We observe an applied potential to have a significant effect on adsorption beyond the transport-limited regime. The apparent adsorption rate constant introduced in and around Eq. 11 - a measure of the rate of adsorption to an empty surface and a physical property depending on protein/surface/solvent characteristics - increases with applied voltage for the negatively charged albumin, decreases somewhat for the positively charged cytochrome c in water, and remains roughly constant for cy-tochrome c in HEPES. Interestingly, we observe the rate ofadsorption onto surfaces of higher coverage to increase significantly with voltage in all systems investigated. Since these measurements occur well beyond the transport-limited regime, this reflects an increased rate of attachment among protein molecules at or near the surface. Since direct alteration of the apparent rate constant by interactions with previously adsorbed proteins is unlikely, the increase in overall adsorption rate is probably due to an increased amount of surface available for adsorption and, at higher coverage, a formation of multilayers. A measure of the available surface is given by the cavity function $ (as introduced in Eq. 11), and contributing factors to its increase are: (1) the adsorption of protein molecules with smaller projected areas, as would occur in an end-on orientation of a nonspher-ical protein, and (2) the formation of protein clusters on the surface. We quantify changes in $ with voltage by considering its first-order density expansion coefficient, C1, obtained from the slopes of the linear regions of dr/ dt versus r curves. As reported in Table 2, we observe C1 to decrease with voltage for albumin, but to be roughly independent of voltage for cytochrome c (see Table 2). A smaller adsorbed molecule projected area, or adsorption directly to the edge of growing clusters, are physical explanations consistent with this observation. Both of these features are engendered by adsorption of protein oriented such that a complementary (in this case negative) charge faces the adsorbing substrate. In this way, even the positively charged cytochrome c may adsorb more rapidly with applied voltage.

Assuming a rectangular array of adsorbed proteins, the dimensions of which are the same as those previously reported [8x8x3 nm for albumin (He and Carter 1992), 3.7 x 2.5 x 2.5 nm for cytochrome c (Lvov et al. 1995)], the maximal densities are approximately 0.46 and 0.33 ^g/cm2 for albumin and cytochrome c, respectively. Clearly, multilayer adsorption under applied voltage is occurring for both proteins in water and possibly, following sufficient time, for cytochrome c in HEPES. As mentioned above, adsorption in the first layer probably involves attachment at a region of complementary charge. This in turn may expose regions of opposite charge, to which charged patches of incoming proteins may be attracted. A plausible cause of multilayer adsorption is therefore the axial interaction between aligned dipoles. One expects this interaction to become weaker with each layer, however, due to incomplete charge reversal. Thus, even systems exhibiting multilayers possess kinetic curves with negative curvature, if not true plateaus.

We observe the overall extent of adsorption and the influence on adsorption by an applied voltage to be greatest when employing a water solvent. One issue here is solvent quality: HEPES is a better solvent, as evidenced by higher protein solubility. Another issue is the higher pH of HEPES (7.4) compared to deionized water (5.5-6.0). For a given potential difference, this works to lower both ITO and platinum potentials (as shown in Fig. 4a,b). However, when comparing adsorption at roughly equal electrode potentials (e. g., water at AV = 1.0 V and HEPES at AV = 1.5 V), we continue to observe a greater degree of adsorption in the water system. A third issue is ionic strength: the ability of charged species in solution to screen electrostatic interactions is well established and this is clearly serving to reduce in magnitude the effective (or "zeta") potential of the proteins and surfaces investigated here. For example, screening of dipolar interactions by ionic species in the HEPES solvent seems to suppress multilayer formation.

An applied potential clearly offers an opportunity to influence the structure and formation kinetics of an adsorbed protein layer. Interestingly, our work, and that of others (Asanov et al. 1997, 1998; Bernabeu and Caprani 1990; Bos et al. 1994; Feng and Andrade 1994; Fievet et al. 1998; Fraaije et al. 1990; Khan and Wernet 1997) shows that observed behavior does not always follow that expected from basic electrostatic considerations. There is little agreement on the cause of such behavior and, therefore, on the very nature of an applied potential's influence on protein adsorption. Proposed explanations invoke surface-bound counterions, local pH effects, interfacial solvent structure, and protein charge heterogeneity. We will now comment upon each of these effects:

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