Challenges in lin-log modelling of glycolysis in Lactococcus lactis

The performance of the lin-log method for modelling the glycolytic pathway in Lactococcus lactis using in vivo time-series data is investigated. The network structure of this pathway has been studied in previous reports and the authors concentrate here on the challenge of fitting the lin- log model parameters to experimental data. To calibrate the estimation methods, the performance of the lin-log method on a simpler model of a small gene regulatory system was first investigated, which has become a benchmark in the field. Two families of optimisation algorithms were employed. One computes the objective function by solving a system of ordinary differential equations (ODEs), whereas the other discretises the ODEs and incorporates them as nonlinear equality constraints in the optimisation problem. Gradient-based, simplex-based and stochastic search algorithms were used to solve the former, whereas only a gradient-based algorithm was used to solve the latter. Although the estimation methods succeeded in determining the parameter values for the small gene network model, they did not yield a satisfactory lin- log model for the glycolytic pathway. The main reasons are apparently that several system variables approach low, and ultimately zero concentrations, which are intrinsically problematic for lin- log models, and that this pathway does not offer a natural non-zero reference state.