First Passage Problems in Biology

Abstract

Applications of first passage times in stochastic processes arise across a wide range of length and time scales in biological settings. After an initial technical overview, we survey representative applications and their corresponding models. Within models that are effectively Markovian, we discuss canonical examples of first passage problems spanning applications to molecular dissociation and self-assembly, molecular search, transcription and translation, neuronal spiking, cellular mutation and disease, and organismic evolution and population dynamics. In this last application, a simple model for stem-cell ageing is presented and some results derived. Various approximation methods and the physical and mathematical subtleties that arise in the chosen applications are also discussed.

40 pages, 90 references, 10 figures

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• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Disease extinction in the presence of non-Gaussian noise
• Narrow escape and leakage of Brownian particles
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Cited by in corpus (25)

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• A hierarchical kinetic theory of birth, death, and fission in age-structured interacting populations
• Asymptotics of extreme statistics of escape time in 1,2 and 3-dimensional diffusions
• A probabilistic approach to extreme statistics of Brownian escape times in dimensions 1, 2, and 3
• Competition between slow and fast regimes for extreme first passage times of diffusion
• Temporal precision of regulated gene expression
• First hitting times to intermittent targets
• Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate
• A Unified Approach to Gated Reactions on Networks
• First passage time study of DNA strand displacement
• Dynamic Looping of a Free-Draining Polymer
• Lagrangian Manifestation of Anomalies in Active Turbulence
• Primordial Sex Facilitates the Emergence of Evolution
• First detection of threshold crossing events under intermittent sensing
• Freezing transitions of Brownian particles in confining potentials
• The narrow escape problem in a circular domain with radial piecewise constant diffusivity
• First-Passage Time Statistics on Surfaces of General Shape: Surface PDE Solvers using Generalized Moving Least Squares (GMLS)
• Exact calculation of the mean first-passage time of continuous-time random walks by nonhomogeneous Wiener-Hopf integral equations
• First-passage times in complex energy landscapes: a case study with nonmuscle myosin II assembly
• Density- and elongation speed-dependent error correction in RNA polymerization
• Mean First Passage Times for Transport Equations
• Inferring phenomenological models of first passage processes
• Slack Reactants: A State-Space Truncation Framework to Estimate Quantitative Behavior of the Chemical Master Equation
• Stochastic elastohydrodynamics of contact and coarsening during membrane adhesion
• A First-Order Gradient Approach for the Connectivity Optimization of Markov Chains