Redemption: Reduced dimensional ensemble modeling and parameter estimation

The creation of kinetic ordinary differential equation (ODE) models of biological networks is often hampered by imprecise knowledge of reaction rate equations and their associated parameters. The model is generally written as: dX/dt = Sv(x,p) (1) where X is the vector of species concentrations, S is the stoichiometric matrix, v(X,p) is the vector of rate equations, and p is the vector of kinetic parameters. Here, the estimation of unknown kinetic parameters from time-series concentration data frequently becomes the bottlenecking step in the model building, motivating the development of a large number of methods [1]. Existing methods can generally be divided into two groups: integral and differential approach, based on whether or not the ODE model is integrated during the estimation. In the integral approach, the parameter estimation is formulated as a constrained optimization to minimize model prediction error. Meanwhile, the differential approach involves a pre-processing step, in which the time-series data are smoothen and differentiated to give estimates of dX/dt and Eq (1) is then used to compute dynamic reaction flux estimates v. Afterwards, the parameters are estimated by minimizing flux prediction errors. The main advantage of the differential over the integral approach is computational speed, as the ODEs need not be integrated and the parameter estimation can be done one flux at a time. However, the differential approach is known to give biased parameter estimates, and the parameter accuracy is sensitive to the data-smoothing step.