Accounting for randomness in measurement and sampling in studying cancer cell population dynamics

Siavash Ghavami; Olaf Wolkenhauer; Farshad Lahouti; Mukhtar Ullah; Michael Linnebacher

Accounting for randomness in measurement and sampling in studying cancer cell population dynamics

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Author(s): Siavash Ghavami ^{1, 2} ; Olaf Wolkenhauer ^{2, 3} ; Farshad Lahouti ¹ ; Mukhtar Ullah ² ; Michael Linnebacher ⁴
- Affiliations: 1: Center for Wireless Multimedia Communications, Center of Excellence in Applied Electromagnetic Systems, School of Electrical & Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran;
  2: Department of Systems Biology and Bioinformatics, University of Rostock, Rostock, Germany;
  3: Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre at Stellenbosch University, Stellenbosch, South Africa;
  4: Department of General, Thoracic, Vascular and Transplantation Surgery, University of Rostock, Rostock, Germany
Source: Volume 8, Issue 5, October 2014, p. 230 – 241
DOI: 10.1049/iet-syb.2013.0031 , Print ISSN 1751-8849, Online ISSN 1751-8857

Received 01/10/2013, Accepted 27/01/2014, Revised 22/12/2013, Published 17/03/2014

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.

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