| Abstract: | ABSTRACT: BACKGROUND: Ordinary differential equations are widely-used in the field of systems biology andchemical engineering to model chemical reaction networks. Numerous techniques havebeen developed to estimate parameters like rate constants, initial conditions or steady stateconcentrations from time-resolved data. In contrast to this countable set of parameters, theestimation of entire courses of network components corresponds to an innumerable set ofparameters. RESULTS: The approach presented in this work is able to deal with course estimation for extrinsicsystem inputs or intrinsic reactants, both not being constrained by the reaction networkitself. Our method is based on variational calculus which is carried out analytically toderive an augmented system of differential equations including the unconstrainedcomponents as ordinary state variables. Finally, conventional parameter estimation isapplied to the augmented system resulting in a combined estimation of courses andparameters. CONCLUSIONS: The combined estimation approach takes the uncertainty in input courses correctly intoaccount. This leads to precise parameter estimates and correct confidence intervals. Inparticular this implies that small motifs of large reaction networks can be analysedindependently of the rest. By the use of variational methods, elements from control theoryand statistics are combined allowing for future transfer of methods between the two fields. |
