{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:47:04Z","timestamp":1758815224727},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"02b","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2007,4]]},"abstract":"<jats:p> Mechanistic models for transcriptional regulation are derived using the methods of equilibrium statistical mechanics, to model equilibrating processes that occur at a fast time scale. These processes regulate slower changes in the synthesis and expression of transcription factors that feed back and cooperatively regulate transcription, forming a gene regulation network (GRN). We rederive and extend two previous quasi-equilibrium models of transcriptional regulation, and demonstrate circumstances under which they can be approximated at each transcription complex by feed-forward artificial neural network (ANN) models. A single-level mechanistic model can be approximated by a successfully applied phenomenological model of GRNs which is based on single-layer analog-valued ANNs. A two-level hierarchical mechanistic model, with separate activation states for modules and for the whole transcription complex, can be approximated by a two-layer feed-forward ANN in several related ways. The sufficient conditions demonstrated for the ANN approximations correspond biologically to large numbers of binding sites each of which have a small effect. A further extension to the single-level and two-level models allows one-dimensional chains of overlapping and\/or energetically interacting binding sites within a module. Partition functions for these models can be constructed from stylized diagrams that indicate energetic and logical interactions between binary-valued state variables. All parameters in the mechanistic models, including the two approximations, can in principle be related to experimentally measurable free energy differences, among other observables. <\/jats:p>","DOI":"10.1142\/s0219720007002874","type":"journal-article","created":{"date-parts":[[2007,7,16]],"date-time":"2007-07-16T11:30:04Z","timestamp":1184585404000},"page":"467-490","source":"Crossref","is-referenced-by-count":13,"title":["ON COOPERATIVE QUASI-EQUILIBRIUM MODELS OF TRANSCRIPTIONAL REGULATION"],"prefix":"10.1142","volume":"05","author":[{"given":"ERIC","family":"MJOLSNESS","sequence":"first","affiliation":[{"name":"Institute for Genomics and Bioinformatics, and Departments of Computer Science and Mathematics, University of California, Irvine, California, 92697, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","first-page":"4047","DOI":"10.1002\/j.1460-2075.1992.tb05498.x","volume":"11","author":"Small S.","journal-title":"The EMBO Journal"},{"key":"rf2","unstructured":"M.\u00a0Gibson and E.\u00a0Mjolsness, Computational Methods in Molecular Biology, eds. 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