Enrico Ravera, Azzurra Carlon, Giacomo Parigi*

Pairwise binding competition experiments for sorting hub-protein/effector interaction hierarchy and simultaneous equilibria

Enrico Ravera, Azzurra Carlon, Giacomo Parigi*

Magnetic Resonance Center (CERM) and Department of Chemistry “Ugo Schiff”, University of Florence, Italy

e-mail:

SUPPLEMENTARY MATERIAL

At first, the dissociation constants between a hub protein R and each of the N binding proteins Y are written:

(S1)

The intensity ratios between pairs of complexes with the binding proteins A and B are related to their dissociationconstants through the relationship:

(1)

By definition, , and ;then, for the experimental setup and assuming that A and B are in large excess with respect to R, and that R binds to either A or B completely within the experimental uncertainty .

Equation 1 thus becomes:

(S2)

so that

(S3)

that leads to the equation of second degree in [RB]

(2)

Since in the presence of multiple binding proteins

(5)

equation S1 yields:

.(6)

Equation 6 can be rearranged into

, (S4)

and, in analogy to what already done, we substitute for

(S5)

that directly recasts into

(S6)

and, after normalization by CR2,

(8)

Rigorous resolution of this and similar systems, representing coupled equilibria, can be accomplished via the Newton method. The relevant expression for the Jacobian matrix elements is:

(S7)

To demonstrate that the relative distribution between the binding partners is independent on their dissociation constant values but only depends on their ratios, equation 7 is obtained from equation 6 as follows:

(S8)

The ratio is taken with another constant, to yield:

(S9)

From this, [RY] can be extracted:

(S10)

(S11)

that directly recasts into equation 7.

Figure S1. Agreement between experimental and back-calculated ratios in the concentration of formed complexes for all pairwise experiments with the wild type RAS. Experiments are numbered as in Tables 2.

Figure S2. Agreement between experimental and back-calculated ratios in the concentration of formed complexes for all pairwise experiments with the G12V mutant. Experiments are numbered as in Table 3.

Figure S3: Concentration profiles calculated for a mixture of competitors in 4:1 excess with respect to wild type RAS. The concentration of one competitor at a time is varied in the mixture (panels A-I) and the percentage of RAS bound to the selected competitor is calculated. Panel J summarizes the concentration of all the competitors as calculated in panels A-I.

Figure S4: Concentration profiles calculated for a mixture of competitors in 4:1 excess with respect to G12V RAS (see Figure S3).