Nanopore Recordings to Quantify Activity-Related Properties of Proteins - Nanopores: Sensing and Fundamental Biological Interactions - page 212

Uram et al . calculated the volume of virus particles before and after the addition of
antibody from DI . Assuming that a typical immunoglobulin G, IgG, antibody has a

volume of 347 nm 3 [ 39 ], the number of antibodies bound to each virus at equilibrium
could be estimated. The results suggested that the majority of the antibodies were
bound to the virus via one of their two binding sites. Thus, this method provided
information about whether the antibodies were attached by a monovalent or divalent
interaction. In addition, this method yielded an estimate for the number of epitopes on a
virus for a specific antibody preparation.
Martin's group demonstrated another technique to determine the stoichiometry of
protein-ligand interactions [ 40 ]. In these experiments, Sexton et al . used the trans-
location time of the protein-ligand complex to estimate the number of antibody-Fab
fragments bound to individual BSA proteins. Upon the addition of increasing
concentrations of Fab fragments to a solution containing BSA, the translocation
time of BSA increased markedly. Based on these results, Sexton et al . estimated that
BSA presents up to three epitopes for the binding of Fab fragments.

9.3.2 Determining Dissociation Constants with Nanopores

Another important characteristic of protein-ligand interactions is the equilibrium
dissociation constant. Two methods have been used to determine this constant
based on current recordings through nanopores, and both methods employ standard
equations for binding equilibria.
For the simple case of a protein, P, binding to a single ligand, L, the binding can
be described by the reaction [ 10 , 35 ]:

k on

Ð

P þ L PL : (9.4)

k off

Once binding has reached equilibrium, the strength of the binding can be
quantified by an equilibrium association constant, K a (M 1 ), which is defined for
this reaction as:

½ PL k on

k off ¼

1
K d ;

K a ¼

[L] ¼

(9.5)

[P]

where [PL] is the concentration of the protein-ligand complex at equilibrium, [P] is
the concentration of unbound protein at equilibrium, [L] is the concentration
of unbound ligand at equilibrium, k on

s 1 ) is the association rate constant,
k off (s 1 ) is the dissociation rate constant, and K d (M) is the dissociation constant.

(M 1