Highly reliable computation of dynamic sensitivities in metabolic reaction systems by a variable‐step Taylor series method

Dynamic sensitivities are useful to characterize time-varying systems efficiently. In metabolic reaction systems, however, analysis using these values is not so popular. This is mainly due to the following two reasons. One is that the calculation of dynamic sensitivities requires us to derive differential equations for sensitivities from those for metabolite concentrations by partial differentiation, and it is not easy for experimentalists to perform this mathematical operation. The other is that the metabolic reaction systems are mostly described by stiff differential equations, from which it may not be easy to obtain reliable numerical solutions. We have previously developed software for calculation of dynamic sensitivities (softcads), in which one can calculate dynamic sensitivities with high accuracy by setting only differential equations for metabolite concentrations. This paper further improves the algorithm of softcads to enhance its performance. The results clearly show that regardless of the degree of stiffness, the improved softcads provides dynamic sensitivities with the super high accuracy that is comparable to the machine accuracy and also completes the calculation in a shorter time. © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

[1]  Yuji Hatoh,et al.  An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory. , 2005 .

[2]  Herbert M Sauro,et al.  Sensitivity analysis of stoichiometric networks: an extension of metabolic control analysis to non-steady state trajectories. , 2003, Journal of theoretical biology.

[3]  M A Savageau,et al.  The tricarboxylic acid cycle in Dictyostelium discoideum. II. Evaluation of model consistency and robustness. , 1992, The Journal of biological chemistry.

[4]  A highly accurate numerical method for calculating apparent kinetic parameters of immobilized enzyme reactions: 1. Theory , 1999 .

[5]  Kansuporn Sriyudthsak,et al.  Calculation errors of time-varying flux control coefficients obtained from elasticity coefficients by means of summation and connectivity theorems in metabolic control analysis. , 2010, Mathematical biosciences.

[6]  Fumihide Shiraishi,et al.  A Taylor-series solution in Cartesian space to GMA-system equations and its application to initial-value problems , 2002, Appl. Math. Comput..

[7]  Fumihide Shiraishi,et al.  A simple and highly accurate numerical differentiation method for sensitivity analysis of large-scale metabolic reaction systems. , 2007, Mathematical biosciences.

[8]  Fumihide Shiraishi,et al.  An efficient method for solving two-point boundary value problems with extremely high accuracy , 1996 .

[9]  M. Kramer,et al.  Sensitivity Analysis in Chemical Kinetics , 1983 .

[10]  A. M. Dunker.  The decoupled direct method for calculating sensitivity coefficients in chemical kinetics , 1984 .

[11]  M A Savageau,et al.  The tricarboxylic acid cycle in Dictyostelium discoideum. I. Formulation of alternative kinetic representations. , 1992, The Journal of biological chemistry.

[12]  Kansuporn Sriyudthsak,et al.  Investigation of the performance of fermentation processes using a mathematical model including effects of metabolic bottleneck and toxic product on cells. , 2010, Mathematical biosciences.

[13]  Matthias Reuss,et al.  Dynamic sensitivity analysis for metabolic systems , 1997 .

[14]  Hiroshi Hirayama,et al.  A reliable Taylor series-based computational method for the calculation of dynamic sensitivities in large-scale metabolic reaction systems: algorithm and software evaluation. , 2009, Mathematical biosciences.

[15]  K Sriyudthsak,et al.  Identification of bottleneck enzymes with negative dynamic sensitivities: ethanol fermentation systems as case studies. , 2010, Journal of biotechnology.

[16]  Michael A. Savageau,et al.  The Tricarboxylic Acid Cycle inDictyostelium discoideum—Two Methods of Analysis Applied to the Same Model☆ , 1996 .

[17]  Kansuporn Sriyudthsak,et al.  Selection of Best Indicators for Ranking and Determination of Bottleneck Enzymes in Metabolic Reaction Systems , 2010 .

[18]  Kansuporn Sriyudthsak,et al.  Instantaneous and Overall Indicators for Determination of Bottleneck Ranking in Metabolic Reaction Networks , 2010 .

[19]  Fumihide Shiraishi,et al.  NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM BY COMBINED TAYLOR SERIES METHOD WITH A TECHNIQUE FOR RAPIDLY SELECTING SUITABLE STEP SIZES , 1995 .

[20]  M A Savageau,et al.  The tricarboxylic acid cycle in Dictyostelium discoideum. III. Analysis of steady state and dynamic behavior. , 1992, The Journal of biological chemistry.

[21]  M A Savageau,et al.  The tricarboxylic acid cycle in Dictyostelium discoideum. IV. Resolution of discrepancies between alternative methods of analysis. , 1992, The Journal of biological chemistry.

[22]  Fumihide Shiraishi,et al.  Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor series method , 2001 .

[23]  M A Savageau,et al.  The tricarboxylic acid cycle in Dictyostelium discoideum. Systemic effects of including protein turnover in the current model. , 1993, The Journal of biological chemistry.