Abstract
Quantification of system dynamics is a central aim of mathematical modelling in biology. Defining experimentally supported functional relationships between molecular entities by mathematical terms enables the application of computational routines to simulate and analyse the underlying molecular system. In many fields of natural sciences and engineering, trigonometric functions are applied to describe oscillatory processes. As biochemical oscillations occur in many aspects of biochemistry and biophysics, Fourier analysis of metabolic functions promises to quantify, describe and analyse metabolism and its reaction towards environmental fluctuations. Here, Fourier polynomials were developed from experimental time-series data and combined with block diagram simulation of plant metabolism to study heat shock response of photosynthetic CO2 assimilation and carbohydrate metabolism in Arabidopsis thaliana. Simulations predicted a stabilising effect of reduced sucrose biosynthesis capacity and increased capacity of starch biosynthesis on carbon assimilation under transient heat stress. Model predictions were experimentally validated by quantifying plant growth under such stress conditions. In conclusion, this suggests that Fourier polynomials represent a predictive mathematical approach to study dynamic plant-environment interactions.
Highlights
Quantification of system dynamics is a central aim of mathematical modelling in biology
I.e., the sum of synthesizing and degrading/consuming reactions of metabolite pools, under dynamic environmental conditions we have previously suggested a method for implicit estimation of metabolic functions[15]
We developed a mathematical model based on Fourier polynomials to simulate and analyze dynamics of photosynthesis and carbohydrate metabolism under transient heat exposure by function superposition
Summary
Quantification of system dynamics is a central aim of mathematical modelling in biology. Model predictions were experimentally validated by quantifying plant growth under such stress conditions This suggests that Fourier polynomials represent a predictive mathematical approach to study dynamic plant-environment interactions. ODE models are frequently applied to simulate enzyme kinetic reactions and, by this, to explain dynamics of observed metabolite concentrations. Dynamics of metabolite concentrations in time-series experiments were used in this approach to derive a time-continuous mathematical function to identify regulatory cascades in metabolic pathways. This approach made use of spline interpolations which were composed of cubic polynomials which were fitted to adjacent pairs of data points in a time-series data set. Model simulations indicated a significant impact of sucrose and starch biosynthesis on the stabilization of carbon assimilation and growth under elevated temperatures
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