Browse
Submit Data
Databases
API
Help

Dataset Information

24 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Network Reconstruction From High-Dimensional Ordinary Differential Equations.

ABSTRACT: We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

SUBMITTER: Chen S

PROVIDER: S-EPMC5880569 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Network Reconstruction From High-Dimensional Ordinary Differential Equations.

Chen Shizhe S Shojaie Ali A Witten Daniela M DM

Journal of the American Statistical Association 20170807 520

We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficie ...[more]

PMID: 29618851

Similar Datasets

Identifying the dynamic gene regulatory network during latent HIV-1 reactivation using high-dimensional ordinary differential equations.

Project description:Reactivation of latently infected cells has emerged as an important strategy for eradication of HIV. However, genetic mechanisms of regulation after reactivation remain unclear. We describe a five-step pipeline to study the dynamics of the gene regulatory network following a viral reactivation using high-dimensional ordinary differential equations. Our pipeline implements a combination of five different methods, by detecting temporally differentially expressed genes (step 1), clustering genes with similar temporal expression patterns into a small number of response modules (step2), performing a functional enrichment analysis within each gene response module (step 3), identifying a network structure based on the gene response modules using ordinary differential equations (ODE) and a high-dimensional variable selection technique (step 4), and obtaining a gene regulatory model based on refined parameter estimates using nonlinear least squares (step 5). We applied our pipeline to a time course gene expression data of latently infected T-cells following a latency-reversion.

| S-EPMC8442249 | biostudies-literature

Modeling genome-wide dynamic regulatory network in mouse lungs with influenza infection using high-dimensional ordinary differential equations.

Project description:The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.

| S-EPMC4011728 | biostudies-literature

Transcriptomic forecasting with neural ordinary differential equations.

Project description:Single-cell transcriptomics technologies can uncover changes in the molecular states that underlie cellular phenotypes. However, understanding the dynamic cellular processes requires extending from inferring trajectories from snapshots of cellular states to estimating temporal changes in cellular gene expression. To address this challenge, we have developed a neural ordinary differential-equation-based method, RNAForecaster, for predicting gene expression states in single cells for multiple future time steps in an embedding-independent manner. We demonstrate that RNAForecaster can accurately predict future expression states in simulated single-cell transcriptomic data with cellular tracking over time. We then show that by using metabolic labeling single-cell RNA sequencing (scRNA-seq) data from constitutively dividing cells, RNAForecaster accurately recapitulates many of the expected changes in gene expression during progression through the cell cycle over a 3-day period. Thus, RNAForecaster enables short-term estimation of future expression states in biological systems from high-throughput datasets with temporal information.

| S-EPMC10435954 | biostudies-literature

Regularized Semiparametric Estimation for Ordinary Differential Equations.

Project description:Ordinary differential equations (ODEs) are widely used in modeling dynamic systems and have ample applications in the fields of physics, engineering, economics and biological sciences. The ODE parameters often possess physiological meanings and can help scientists gain better understanding of the system. One key interest is thus to well estimate these parameters. Ideally, constant parameters are preferred due to their easy interpretation. In reality, however, constant parameters can be too restrictive such that even after incorporating error terms, there could still be unknown sources of disturbance that lead to poor agreement between observed data and the estimated ODE system. In this paper, we address this issue and accommodate short-term interferences by allowing parameters to vary with time. We propose a new regularized estimation procedure on the time-varying parameters of an ODE system so that these parameters could change with time during transitions but remain constants within stable stages. We found, through simulation studies, that the proposed method performs well and tends to have less variation in comparison to the non-regularized approach. On the theoretical front, we derive finite-sample estimation error bounds for the proposed method. Applications of the proposed method to modeling the hare-lynx relationship and the measles incidence dynamic in Ontario, Canada lead to satisfactory and meaningful results.

| S-EPMC4574313 | biostudies-literature

Solving the initial value problem of ordinary differential equations by Lie group based neural network method.

Project description:To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing the Lie group expressions of the solution, the trial solution of ODEs is split into two parts. The first part is a solution of other ODEs with initial values of original IVP. This is easily solved using the Lie group and known symbolic or numerical methods without any network parameters (weights and biases). The second part consists of an FNN with adjustable parameters. This is trained using the error back propagation method by minimizing an error (loss) function and updating the parameters. The method significantly reduces the number of the trainable parameters and can more quickly and accurately learn the real solution, compared to the existing similar methods. The numerical method is applied to several cases, including physical oscillation problems. The results have been graphically represented, and some conclusions have been made.

| S-EPMC8985966 | biostudies-literature

A variational approach to parameter estimation in ordinary differential equations.

Project description:BackgroundOrdinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters.ResultsThe approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters.ConclusionsThe combined estimation approach takes the uncertainty in input courses correctly into account. This leads to precise parameter estimates and correct confidence intervals. In particular this implies that small motifs of large reaction networks can be analysed independently of the rest. By the use of variational methods, elements from control theory and statistics are combined allowing for future transfer of methods between the two fields.

| S-EPMC3534504 | biostudies-literature

A unique transformation from ordinary differential equations to reaction networks.

