Langmuir 1:1 kinetics

Hi, first post here. I'd just like to say I love the site. Heres my query..

Langmuir 1:1 kinetics. This is a phrase commonly bandied around when fitting curves.

So am I right in assuming that when a range of binding curves fit this criterion (using the standard Biaevaluation software - integrated non-linear differential rate equation) - a 1:1 binding ratio for ligand:receptor is demonstrated ?

I just find it a little difficult to grasp this concept when the level of chip-immobilised ligand is not accounted for ?

Am I correct when I assume that its the SHAPE of the binding curve that is sufficient to demonstrate a 1:1 binding stoichiometry ?

Thanks

Gordon

>So am I right in assuming that when a range of binding curves fit this criterion (using the standard Biaevaluation software - integrated non-linear differential rate equation) - a 1:1 binding ratio for ligand:receptor is demonstrated ?

The point is when you immobilise a bivalent analyte (like an IgG) you find a 1:1 binding ratio. When you reverse the system you find a 1:2. Thus in my opinion, just curve fitting is not sufficient.

>I just find it a little difficult to grasp this concept when the level of chip-immobilised ligand is not accounted for ?

Binding an analyte (A) to a ligand (L) can be described by:

d[LA]/dt= ka.[L][A]-kd.[LA]

During binding the concentration [L] = [L]o [LA] ([L]o are all free binding places) and is assumed that [A] is constant (C). Thus:

d[LA]/dt = ka.C.([L]o-[LA])-ka[LA]

In SPR the response (Rt) is proportional to [LA] and at saturation [LA] reaches Rmax which is equivalent to [L]o. Thus:

dR/dt = ka.C.(Rmax-Rt) kd.Rt

So effectively the starting value of free ligand sites is converted to the maximum signal at saturation. The point is that the maximum signal depends on the size of the analyte and is generally reached with analyte concentration above 50 times KD of the interaction.

Look also at the SPR Pages Datafittig theory

> Am I correct when I assume that its the SHAPE of the binding curve that is sufficient to demonstrate a 1:1 binding stoichiometry ?

Yes and NO: with variables such as ka, kd, C and Rmax there are many curves which can be drawn resembling 1:1 stoichiometry. Within one system ka, kd, and Rmax should be fixed and only the analyte concentration will determine the shape of the curve.