A novel cost function for parameters estimation in oscillatory biochemical systems

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, cannot be measured directly and most of them have to be estimated using 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 cost function to address these issues by integrating temporal information with periodic information embedded in the measurements. This new cost function has better surface properties leading to fewer local minima and better performance of global optimization algorithms. We verified for two oscillatory biochemical systems that our method results in an increased ability to estimate accurate kinetic parameters as compared to the traditional LS cost function. This will eventually lead to biochemical models that are more precise, predictable and controllable.