{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T12:52:26Z","timestamp":1773665546332,"version":"3.50.1"},"reference-count":21,"publisher":"Oxford University Press (OUP)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,3,1]]},"abstract":"<jats:p>Motivation: We propose the third-order model equation of the Jeffreys type for concentrations of gap gene proteins in order to take into account particle inertia. Gap genes are responsible for formation of body segments in Drosophila melanogaster embryo during its early development. Usually the expression of the genes is described by the model of protein transport based on conventional diffusion equation. However, the model is known to govern the Brownian (non-inertial) motion of particles; hence, it is hardly applicable to the description of protein transport.<\/jats:p>\n               <jats:p>Results: Analysis of the Jeffreys-type equation results in the necessary condition for the problem to be well-posed. Application of the Jeffreys-type equation with non-linear terms to description of the dynamics of gap gene network demonstrates better fitting to experimental data than the conventional model.<\/jats:p>\n               <jats:p>Availability and implementation: Implementation of solver algorithms and the software are freely available from: https:\/\/github.com\/wswgG\/solver-for-the-Jeffreys-type-equations-system<\/jats:p>\n               <jats:p>Contact: \u00a0gula@mail.ioffe.ru<\/jats:p>\n               <jats:p>Supplementary information: \u00a0Supplementary Data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btu695","type":"journal-article","created":{"date-parts":[[2014,10,23]],"date-time":"2014-10-23T00:08:46Z","timestamp":1414022926000},"page":"714-719","source":"Crossref","is-referenced-by-count":4,"title":["A model for the expression of <i>gap<\/i> genes based on the Jeffreys-type equation"],"prefix":"10.1093","volume":"31","author":[{"given":"Igor A.","family":"Gula","sequence":"first","affiliation":[{"name":"1 \u00a01The Ioffe Physical Technical Institute, St. Petersburg, 194021 Russia and 2State Polytechnical University, St. Petersburg, 195251 Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander M.","family":"Samsonov","sequence":"additional","affiliation":[{"name":"1 \u00a01The Ioffe Physical Technical Institute, St. Petersburg, 194021 Russia and 2State Polytechnical University, St. Petersburg, 195251 Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2014,10,22]]},"reference":[{"key":"2023020116165264600_btu695-B1","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0092-8674(88)90182-1","article-title":"A gradient of bicoid protein in Drosphila embryos","volume":"54","author":"Driever","year":"1988","journal-title":"Cell"},{"key":"2023020116165264600_btu695-B2","doi-asserted-by":"crossref","DOI":"10.1088\/1478-3975\/9\/5\/055004","article-title":"The synthesis-diffusion-degradation model explains Bicoid gradient formation in unfertilized eggs","volume":"9","author":"Drocco","year":"2012","journal-title":"Phys. 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