{"title":"Variance bounds for a class of biochemical birth/death like processes via a discrete expansion and spectral properties of the Master equation","authors":"Giovanni Pugliese Carratelli, Ioannis Leastas","doi":"arxiv-2409.05667","DOIUrl":null,"url":null,"abstract":"We consider a class of birth/death like process corresponding to coupled\nbiochemical reactions and consider the problem of quantifying the variance of\nthe molecular species in terms of the rates of the reactions. In particular, we\naddress this problem in a configuration where a species is formed with a rate\nthat depends nonlinearly on another spontaneously formed species. By making use\nof an appropriately formulated expansion based on the Newton series, in\nconjunction with spectral properties of the master equation, we derive an\nanalytical expression that provides a hard bound for the variance. We show that\nthis bound is exact when the propensities are linear, with numerical\nsimulations demonstrating that this bound is also very close to the actual\nvariance. An analytical expression for the covariance of the species is also\nderived.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"46 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05667","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a class of birth/death like process corresponding to coupled
biochemical reactions and consider the problem of quantifying the variance of
the molecular species in terms of the rates of the reactions. In particular, we
address this problem in a configuration where a species is formed with a rate
that depends nonlinearly on another spontaneously formed species. By making use
of an appropriately formulated expansion based on the Newton series, in
conjunction with spectral properties of the master equation, we derive an
analytical expression that provides a hard bound for the variance. We show that
this bound is exact when the propensities are linear, with numerical
simulations demonstrating that this bound is also very close to the actual
variance. An analytical expression for the covariance of the species is also
derived.