Bounding Mean First Passage Times in Population Continuous-Time Markov Chains

Backenköhler, Michael; Bortolussi, Luca; Wolf, Verena

doi:10.1007/978-3-030-59854-9_13

Cited by 8 publications

(7 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, it has become increasingly popular to study probabilities or timing of cellular events, for instance by calculating the waiting time distribution for a certain protein in the cell to reach a particular threshold level given some initial amount of protein [35][36][37] .…”

Section: Please Cite This Article Asmentioning

confidence: 99%

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Ruess,

Ballif,

Aditya

2023

The Journal of Chemical Physics

View full text Add to dashboard Cite

Stochastic chemical kinetics is a widely used formalism for studying stochasticity of chemical reactions inside single cells. Experimental studies of reaction networks are generally performed with cells that are part of a growing population, yet the population context is rarely taken into account when models are developed. Models that neglect the population context lose their validity whenever the studied system influences traits of cells that can be selected in the population, a property that naturally arises in the complex interplay between single-cell and population dynamics of cell fate decision systems. Here, we represent such systems as absorbing continuous-time Markov chains. We show that conditioning on non-absorption allows one to derive a modified master equation that tracks the time evolution of the expected population composition within a growing population. This allows us to derive consistent population dynamics models from a specification of the single-cell process. We use this approach to classify cell fate decision systems into two types that lead to different characteristic phases in emerging population dynamics. Subsequently, we deploy the gained insights to experimentally study a recurrent problem in biology: how to link plasmid copy number fluctuations and plasmid loss events inside single cells to growth of cell populations in dynamically changing environments.

show abstract

Section: Please Cite This Article Asmentioning

confidence: 99%

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Ruess,

Ballif,

Aditya

2023

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…Approaches for first-passage times are often of heuristic nature [42,22,8]. Rigorous approaches yielding guaranteed bounds are currently limited by the performance of state-of-the-art optimization software [6]. In biological applications, rare events of interest are typically related to the reachability of certain thresholds on molecule counts or mode switching [45].…”

Section: Related Workmentioning

confidence: 99%

Analysis of Markov Jump Processes under Terminal Constraints

Backenköhler

Bortolussi

Großmann

et al. 2021

Tools and Algorithms for the Construction and Analysis of Systems

Self Cite

View full text Add to dashboard Cite

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method’s applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.

show abstract

“…Even in simple models such as a birth-death Process (Model 1), the reachable state-space is countably infinite. Direct analyzes of backward (6) and forward equations (4) are often infeasible. Instead, the integration of these differential equations requires working with a finite subset of the infinite state-space [37].…”

Section: Finite State Projectionmentioning

confidence: 99%

Analysis of Markov Jump Processes under Terminal Constraints

Backenköhler

Bortolussi

Großmann

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method's applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.

show abstract

Bounding Mean First Passage Times in Population Continuous-Time Markov Chains

Cited by 8 publications

References 46 publications

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Stochastic chemical kinetics of cell fate decision systems: From single cells to populations and back

Analysis of Markov Jump Processes under Terminal Constraints

Analysis of Markov Jump Processes under Terminal Constraints

Contact Info

Product

Resources

About