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Assessing uncertainty in model parameters based on sparse and noisy experimental data.

ABSTRACT: To perform parametric identification of mathematical models of biological events, experimental data are rare to be sufficient to estimate target behaviors produced by complex non-linear systems. We performed parameter fitting to a cell cycle model with experimental data as an in silico experiment. We calibrated model parameters with the generalized least squares method with randomized initial values and checked local and global sensitivity of the model. Sensitivity analyses showed that parameter optimization induced less sensitivity except for those related to the metabolism of the transcription factors c-Myc and E2F, which are required to overcome a restriction point (R-point). We performed bifurcation analyses with the optimized parameters and found the bimodality was lost. This result suggests that accumulation of c-Myc and E2F induced dysfunction of R-point. We performed a second parameter optimization based on the results of sensitivity analyses and incorporating additional derived from recent in vivo data. This optimization returned the bimodal characteristics of the model with a narrower range of hysteresis than the original. This result suggests that the optimized model can more easily go through R-point and come back to the gap phase after once having overcome it. Two parameter space analyses showed metabolism of c-Myc is transformed as it can allow cell bimodal behavior with weak stimuli of growth factors. This result is compatible with the character of the cell line used in our experiments. At the same time, Rb, an inhibitor of E2F, can allow cell bimodal behavior with only a limited range of stimuli when it is activated, but with a wider range of stimuli when it is inactive. These results provide two insights; biologically, the two transcription factors play an essential role in malignant cells to overcome R-point with weaker growth factor stimuli, and theoretically, sparse time-course data can be used to change a model to a biologically expected state.

SUBMITTER: Hiroi N

PROVIDER: S-EPMC3983526 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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Assessing uncertainty in model parameters based on sparse and noisy experimental data.

Hiroi Noriko N Swat Maciej M Funahashi Akira A

Frontiers in physiology 20140404

To perform parametric identification of mathematical models of biological events, experimental data are rare to be sufficient to estimate target behaviors produced by complex non-linear systems. We performed parameter fitting to a cell cycle model with experimental data as an in silico experiment. We calibrated model parameters with the generalized least squares method with randomized initial values and checked local and global sensitivity of the model. Sensitivity analyses showed that parameter ...[more]

PMID: 24772089

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Project description:Tuning curves are the functions that relate the responses of sensory neurons to various values within one continuous stimulus dimension (such as the orientation of a bar in the visual domain or the frequency of a tone in the auditory domain). They are commonly determined by fitting a model e.g. a Gaussian or other bell-shaped curves to the measured responses to a small subset of discrete stimuli in the relevant dimension. However, as neuronal responses are irregular and experimental measurements noisy, it is often difficult to determine reliably the appropriate model from the data. We illustrate this general problem by fitting diverse models to representative recordings from area MT in rhesus monkey visual cortex during multiple attentional tasks involving complex composite stimuli. We find that all models can be well-fitted, that the best model generally varies between neurons and that statistical comparisons between neuronal responses across different experimental conditions are affected quantitatively and qualitatively by specific model choices. As a robust alternative to an often arbitrary model selection, we introduce a model-free approach, in which features of interest are extracted directly from the measured response data without the need of fitting any model. In our attentional datasets, we demonstrate that data-driven methods provide descriptions of tuning curve features such as preferred stimulus direction or attentional gain modulations which are in agreement with fit-based approaches when a good fit exists. Furthermore, these methods naturally extend to the frequent cases of uncertain model selection. We show that model-free approaches can identify attentional modulation patterns, such as general alterations of the irregular shape of tuning curves, which cannot be captured by fitting stereotyped conventional models. Finally, by comparing datasets across different conditions, we demonstrate effects of attention that are cell- and even stimulus-specific. Based on these proofs-of-concept, we conclude that our data-driven methods can reliably extract relevant tuning information from neuronal recordings, including cells whose seemingly haphazard response curves defy conventional fitting approaches.

Dataset Information

Assessing uncertainty in model parameters based on sparse and noisy experimental data.

Publications

Assessing uncertainty in model parameters based on sparse and noisy experimental data.

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