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Volume 13   Issue 2   Year 2018
Markov Chain Monte Carlo Parameter Estimation of the ODE Compartmental Cell Growth Model

Tatyana Luzyanina, Gennady Bocharov

Institute of Mathematical Problems of Biology RAS – The Branch of Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Pushchino, Russian Federation
Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russian Federation

Abstract. We use a Markov chain Monte Carlo (MCMC) method to quantify uncertainty in parameters of the heterogeneous linear compartmental model of cell population growth, described by a system of ordinary differential equations. This model allows division number-dependent rates of cell proliferation and death and describes the rate of changes in the numbers of cells having undergone j divisions. The experimental data set specifies the following characteristics of the kinetics of human T lymphocyte proliferation assay in vitro: the total number of live cells and dead but not disintegrated cells and the number of cells divided j times. Our goal is to compare results of the MCMC analysis of the uncertainty in the best-fit parameter estimates with the ones obtained earlier, using the variance-covariance approach, the profile-likelihood based approach and the bootstrap technique. We show that the computed posterior probability density functions are Gaussian for most of the model parameters and they are close to Gaussian ones for other parameters except one. We present posterior uncertainty limits for the model solution and new observations.
Key words: cell population dynamics, Markov chain Monte Carlo analysis, CFSE assay, heterogenous compartmental model, parameter estimation, uncertainty.
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2018.13.376
published in English

Abstract (eng.)
Abstract (rus.)
Full text (eng., pdf)


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