A novel cost function to estimate parameters of oscillatory biochemical systems

Oscillatory biochemical pathways are an important class of biochemical systems [1,2] that play significant roles in living systems. For instance, "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 sleep-wake cycle in mammals [4]. "Cell cycles" are also another vital class of biochemical oscillations. The cell cycle is the sequence of events by which a growing cell replicates all its components and divides into two daughter cells [5]. Inappropriate cell proliferation due to malfunctioning cell cycle control mechanisms can cause development of certain types of cancers [5]. There are also 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.A complete modeling of a biochemical system includes characterization of all nonlinear structures of the network along with the associated kinetic rates. In other words, without fully identifying all the kinetic parameter values, these models are still incomplete even if the full structure of the model has been determined. Few kinetic rates are available directly from experimentation or literature. Most of them, however, have to be estimated by parameter fitting techniques to complete the modeling of the biochemical pathway. Thus, a mathematical framework is needed to fit the kinetic parameters using the observables. Optimization frameworks that focus specifically on estimating parameters associated with biochemical pathways have received much attention in recent years [9-14].Two main issues in estimating kinetic parameters in biochemical systems are data related issues and computational issues [14]. The measurement dataset used to fit these parameters are usually noisy and incomplete. Measurement datasets are also affected by uncertainties rela