Models Of Biological Pathways Research Articles

Identifying Bayesian optimal experiments for uncertain biochemical pathway models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.

A data-driven approach for timescale decomposition of biochemical reaction networks.

Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for the timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies timescale hierarchies, concentration pools, and coherent structures from time-series data, providing a system-level description of reaction networks at physiologically important timescales. We apply this technique to kinetic models of hypothetical and biological pathways, validating it by reproducing analytically characterized or previously known concentration pools of these pathways. Moreover, by analyzing the timescale hierarchy of the glycolytic pathway, we elucidate the connections between the stoichiometric and dissipative structures of reaction networks and the temporal organization of coherent structures. Specifically, we show that glycolysis is a cofactor-driven pathway, the slowest dynamics of which are described by a balance between high-energy phosphate bond and redox trafficking. Overall, this approach provides more biologically interpretable characterizations of network dynamics than large-scale kinetic models, thus facilitating model reduction and personalized medicine applications. IMPORTANCE Complex interactions within interconnected biochemical reaction networks enable cellular responses to a wide range of unpredictable environmental perturbations. Understanding how biological functions arise from these intricate interactions has been a long-standing problem in biology. Here, we introduce a computational approach to dissect complex biological systems' dynamics in evolving environments. This approach characterizes the timescale hierarchies of complex reaction networks, offering a system-level understanding at physiologically relevant timescales. Analyzing various hypothetical and biological pathways, we show how stoichiometric properties shape the way energy is dissipated throughout reaction networks. Notably, we establish that glycolysis operates as a cofactor-driven pathway, where the slowest dynamics are governed by a balance between high-energy phosphate bonds and redox trafficking. This approach enhances our understanding of network dynamics and facilitates the development of reduced-order kinetic models with biologically interpretable components.

Targeted proteomics-driven computational modeling of the mouse macrophage toll-like receptor signaling pathway

Abstract The Toll-like receptor (TLR) signaling pathway is crucial for the initiation of effective immune responses. Computational modeling of biological pathways can test mechanistic hypotheses about how regulation is achieved and why it sometimes fails, causing disease (e.g., sepsis). In this investigation, mass spectrometry (LC-MS) and computational modeling are being integrated to develop a model of the TLR4 pathway. TLR4 pathway proteins within mouse macrophages were quantitated using targeted LC-MS and stable-isotope labeled internal (phospho)peptide standards (136 unmodified peptides and 29 phosphopeptides for 54 (phospho)proteins). AlphaFold-Multimer was used to predict protein complex structures, Rosetta was used to idealize and relax the structures, and Simulation of Diffusional Association (SDA) and TransComp were used to estimate protein-protein association rates. Simmune was used to perform rule-based pathway modeling, simulation, and training. LPS stimulation altered proteins known to be affected by TLR4 pathway activation (e.g., phosphorylated ERK1 increased from 30,000 to 250,000 copies per cell). Hundreds of protein-protein association rates were predicted. The (phospho)protein absolute abundance values and protein-protein association rates are being used as parameters for TLR4 pathway models. The parameter space is being explored to identify parameter sets that accurately reproduce the experimental data. Experimental and computational techniques are being integrated to generate a strongly data driven model of the TLR pathway. This work was supported by the Intramural Research Program of NIAID, NIH. This work was supported by the Intramural Research Program of NIAID, NIH.

Effect of weak alternating magnetic fields on neutrophilic granulocytes. An analytical review

The article discusses the main achievements in recent years in studying the biological effects of weak and superweak low-frequency magnetic fields, either variable or combined with constant ones. Considered are neutrophil granulocytes activated by chemical stimulants or intact when the magnetic fields affect isolated cells, blood, and whole organisms. The methods include recording changes in ROS concentration levels (the most noticeable effect of exposure to a weak magnetic field), priming index, calcium homeostasis, proliferative activity, immune status, as well as the influence of various chemical agents on these indicators. The leading methods in this field are fluorescence spectrometry and chemiluminescence analysis. The experimental results indicate the biological effectiveness of this physical factor, the specific effect of which depends on the type of biosystem, its functional status, the environment, and the parameters of the fields themselves. The data obtained can have applied significance in magnetotherapy, immune response optimization in various diseases, acceleration of tissue regeneration and repair, and increasing the body's resistance to infections. They also can have academic significance since they help to identify the primary field acceptors and magnetic targets and their localization in the cell, study relationships with signal cascades, build models of biological signal amplification pathways, and find biologically significant frequencies and field amplitudes.

Introducing Parameter Clustering to the OED Procedure for Model Calibration of a Synthetic Inducible Promoter in S. cerevisiae

In recent years, synthetic gene circuits for adding new cell features have become one of the most powerful tools in biological and pharmaceutical research and development. However, because of the inherent non-linearity and noisy experimental data, the experiment-based model calibration of these synthetic parts is perceived as a laborious and time-consuming procedure. Although the optimal experimental design (OED) based on the Fisher information matrix (FIM) has been proved to be an effective means to improve the calibration efficiency, the required calculation increases dramatically with the model size (parameter number). To reduce the OED complexity without losing the calibration accuracy, this paper proposes two OED approaches with different parameter clustering methods and validates the accuracy of calibrated models with in-silico experiments. A model of an inducible synthetic promoter in S. cerevisiae is adopted for bench-marking. The comparison with the traditional off-line OED approach suggests that the OED approaches with both of the clustering methods significantly reduce the complexity of OED problems (for at least 49.0%), while slightly improving the calibration accuracy (11.8% and 19.6% lower estimation error in average for FIM-based and sensitivity-based approaches). This study implicates that for calibrating non-linear models of biological pathways, cluster-based OED could be a beneficial approach to improve the efficiency of optimal experimental design.

Reaction Systems for Modeling and Validation of Biological Signaling Pathways: G1/S Checkpoint of the Cell Cycle

Reaction Systems for Modeling and Validation of Biological Signaling Pathways: G1/S Checkpoint of the Cell Cycle

Logic-based analysis of gene expression data predicts association between TNF, TGFB1 and EGF pathways in basal-like breast cancer.

For breast cancer, clinically important subtypes are well characterized at the molecular level in terms of gene expression profiles. In addition, signaling pathways in breast cancer have been extensively studied as therapeutic targets due to their roles in tumor growth and metastasis. However, it is challenging to put signaling pathways and gene expression profiles together to characterize biological mechanisms of breast cancer subtypes since many signaling events result from post-translational modifications, rather than gene expression differences. We designed a logic-based computational framework to explain the differences in gene expression profiles among breast cancer subtypes using Pathway Logic and transcriptional network information. Pathway Logic is a rewriting-logic-based formal system for modeling biological pathways including post-translational modifications. Our method demonstrated its utility by constructing subtype-specific path from key receptors (TNFR, TGFBR1 and EGFR) to key transcription factor (TF) regulators (RELA, ATF2, SMAD3 and ELK1) and identifying potential association between pathways via TFs in basal-specific paths, which could provide a novel insight on aggressive breast cancer subtypes. Codes and results are available at http://epigenomics.snu.ac.kr/PL/.

Setting the basis of best practices and standards for curation and annotation of logical models in biology-highlights of the [BC]2 2019 CoLoMoTo/SysMod Workshop.

The fast accumulation of biological data calls for their integration, analysis and exploitation through more systematic approaches. The generation of novel, relevant hypotheses from this enormous quantity of data remains challenging. Logical models have long been used to answer a variety of questions regarding the dynamical behaviours of regulatory networks. As the number of published logical models increases, there is a pressing need for systematic model annotation, referencing and curation in community-supported and standardised formats. This article summarises the key topics and future directions of a meeting entitled 'Annotation and curation of computational models in biology', organised as part of the 2019 [BC]2 conference. The purpose of the meeting was to develop and drive forward a plan towards the standardised annotation of logical models, review and connect various ongoing projects of experts from different communities involved in the modelling and annotation of molecular biological entities, interactions, pathways and models. This article defines a roadmap towards the annotation and curation of logical models, including milestones for best practices and minimum standard requirements.

