scholarly journals Identifiability of stochastically modelled reaction networks

2021 ◽  
pp. 1-23 ◽  
Author(s):  
GERMAN ENCISO ◽  
RADEK ERBAN ◽  
JINSU KIM
Keyword(s):  
System Dynamics ◽  
Network Structure ◽  
Network Inference ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Stochastic Simulations ◽  
Reaction Networks ◽  
Data Types ◽  
Biochemical System ◽  
Underlying Network

Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous-time Markov processes. In this manuscript, the identifiability of the underlying network structure with a given stochastic system dynamics is studied. It is shown that some data types related to the associated stochastic dynamics can uniquely identify the underlying network structure as well as the system parameters. The accuracy of the presented network inference is investigated when given dynamical data are obtained via stochastic simulations.

Inference of Chemical Reaction Networks Using Hybrid S-system Models

2007 ◽  
Vol 2 (1) ◽  
Author(s):  
Dominic P Searson ◽  
Mark J Willis ◽  
Simon J Horne ◽  
Allen R Wright
Keyword(s):  
Chemical Reaction ◽  
Power Law ◽  
Network Inference ◽  
Batch Reactor ◽  
Reaction Network ◽  
Chemical Reaction Networks ◽  
Chemical Reaction Network ◽  
Reaction Networks ◽  
Fed Batch ◽  
System Equations

This article demonstrates, using simulations, the potential of the S-system formalism for the inference of unknown chemical reaction networks from simple experimental data, such as that typically obtained from laboratory scale reaction vessels. Virtually no prior knowledge of the products and reactants is assumed. S-systems are a power law formalism for the canonical approximate representation of dynamic non-linear systems. This formalism has the useful property that the structure of a network is dictated only by the values of the power law parameters. This means that network inference problems (e.g. inference of the topology of a chemical reaction network) can be recast as parameter estimation problems. The use of S-systems for network inference from data has been reported in a number of biological fields, including metabolic pathway analysis and the inference of gene regulatory networks. Here, the methodology is adapted for use as a hybrid modelling tool to facilitate the reverse engineering of chemical reaction networks using time series concentration data from fed-batch reactor experiments. The principle of the approach is demonstrated with noisy simulated data from fed-batch reactor experiments using a hypothetical reaction network comprising 5 chemical species involved in 4 parallel reactions. A co-evolutionary algorithm is employed to evolve the structure and the parameter values of the S-system equations concurrently. The S-system equations are then interpreted in order to construct a network diagram that accurately reflects the underlying chemical reaction network.

scholarly journals Neural network aided approximation and parameter inference of non-Markovian models of gene expression

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qingchao Jiang ◽  
Xiaoming Fu ◽  
Shifu Yan ◽  
Runlai Li ◽  
Wenli Du ◽  
...  
Keyword(s):  
Neural Network ◽  
Stochastic Dynamics ◽  
Stochastic Simulations ◽  
Parameter Inference ◽  
Biochemical Processes ◽  
Markovian Models ◽  
The Neural Network ◽  
Large Numbers ◽  
Small Set ◽  
Noisy Measurements

AbstractNon-Markovian models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system’s history. Here we use an artificial neural network to approximate the time-dependent distributions of non-Markovian models by the solutions of much simpler time-inhomogeneous Markovian models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markovian model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markovian models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

scholarly journals Uncertainty quantification for quantum chemical models of complex reaction networks

2016 ◽  
Vol 195 ◽  
pp. 497-520 ◽  
Author(s):  
Jonny Proppe ◽  
Tamara Husch ◽  
Gregor N. Simm ◽  
Markus Reiher
Keyword(s):  
Free Energy ◽  
Electronic Structure ◽  
State Space ◽  
Time Scales ◽  
Reaction Network ◽  
Reaction Networks ◽  
Multiple Time Scales ◽  
Complex Reaction ◽  
Discrete State ◽  
Continuous State

