Electrostatic patch model

The two major theories of flocculation, the bridging model (1) and the electrostatic patch model (2, 3 ), provide the conceptual framework for the understanding of polymer-aided flocculation, but they do not directly address the kinetics of the process. Smellie and La Mer (4) incorporated the bridging concept into a kinetic model of flocculation. They proposed that the collision efficiency in the flocculation process should be a function of the fractional surface coverage, 0. Using a modified Smoluchowski equation, they wrote for the initial flocculation rate... 

The results of the contact force measurements, p, between cellulosic fibers in the presence of PEI are shown in Figure 2.23. The observed trends are similar to those shown in Figure 2.21 for the friction coefficient measurements and are also in good agreanent with the patch model of flocculation by the PEI, and the previously mentioned electrokinetic studies, as reflected by the maximum in the cohesive force at low concentrations of PEI. As expected, after reaching the maximum, the cohesive forces decrease with a further increase in the PEI concentration. This corresponds to the decrease in the fraction of available negatively charged patches for interaction with PEI and the increase in the electrostatic repulsion due to a continued adsorption of PEI. 

FIGURE 3. Hypotctical structural model of the ternary complex formed between one molecule of D. salexigens flavodoxin and two molecules of Z). gigas cytochrome cj. Represented as thick black lines are possible intermolecular salt bridges formed between flavodoxin and the cytochromes and also between both hemic proteins. The FMN on flavodoxin and the heme surrounded by a patch of positive electrostatic potential (see text) are also shown as thick black lines, while the remaining hemes are represented by thick gray lines. 

The electrical properties of OmpF have been measured for long times, both with patch-clamp techniques and on planar lipid membranes." A high-resolution electrostatic mapping of the trimer was obtained with atomic probe microscopy,while a systematic electrostatic modeling of the pore lumen has been recently performed by two groups who did not limit their study to the wild protein, but comparatively analyzed several mutants. The electrostatic landscape of OmpF is a typical example of how the balance between strong interactions finely tunes the properties of a channel. Ionic trajectories have been simulated both with Brownian and molecular dynamics simulation codes,and the role of ion-ion interaction within the pore has been stressed as being important. 

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