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Macarron, R., Banks, M.N., Bojanic, D., Burns, D.J., Cirovic, D.A., Garyantes, T., Green, D.V., Hertzberg, R.P., Janzen, W.P., Paslay, J.W., Schopfer, U. and Sittampalam, G.S. (2011) Impact of High-Throughput Screening in Biomedical Research. Nature Reviews Drug Discovery, 10, 188-195.
https://doi.org/10.1038/nrd3368

has been cited by the following article:

• TITLE: An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology

  AUTHORS: Yohei Motomura, Hiroyuki Hamada, Masahiro Okamoto

  KEYWORDS: Finite Difference Method, Stiff Equation, Multi-Time-Scale, Systems Biology, Mathematical Analysis

  JOURNAL NAME: Applied Mathematics, Vol.7 No.17, November 23, 2016

  ABSTRACT: The improvements of high-throughput experimental devices such as microarray and mass spectrometry have allowed an effective acquisition of biological comprehensive data which include genome, transcriptome, proteome, and metabolome (multi-layered omics data). In Systems Biology, we try to elucidate various dynamical characteristics of biological functions with applying the omics data to detailed mathematical model based on the central dogma. However, such mathematical models possess multi-time-scale properties which are often accompanied by time-scale differences seen among biological layers. The differences cause time stiff problem, and have a grave influence on numerical calculation stability. In the present conventional method, the time stiff problem remained because the calculation of all layers was implemented by adaptive time step sizes of the smallest time-scale layer to ensure stability and maintain calculation accuracy. In this paper, we designed and developed an effective numerical calculation method to improve the time stiff problem. This method consisted of ahead, backward, and cumulative algorithms. Both ahead and cumulative algorithms enhanced calculation efficiency of numerical calculations via adjustments of step sizes of each layer, and reduced the number of numerical calculations required for multi-time-scale models with the time stiff problem. Backward algorithm ensured calculation accuracy in the multi-time-scale models. In case studies which were focused on three layers system with 60 times difference in time-scale order in between layers, a proposed method had almost the same calculation accuracy compared with the conventional method in spite of a reduction of the total amount of the number of numerical calculations. Accordingly, the proposed method is useful in a numerical analysis of multi-time-scale models with time stiff problem.