Multiset sparse partial least squares path modeling for high dimensional omics data analysis

BackgroundRecent technological developments have enabled the measurement of a plethora of biomolecular data from various omics domains, and research is ongoing on statistical methods to leverage these omics data to better model and understand biological pathways and genetic architectures of complex phenotypes. Current reviews report that the simultaneous analysis of multiple (i.e. three or more) high dimensional omics data sources is still challenging and suitable statistical methods are unavailable. Often mentioned challenges are the lack of accounting for the hierarchical structure between omics domains and the difficulty of interpretation of genomewide results. This study is motivated to address these challenges. We propose multiset sparse Partial Least Squares path modeling (msPLS), a generalized penalized form of Partial Least Squares path modeling, for the simultaneous modeling of biological pathways across multiple omics domains. msPLS simultaneously models the effect of multiple molecular markers, from multiple omics domains, on the variation of multiple phenotypic variables, while accounting for the relationships between data sources, and provides sparse results. The sparsity in the model helps to provide interpretable results from analyses of hundreds of thousands of biomolecular variables.ResultsWith simulation studies, we quantified the ability of msPLS to discover associated variables among high dimensional data sources. Furthermore, we analysed high dimensional omics datasets to explore biological pathways associated with Marfan syndrome and with Chronic Lymphocytic Leukaemia. Additionally, we compared the results of msPLS to the results of Multi-Omics Factor Analysis (MOFA), which is an alternative method to analyse this type of data.ConclusionsmsPLS is an multiset multivariate method for the integrative analysis of multiple high dimensional omics data sources. It accounts for the relationship between multiple high dimensional data sources while it provides interpretable results through its sparse solutions. The biomarkers found by msPLS in the omics datasets can be interpreted in terms of biological pathways associated with the pathophysiology of Marfan syndrome and of Chronic Lymphocytic Leukaemia. Additionally, msPLS outperforms MOFA in terms of variation explained in the chronic lymphocytic leukaemia dataset while it identifies the two most important clinical markers for Chronic Lymphocytic LeukaemiaAvailabilityhttp://uva.csala.me/mspls.https://github.com/acsala/2018_msPLS

Flux prediction using artificial neural network (ANN) for the upper part of glycolysis.

The selection of optimal enzyme concentration in multienzyme cascade reactions for the highest product yield in practice is very expensive and time-consuming process. The modelling of biological pathways is a difficult process because of the complexity of the system. The mathematical modelling of the system using an analytical approach depends on the many parameters of enzymes which rely on tedious and expensive experiments. The artificial neural network (ANN) method has been successively applied in different fields of science to perform complex functions. In this study, ANN models were trained to predict the flux for the upper part of glycolysis as inferred by NADH consumption, using four enzyme concentrations i.e., phosphoglucoisomerase, phosphofructokinase, fructose-bisphosphate-aldolase, triose-phosphate-isomerase. Out of three ANN algorithms, the neuralnet package with two activation functions, “logistic” and “tanh” were implemented. The prediction of the flux was very efficient: RMSE and R2 were 0.847, 0.93 and 0.804, 0.94 respectively for logistic and tanh functions using a cross validation procedure. This study showed that a systemic approach such as ANN could be used for accurate prediction of the flux through the metabolic pathway. This could help to save a lot of time and costs, particularly from an industrial perspective. The R-code is available at: https://github.com/DSIMB/ANN-Glycolysis-Flux-Prediction.

Modeling Variability in Populations of Cells Using Approximated Multivariate Distributions.

We are interested in studying the evolution of large homogeneous populations of cells, where each cell is assumed to be composed of a group of biological players (species) whose dynamics is governed by a complex biological pathway, identical for all cells. Modeling the inherent variability of the species concentrations in different cells is crucial to understand the dynamics of the population. In this work, we focus on handling this variability by modeling each species by a random variable that evolves over time. This appealing approach runs into the curse of dimensionality since exactly representing a joint probability distribution involving a large set of random variables quickly becomes intractable as the number of variables grows. To make this approach amenable to biopathways, we explore different techniques to (i) approximate the exact joint distribution at a given time point, and (ii) to track its evolution as time elapses. We start with the problem of approximating the probability distribution of biological species in a population of cells at some given time point. Data come from different fine-grained models of biological pathways of increasing complexities, such as (perturbed) Ordinary Differential Equations (ODEs). Classical approximations rely on the strong and unrealistic assumption that variables/species are independent, or that they can be grouped into small independent clusters. We propose instead to use the Chow-Liu tree representation, based on overlapping clusters of two variables, which better captures correlations between variables. Our experiments show that the proposed approximation scheme is more accurate than existing ones to model probability distributions deriving from biopathways. Then we address the problem of tracking the dynamics of a population of cells, that is computing from an initial distribution the evolution of the (approximate) joint distribution of species over time, called the inference problem. We evaluate several approximate inference algorithms (e.g., [14] , [17] ) for coarse-grained abstractions [12], [16] of biological pathways. Using the Chow-Liu tree approximation, we develop a new inference algorithm which is very accurate according to the experiments we report, for a minimal computation overhead. Our implementation is available at https://codeocean.com/capsule/6491669/tree.