Project description:Many models in Systems Biology are described as a system of Ordinary Differential Equations, which allows for transient, steady-state or bifurcation analysis when kinetic information is available. Complementary structure-related qualitative analysis techniques have become increasingly popular in recent years, like qualitative model checking or pathway analysis (elementary modes, invariants, flux balance analysis, graph-based analyses, chemical organization theory, etc.). They do not rely on kinetic information but require a well-defined structure as stochastic analysis techniques equally do. In this article, we look into the structure inference problem for a model described by a system of Ordinary Differential Equations and provide conditions for the uniqueness of its solution. We describe a method to extract a structured reaction network model, represented as a bipartite multigraph, for example, a continuous Petri net (CPN), from a system of Ordinary Differential Equations (ODEs). A CPN uniquely defines an ODE, and each ODE can be transformed into a CPN. However, it is not obvious under which conditions the transformation of an ODE into a CPN is unique, that is, when a given ODE defines exactly one CPN. We provide biochemically relevant sufficient conditions under which the derived structure is unique and counterexamples showing the necessity of each condition. Our method is implemented and available; we illustrate it on some signal transduction models from the BioModels database. A prototype implementation of the method is made available to modellers at http://contraintes.inria.fr/~soliman/ode2pn.html, and the data mentioned in the "Results" section at http://contraintes.inria.fr/~soliman/ode2pn_data/. Our results yield a new recommendation for the import/export feature of tools supporting the SBML exchange format.

| S-EPMC3008708 | biostudies-literature

Investigation of singular ordinary differential equations by a neuroevolutionary approach.

Project description:In this research, we have investigated doubly singular ordinary differential equations and a real application problem of studying the temperature profile in a porous fin model. We have suggested a novel soft computing strategy for the training of unknown weights involved in the feed-forward artificial neural networks (ANNs). Our neuroevolutionary approach is used to suggest approximate solutions to a highly nonlinear doubly singular type of differential equations. We have considered a real application from thermodynamics, which analyses the temperature profile in porous fins. For this purpose, we have used the optimizer, namely, the fractional-order particle swarm optimization technique (FO-DPSO), to minimize errors in solutions through fitness functions. ANNs are used to design the approximate series of solutions to problems considered in this paper. We find the values of unknown weights such that the approximate solutions to these problems have a minimum residual error. For global search in the domain, we have initialized FO-DPSO with random solutions, and it collects best so far solutions in each generation/ iteration. In the second phase, we have fine-tuned our algorithm by initializing FO-DPSO with the collection of best so far solutions. It is graphically illustrated that this strategy is very efficient in terms of convergence and minimum mean squared error in its best solutions. We can use this strategy for the higher-order system of differential equations modeling different important real applications.

| S-EPMC7347205 | biostudies-literature

Predicting metabolomic profiles from microbial composition through neural ordinary differential equations.

Project description:Characterizing the metabolic profile of a microbial community is crucial for understanding its biological function and its impact on the host or environment. Metabolomics experiments directly measuring these profiles are difficult and expensive, while sequencing methods quantifying the species composition of microbial communities are well-developed and relatively cost-effective. Computational methods that are capable of predicting metabolomic profiles from microbial compositions can save considerable efforts needed for metabolomic profiling experimentally. Yet, despite existing efforts, we still lack a computational method with high prediction power, general applicability, and great interpretability. Here we develop a method - mNODE (Metabolomic profile predictor using Neural Ordinary Differential Equations), based on a state-of-the-art family of deep neural network models. We show compelling evidence that mNODE outperforms existing methods in predicting the metabolomic profiles of human microbiomes and several environmental microbiomes. Moreover, in the case of human gut microbiomes, mNODE can naturally incorporate dietary information to further enhance the prediction of metabolomic profiles. Besides, susceptibility analysis of mNODE enables us to reveal microbe-metabolite interactions, which can be validated using both synthetic and real data. The presented results demonstrate that mNODE is a powerful tool to investigate the microbiome-diet-metabolome relationship, facilitating future research on precision nutrition.

| S-EPMC10786629 | biostudies-literature

Generation of realistic synthetic data using Multimodal Neural Ordinary Differential Equations

Project description:Individual organizations, such as hospitals, pharmaceutical companies, and health insurance providers, are currently limited in their ability to collect data that are fully representative of a disease population. This can, in turn, negatively impact the generalization ability of statistical models and scientific insights. However, sharing data across different organizations is highly restricted by legal regulations. While federated data access concepts exist, they are technically and organizationally difficult to realize. An alternative approach would be to exchange synthetic patient data instead. In this work, we introduce the Multimodal Neural Ordinary Differential Equations (MultiNODEs), a hybrid, multimodal AI approach, which allows for generating highly realistic synthetic patient trajectories on a continuous time scale, hence enabling smooth interpolation and extrapolation of clinical studies. Our proposed method can integrate both static and longitudinal data, and implicitly handles missing values. We demonstrate the capabilities of MultiNODEs by applying them to real patient-level data from two independent clinical studies and simulated epidemiological data of an infectious disease.

| S-EPMC9391444 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data