Reconstructing dynamic molecular states from single-cell time series.
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.
Institute of Molecular Systems Biology, D-BIOL, ETH Zurich, Zurich, Switzerland.
Lirong
0000-0002-6441-3918
L
Huang
Laboratoire de Recherche en Informatique, Université Paris-Sud, Orsay, France.
Loic
L
Pauleve
Department of Biosystems Science and Engineering, ETH Zurich, Zurich, Switzerland.
Christoph
C
Zechner
Institute of Biochemistry, ETH Zurich, Zurich, Switzerland.
Michael
M
Unger
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA.
Anders S
0000-0001-7540-7858
AS
Hansen
Department of Electrical Engineering and Information Technology, Technische Universität Darmstadt, Darmstadt, Germany Department of Biology, Technische Universität Darmstadt, Darmstadt, Germany heinz.koeppl@bcs.tu-darmstadt.de.
Heinz
H
Koeppl
D015966:Gene Expression Regulation, Fungal / Q000502:physiology*; D008390:Markov Chains; D008954:Models, Biological; D011401:Promoter Regions, Genetic / Q000502:physiology*; D012331:RNA, Fungal / Q000096:biosynthesis*; D012333:RNA, Messenger / Q000096:biosynthesis*; D012441:Saccharomyces cerevisiae / Q000166:cytology / Q000378:metabolism*
D012331:RNA, Fungal; D012333:RNA, Messenger
chemical master equation; continuous time Markov chains; gene expression; moment dynamics; optimal filtering