A modular approach for assembly of quantitative adverse outcome pathways.

The adverse outcome pathway (AOP) framework is a conceptual construct that mechanistically links molecular initiating events to adverse biological outcomes through a series of causal key events (KEs) that represent the perturbation of the biological system. Quantitative, predictive AOPs are necessary for screening emerging contaminants and potential substitutes to inform their prioritization for testing. In practice, they are not widely used because they can be costly to develop and validate. A modular approach for assembly of quantitative AOPs, based on existing knowledge, would allow for rapid development of biological pathway models to screen contaminants for potential hazards and prioritize them for subsequent testing and modeling. For each pair of KEs, a quantitative KE relationship (KER) can be derived as a response-response function or a conditional probability matrix describing the anticipated change in a KE based on the response of the prior KE. This transfer of response across KERs can be used to assemble a quantitative AOP. Here we demonstrate the use of proposed approach in two cases: inhibition of cytochrome P450 aromatase leading to reduced fecundity in fathead minnows and ionic glutamate receptor mediated excitotoxicity leading to memory impairment in rodents. The model created from these chains have value in characterizing the pathway and the potential or relative level of toxicological effect anticipated. This approach to simplistic, modular AOP models has wide applicability for rapid development of biological pathway models.

Comparative Models of Biological and Social Pathways to Predict Child Growth through Age 2 Years from Birth Cohorts in Brazil, India, the Philippines, and South Africa

BackgroundEarly growth faltering accounts for one-third of child deaths, and adversely impacts the health and human capital of surviving children. Social as well as biological factors contribute to growth faltering, but their relative strength and interrelations in different contexts have not been fully described.ObjectiveThe aim of this study was to use structural equation modelling to explore social and biological multidetermination of child height at age 2 y in longitudinal data from 4 birth cohort studies in low- and middle-income countries.MethodsWe analyzed data from 13,824 participants in birth cohort studies in Brazil, India, the Philippines, and South Africa. We used exploratory structural equation models, with height-for-age at 24 mo as the outcome to derive factors, and path analysis to estimate relations among a wide set of social and biological variables common to the 4 sites.ResultsThe prevalence of stunting at 24 mo ranged from 14.0% in Brazil to 67.7% in the Philippines. Maternal height and birthweight were strongly predictive of height-for-age at 24 mo in all 4 sites (all P values <0.001). Three social-environmental factors, which we characterized as “child circumstances,” “family socioeconomic status,” and “community facilities,” were identified in all sites. Each social-environmental factor was also strongly predictive of height-for-age at 24 mo (all P values <0.001), with some relations partly mediated through birthweight. The biological pathways accounted for 59% of the total explained variance and the social-environmental pathways accounted for 41%. The resulting path coefficients were broadly similar across the 4 sites.ConclusionsEarly child growth faltering is determined by both biological and social factors. Maternal height, itself a marker of intergenerational deprivation, strongly influences child height at 2 y, including indirect effects through birthweight and social factors. However, concurrent social factors, many of which are modifiable, directly and indirectly contribute to child growth. This study highlights opportunities for interventions that address both biological and social determinants over the long and short term.

A graphical and computational modeling platform for biological pathways.

