[Paper Review] A sequential algorithm with a built in tension-propagation mechanism for modeling the chain-like bodies dynamics

Andrzej Z. Grzybowski, Zbigniew Domański|arXiv (Cornell University)|Dec 15, 2013

Theoretical and Computational Physics4 citations

TL;DR

This paper introduces a novel sequential stochastic algorithm for simulating chain-like body (CLB) dynamics with an embedded tension-propagation mechanism, enabling efficient, high-acceptance conformational transitions. The method models translocation through a pore using virtual steps that propagate tension, and identifies the Moyal distribution as an accurate model for translocation time distributions in 2D self-avoiding polymers.

ABSTRACT

In the paper a novel stochastic algorithm designed to study of chain-like bodies dynamics is introduced. This algorithm models chain movements induced by the tension propagation and its main idea relies on the sequentialization of each movement into a sequence of virtual steps made by chain's segments. In this spirit, any accepted chain's new position is achieved by a move that is initiated by a shift of one segment picked randomly according to a problem-specific probability distribution and then followed by a cascade of some other segments' position rearrangements. The rearrangement process terminates when the tension in the chain induced by the initial shift is released. A considerable gain in the volume of allocated memory is achieved because the virtual steps lead to new conformations that are very likely to be acceptable by nature. We validate the algorithm by comparing passage times for polymer translocation through a pore obtained within this algorithm with their counterparts reported in the literature. In this paper we focus on a fluctuating-bond model of self-avoiding polymers on 2D square lattice. Based on the large data sets received in our simulations we have found that the transolaction time is distributed according to the Moyal probability distribution. This novel finding enables us to identify the theoretical form of various distributions of translocation time reported in literature by expressing them very accurately with the help of this two-parameter family of probability distributions

Motivation & Objective

• To develop a computationally efficient algorithm for simulating chain-like body dynamics with inherent tension propagation.
• To address the lack of existing stochastic algorithms that simultaneously ensure high acceptance rates, self-avoidance, and proper tension response.
• To validate the algorithm by comparing simulated translocation times with literature data.
• To identify the theoretical distribution underlying translocation time data from large-scale simulations.
• To enable large-scale data generation for robust statistical analysis of polymer dynamics.

Proposed method

• The algorithm sequentially updates chain conformations by initiating a random shift in one segment based on a problem-specific probability distribution.
• Following the initial shift, a cascade of segment rearrangements propagates tension through the chain until equilibrium is reached.
• Each virtual step ensures self-avoidance and maintains ergodicity by only accepting physically plausible conformations.
• The method reduces memory usage and search space by favoring high-acceptance transitions that reflect natural tension relaxation.
• Translocation times are collected from simulations on a 2D square lattice using a fluctuating-bond, self-avoiding polymer model.
• The Moyal probability distribution is fitted to translocation time data to assess its accuracy as a theoretical model.

Experimental results

Research questions

• RQ1 Can a sequential stochastic algorithm with built-in tension propagation efficiently simulate chain-like body dynamics with high acceptance rates?
• RQ2 How does the proposed algorithm compare to existing methods in terms of computational efficiency and memory usage?
• RQ3 What is the underlying probability distribution of translocation times in 2D self-avoiding polymers under the proposed algorithm?
• RQ4 Can the Moyal distribution accurately model translocation time data from both simulations and experimental literature?
• RQ5 How do parameters such as chain length and tension propagation range affect translocation time distributions?

Key findings

• The proposed algorithm achieves significant memory and computational efficiency by favoring high-acceptance conformations through tension-propagation mechanics.
• Translocation times in the simulations follow the Moyal probability distribution with high accuracy, as confirmed by fitting to large data sets.
• The Moyal distribution provides a superior fit to translocation time data compared to alternative models such as $ t^{a_1} ext{exp}(-a_2 t) $, especially at small time values.
• The Moyal distribution accurately models translocation time data from multiple sources, including voltage-driven DNA translocations and Langevin dynamics simulations.
• The parameter $ b \approx 0.21 $ was derived from experimental histograms of DNA translocation, confirming the Moyal distribution's relevance to real-world data.
• The algorithm enables the generation of large, reliable data sets, facilitating the identification of the Moyal distribution as a universal model for translocation times.