Abstract
Oscillatory pathways are among the most important classes of biochemical systems with examples ranging from circadian rhythms and cell cycle maintenance. Mathematical modeling of these highly interconnected biochemical networks is needed to meet numerous objectives such as investigating, predicting and controlling the dynamics of these systems. Identifying the kinetic rate parameters is essential for fully modeling these and other biological processes. These kinetic parameters, however, are not usually available from measurements and most of them have to be estimated by parameter fitting techniques. One of the issues with estimating kinetic parameters in oscillatory systems is the irregularities in the least square (LS) cost function surface used to estimate these parameters, which is caused by the periodicity of the measurements. These irregularities result in numerous local minima, which limit the performance of even some of the most robust global optimization algorithms. We proposed a parameter estimation framework to address these issues that integrates temporal information with periodic information embedded in the measurements used to estimate these parameters. This periodic information is used to build a proposed cost function with better surface properties leading to fewer local minima and better performance of global optimization algorithms. We verified for three oscillatory biochemical systems that our proposed cost function results in an increased ability to estimate accurate kinetic parameters as compared to the traditional LS cost function. We combine this cost function with an improved noise removal approach that leverages periodic characteristics embedded in the measurements to effectively reduce noise. The results provide strong evidence on the efficacy of this noise removal approach over the previous commonly used wavelet hard-thresholding noise removal methods. This proposed optimization framework results in more accurate kinetic parameters that will eventually lead to biochemical models that are more precise, predictable, and controllable.
Highlights
Oscillatory biochemical pathways are an important class of biochemical systems [1,2] that play significant roles in living systems
We show that periodicity in the measurements of oscillatory systems results in irregularly surface properties of the least square (LS) cost function leading to numerous local minima
This study considers deterministic, nonlinear oscillatory biochemical pathways described by ordinary differential equations (ODEs) as shown in (1): x(t) = f(x(t), p) t0 < t < te, (1)
Summary
Oscillatory biochemical pathways are an important class of biochemical systems [1,2] that play significant roles in living systems. “circadian rhythms” are fundamental daily time-keeping mechanisms in a wide range of species from unicellular organisms to complex eukaryotes [3]. One of their most important roles is in regulating physiological processes such as the sleepwake cycle in mammals [4]. “Cell cycles” are another vital class of biochemical oscillations. There are other classes of biochemical rhythms such as cardiac rhythms [6], ovarian cycles [7] and cAMP oscillations [8] that have their own significance in systems biology
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