Trapping of Planar Brownian Motion: Full First Passage Time Distributions by Kinetic Monte Carlo, Asymptotic, and Boundary Integral Methods

Cherry, Jake; Lindsay, Alan E.; Hernández, Adrián Navarro; Quaife, Bryan

doi:10.1137/21m146380x

Cited by 5 publications

(22 citation statements)

References 47 publications

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“…This result is in agreement with those previously determined for steady state [45,39] quantities, but is obtained here for all dynamic modes, demonstrating that homogenization has much broader e cacy. This has been recently observed in the first passage time distribution of capture to planar absorbers [16]. 9 2.4.…”

Section: Homogenizationsupporting

confidence: 54%

“…In the previous sections we alluded to the usefulness of the dynamic fluxes to source inference. To obtain these dynamic quantities (3), we proceed by applying a "hybrid numerical-asymptotic" method [16,10] to the parabolic problem (2). The steps of this method are to first apply a Laplace transform to the underlying parabolic equation, following by matched asymptotic solution of the elliptic transform problem.…”

Section: Receptor Arrival Statisticsmentioning

confidence: 99%

“…Following the hybrid-asymptotic approach [40,16], we solve ( 18) by means of matched asymptotic expansion in the limit " ! 0 and as such, replace each absorbing site @⌦ j with the local behavior p ⇠ A j (s)⌫ j log |x x j | + A j (s) as x !…”

Section: Receptor Arrival Statisticsmentioning

confidence: 99%

“…1). The applicability of this work to a half plane scenario, which has previously been studied in source localization [17], is demonstrated in appendix D. To corroborate results from the hybrid numerical-asymptotic approach, we employ a recently developed Kinetic Monte Carlo (KMC) which can rapidly and accurately sample all relevant arrival statistics [16]. To perform inference on the source location, we develop in Sec.…”

mentioning

confidence: 92%

“…Asymptotic construction of splitting probabilities and dynamic fluxes. In this section, we obtain an asymptotic representation [29,28,16,58,8,10] of the solution of (1) and (2) as " ! 0.…”

mentioning

confidence: 99%

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Short time diffusive fluxes over membrane receptors yields the direction of a signaling source

Lindsay

Bernoff

Hernández

2023

Preprint

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An essential ability of many cell types is to detect stimuli in the form of shallow chemical gradients. Such cues may indicate the direction that new growth should occur, or the location of a mate. Amplification of these faint signals is due to intra cellular mechanisms while the cue itself is generated by the noisy arrival of signaling molecules to surface bound membrane receptors. We employ a new hybrid numerical-asymptotic technique coupling matched asymptotic analysis and numerical inverse Laplace transform to rapidly and accurately solve the parabolic exterior problem describing the dynamic diffusive fluxes to receptors. We observe that equilibration occurs on long timescales, potentially limiting the usefulness of steady state quantities for localization at practical biological timescales. We demonstrate that directional information is encoded primarily in early arrivals to the receptors, while equilibrium quantities inform on source distance. We develop a new homogenization result showing that complex receptor configurations can be replaced by a uniform effective condition. In the extreme scenario where the cell adopts the angular direction of the first impact, we show this estimate to be surprisingly accurate.

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Section: Homogenizationsupporting

confidence: 54%

Section: Receptor Arrival Statisticsmentioning

confidence: 99%

Section: Receptor Arrival Statisticsmentioning

confidence: 99%

mentioning

confidence: 92%

“…Asymptotic construction of splitting probabilities and dynamic fluxes. In this section, we obtain an asymptotic representation [29,28,16,58,8,10] of the solution of (1) and (2) as " ! 0.…”

mentioning

confidence: 99%

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