A major endeavor of systems biology is the construction of graphical and computational models of biological pathways as a means to better understand their structure and function. Here, we present a protocol for a biologist-friendly graphical modeling scheme that facilitates the construction of detailed network diagrams, summarizing the components of a biological pathway (such as proteins and biochemicals) and illustrating how they interact. These diagrams can then be used to simulate activity flow through a pathway, thereby modeling its dynamic behavior. The protocol is divided into four sections: (i) assembly of network diagrams using the modified Edinburgh Pathway Notation (mEPN) scheme and yEd network editing software with pathway information obtained from published literature and databases of molecular interaction data; (ii) parameterization of the pathway model within yEd through the placement of 'tokens' on the basis of the known or imputed amount or activity of a component; (iii) model testing through visualization and quantitative analysis of the movement of tokens through the pathway, using the network analysis tool Graphia Professional and (iv) optimization of model parameterization and experimentation. This is the first modeling approach that combines a sophisticated notation scheme for depicting biological events at the molecular level with a Petri net-based flow simulation algorithm and a powerful visualization engine with which to observe the dynamics of the system being modeled. Unlike many mathematical approaches to modeling pathways, it does not require the construction of a series of equations or rate constants for model parameterization. Depending on a model's complexity and the availability of information, its construction can take days to months, and, with refinement, possibly years. However, once assembled and parameterized, a simulation run, even on a large model, typically takes only seconds. Models constructed using this approach provide a means of knowledge management, information exchange and, through the computation simulation of their dynamic activity, generation and testing of hypotheses, as well as prediction of a system's behavior when perturbed.

Stability of Signaling Pathways during Aging-A Boolean Network Approach.

Biological pathways are thought to be robust against a variety of internal and external perturbations. Fail-safe mechanisms allow for compensation of perturbations to maintain the characteristic function of a pathway. Pathways can undergo changes during aging, which may lead to changes in their stability. Less stable or less robust pathways may be consequential to or increase the susceptibility of the development of diseases. Among others, NF-B signaling is a crucial pathway in the process of aging. The NF-B system is involved in the immune response and dealing with various internal and external stresses. Boolean networks as models of biological pathways allow for simulation of signaling behavior. They can help to identify which proposed mechanisms are biologically representative and which ones function but do not mirror physical processes—for instance, changes of signaling pathways during the aging process. Boolean networks can be inferred from time-series of gene expression data. This allows us to get insights into the changes of behavior of pathways such as NF-B signaling in aged organisms in comparison to young ones.

A parallel metaheuristic for large mixed-integer dynamic optimization problems, with applications in computational biology.

BackgroundWe consider a general class of global optimization problems dealing with nonlinear dynamic models. Although this class is relevant to many areas of science and engineering, here we are interested in applying this framework to the reverse engineering problem in computational systems biology, which yields very large mixed-integer dynamic optimization (MIDO) problems. In particular, we consider the framework of logic-based ordinary differential equations (ODEs).MethodsWe present saCeSS2, a parallel method for the solution of this class of problems. This method is based on an parallel cooperative scatter search metaheuristic, with new mechanisms of self-adaptation and specific extensions to handle large mixed-integer problems. We have paid special attention to the avoidance of convergence stagnation using adaptive cooperation strategies tailored to this class of problems.ResultsWe illustrate its performance with a set of three very challenging case studies from the domain of dynamic modelling of cell signaling. The simpler case study considers a synthetic signaling pathway and has 84 continuous and 34 binary decision variables. A second case study considers the dynamic modeling of signaling in liver cancer using high-throughput data, and has 135 continuous and 109 binaries decision variables. The third case study is an extremely difficult problem related with breast cancer, involving 690 continuous and 138 binary decision variables. We report computational results obtained in different infrastructures, including a local cluster, a large supercomputer and a public cloud platform. Interestingly, the results show how the cooperation of individual parallel searches modifies the systemic properties of the sequential algorithm, achieving superlinear speedups compared to an individual search (e.g. speedups of 15 with 10 cores), and significantly improving (above a 60%) the performance with respect to a non-cooperative parallel scheme. The scalability of the method is also good (tests were performed using up to 300 cores).ConclusionsThese results demonstrate that saCeSS2 can be used to successfully reverse engineer large dynamic models of complex biological pathways. Further, these results open up new possibilities for other MIDO-based large-scale applications in the life sciences such as metabolic engineering, synthetic biology, drug scheduling.

SiGNet: A signaling network data simulator to enable signaling network inference.

