Statistical multivalency

F la-e Some possible modes of multivalent binding events, a Statistical multivalency, b Chelating, c Clustering, d Adhesion, e Sub-site binding... 

Tiller and O Melia (1993) compared their polymer adsorption statistics calculations with data from laboratory experiments on the interaction of polyacrylic and polyaspartic acid as well as of humic acids with hematite. Their conclusion is that, at low ionic strength, anionic polyelectrolytes affect the coagulation of positively charged particles by altering the net surface charge in a way similar to that of multivalent, monomeric anions. Steric repulsion, at low ionic strength (i.e., in fresh water), plays little or no role in the stabilization of hematite colloids by the organic macromolecules used in their work calcium... 

Equation 3.108 predicts a higher local concentration of cations near a negatively charged clay surface than in bulk solution, and a lower concentration of anions near the surface than in solution. Figure 3.24 shows this predicted distribution of monovalent cations and anions near the clay surface for two different concentrations of electrolyte in solution. More modem statistical mechanical models of this clay interfacial region have predicted that ion-ion correlation (electrostatic) effects should cause deviations from this classical picture, such as the positive adsorption of anions at intermediate distances from the surface when the cation is divalent or multivalent. 

Lombardo F, Obach RS, Shalaeva MY and Gao F, Prediction of human volume of distribution values for neutral and basic drugs. 2. Extended data set and leave-class-out statistics, J. Med. Chem., 47,1242-1250 (2004). Ref. 304 Hasegawa J, Fujita T, Hayashi Y, Iwamoto K and Watanabe J, pJC determination of verapamil by liquid-liquid partition, J. Pharm. Sci., 73, 442-445 (1984). At 31 C, the value was 8.79, and at 37 °C, die value was 8.68 305 Ishihama Y, Oda Y and Asakawa N, Microscale determination of dissociation constants of multivalent pharmaceuticals by capillary electrophoresis,... 

Ercolani G, Piguet P, Borkovec M, HamacekJ. Symmetry numbers and statistical factors in self-assembly and multivalency. J Phys Chem B. 2007 111 12195-12203. 

These results unequivocally demonstrated the existence of tailored presentation of peripheral recognition moieties insured by the rigid central scaffold. Clear multivalent effects beyond the expected statistical rebinding and local concentration effects was observed. In addition, the plausible implication of a sliding mechanism of the inhibitors in the enzyme active site or an additional binding process at a close allosteric site might explain the distinct specificity enhancement. 

Here, n is the valency number, F is statistical factor defined by the system, and s = 30/(interreceptor distance (A)). An application is illustrated by a monovalent P trisaccharide ligand, which binds to pentavalent Shiga toxin (AB5) with a Ka of 10 M . If this monovalent ligand is converted to a polyvalent ligand through conjugation to polyacrylamide, a binding constant can be estimated for the multivalent interaction with the toxin pentamer as follows in (8). 

The contribution of the statistical rebinding of multivalent ligands to multivalent receptors is essential to the mechanism of multivalent binding. A critical parameter for assessment of this statistical rebinding is effective concentration. Effective concentration is a theoretical parameter that allows for the estimation of the kinetics and thermodynamics of ring closure for intramolecular reactions. ... 

Multivalency effect due to high local concentration (statistical rebinding)... 

Perel, V. I. and B. I. Shklovskii. 1999. Screening of a macroion by multivalent ions A new boundary condition for the Poisson-Boltzmann equation and charge inversion. Physica A Statistical Mechanics and its Applications 21A (3) 446-453. 

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