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Mixed association models

These models are only implemented for sedimentation equilibrium data.

mixed association:  incompetent species are incompetent for both monomer-dimer and heterogeneous association

* log or lg means log10

* a species not participating in the association can be specified (check the 'add non-participating species' field) This is simply an additional component, perhaps an impurity, which has nothing to do with the associating molecules.

1) Monomer-Dimer A, A2 binding B, forming heterogeneous complexes AB, AAB, and BAAB

with K_A12: monomer-dimer association constant (microscopic = macroscopic)

K_AB: microscopic heterogeneous binding constant of B to A 

a_A:  macroscopic cooperativity constant of K_[AA]B/K_AB, i.e. enhancement of AB interface through the dimerization of A. If there's no microscopic cooperativity here, the macroscopic value of this parameter is the statistical factor 2 (or log10(a_A) = 0.30103).

a_A^M: macroscopic cooperativity constant K_[BAA]B/K_[AA]B, i.e. enhancement of binding of the second B to the free A of a preformed AAB complex through the presence of a prior B (either via B-B interactions, or modifications of the free protomer of A in the AAB complex) (microscopic = macroscopic).  If there's no microscopic cooperativity here, the macroscopic value of this parameter is the statistical factor 1/4 (or log10(a_A^M) = -0.60206).

1) Monomer-dimer A, A2, and monomer-dimer B, B2, forming heterogeneous complexes AB, AAB, BBA, and BAAB

with K_A12: monomer-dimer association constant of A (microscopic = macroscopic)

with K_B12: monomer-dimer association constant of B (microscopic = macroscopic)

K_AB: microscopic heterogeneous binding constant of B to A 

a_A:  macroscopic cooperativity constant of K_[AA]B/K_AB, i.e. enhancement of AB interface through the dimerization of A. If there's no microscopic cooperativity here, the macroscopic value of this parameter is the statistical factor 2 (or log10(a_A) = 0.30103).

a_B:  analogous to a_A - macroscopic cooperativity constant of K_[BB]A/K_AB, i.e. enhancement of AB interface through the dimerization of B. If there's no microscopic cooperativity here, the macroscopic value of this parameter is the statistical factor 2 (or log10(a_B) = 0.30103).

a_A^M: macroscopic cooperativity constant K_[BAA]B/K_[AA]B, i.e. enhancement of binding of the second B to the free A of a preformed AAB complex through the presence of a prior B (either via B-B interactions, or modifications of the free protomer of A in the AAB complex). If there's no microscopic cooperativity here, the macroscopic value of this parameter is the statistical factor 1/4 (or log10(a_A^M) = -0.60206).

a_B^M: macroscopic cooperativity constant K_[BBA]A/K_[BB]A, i.e. enhancement of binding of the second A to the free B of a preformed BBA complex through the presence of a prior A (either via A-A interactions, or modifications of the free protomer of B in the BBA complex). If there's no microscopic cooperativity here, the macroscopic value of this parameter is the statistical factor 1/4 (or log10(a_A^M) = -0.60206).

There is the relationship: 

All models provide the possibility of adding an additional species that is unrelated to the reactive species. 

This can be used to describe, for example, a contaminant, or IF signals from sedimenting buffer salts.  The presence of such components, and their estimated molar mass and s-value may be obtained from c(s) analysis with sedfit.  The purpose of the vbar in this section allows this species to be used in a flexible way in density contrast experiments (e.g. to describe the free detergent micelle).