Concept maps and canonical models in neuropsychiatry.

Most bioscientists engage in informal modelling in their research and explicitly document this activity's results in diagrams or "concept maps". While canonical modelling approaches such as Biochemical Systems Theory (BST) immediately allow the construction of a corresponding system of equations, the problem of determining appropriate parameter values remains. Goel et al. introduced Concept Map Modelling (CMM) as a framework to address this problem through an interactive dialogue between experimenters and modellers. The CMM dialogue extracts the experimenters' implicit knowledge about dynamical behaviour of the parts of the system being modelled in form of rough sketches and verbal statements, e.g. value ranges. These are then used as inputs for parameter and initial value estimates for the symbolic canonical model based on the diagram. Canonical models have the big advantage that a great variety of parameter estimation methods have been developed for them in recent years. The paper discusses the suitability of this approach for neuropsychiatry using recent work of Qi et al. on a canonical model of presynaptic dopamine metabolism. Due to the complexity of systems encountered in neuropsychiatry, hybrid models are often used to complement the canonical models discussed here.

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. [Includes supplementary material.].

Modelling the CheY(D10K,Yl00W) Halobacterium salinarum mutant: sensitivity analysis allows choice of parameter to be modified in the phototaxis model.

A recent phototaxis model of Halobacterium salinarum composed of the signalling pathway and the switch complex of the motor explained all considered experimental data on spontaneous switching and response time to repellent or attractant light stimuli. However, the model which considers symmetric processes in the clockwise and counter-clockwise rotations of the motor cannot explain the behaviour of a CheY(D10K,Yl00W) mutant which always moves forward and does not respond to light. We show that the introduction of asymmetry in the motor switch model can explain this behaviour. Sensitivity analysis allowed us to choose parameters for which the model is sensitive and whose values we then change in either direction to obtain an asymmetric model. We also demonstrate numerically that at low concentrations of CheYP, the symmetric and asymmetric models behave similarly, but at high concentrations, differences in the clockwise and counter-clockwise modes become apparent. Thus, those experimental data that could previously be explained only by ad hoc assumptions are now obtained 'naturally' from the revised model.