Reconstructing dynamic molecular states from single-cell time series

• Published in: Journal of the Royal Society interface Vol. 13; no. 122; p. 20160533
• Main Authors: Huang, Lirong, Pauleve, Loic, Zechner, Christoph, Unger, Michael, Hansen, Anders S., Koeppl, Heinz
• Format: Journal Article
• Language: English
• Published: England The Royal Society 01.09.2016; the Royal Society
• Subjects: Bioinformatics; Chemical Master Equation; Computer Science; Continuous Time Markov Chains; Dynamical Systems; Gene Expression; Gene Expression Regulation, Fungal - physiology; Life Sciences–Mathematics interface; Markov Chains; Mathematics; Models, Biological; Moment Dynamics; Optimal Filtering; Promoter Regions, Genetic - physiology; RNA, Fungal - biosynthesis; RNA, Messenger - biosynthesis; Saccharomyces cerevisiae - cytology; Saccharomyces cerevisiae - metabolism; Systems and Control; chemical master equation; optimal filtering; moment dynamics; gene expression; continuous time Markov chains; continuous-time Markov chains; Optimal filtering
• ISSN: 1742-5689; 1742-5662
• DOI: 10.1098/rsif.2016.0533

The notion of state for a system is prevalent in the quantitative sciences and refers to the minimal system summary sufficient to describe the time evolution of the system in a self-consistent manner. This is a prerequisite for a principled understanding of the inner workings of a system. Owing to the complexity of intracellular processes, experimental techniques that can retrieve a sufficient summary are beyond our reach. For the case of stochastic biomolecular reaction networks, we show how to convert the partial state information accessible by experimental techniques into a full system state using mathematical analysis together with a computational model. This is intimately related to the notion of conditional Markov processes and we introduce the posterior master equation and derive novel approximations to the corresponding infinite-dimensional posterior moment dynamics. We exemplify this state reconstruction approach using both in silico data and single-cell data from two gene expression systems in Saccharomyces cerevisiae, where we reconstruct the dynamic promoter and mRNA states from noisy protein abundance measurements.