23.8 In Vitro Experimental Methods

329

detect 1 protein per 50muµmsquared² using grating couplers. Provided adequate tempera-

ture stabilization can be achieved, interferometry (i.e., optical waveguide lightmode

interferometry—OWLI—for which there are various schemes, including allowing

orthogonal (transverse magnetic and transverse electric) modes to propagate within

the same waveguide, and dual polarization interferometry, in which the modes prop-

agate in separate waveguides and are allowed to interfere in the far field) and the

hybrid GCI can potentially achieve several orders of magnitude more sensitivity by

using extended path lengths, although this may complicate the kinetic analysis of

any processes being monitored.

Both QCM and SPR present a metal surface to the recreated cytoplasm, to which

it can be problematical to immobilize one of the binding partners. ³² OWLS, OWLI

and GCI have no such restriction since the transducer surface can be any high refrac-

tive index transparent material (titania is a popular choice). Moreover, the risk of

denaturing the protein by the immobilization procedure can be avoided by coating

the transducer (the optical waveguide) with a natural bilayer lipid membrane and

choosing a membrane-associated protein as the target.

For measuring the interaction, one simply causes a solution of the putative binding

protein (A) to flow over its presumed partner (B) immobilized at the transducer

surface; the binding of A to B can be recorded with very high time resolution.

The real power of this approach lies in the comprehensive characterization (i.e.,

precise determination of the number of associated proteins with good time resolution)

of the association that it can deliver. A major defect of the description built around

Eq. (23.6) is that the dissociation of A from B is only very rarely correctly given by

an equation of the typed nu slash d t tilde e Superscript minus k Super Subscript normal d Superscript tdν/dt ∼e^−kdt, wherenuν is the number of associated proteins

(i.e., a pure Poisson process without memory), since most proteins remember how

long they have been associated. This is a consequence of the fact that they have

several stable states, and transitions between the states can be induced by a change

in external conditions, such as binding to another protein. The correct approach is

to consider that during a small interval of time Delta t 1Δt1 at epoch t 1t1, a number Delta nuΔν of

molecules of A will be bound to B; hence,

Delta nu equals k Subscript normal a Baseline left parenthesis nu comma t 1 right parenthesis c Subscript normal upper A Baseline left parenthesis nu comma t 1 right parenthesis phi left parenthesis nu comma t 1 right parenthesis Delta t 1 commaΔν = ka(ν, t1) cA(ν, t1) φ(ν, t1) Δt1 ,

(23.20)

where c Subscript normal upper AcA is the concentration of free (unassociated) A and phiφ is the probability that

there is room to bind (we recall that the cell is a very crowded milieu). The memory

functionupper Q left parenthesis t comma t 1 right parenthesisQ(t, t1) gives the probability that a molecule bound at epocht 1t1 is still bound

32 A popular way to avoid the bioincompatibility of the gold or silver surface of the transducer

required with SPR has been to coat it with a thick (tilde 200∼200 nm) layer of a biocompatible polysaccharide

such as dextran, which forms a hydrogel, to which the target protein is bound. Unfortunately, this

drastically changes the transport properties of the solution in the vicinity of the target (bound) protein

(see Schuck 1996), which can lead to errors of up to several orders of magnitude in apparent binding

constants (via a differential effect onk Subscript normal aka andk Subscript normal dkd). Furthermore, such materials interact very strongly

(via hydrogen bonds) with water, altering its hydrophilicity, with concomitant drastic changes to

protein affinity, leading to further, possibly equally large, distortions in binding constant via its link

to the free energy of interaction (Delta upper G equals minus upper R upper T ln upper KΔG = −RT ln K).