The relative importance of data points in systems biology and parameter estimation

Estimating model parameters is a crucial step to understand the behavior of biological systems. To perform parameter estimation, a commonly used formulation is the least square method that minimizes the mean squared error. This method finds the model parameters that minimize the sum of the squared error between experimental data and model predictions. However, such a formulation can misguide parameter estimation and the understanding of the system. This is mainly because least square formulation typically treats all data points equally, while the reality is that not all data points are of equal importance. Another common issue in systems biology is that the amount of experimental data is almost always limited compared to the model complexity, making parameter estimation challenging and ill-conditioned. Ignoring the relative importance of data points may amplify the ill-conditioned nature of the problem. Therefore, we propose to give different weight to each data point when formulating the least square cost function. The weight of each data point is defined by an uncertainty measure for the data point given the others, quantifying each data point's unique information that cannot be inferred from other data points. To test our algorithm, we used a G1/S transition model with two dynamic variables and 12 parameters, developed a sampling algorithm to obtain collections of parameter settings close to the best fit, and demonstrated the benefits of the proposed weighted cost function formulation.