- 4:45 PM

Stochastic Simulation and Systems Analysis of Insulin-Stimulated GLUT4 Translocation

Eric C. Kwei1, Kevin R. Sanft2, Jason E. Shoemaker1, Linda R. Petzold2, and Francis J. Doyle III1. (1) Department of Chemical Engineering, University of California, Santa Barbara, Santa Barbara, CA 93106-5080, (2) Department of Computer Science, University of California, Santa Barbara, Santa Barbara, CA 93106-5070

The estimated number of people in the US with diagnosed diabetes has more than doubled in the last 15 years to 14.6 million, with associated annual medical costs of $174 billion; type 2 diabetes mellitus (T2DM) represents 90 to 95% of these cases [1].

T2DM is characterized by insulin resistance, which has been linked to defects in the insulin signaling pathway. Analysis of detailed mathematical models of insulin signaling should yield a better understanding of the underlying mechanisms of insulin resistance and its subsequent progression to T2DM. This may be very relevant for maximizing treatment efficacy and minimizing side effects, which can ultimately improve the quality of life for those who suffer from T2DM.

We have brought a variety of engineering tools, including stochastic modeling, parameter sensitivity analysis, and robust performance analysis, to bear on an existing insulin signaling model [2]. This differential equation model, based largely on mass action kinetics, describes the mechanisms in adipocytes (fat cells) that transduce an insulin input signal to movement of GLUT4, a glucose transporter responsible for glucose uptake, to the cell surface.

The precision of a deterministic model fitted to data depends on measurement precision, which is limited by, among other factors, stochastic fluctuation magnitude. Because modern experimental methods can quantify the dynamic response of single target cells to insulin, we became interested in establishing if a deterministic model can completely describe such a system. Upon scaling the model for typical adipocyte cell volumes, conversion to molecule counts revealed that several model species were present in small numbers (O(1) in some instances). When such small populations are involved, stochastic fluctuations may have significant effects on system behavior. To investigate, we developed and simulated a stochastic version of this model.

Significant fluctuations from the deterministic results were observed at cell-scale volumes for a number of states. For an average adipocyte volume, 10% peak fluctuations are observed for cell-surface GLUT4. Fluctuations in surface GLUT4 are fairly sensitive to the system volume parameter, changing from 40% to less than 5% over a range of two orders of magnitude in system volume. These simulations provide insight into the inherent fluctuations in system behavior and highlight potential areas for improvement on the model.

Because experimental measurements can be sparse in biological systems, it is vital to develop an experimental design that can maximize the amount of information about model parameter values from limited data. Towards this goal we developed an optimized experimental design with parameter sensitivity analysis.

The Fisher information matrix (FIM) was used to predict the maximum accuracy of parameter estimation for a model using parameter sensitivities and estimates of state measurement error (using our simulated stochastic variances) [3]. With the FIM, we minimized the standard deviation of model parameter estimates by varying the insulin input profile and the choice of measured states. Using an optimized input profile (1-minute insulin pulse at 1E-7 M) and measured state selection (4 out of a possible 21 states in the model), an ideal parameter estimator can identify 21 of 31 model parameters with 95% confidence.

With our insights to the insulin signaling model from stochastic modeling and sensitivity analysis, we performed a structured singular value (SSV) analysis. This SSV analysis quantifies the range of fluctuation a set of parameters can tolerate while maintaining robust insulin signaling; this allows us to identify cellular targets suitable for single or multi-drug therapies that maximally manipulate sensitivity of GLUT4 response to insulin while minimizing impact on signaling components possibly shared with other pathways [4]. Furthermore, SSV analysis of the deterministic system provides fundamental insight into the state distributions observed in the stochastic regime and reveals that distributions in cell-surface GLUT4 levels observed can be well bounded by the deterministic model if suitable variation in the most sensitive parameters, including stochastic system volume, is allowed.

For this system, one set of performance criteria include maximizing insulin sensitivity of GLUT4 translocation while minimizing impact on Akt (a protein kinase upstream of GLUT4) because Akt is shared with several other signaling pathways. Early results indicate that GLUT4 translocation is sensitive to parameter perturbation in receptor recycling, while Akt phosphorylation is relatively robust to these perturbations.

1. Centers for Disease Control and Prevention, Diabetes: Disabling Disease to Double by 2050. 2008.

2. Sedaghat, A.R., A. Sherman, and M.J. Quon, A mathematical model of metabolic insulin signaling pathways. American Journal of Physiology-Endocrinology and Metabolism, 2002. 283(5): p. E1084-E1101.

3. Zak, D.E., et al., Importance of input perturbations and stochastic gene expression in the reverse engineering of genetic regulatory networks: Insights from an identifiability analysis of an in silico network. Genome Research, 2003. 13(11): p. 2396-2405.

4. Doyle, J., Analysis of Feedback-Systems with Structured Uncertainties. IEE Proceedings-D Control Theory and Applications, 1982. 129(6): p. 242-250.