Comparison of mechanisms of kinetochore capture with varying number of spindle microtubules

Nayak, Indrani; Das, Dibyendu; Nandi, Amitabha

doi:10.1103/physrevresearch.2.013114

Cited by 18 publications

(14 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our work indicates new avenues for understanding the nonequilibrium features of resetting, e.g., in the study of optimization of resetting pathways for efficient particle transport. Furthermore, we expect that our formalism could be extended to shed light on various biophysical problems described by onedimensional diffusion with suitable boundary and/or resetting conditions, such as microtubule dynamics [43,44], molecular motors [2,45,46], single-file diffusion of water in carbon nanorings [47], or polymer translocation through nanopores [48,49] In this Appendix, we report the solution for the Laplace transform of Eq. (1) for P(x, t|x 0 , x r ), the probability distribution of the Brownian particle position in one dimension, initially at x 0 , resetting to x r according the space-dependent resetting rate r c (x).…”

Section: Discussionmentioning

confidence: 99%

Controlling particle currents with evaporation and resetting from an interval

Tucci

Gambassi

Gupta

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

We investigate the Brownian diffusion of particles in one spatial dimension and in the presence of finite regions within which particles can either evaporate or be reset to a given location. For open boundary conditions, we highlight the appearance of a Brownian yet non-Gaussian diffusion: At long times, the particle distribution is non-Gaussian but its variance grows linearly in time. Moreover, we show that the effective diffusion coefficient of the particles in such systems is bounded from below by 1 − 2/π times their bare diffusion coefficient. For periodic boundary conditions, i.e., for diffusion on a ring with resetting, we demonstrate a "gauge invariance" of the spatial particle distribution for different choices of the resetting probability currents, in both stationary and nonstationary regimes. Finally, we apply our findings to a stochastic biophysical model for the motion of RNA polymerases during transcriptional pauses, deriving analytically the distribution of the length of cleaved RNA transcripts and the efficiency of RNA cleavage in backtrack recovery.

show abstract

Section: Discussionmentioning

confidence: 99%

Controlling particle currents with evaporation and resetting from an interval

Tucci

Gambassi

Gupta

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…For any stochastic system, the first passage time is a random variable that denotes the first time some event occurred [23]. Examples of such events may be like a passive or active particle reaching a boundary [24,25], a protein binding to a specific patch on DNA [26], a moving kinetochore being captured by microtubules [27], or as in this case protein levels reaching a pre-determined threshold. The papers [21,22], showed that a model based on the statistics of first passage times to reach a critical protein concentration could reproduce the observed data.…”

Section: Introductionmentioning

confidence: 99%

The Protein Hourglass: Exact First Passage Time Distributions for Protein Thresholds

Rijal

Prasad

Das

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Protein thresholds have been shown to act as an ancient timekeeping device, such as in the time to lysis of E. coli infected with bacteriophage lambda. The time taken for protein levels to reach a particular threshold for the first time is defined as the first passage time of the protein synthesis system, which is a stochastic quantity. It had been shown previously that it was possible to obtain the mean and higher moments of the distribution of first passage times, but an analytical expression for the full distribution was not available. In this work, we derive an analytical expression for the first passage times for a long-lived protein. This expression allows us to calculate the full distribution not only for cases of no self-regulation, but also for both positive and negative self-regulation of the threshold protein. We show that the shape of the distribution matches previous experimental data on lambda-phage lysis time distributions. We study the noise in the precision of the first passage times by calculating the coefficient of variation (CV) of the distribution under various conditions. In agreement with previous results, we show that the CV of a protein that is not self-regulated is less than that of a self-regulated protein for both positive and negative regulation. We show that under conditions of positive self-regulation, the CV declines sharply and then roughly plateaus with increasing protein threshold, while under conditions of negative self-regulation, the CV declines steeply and then increases with increasing protein threshold. In the latter case therefore there is an optimal protein threshold that minimizes the noise in the first passage times. We also provide analytical expressions for the FPT distribution with non-zero degradation in Laplace space. These analytical distributions will have applications in understanding the stochastic dynamics of threshold determined processes in molecular and cell biology.

show abstract

“…Search and capture processes are ubiquitous in nature and have been an important topic in stochastic processes [1][2][3]. Such processes find application in a wide range of fields [4][5][6][7][8][9][10][11][12][13][14], and the list is still growing. Theoretical techniques to study a search and capture process involve the statistics of the first encounter with the target -commonly known as the first passage times (FPT).…”

Section: Introductionmentioning

confidence: 99%

“…While open space is relevant in many physical problems, on the other hand, there are many diffusive processes in nature that occur in confined spaces. Transport inside living cells are limited by the cellular dimensions -relevant examples in this context are proteins binding to a target site on DNA [45] or microtubules trying to capture a kinetochore [11]. Likewise, neutrophils chase and engulf diffusing bacteria or foreign particles within a finite region of the bloodstream [46].…”

Section: Introductionmentioning

confidence: 99%

Capture of a diffusive prey by multiple predators in confined space

Nayak,

Nandi,

Das

2020

Preprint

Self Cite

View full text Add to dashboard Cite

The first passage search of a diffusing target (prey) by multiple searchers (predators) in confinement is an important problem in the stochastic process literature. While the analogous problem in open space has been studied in some details, a systematic study in confined space is still lacking. In this paper, we study the first passage times for this problem in 1,2 and 3−dimensions. Due to confinement, the survival probability of the target takes a form ∼ e −t/τ at large times t. The characteristic capture timescale τ associated with the rare capture events are rather challenging to measure. We use a computational algorithm that allows us to estimate τ with high accuracy. We study in details the behavior of τ as a function of the system parameters, namely, the number of searchers N , the relative diffusivity r of the target with respect to the searcher, and the system size. We find that τ deviates from the ∼ 1/N scaling seen in the case of a static target, and this deviation varies continuously with r and the spatial dimensions.

show abstract

Comparison of mechanisms of kinetochore capture with varying number of spindle microtubules

Cited by 18 publications

References 67 publications

Controlling particle currents with evaporation and resetting from an interval

Controlling particle currents with evaporation and resetting from an interval

The Protein Hourglass: Exact First Passage Time Distributions for Protein Thresholds

Capture of a diffusive prey by multiple predators in confined space

Contact Info

Product

Resources

About