{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:12:28Z","timestamp":1768738348291,"version":"3.49.0"},"reference-count":48,"publisher":"Oxford University Press (OUP)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivation: Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment.<\/jats:p><jats:p>Results: In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy.<\/jats:p><jats:p>Contact: \u00a0tian@maths.uq.edu.au<\/jats:p>","DOI":"10.1093\/bioinformatics\/btl552","type":"journal-article","created":{"date-parts":[[2006,10,27]],"date-time":"2006-10-27T00:26:52Z","timestamp":1161908812000},"page":"84-91","source":"Crossref","is-referenced-by-count":87,"title":["Simulated maximum likelihood method for estimating kinetic rates in gene expression"],"prefix":"10.1093","volume":"23","author":[{"given":"Tianhai","family":"Tian","sequence":"first","affiliation":[{"name":"Advanced Computational Modelling Centre, University of Queensland 1 \u00a0 1 \u00a0 \u00a0 Brisbane, QLD 4072, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Songlin","family":"Xu","sequence":"additional","affiliation":[{"name":"Advanced Computational Modelling Centre, University of Queensland 1 \u00a0 1 \u00a0 \u00a0 Brisbane, QLD 4072, Australia"},{"name":"Department of Mathematics, Hubei University of Technology 2 \u00a0 2 \u00a0 \u00a0 Wuhan, Hubei 430068, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junbin","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Information Technology, Charles Sturt University 3 \u00a0 3 \u00a0 \u00a0 Bathurst, NSW 2795, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kevin","family":"Burrage","sequence":"additional","affiliation":[{"name":"Advanced Computational Modelling Centre, University of Queensland 1 \u00a0 1 \u00a0 \u00a0 Brisbane, QLD 4072, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2006,10,26]]},"reference":[{"key":"2023041105092728800_","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1093\/bioinformatics\/16.8.727","article-title":"Inferring qualitative relations in genetic networks and metabolic pathways","volume":"16","author":"Akutsu","year":"2000","journal-title":"Bioinformatics"},{"key":"2023041105092728800_","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.csda.2003.11.025","article-title":"A genetic estimation algorithm for parameters of stochastic ordinary differential equations","volume":"47","author":"Alcock","year":"2004","journal-title":"Comput. 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Phys."},{"key":"2023041105092728800_","doi-asserted-by":"crossref","DOI":"10.1002\/9780470316849","article-title":"Multivariate Density Estimation: Theory, Practice and Visualization","author":"Scott","year":"1992"},{"key":"2023041105092728800_","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.biosystems.2004.11.003","article-title":"Reverse engineering of biochemical equations from time-course data by means of genetic programming","volume":"80","author":"Sugimoto","year":"2005","journal-title":"Biosystems"},{"key":"2023041105092728800_","doi-asserted-by":"crossref","first-page":"12795","DOI":"10.1073\/pnas.162041399","article-title":"Intrinsic and extrinsic contributions to stochasticity in gene expression","volume":"99","author":"Swain","year":"2002","journal-title":"Proc. Natl Acad. Sci. 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