From owner-biophysics@net.bio.net Mon Jan 19 22:00:00 1998 Path: biosci!daresbury!uninett.no!Cabal.CESspool!bofh.vszbr.cz!lyra.csx.cam.ac.uk!hgmp.mrc.ac.uk!mail.dcs.warwick.ac.uk!warwick!leicester!usenet From: "Dr E. Buxbaum" Newsgroups: bionet.biophysics Subject: Re: Quadratic binding equation Date: Tue, 20 Jan 1998 16:23:34 -0800 Organization: University of Leicester (PCFS User) Lines: 24 Message-ID: <34C54006.4535@le.ac.uk> References: <34C3B0DF.3B24@york.ac.uk> NNTP-Posting-Host: pc47.msb.le.ac.uk Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Mailer: Mozilla 3.01 (Win16; I) David Scott wrote: > > Hia > Here's one for all you all: > Binding of a ligand can be characterised by the hyperbolic binding curve > as we all know. However, under certain circumstances, we tend to use the > quadratic binding equation, or tight binding relationship: > v=(-(Kd+t+Cap)+/- sqr((Kd+t+Cap)^2+4.t.Cap))/2 > where v is amount bound, t is total ligand conc, Cap is total binding > capacity and Kd is dissn constant. > Now I've been happily using this for years for the appropriate cases, > but where does it come from and who derived it first? As far as I know, the first to derive quantitative relationships between total ligand and enzyme activity (equivalent to binding) was Victor Henry in 1902. He published his results in an exotic journal (Comptes rendues de l'Academie des Sciences) in an even more exotic language (french), so his work was largely ignored. 12 Years later Michaelis and Menten published similar work, using the free ligand concentration. They used a main stream journal (Biochem. Z.) and the language of science (german), so everybody knows about them. Note however that the Henry equation and the Michaelis-Menten equation are directly related: Replace in the MM-eq. the free ligand by (Total - Bound) and you get a quadratic equation, the positive root of which is the Henry equation. .