An algorithmic method for reducing conductance-based neuron models

Decoding complex biological networks - tracing essential and modulatory parameters in complex and simplified models of the cell cycle

Background

One of the most well described cellular processes is the cell cycle, governing cell division. Mathematical models of this gene-protein network are therefore a good test case for assessing to what extent we can dissect the relationship between model parameters and system dynamics. Here we combine two strategies to enable an exploration of parameter space in relation to model output. A simplified, piecewise linear approximation of the original model is combined with a sensitivity analysis of the same system, to obtain and validate analytical expressions describing the dynamical role of different model parameters.

Results

We considered two different output responses to parameter perturbations. One was qualitative and described whether the system was still working, i.e. whether there were oscillations. We call parameters that correspond to such qualitative change in system response essential. The other response pattern was quantitative and measured changes in cell size, corresponding to perturbations of modulatory parameters. Analytical predictions from the simplified model concerning the impact of different parameters were compared to a sensitivity analysis of the original model, thus evaluating the predictions from the simplified model. The comparison showed that the predictions on essential and modulatory parameters were satisfactory for small perturbations, but more discrepancies were seen for larger perturbations. Furthermore, for this particular cell cycle model, we found that most parameters were either essential or modulatory. Essential parameters required large perturbations for identification, whereas modulatory parameters were more easily identified with small perturbations. Finally, we used the simplified model to make predictions on critical combinations of parameter perturbations.

Conclusions

The parameter characterizations of the simplified model are in large consistent with the original model and the simplified model can give predictions on critical combinations of parameter perturbations. We believe that the distinction between essential and modulatory perturbation responses will be of use for sensitivity analysis, and in discussions of robustness and during the model simplification process.

Functional consequences of model complexity in rhythmic systems: I. Systematic reduction of a bursting neuron model

Neural models are increasingly being used as design components of physical systems. In order to most effectively utilize neuronal models in these novel contexts, we need to develop design rules for neuronal systems that relate how model design affects overall system performance. In this paper and a companion article, we investigate how the complexity of a neural model affects the performance of a two-cell oscillator built from the model. In this paper, we create a series of related neuron models with different mathematical complexity. Starting with a complex mechanistic model of a bursting neuron, we use a variety of techniques to create a series of simplified neuron models. These three reduced models produce bursting activity that is qualitatively very similar to the original model. In the following companion article, we investigate the functional performance of oscillators built from these models.