From owner-biophysics@net.bio.net Sun Jan 18 22:00:00 1998 Path: biosci!agate!logbridge.uoregon.edu!news.uoregon.edu!news.acsu.buffalo.edu!newsstand.cit.cornell.edu!varnafc.vet.cornell.edu!user From: alb2@cornell.edu (Allan Berger) Newsgroups: bionet.biophysics Subject: Re: Quadratic binding equation Date: Mon, 19 Jan 1998 10:55:54 -0500 Organization: Cornell University Lines: 39 Sender: alb2@cornell.edu (Verified) Message-ID: References: <34C3B0DF.3B24@york.ac.uk> NNTP-Posting-Host: varnafc.vet.cornell.edu X-Newsreader: Value-Added NewsWatcher 2.0b24.0+ In article <34C3B0DF.3B24@york.ac.uk>, 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? > > Dave. The hyperbolic binding curve comes from standard pharmacological research where one assumes that the total ligand [] = the free ligand [] (i.e. the amount bound by receptor is insignificant and does not change the free concentration of ligand). If you have a situation in which receptor depletes the ligand from solution as it binds, then you can't use the standard hyperbolic. Go ahead and substitute L(free) = L(total) - RL(bound) for L in the standard hyperbolic and you'll wind up with the quadratic (RL^2 term). I'm not sure who derived it first; certainly many have derived it independently. Check Lundblad et al., Mol Endocrinology 10:607-612 for a published derivation. Each time I use the formula I derive it from scratch because I've forgotten it. :-) AB Allan Berger Dept. of Pharmacology College of Veterinary Medicine Cornell University Ithaca, NY 14853 (607) 253-3878 (voice) (607) 253-3659 (fax) .