Analysis of Mitotic Spindle Mathematical Model Sensitivity using Monte Carlo Simulation (2013)

Undergraduates: Patrick Short, Dr. Greg Forest, Dr. Paula Vasquez, Dr. Kerry Bloom Ying Zhou, Kelly Brannigan

Faculty Advisor: Greg Forest
Department: Mathematics

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Mathematical models serve as incredibly powerful tools that provide insight into the mathematical underpinnings of a system as well as offer the opportunity to tweak parameters, fit to data, or predict real experimental results. The robustness of a mathematical model depends not only on its ability to fit to experimental data and serve as a virtual laboratory for in silico experiments, but also on the way it responds to changes in input parameters. Using an existing mathematical model of the mitotic spindle in metaphase from Stephens et al [JCB 2013], we perform a sensitivity analysis first varying input parameters independently, and then using a Monte Carlo simulation approach coupled with principle component analysis to determine the effect on system variation from each of the sensitive parameters. Our analysis identified 10 of the 14 model input parameters to be sensitive, defined as a variation of more than 10% from the expected output value over an order of magnitude variation about the model¿s default input value. The Monte Carlo simulation coupled with PCA revealed that one system input, the number of molecular motors, accounted for nearly 97.5% of the system variation. These results have important implications for parameter input¿highly sensitive variables must have their values confirmed by experimental evidence. Likewise, if a model is able to robustly predict experimental outcome, much can be learned from the input value of highly sensitive parameters.