Accounting for randomness in measurement and sampling in studying cancer cell population dynamics. Issue 5 (1st October 2014)

• Record Type: Journal Article
• Authors: Ghavami, Siavash; Wolkenhauer, Olaf; Lahouti, Farshad; Ullah, Mukhtar; Linnebacher, Michael
• Is Part Of: IET systems biology. Volume 8:Issue 5(2014)
• Page Start: 230
• Page End: 241
• Publication Date: 2014-10-01
• Subjects: cancer -- tumours -- cellular biophysics -- biomedical measurement -- Gaussian distribution -- maximum likelihood estimation -- mean square error methods -- hidden Markov models -- fluorescence -- random processes -- convergence of numerical methods; cancer cell population dynamics -- malignant tumours -- tissue samples -- normal tissue cells -- disease -- drugs -- Markov process -- cell population size measurement -- hidden Markov model -- noisy measurement -- state transition probability -- fluorescence‐activated cell sorting measurement -- minimum mean square error estimator -- maximum likelihood estimator -- transition probability matrix -- noise distributions -- Gaussian distributions -- MMSE -- convergence mechanism -- standard deterministic approach -- stochastic phenomena -- random variable; Systems biology -- Periodicals; Cell physiology -- Periodicals; Biological systems -- Mathematical models -- Periodicals; Genetics -- Mathematical models -- Periodicals; Computational biology -- Periodicals; 573
• DOI: 10.1049/iet-syb.2013.0031
• Languages: English
• ISSNs: 1751-8849

Abstract

Abstract : Knowing the expected temporal evolution of the proportion of different cell types in sample tissues gives an indication about the progression of the disease and its possible response to drugs. Such systems have been modelled using Markov processes. We here consider an experimentally realistic scenario in which transition probabilities are estimated from noisy cell population size measurements. Using aggregated data of FACS measurements, we develop MMSE and ML estimators and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes. Our numerical results show that the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach for noisy measurements. This provides support for our argument that for the analysis of FACS data one should consider the observed state as a random variable. The second problem we address is about the consequences of estimating the probability of a cell being in a particular state from measurements of small population of cells. We show how the uncertainty arising from small sample sizes can be captured by a distribution for the state probability.