Competitive DNA binding of Ru ( bpy ) 2 dppz 2 + enantiomers studied with isothermal titration calorimetry ( ITC ) using a direct and general binding isotherm algorithm

While isothermal titration calorimetry (ITC) is widely used and sometimes referred to as the "gold standard" for quantitative measurements of biomolecular interactions, its usage has so far been limited to the analysis of the binding to isolated, non-cooperative binding sites. Studies on more complicated systems, where the binding sites interact, causing either cooperativity or anti-cooperativity between neighboring bound ligands, are rare, probably due to the complexity of the methods currently available. Here we have developed a simple algorithm not limited by the complexity of a binding system, meaning that it can be implemented by anyone, from analyzing systems of simple, isolated binding sites to complicated interactive multiple-site systems. We demonstrate here that even complicated competitive binding calorimetric isotherms can be properly analyzed, provided that ligand-ligand interactions are taken into account. As a practical example, the competitive binding interactions between the two enantiomers of Ru(bpy)2dppz2+ (Ru-bpy) and poly(dAdT)2 (AT-DNA) are analyzed using our new algorithm, which provided an excellent global fit for the ITC experimental data.

Note that in the following programs, the total concentration of binding sites, denoted B 0 in the main text, is now denoted D0.
GeneralAlgorithm.m function [conc,x,f,P,r]=GeneralAlgorithm(C0,M,T,Y,K,n,r) %General algortihm for solving the mass balance for %ligands interacting with a linear polymer of identical binding site units %D with explicit nearest neighbor interaction.
%INPUT: %CO=[D0 A0 B0...] 1x(1+L) vector with total concentration of %binding site units D and L ligands A, B... %M = mxL matrix of the stoichiometric coefficients for the m ligandcontaing elementary %units.%T = mxm non-singular matrix transforming M such that in the product T*M no column is %zero, and each row only contains one 1, the rest being zeros.%Y =(m+1)x(m+1)matrix containg the cooperativity parameters for nearest %neighbor interactions between the elementary units, the first row and %column being the interactions with the ligand-free elementary unit.%K = Intrinsic binding constants of the elementary units.%n = Number of binding site units made inaccesible by formation of the elementary unit.%r = Guess for vector r %OUTPUT %conc = [[Afree; Bfree ...][ Abound; Bbound ...]] %x = binding potentials of elementary units %f = binding densities of elementary units %P = matrix of conditional probabilities %r = vector r that solves the mass balance equations [m,l]

Figure S1 :
Figure S1: Fit of (7+5) parameter Model 3 (red) and (5+4) parameter model 4* (blue) to the ITC data.Note that in addition to an inferior fit, the enthalpy values obtained from Model 4 are of an unrealistically high magnitude.
'; %For each of the 4 titrations, appropriate submatrices are constructed.Here La only titration.