A further extremely important extension of the basic experiment of allowing one protein to adsorb from solution at a single bulk concentration is to suddenly flood the system with protein-free solvent, which in practice generally means replacing flow of the protein solution by flow of protein-free solvent. In that case Eq. 35 becomes simply dM/dt = -kdM . (53)

As already pointed out, in general, kd is not a true constant. Only in the case of pure exponential decay of M can ideal, memory-free desorption be inferred, and another characteristic time, Td = 1/kd, be defined. Usually M(t)cb=0 is strongly non-exponential. In this case it is convenient to use a memory function to characterize the adsorption behaviour. The amount of protein bound, v(t), can be represented by the integral (Talbot 1996)

The memory kernel Q denotes the fraction of protein bound at epoch ti that remains adsorbed at epoch t (if dissociation is indeed a first order (Poisson) process then Q(t) = exp(-kdt)). A necessary condition for the system to reach equilibrium is lim Q(t) = 0 . (55)

The dissociation coefficient is time dependent and is given by the quotient k (t) ยก0 0(ti)Q/(t> ti)dti (56)

Cooperative effects are not uncommon in densely packed protein monolayers. An example in which the desorption of an individual particle is influenced by its adsorbed neighbours is described by Kurrat et al. (i994).

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