For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

scholarly journals Biological Network Inference with GRASP: A Bayesian Network Structure Learning Method Using Adaptive Sequential Monte Carlo

2021 ◽  
Author(s):  
Kaixian Yu ◽  
Zihan Cui ◽  
Xin Sui ◽  
Xing Qiu ◽  
Jinfeng Zhang
Keyword(s):  
Monte Carlo ◽  
Network Structure ◽  
Network Inference ◽  
Sequential Monte Carlo ◽  
Structure Learning ◽  
Biomedical Science ◽  
Optimal Network ◽  
Genomic Studies ◽  
Complex Correlation ◽  
Open Question

Abstract Bayesian networks (BNs) provide a probabilistic, graphical framework for modeling high-dimensional joint distributions with complex correlation structures. BNs have wide applications in many disciplines, including biology, social science, finance and biomedical science. Despite extensive studies in the past, network structure learning from data is still a challenging open question in BN research. In this study, we present a sequential Monte Carlo (SMC)-based three-stage approach, GRowth-based Approach with Staged Pruning (GRASP). A double filtering strategy was first used for discovering the overall skeleton of the target BN. To search for the optimal network structures we designed an adaptive SMC (adSMC) algorithm to increase the quality and diversity of sampled networks which were further improved by a third stage to reclaim edges missed in the skeleton discovery step. GRASP gave very satisfactory results when tested on benchmark networks. Finally, BN structure learning using multiple types of genomics data illustrates GRASP’s potential in discovering novel biological relationships in integrative genomic studies.

Feedback mechanisms in mineral replacement networks: an experimental investigation of the ultramafic model system

2021 ◽  
Author(s):  
Ingvild Aarrestad ◽  
Oliver Plümper ◽  
Desiree Roerdink ◽  
Andreas Beinlich
Keyword(s):  
Reaction Rate ◽  
Energy Transport ◽  
Kinetic Modelling ◽  
Indirect Evidence ◽  
Reaction Network ◽  
Reaction Networks ◽  
Silicate System ◽  
Rock Interaction ◽  
Feedback Mechanisms ◽  
Salinity Effect

<p>The overall rates of multi-component reaction networks are known to be controlled by feedback mechanisms. Feedback mechanisms represent loop systems where the output of the system is conveyed back as input and the system is either accelerated or regulated (positive and negative feedback respectively). In other words, feedback mechanisms control the rate of a reaction network without external influences. Feedback mechanisms are well-studied in a variety of reaction networks (e.g. bio-chemical, atmospheric); however, in fluid-rock interaction systems they are not researched as such. Still, indirect evidence, theoretical considerations and direct observations attest to their existence [e.g. 1, 2, 3]. It remains unknown how mass and energy transport between distinct reaction sites affect the overall reaction rate and outcome through feedback mechanisms. We propose that feedback mechanisms are a missing critical ingredient to understand reaction progress and timescales of fluid-rock interactions. We apply the serpentinization of ultramafic silicates as a relatively simple reaction network to investigate feedback mechanisms during fluid-rock interactions. Recent studies show that theoretical timescale-predictions appear inconsistent with natural observations [e.g. 4, 5]. The ultramafic silicate system is ideal for investigating feedback mechanisms as it is relevant to natural processes, is reactive on timescales that can be explored in the laboratory, and natural peridotite typically consists of less than four phases. Our preliminary observations indicate a feedback between pyroxene dissolution and olivine serpentinization. Olivine serpentinization appears to proceed faster in the presence of pyroxene. Furthermore, the bulk system reaction rate increases with increasing fluid salinity, which is opposite to the salinity effect on the monomineralic olivine system. Dunite (>90% olivine) is rare, which is why it is crucial to explore the more common pyroxene-bearing systems. The salinity effect is important to investigate due to the inevitable increase in fluid salinity from the boiling-induced phase separation and OH-uptake in the formation of serpentine. Here we present preliminary textural and chemical observations, which will subsequently be used for kinetic modelling of feedback.</p><p>[1] Ortoleva P., Merino, E., Moore, C. & Chadam, J. (1987). American Journal of Science <strong>287</strong>, 997-1007.</p><p>[2] Centrella, S., Austrheim, H., & Putnis, A. (2015). Lithos <strong>236–237</strong>, 245–255.</p><p>[3] Nakatani, T. & Nakamura, M. (2016). Geochemistry, Geophysics, Geosystems <strong>17</strong>, 3393-3419.</p><p>[4] Ingebritsen, S. E. & Manning, C. E. (2010). Geofluids <strong>10</strong>, 193-205.</p><p>[5] Beinlich, A., John, T., Vrijmoed, J.C., Tominaga, M., Magna, T. & Podladchikov, Y.Y. (2020). Nature Geoscience <strong>13</strong>, 307–311.</p>

