An improved curvilinear gradient method for parameter optimization in complex biological models

Mathematical modeling is an often used approach in biological science which, given some understanding of a system, is employed as a means of predicting future behavior and quantitative hypothesis testing. However, as our understanding of processes becomes more in depth, the models we use to describe them become correspondingly more complex. There is a paucity of effective methods available for sampling the vast objective surfaces associated with complex multiparameter models while at the same time maintaining the accuracy needed for local evaluation of minima-all in a practical time period. We have developed a series of modifications to the curvilinear gradient method for parameter optimization. We demonstrate the power and efficiency of our routine through fitting of a 22 parameter Markov state model to an electrophysiological recording of a cardiac ion channel. Our method efficiently and accurately locates parameter minima which would not be easily identified using the currently available means. While the computational overhead involved in implementing the curvilinear gradient method may have contributed to resistance to adopting this technique, the performance improvements allowed by our modifications make this an extremely valuable tool in development of models of complex biological systems.