Evaluation of Lateral Diffusivity and 2D Crystal Unit Cell Size

Extremely valuable information may be obtained by repeating adsorption measurements at different bulk concentrations. We consider three cases, A, B and C:

A. In this, the simplest case, the same behaviour is obtained at all cb and the (M, t) curves may be superimposed upon each other by rescaling time as the product cbt.

B. The shape of the v vs v plot is the same for all cb, but a varies (usually increasing with decreasing cb) (Ramsden 1993c). This implies that

adsorbed proteins are occupying more area after initial attachment, via orientational or conformational rearrangement. Let kr be the rate of rearrangement. The characteristic time for rearrangement Tr = 1/kr may be supposed equal to the characteristic time for adsorption Ta = 1/(Jcb$a) at the bulk concentration corresponding to the mid-point between the limiting lower and higher areas a, where J is the protein flux to the empty surface normalized to unit adsorbent area and unit bulk concentration. A more sophisticated approach involves simultaneously fitting the adsorption data to the equations explicitly taking rearrangement into account (Van Tassel et al. 1998), see Eqs. 51 and 52.

C. The adsorption changes from RSA at high cb to Langmuir at low cb (Ramsden etal. 1994). Atlowbulk concentration, Ta is long and adsorbed proteins have time to diffuse laterally, for which the characteristic time t2 = 1/(D2v), and crystallize. t2 can be obtained from the value of cb at the crossover point when the series of v vs v curves changes from RSA to Langmuir, at which point it may be supposed that t2 = Ta. The next step is to compare a obtained at high cb with that obtained at low cb. Near equivalence means that the proteins are forming a random cluster. If the value at low cb is much greater than at high cb, two dimensional crystallization maybe inferred and the value of a at low cb corresponds to unit cell size.

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