Sajad Shafiekhani - Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences- Research Center for Biomedical Technologies and Robotics, Tehran University of Medical Sciences - ۳Students’ Scientific Research Center, Tehran University of
Mojtaba Shafiekhani - Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran
Sara Rahbar - Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences- Research Center for Biomedical Technologies and Robotics, Tehran University of Medical Sciences
Amir Homayoun Jafari - Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences- Research Center for Biomedical Technologies and Robotics, Tehran University of Medical Sciences

Background: How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling. Methods: We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G۱, S, G۲, M, and stationary G۱. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable. Results: Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G۱ increased from ۸۶% to ۹۶.۴۸% while the number of attractors decreased from ۷ in the original model to ۵ in the extended one. Hence, an increase in the robustness of the system has been achieved. Conclusion: The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.

Boolean network, budding yeast cell cycle, genetic algorithm, Markov chain model