Hybrid Dynamic Optimization Methods for Systems Biology with Efficient Sensitivities

Abstract

Abstract:In recent years, model optimization in the field of computational biology has become a prominent area for development of pharmaceutical drugs. The increased amount of experimental data leads to the increase in complexity of proposed models. With increased complexity comes a necessity for computational algorithms that are able to handle the large datasets that are used to fit model parameters. In this study the ability of simultaneous, hybrid simultaneous, and sequential algorithms are tested on two models representative of computational systems biology. The first case models the cells affected by a virus in a population and serves as a benchmark model for the proposed hybrid algorithm. The second model is the ErbB model and shows the ability of the hybrid sequential and simultaneous method to solve large-scale biological models. Post-processing analysis reveals insights into the model formulation that are important for understanding the specific parameter optimization. A parameter sensitivity analysis reveals shortcomings and difficulties in the ErbB model parameter optimization due to the model formulation rather than the solver capacity. Suggested methods are model reformulation to improve input-to-output model linearity, sensitivity ranking, and choice of solver.

GEKKO Optimization Suite

“…The first method is to specify an option in GEKKO (sensitivity) to generate a local sensitivity at the solution. This is performed by inverting the sparse Jacobian at the solution [44]. The second method is to perform a finite difference evaluation of the solution after the initial optimization problem is complete.…”

“…Additional example problems are shown in the back matter, with an example of an artificial neural network in Appendix A and several dynamic optimization benchmark problems shown in Appendix B. Since the GEKKO Fortran backend is the successor to APMonitor [37], the many applications of APMonitor are also possible within this framework, including recent applications in combined scheduling and control [46], industrial dynamic estimation [43], drilling automation [47,48], combined design and control [49], hybrid energy storage [50], batch distillation [51], systems biology [44], carbon capture [52], flexible printed circuit boards [53], and steam distillation of essential oils [54].…”

Model predictive automatic control of sucker rod pump system with simulation case study

“…MHE is a dynamic optimization technique that looks back at a time horizon and fits model parameters to historical data. MHE approximates uncertain parameters or variables, and performs well on systems that include large amounts of noise in the data set [37]. MHE also allows process information to be directly considered during optimization [55].…”

Optimal combined long-term facility design and short-term operational strategy for CHP capacity investments

“…DAE models are used in nonlinear predictive control and estimation applications such as industrial process fouling [73], unmanned aerial systems [74], drilling automation [75], systems biology [76], batch distillation [77], pipeline flow assurance [78] and many other applications. In a control environment, multiple objectives may be desired within a single control application.…”