{"title":"Note on two-point mean square displacement.","authors":"Naoya Katayama, Takahiro Sakaue","doi":"10.1039/d5sm00555h","DOIUrl":null,"url":null,"abstract":"<p><p>When probe molecules of interest are embedded in a substrate or aggregate under stochastic motion, one needs to rely on the so-called two-point mean square displacement (MSD) measurement to extract the intrinsic mobility of the probes. We discuss two versions, based on the time series of relative vector or distance between two probes, and summarize their basic properties compared to the standard MSD. We also propose a way to extract (i) the non-Gaussianity in the displacement statistics and (ii) the motional correlation between probes from the two-point MSD. The results are presented not only for independent probes, but also for intramolecular probes within a long polymer, which could be useful in quantifying the dynamics of chromatin loci in a living cell nucleus.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" ","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Soft Matter","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1039/d5sm00555h","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
Abstract
When probe molecules of interest are embedded in a substrate or aggregate under stochastic motion, one needs to rely on the so-called two-point mean square displacement (MSD) measurement to extract the intrinsic mobility of the probes. We discuss two versions, based on the time series of relative vector or distance between two probes, and summarize their basic properties compared to the standard MSD. We also propose a way to extract (i) the non-Gaussianity in the displacement statistics and (ii) the motional correlation between probes from the two-point MSD. The results are presented not only for independent probes, but also for intramolecular probes within a long polymer, which could be useful in quantifying the dynamics of chromatin loci in a living cell nucleus.
期刊介绍:
Soft Matter is an international journal published by the Royal Society of Chemistry using Engineering-Materials Science: A Synthesis as its research focus. It publishes original research articles, review articles, and synthesis articles related to this field, reporting the latest discoveries in the relevant theoretical, practical, and applied disciplines in a timely manner, and aims to promote the rapid exchange of scientific information in this subject area. The journal is an open access journal. The journal is an open access journal and has not been placed on the alert list in the last three years.