Estimation of component concentrations in biological systems via Interval Analysis

The estimation of state variables and parameters is an important and necessary step when modeling biological systems. Uncertainty has to be included to obtain results that are consistent with the true dynamics of the system. Classically, the estimation problem with uncertainty was addressed by methods such as the Kalman filter. In biological systems however, the probabilistic information about uncertainties is unknown, and bounded error estimation algorithms are better suited. The latter consider bounded uncertainties to produce results that are consistent with these uncertainties. These methods have been applied to a multitude of areas. To our knowledge, they have not been specifically developed to address the issues associated with state and parameter estimation of biological systems. The purpose of this work has been to generate an estimation algorithm that improves the amount of uncertainty that traditional methods can handle in scenarios typically encountered in biological systems. In those scenarios, knowledge about the system through measurements is rather small. The developed method is based on Interval Analysis. We present in this paper the developed method, followed by the results of applying it to a biological pathway. A comparison of our results with those from different methods are also presented.