[Paper Review] Parameter inference method for stochastic single-cell dynamics from tree-structured data

Irena Kuzmanovska, Andreas Milias‐Argeitis+2 more|arXiv (Cornell University)|May 18, 2016

Gene Regulatory Network Analysis16 references3 citations

TL;DR

This paper proposes a Bayesian parameter inference framework for stochastic single-cell dynamics using tree-structured lineage data from time-lapse microscopy. By combining Sequential Monte Carlo for likelihood approximation and Markov Chain Monte Carlo for posterior sampling, the method leverages mother-daughter correlations to improve parameter estimation—especially for slow-switching or division-dependent processes—where independent trajectory analysis fails due to limited temporal information.

ABSTRACT

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. However, most of the currently available methods treat single-cell trajectories independently, ignoring the mother-daughter relationships and the information provided by population structure. This information is however essential if a process of interest happens at cell division, or if it evolves slowly compared to the duration of the cell cycle. In this work, we highlight the importance of tracking cell lineage trees and propose a Bayesian framework for parameter inference on tree-structured data. Our method relies on a combination of Sequential Monte Carlo for likelihood approximation and Markov Chain Monte Carlo for parameter sampling. We demonstrate the capabilities of our inference framework on two simple examples in which the lineage tree information is necessary: one in which the cell phenotype can only switch at cell division and another where the cell type fluctuates randomly over timescales that extend well beyond the lifetime of a single cell.

Motivation & Objective

• Address the limitation of existing methods that treat single-cell trajectories as independent, ignoring lineage information.
• Develop a parameter inference framework that explicitly incorporates tree-structured data from time-lapse microscopy to improve accuracy in stochastic systems.
• Enable reliable inference for processes that switch only at cell division or evolve on timescales comparable to or longer than the cell cycle.
• Overcome the bias and uncertainty in parameter estimates when switching rates are low and data per cell is limited.
• Provide a scalable and generalizable method applicable to complex systems such as bacterial phenotype switching and stem cell fate decisions.

Proposed method

• Formulate the inference problem using a continuous-time stochastic model with hidden internal states and fluorescent reporter readouts.
• Use Sequential Monte Carlo (SMC) to recursively approximate the intractable likelihood by marginalizing over unobserved state trajectories.
• Apply Markov Chain Monte Carlo (MCMC) to sample from the posterior distribution of system parameters, even with noisy SMC-based likelihood estimates.
• Incorporate lineage structure by propagating posterior distributions of mother cells as priors for daughter cells, reducing uncertainty in initial conditions.
• Handle variable cell cycle durations and irregular measurement times across the tree by modeling each cell’s trajectory with its own time index and division time.
• Ensure convergence to the correct posterior by using MCMC with a likelihood estimator that is consistent despite statistical noise.

Experimental results

Research questions

• RQ1 Can lineage information in tree-structured single-cell data significantly improve parameter inference for stochastic biochemical processes?
• RQ2 How does incorporating mother-daughter correlations affect the accuracy and uncertainty of parameter estimates in systems with slow switching dynamics?
• RQ3 To what extent does the proposed method outperform independent trajectory analysis when switching events are rare or occur only at cell division?
• RQ4 How does the method handle variable cell cycle durations and irregular measurement times in real experimental data?
• RQ5 What is the impact of lineage structure on the estimation of switching rates in Markovian processes with long holding times?

Key findings

• The method successfully infers parameters of stochastic systems using tree-structured data, achieving accurate posterior estimates even when switching rates are low.
• Inference based on independent trajectories underestimates low switching rates because each cell’s history is limited to its own lifetime, while lineage data provides longer effective observation windows.
• The posterior uncertainty for initial conditions is significantly reduced in the tree-based approach, as daughter cells inherit state distributions from their mothers.
• For systems with fast switching (mean holding times comparable to or shorter than cell cycle), both tree-structured and independent trajectory methods yield similar performance.
• The framework enables accurate inference in systems where switching is triggered by DNA replication at division, such as epigenetic regulation in E. coli and Salmonella.
• The method is generalizable to complex models, though computational cost increases with state and parameter dimensionality, requiring more particles in SMC for accurate likelihood estimation.