Fast calcium transients in dendritic spines driven by extreme statistics

Basnayake, Kanishka; Mazaud, David; Bémelmans, Alexis; Rouach, Nathalie; Korkotian, Eduard; Holcman, David

doi:10.1371/journal.pbio.2006202

Cited by 43 publications

(61 citation statements)

References 66 publications

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“…We will return to the question of the existence of such a function S b in the subsection below. Using (23)- (25) yields that for small t,…”

Section: Partially Absorbing Boundarymentioning

confidence: 99%

Universal formula for extreme first passage statistics of diffusion

Lawley

2020

Phys. Rev. E

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The timescales of many physical, chemical, and biological processes are determined by first passage times (FPTs) of diffusion. The overwhelming majority of FPT research studies the time it takes a single diffusive searcher to find a target. However, the more relevant quantity in many systems is the time it takes the fastest searcher to find a target from a large group of searchers. This fastest FPT depends on extremely rare events and has a drastically faster timescale than the FPT of a given single searcher. In this paper, we prove a simple explicit formula for every moment of the fastest FPT. The formula is remarkably universal, as it holds for d-dimensional diffusion processes (i) with general space-dependent diffusivities and force fields, (ii) on any smooth Riemannian manifold, (iii) in the presence of reflecting obstacles, and (iv) with partially absorbing targets. Our results rigorously confirm, generalize, correct, and unify various conjectures and heuristics about the fastest FPT.S l (t) ≈ 1 − e −l 2 /t for t 1.

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“…We will return to the question of the existence of such a function S b in the subsection below. Using (23)- (25) yields that for small t,…”

Section: Partially Absorbing Boundarymentioning

confidence: 99%

Universal formula for extreme first passage statistics of diffusion

Lawley

2020

Phys. Rev. E

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“…For example, roughly N = 10 8 sperm cells search for an egg in human reproduction, but fertilization occurs as soon as a single sperm cell finds the egg [21,22,23,24]. Similarly, a calcium-induced calcium release in a dendritic spine occurs when the two fastest calcium ions out of roughly N = 10 3 calcium ions find small Ryanodyne receptors at the base of the spine [25]. Importantly, the time it takes the fastest searcher(s) out of many searchers to find a target is much less than the time it takes a given single searcher to find a target.…”

Section: Introductionmentioning

confidence: 99%

Distribution of extreme first passage times of diffusion

Lawley

2020

J. Math. Biol.

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Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme FPT. In this paper, we apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion. This approximation can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT. We find this distribution by proving that a careful rescaling of extreme FPTs converges in distribution as the number of searchers grows. This limiting distribution is a type of Gumbel distribution and involves the LambertW function. This analysis yields new explicit formulas for approximations of statistics of extreme FPTs (mean, variance, moments, etc.) which are highly accurate and are accompanied by rigorous error estimates.

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“…In summary, our computational models using idealized and realistic geometries of dendritic spines have identified potential relationships between spine geometry and synaptic weight change that emerge despite the inherent stochasticity of calcium transients. The advances in computational modeling and techniques have set the stage for a detailed exploration of biophysical processes in dendritic spines (57,61,62). Such efforts are critical for identifying emergent properties of systems behavior and also eliminating hypotheses that are physically infeasible (63,64).…”

Section: Discussionmentioning

confidence: 99%

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Lee

et al. 2021

Preprint

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Dendritic spines act as computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can separately modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

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Fast calcium transients in dendritic spines driven by extreme statistics

Cited by 43 publications

References 66 publications

Universal formula for extreme first passage statistics of diffusion

Universal formula for extreme first passage statistics of diffusion

Distribution of extreme first passage times of diffusion

Dendritic spine morphology regulates calcium-dependent synaptic weight change

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