Related Experiment Video
Updated: Aug 11, 2026

Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
Published on: April 27, 2021
Efficient computation of the first passage time distribution of the generalized master equation by steady-state
David Shalloway1, Anton K Faradjian
1Biophysics Program, Department of Molecular Biology and Genetics, Cornell University, Ithaca, New York 14853, USA. dis2@cornell.edu
Abstract:
The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a gamma distribution or rational function approximation to its Laplace transform.
Related Concept Videos
Reaction Mechanisms: The Steady-State Approximation
Atomic Nuclei: Types of Nuclear Relaxation
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
Fast Reactions
First Order Systems
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Standard Entropy Change for a Reaction
One-Compartment Open Model for Extravascular Administration: First-Order Absorption Model
