approximate Bayesian computation.

To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is that parameter inference must generally rely on summary statistics of the data. This is particularly the case for problems involving high-dimensional data, such as biological imaging experiments. However, some summary statistics contain more information about parameters of interest than others, and it is not always clear how to weight their contributions within the ABC framework. We address this problem by developing an automatic, adaptive algorithm that chooses weights for each summary statistic. Our algorithm aims to maximize the distance between the prior and the approximate posterior by automatically adapting the weights within the ABC distance function. Computationally, we use a nearest neighbour estimator of the distance between distributions. We justify the algorithm theoretically based on properties of the nearest neighbour distance estimator. To demonstrate the effectiveness of our algorithm, we apply it to a variety of test problems, including several stochastic models of biochemical reaction networks, and a spatial model of diffusion, and compare our results with existing algorithms.

A biochemical network modeling of a whole-cell

All cellular processes can be ultimately understood in terms of respective fundamental biochemical interactions between molecules, which can be modeled as networks. Very often, these molecules are shared by more than one process, therefore interconnecting them. Despite this effect, cellular processes are usually described by separate networks with heterogeneous levels of detail, such as metabolic, protein–protein interaction, and transcription regulation networks. Aiming at obtaining a unified representation of cellular processes, we describe in this work an integrative framework that draws concepts from rule-based modeling. In order to probe the capabilities of the framework, we used an organism-specific database and genomic information to model the whole-cell biochemical network of the Mycoplasma genitalium organism. This modeling accounted for 15 cellular processes and resulted in a single component network, indicating that all processes are somehow interconnected. The topological analysis of the network showed structural consistency with biological networks in the literature. In order to validate the network, we estimated gene essentiality by simulating gene deletions and compared the results with experimental data available in the literature. We could classify 212 genes as essential, being 95% of them consistent with experimental results. Although we adopted a relatively simple organism as a case study, we suggest that the presented framework has the potential for paving the way to more integrated studies of whole organisms leading to a systemic analysis of cells on a broader scale. The modeling of other organisms using this framework could provide useful large-scale models for different fields of research such as bioengineering, network biology, and synthetic biology, and also provide novel tools for medical and industrial applications.

A Probabilistic Approach to Explore Signal Execution Mechanisms With Limited Experimental Data.

Mathematical models of biochemical reaction networks are central to the study of dynamic cellular processes and hypothesis generation that informs experimentation and validation. Unfortunately, model parameters are often not available and sparse experimental data leads to challenges in model calibration and parameter estimation. This can in turn lead to unreliable mechanistic interpretations of experimental data and the generation of poorly conceived hypotheses for experimental validation. To address this challenge, we evaluate whether a Bayesian-inspired probability-based approach, that relies on expected values for quantities of interest calculated from available information regarding the reaction network topology and parameters can be used to qualitatively explore hypothetical biochemical network execution mechanisms in the context of limited available data. We test our approach on a model of extrinsic apoptosis execution to identify preferred signal execution modes across varying conditions. Apoptosis signal processing can take place either through a mitochondria independent (Type I) mode or a mitochondria dependent (Type II) mode. We first show that in silico knockouts, represented by model subnetworks, successfully identify the most likely execution mode for specific concentrations of key molecular regulators. We then show that changes in molecular regulator concentrations alter the overall reaction flux through the network by shifting the primary route of signal flow between the direct caspase and mitochondrial pathways. Our work thus demonstrates that probabilistic approaches can be used to explore the qualitative dynamic behavior of model biochemical systems even with missing or sparse data.