Michio Iwata

A reliable Taylor series-based computational method for the calculation of dynamic sensitivities in large-scale metabolic reaction systems: Algorithm and software evaluation

Dynamic sensitivity analysis has become an important tool to successfully characterize all sorts of biological systems. However, when the analysis is carried out on large scale systems, it becomes imperative to employ a highly accurate computational method in order to obtain reliable values. Furthermore, the preliminary laborious mathematical operations required by current software before the computation of dynamic sensitivities makes it inconvenient for a significant number of unacquainted users. To satisfy these needs, the present work investigates a newly developed algorithm consisting of a combination of Taylor series method that can directly execute Taylor expansions for simultaneous non-linear-differential equations and a simple but highly-accurate numerical differentiation method based on finite-difference formulas. Applications to three examples of biochemical systems indicate that the proposed method makes it possible to compute the dynamic sensitivity values with highly-reliable accuracies and also allows to readily compute them by setting up only the differential equations for metabolite concentrations in the computer program. Also, it is found that the Padé approximation introduced in the Taylor series method shortens the computation time greatly because it stabilizes the computation so that it allows us to use larger stepsizes in the numerical integration. Consequently, the calculated results suggest that the proposed computational method, in addition to being user-friendly, makes it possible to perform dynamic sensitivity analysis in large-scale metabolic reaction systems both efficiently and reliably.

Elucidating the modes of action for bioactive compounds in a cell-specific manner by large-scale chemically-induced transcriptomics

The identification of the modes of action of bioactive compounds is a major challenge in chemical systems biology of diseases. Genome-wide expression profiling of transcriptional responses to compound treatment for human cell lines is a promising unbiased approach for the mode-of-action analysis. Here we developed a novel approach to elucidate the modes of action of bioactive compounds in a cell-specific manner using large-scale chemically-induced transcriptome data acquired from the Library of Integrated Network-based Cellular Signatures (LINCS), and analyzed 16,268 compounds and 68 human cell lines. First, we performed pathway enrichment analyses of regulated genes to reveal active pathways among 163 biological pathways. Next, we explored potential target proteins (including primary targets and off-targets) with cell-specific transcriptional similarity using chemical–protein interactome. Finally, we predicted new therapeutic indications for 461 diseases based on the target proteins. We showed the usefulness of the proposed approach in terms of prediction coverage, interpretation, and large-scale applicability, and validated the new prediction results experimentally by an in vitro cellular assay. The approach has a high potential for advancing drug discovery and repositioning.

Estimation of kinetic parameters in an S-system equation model for a metabolic reaction system using the Newton–Raphson method

Metabolic reaction systems can be modeled easily in terms of S-system type equations if their metabolic maps are available. This study therefore proposes a method for estimating parameters in decoupled S-system equations on the basis of the Newton-Raphson method and elucidates the performance of this estimation method. Parameter estimation from the time-course data of metabolite concentrations reveals that the parameters estimated are highly accurate, indicating that the estimation algorithm has been constructed correctly. The number of iterations is small and the calculation converges in a very short time (usually less than 1s). The method is also applied to time course data with noise and found to estimate parameters efficiently. Results indicate that the present method has the potential to be extended to a method for estimating parameters in large-scale metabolic reaction systems.

PENDISC: A Simple Method for Constructing a Mathematical Model from Time-Series Data of Metabolite Concentrations

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (arameter stimation in a on-mensionalized -system with onstraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Highly accurate computation of dynamic sensitivities in metabolic reaction systems by a Taylor series method

We have previously developed the software for calculation of dynamic sensitivities, SoftCADS, in which one can calculate dynamic sensitivities with high accuracy by just setting the differential equations for metabolite concentrations. However, SoftCADS did not always provide calculated values with the machine accuracy of a computer, although a Taylor series method was employed to numerically solve the differential equations. This is because numerical derivatives calculated from an approximate formula were directly used in the derivation of the differential equations for sensitivities from those for metabolite concentrations. The present work therefore attempts to further enhance the performance of SoftCADS, including not only the accuracies of the calculated values but also the calculation time. To overcome the problem, the approximate formula is expanded into a Taylor series in time and the first-term value of the series is replaced by the exact coefficient on the second term of the flux function expanded into a Taylor series in an independent or dependent variable. The result reveals that this replacement certainly provides not only numerical derivatives but also dynamic sensitivities with superhigh accuracies comparable to the machine accuracy, regardless of the degree of stiffness of the differential equations. Moreover, a comparison indicates that the improved SoftCADS shortens the calculation time of the dynamic sensitivities without reducing their accuracies, even when the simplest approximate derivative formula is used.

Predicting inhibitory and activatory drug targets by chemically and genetically perturbed transcriptome signatures

Genome-wide identification of all target proteins of drug candidate compounds is a challenging issue in drug discovery. Moreover, emerging phenotypic effects, including therapeutic and adverse effects, are heavily dependent on the inhibition or activation of target proteins. Here we propose a novel computational method for predicting inhibitory and activatory targets of drug candidate compounds. Specifically, we integrated chemically-induced and genetically-perturbed gene expression profiles in human cell lines, which avoided dependence on chemical structures of compounds or proteins. Predictive models for individual target proteins were simultaneously constructed by the joint learning algorithm based on transcriptomic changes in global patterns of gene expression profiles following chemical treatments, and following knock-down and over-expression of proteins. This method discriminates between inhibitory and activatory targets and enables accurate identification of therapeutic effects. Herein, we comprehensively predicted drug–target–disease association networks for 1,124 drugs, 829 target proteins, and 365 human diseases, and validated some of these predictions in vitro. The proposed method is expected to facilitate identification of new drug indications and potential adverse effects.

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton-Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks.