{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:33:06Z","timestamp":1787340786715,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2007,1]]},"abstract":"<jats:p>Changes to the relative separation of molecules or other interacting species on account of diffusion accompany their associative or dissociative reaction. The molecules are symbolized, for two distinct types, $A,B$, by the relations $A+B \\leftrightharpoons AB$, and, if $[A]$, $[B]$, and $[AB]$ denote the corresponding densities, the equation $\\frac{d}{dt} [AB] = k_+ [A][B]$ specifies an associative process with forward rate constant $k_+$. An approximate version of the preceding takes the form of a linear differential equation, which can be employed to obtain significant estimates for both $k_+$ and the flux function $d [AB]\/dt$. Such estimates are presented in different circumstances, including the localization of $A,B$ on a common planar surface or their distribution in space, and also when the domain of A is a half space whereas that of B is a bounding planar surface. It proves advantageous to reformulate the last, a mixed boundary value problem, in terms of a linear integral equation. Biological applications are discussed, including the mechanism for the observed phosphorylation of proteins in resting cells and the incipience of phototransduction in rod photoreceptors.<\/jats:p>","DOI":"10.1137\/060655018","type":"journal-article","created":{"date-parts":[[2007,5,14]],"date-time":"2007-05-14T18:00:27Z","timestamp":1179165627000},"page":"1147-1165","source":"Crossref","is-referenced-by-count":5,"title":["Diffusion Limited Reactions"],"prefix":"10.1137","volume":"67","author":[{"given":"Byron","family":"Goldstein","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Harold","family":"Levine","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David","family":"Torney","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2007,5,14]]},"reference":[{"key":"R1","unstructured":"E. Beltrami,\n                      On the theory of potential functions symmetrical about an axis of revolution\n                      , R. Accad. Sci. Bologna, Ser. IV, Vol. II, 1881, pp. 461\u2013498."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0006-3495(77)85544-6"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01010841"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1017\/S0033583500001657"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1063\/1.454362"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.4049\/jimmunol.170.7.3769"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"A. N. Gorban and I. V. Karlin,\n                      Invariant Manifolds for Physical and Chemical Kinetics\n                      , Springer\u2010Verlag, Berlin, 2005.","DOI":"10.1007\/b98103"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1021\/j100223a004"},{"key":"R9","unstructured":"T. D. Lamb,\n                      Gain and kinetics of activation in the G\u2010protein cascade of phototransduction\n                      , in Vision: From Photon to Perception (May 20\u201322, 1995), National Academy of Sciences Colloquium, National Academy Press, Washington, DC, 1999, pp. 10\u201314."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1083\/jcb.102.2.534"},{"key":"R11","unstructured":"P. M. Morse and H. Feshbach,\n                      Methods of Mathematical Physics, Part I\n                      , McGraw\u2010Hill, New York, 1953."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100036987"},{"key":"R13","first-page":"129","volume":"1","author":"Noyes R. M.","year":"1961","journal-title":"Prog. React. Kinet.","ISSN":"https:\/\/id.crossref.org\/issn\/0079-6743","issn-type":"print"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1126\/science.283.5404.990"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1038\/ncb981"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(93)90317-S"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1038\/264550a0"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1021\/bi0027534"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1177\/109434208700100204"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1063\/1.445022"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.107.463"},{"key":"R22","unstructured":"C. Wofsy,\n                      private communication\n                      ."}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060655018","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:47:52Z","timestamp":1787338072000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060655018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,1]]}},"alternative-id":["10.1137\/060655018"],"URL":"https:\/\/doi.org\/10.1137\/060655018","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1]]}}}