A Constrained Mixed Effects Model Based on Semi-Linear Deferential Equation for Cell Polarity Signaling in Tip Growth of Pollen Tubes

• Activity Number: 231
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Zhen Xiao*+
• Companies: University of California, Riverside
• Keywords: Constrained Maximum Likelihood ; Mixed model ; Semi linear Differential Equation ; Integro-Differential EquationIntegro-Differential Equation ; Cell Polarity ; Tip Growth

Abstract

The key of tip growth in eukaryotes is the polarized distribution on plasma membrane of a particle named ROP1. This distribution is a result of a positive feedback loop, whose mechanism can be described by a Integro-Differential Equation parametrized by two meaningful parameters knf and kpf. In this presentation, we first provided an existence and uniqueness result for the solution of our IDE model under certain conditions. Quite interestingly, this analysis gives a tractable expression for the likelihood, and our approach can be seen as the estimation of a constrained nonlinear model. Moreover, we introduced a population variability by introducing a constrained nonlinear mixed model. We then proposed a Constrained Nonlinear Least Square method to fit the model under single subject, and two methods, Constrained Method of Moments and Constrained Restricted Maximum Likelihood to fit the model under multiple subjects case. The asymptotic results of these three methods were also be discussed. The performances of the three methods were studied in a simulation example and a real multiple subjects dataset.