Network models are widely used to describe complex signaling systems. Cellular wiring varies in different cellular contexts and numerous inference techniques have been developed to infer the structure of a network from experimental data of the network’s behavior. To objectively identify which inference strategy is best suited to a specific network, a gold standard network and dataset are required. However, suitable datasets for benchmarking are difficult to find. Numerous tools exist that can simulate data for transcriptional networks, but these are of limited use for the study of signaling networks. Here, we describe SiGNet (Signal Generator for Networks): a Cytoscape app that simulates experimental data for a signaling network of known structure. SiGNet has been developed and tested against published experimental data, incorporating information on network architecture, and the directionality and strength of interactions to create biological data in silico. SiGNet is the first tool to simulate biological signaling data, enabling an accurate and systematic assessment of inference strategies. SiGNet can also be used to produce preliminary models of key biological pathways following perturbation.

Translational Targeted Proteomics Profiling of Mitochondrial Energy Metabolic Pathways in Mouse and Human Samples.

Absolute measurements of protein abundance are important in the understanding of biological processes and the precise computational modeling of biological pathways. We developed targeted LC-MS/MS assays in the selected reaction monitoring (SRM) mode to quantify over 50 mitochondrial proteins in a single run. The targeted proteins cover the tricarboxylic acid cycle, fatty acid β-oxidation, oxidative phosphorylation, and the detoxification of reactive oxygen species. Assays used isotopically labeled concatemers as internal standards designed to target murine mitochondrial proteins and their human orthologues. Most assays were also suitable to quantify the corresponding protein orthologues in rats. After exclusion of peptides that did not pass the selection criteria, we arrived at SRM assays for 55 mouse, 52 human, and 51 rat proteins. These assays were optimized in isolated mitochondrial fractions from mouse and rat liver and cultured human fibroblasts and in total liver extracts from mouse, rat, and human. The developed proteomics approach is suitable for the quantification of proteins in the mitochondrial energy metabolic pathways in mice, rats, and humans as a basis for translational research. Initial data show that the assays have great potential for elucidating the adaptive response of human patients to mutations in mitochondrial proteins in a clinical setting.

Agent-Based Modeling of Biological Pathways - A Case-Study on mRNA Export and Quality Control Mechanism

Currently, a substantial gap exists between the methods utilized for modeling biological pathways. While some methods rely heavily on assumptions that prevent them from capturing the spatial detail and stochastic behavior observed in nature, others are designed to account for deeper levels of spatial details and stochasticity but at the cost of increased computational time and resources. Agent-based modeling (ABM) is a highly promising approach that brings together the advantages of detailed spatiotemporal approaches and computationally inexpensive methods. ABMs consist of a collection of agents with governing rules that dictate local behavior and interactions with adjacent agents, eventually predicting the complex behavior that may not be obvious from the individual rules. Our recently developed ABM platform, called BioABM, is primarily designed to capture the dynamics of molecular-scale complex systems by associating diffusion and binding/unbinding constants of biological species to movement and interaction probabilities in ABM. In order to showcase its potential impact as a predictive tool, we apply BioABM to an important, yet not well understood, biological pathway, i.e. messenger ribonucleic acid (mRNA) export and quality control mechanism. mRNAs are transported to the cytoplasm to transfer genetic information and direct synthesis of functional proteins. Multiple proteins and complexes are involved and the process is meticulously quality controlled by various sophisticated, yet highly efficient, mechanisms in eukaryotic cells. Using BioABM, we explored the dynamics of mRNA export and the mechanism through which aberrant mRNAs are distinguished and retained inside the nucleus. Our results shed light on different aspects of this pathway; addressing factors such as the significance of the expression level of mRNA export factor and the length of mRNA as well as presence of a nuclear basket-associated quality control complex on mRNA export dynamics.

Gradient Matching Methods for Computational Inference in Mechanistic Models for Systems Biology: A Review and Comparative Analysis.

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem in contemporary systems biology. Conventional methods involve repeatedly solving the ODEs by numerical integration, which is computationally onerous and does not scale up to complex systems. Aimed at reducing the computational costs, new concepts based on gradient matching have recently been proposed in the computational statistics and machine learning literature. In a preliminary smoothing step, the time series data are interpolated; then, in a second step, the parameters of the ODEs are optimized, so as to minimize some metric measuring the difference between the slopes of the tangents to the interpolants, and the time derivatives from the ODEs. In this way, the ODEs never have to be solved explicitly. This review provides a concise methodological overview of the current state-of-the-art methods for gradient matching in ODEs, followed by an empirical comparative evaluation based on a set of widely used and representative benchmark data.