Parameter inference for stochastic single-cell dynamics from lineage tree data

Kuzmanovska et al. BMC Systems Biology (2017) 11:52 DOI 10.1186/s12918-017-0425-1 METHODOLOGY ARTICLE Open Access Parameter inference for stochastic single-cell dynamics from lineage tree data Irena Kuzmanovska1 , Andreas Milias-Argeitis1,2 , Jan Mikelson1 , Christoph Zechner1,3 and Mustafa Khammash1* Abstract Background: With the advance of experimental techniques such as time-lapse fluorescence microscopy, the availability of single-cell trajectory data has vastly increased, and so has the demand for computational methods suitable for parameter inference with this type of data. Most of currently available methods treat single-cell trajectories independently, ignoring the mother-daughter relationships and the information provided by the population structure. However, this information is essential if a process of interest happens at cell division, or if it evolves slowly compared to the duration of the cell cycle. Results: In this work, we propose a Bayesian framework for parameter inference on single-cell time-lapse data from lineage trees. Our method relies on a combination of Sequential Monte Carlo for approximating the parameter likelihood function and Markov Chain Monte Carlo for parameter exploration. We demonstrate our inference framework on two simple examples in which the lineage tree information is crucial: one in which the cell phenotype can only switch at cell division and another where the cell state fluctuates slowly over timescales that extend well beyond the cell-cycle duration. Conclusion: There exist several examples of biological processes, such as stem cell fate decisions or epigenetically controlled phase variation in bacteria, where the cell ancestry is expected to contain important information about the underlying system dynamics. Parameter inference methods that discard this information are expected to perform poorly for such type of processes. Our method provides a simple and computationally efficient way to take into account single-cell lineage tree data for the purpose of parameter inference and serves as a starting point for the development of more sophisticated and powerful approaches in the future. Keywords: Parameter inference, Cell lineages, Single cell, Stochastic systems, Monte Carlo methods Background Biochemical processes in isogenic cells exhibit substantial heterogeneity [1, 2]. Understanding the latter demands experimental techniques that can resolve such processes at the single-cell level. In contrast to bulk measurements, these techniques provide not only access to the average behavior of intracellular dynamics, but also its variability across cells and over time. Most single-cell techniques, however, reveal only very few components simultaneously that are often multiple steps away from the actual quantities of interest. The dynamics of a promoter, for instance, *Correspondence: Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland Full list of author information is available at the end of the article 1 may not be accessible directly, but only indirectly through a fluorescent reporter that is expressed upon activation of this promoter [3]. Statistical inference in combination with mathematical models provide a means to reconstruct inaccessible parameters from available measurements, making them instrumental for studying biochemical processes based on single-cell data. How such inference can be performed depends strongly on the way the data has been collected: flow cytometry measurements, for instance, reveal fluorescence values across a population but individual cells cannot be tracked over time. Consequently, measurements at two different time instances are considered statistically independent. Time-lapse microscopy techniques permit tracking of single-cell trajectories over the duration of a whole experiment [4], which in turn provides a handle also on the © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Kuzmanovska et al. BMC Systems Biology (2017) 11:52 temporal correlation of the underlying process. This additional degree of information can dramatically improve the inference of unknown process parameters [5]. Most existing inference approaches consider single-cell trajectories to be statistically independent of each other [3, 5–7]. This way, however, important information stemming from the ancestry of a cell is lost: shortly after cell division, for example, two daughter cells are likely to exhibit substantial correlations, which cannot be captured by a model that assumes independence among cells. This can yield incomplete and biased results, especially when the time scale of the process under study is slow compared with the cell cycle duration. In addition, stochastic processes of interest such as epigenetically regulated phase variation in bacteria are often driven by DNA replication just before cell division. Examples in this category are the regulation of agn43 [8, 9] and Pap [10, 11] systems in E.coli, and the glucosyltransferase (gtr) gene cluster in Salmonella [12]. Due to the non-reversibility of the epigenetic modifications, gene replication (and consequently cell division) is crucial for phase variation to happen. Cell lineage information has to be therefore taken into account in single-cell studies of these systems. Until recently, there existed little work on statistical inference using tree-based single-cell data. In [13], the authors proposed a method for parameter inference from single-cell trajectories based on Approximate Bayesian Computation (ABC). Their approach is applicable to treestructured data as well, although it requires all trajectories to have the same length and sampling resolution. In [14] the authors proposed an observer-based method for state and parameter estimation in stochastic chemical reaction networks, which is also able to handle lineage tree data. However, its applicability is limited to small systems since it requires the full probability distributions from the solution of the chemical master equation. Another alternative was proposed in [15], which presented an inference algorithm for Hidden Markov Trees using variational Bayesian Expectation Maximization. This class of models is similar to the one considered here, but cannot incorporate dynamic readouts or dynamically evolving single-cell states. In more recent work, the authors of [16] presented a method for inferring tra (...truncated)