The Present and the Future Perspectives of Biological Network Inference

2011 ◽  
pp. 118-140 ◽  
Author(s):  
Paola Lecca ◽  
Alida Palmisano
Keyword(s):  
Reaction Kinetics ◽  
Network Structure ◽  
Network Inference ◽  
Biological Network ◽  
Reaction Pathway ◽  
Model Identification ◽  
Chemical Species ◽  
Kinetics Parameters ◽  
Common Opinion ◽  
Genomic Biology

Biological network inference is based on a series of studies and computational approaches to the deduction of the connectivity of chemical species, the reaction pathway, and the reaction kinetics of complex reaction systems from experimental measurements. Inference for network structure and reaction kinetics parameters governing the dynamics of a biological system is currently an active area of research. In the era of post-genomic biology, it is a common opinion among scientists that living systems (cells, tissues, organs and organisms) can be understood in terms of their network structure as well as in term of the evolution in time of this network structure. In this chapter, the authors make a survey of the recent methodologies proposed for the structure inference and for the parameter estimation of a system of interacting biological entities. Furthermore, they present the recent works of the authors about model identification and calibration.

scholarly journals Inferring reaction network structure from single-cell, multiplex data, using toric systems theory

2019 ◽  
Vol 15 (12) ◽  
pp. e1007311 ◽  
Author(s):  
Shu Wang ◽  
Jia-Ren Lin ◽  
Eduardo D. Sontag ◽  
Peter K. Sorger
Keyword(s):  
Single Cell ◽  
Systems Theory ◽  
Network Structure ◽  
Reaction Network

scholarly journals Learning Diverse Bayesian Networks

2019 ◽  
Vol 33 ◽  
pp. 7793-7800
Author(s):  
Cong Chen ◽  
Changhe Yuan
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Network Structure ◽  
Search Algorithm ◽  
Noisy Data ◽  
Local Neighborhood ◽  
Causal Ordering ◽  
True Model ◽  
Underlying Network ◽  
Novel Method

Much effort has been directed at developing algorithms for learning optimal Bayesian network structures from data. When given limited or noisy data, however, the optimal Bayesian network often fails to capture the true underlying network structure. One can potentially address the problem by finding multiple most likely Bayesian networks (K-Best) in the hope that one of them recovers the true model. However, it is often the case that some of the best models come from the same peak(s) and are very similar to each other; so they tend to fail together. Moreover, many of these models are not even optimal respective to any causal ordering, thus unlikely to be useful. This paper proposes a novel method for finding a set of diverse top Bayesian networks, called modes, such that each network is guaranteed to be optimal in a local neighborhood. Such mode networks are expected to provide a much better coverage of the true model. Based on a globallocal theorem showing that a mode Bayesian network must be optimal in all local scopes, we introduce an A* search algorithm to efficiently find top M Bayesian networks which are highly probable and naturally diverse. Empirical evaluations show that our top mode models have much better diversity as well as accuracy in discovering true underlying models than those found by K-Best.

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