Analysis of drug-DNA binding isotherms: a Monte Carlo approach

Monte Carlo simulations of neighbor exclusion models have been used to demonstrate the importance of collecting and fitting data over a wide range of saturation. Low saturation data are important for good estimates of the affinity K of a drug or protein for the lattice site. High saturation data are important for distinguishing between negatively cooperative and noncooperative binding modes. Neglect of negative cooperativity (omega < 1) has in general little effect on the estimation of K. The error is mostly absorbed by increasing the value of n. This kind of behavior was previously observed with the fitting of nonideal, monomer-dimer, ultracentrifugation data where variations in B, the second virial coefficient, and K2, the dimerization equilibrium constant, are highly correlated, thus making their individual determination difficult. Within experimental error the distinction between a noncooperative model [Eq. (1)] and a negatively cooperative model [Eq. (3) or (4) with omega < 1] may require additional evidence to justify the choice of one model over another. For example, for homogeneous lattices of synthetic deoxyoligonucleotides, n may be constrained with some validity, thus allowing a more accurate and precise determination of K and omega. In fact, n may be established independently, for example, by nuclear magnetic resonance (NMR) methods. However, the assumption of an integral value of n for natural DNA samples may not be valid because of sequence heterogeneity. Unconstrained fitting of negatively cooperative data to Eq. (4) will thus be a very difficult problem (Table V). At an experimental error of only 2.3%, n and K can be reasonably determined but with a large error in omega. Data from the final 20% of saturation are essential in extracting omega. This may in part explain the absence of more reports of negatively cooperative behavior in the literature. This analysis is independent of the systematic error that may be induced by the transformation of data to the Scatchard plot, or the omission of drug self-association, or the occurrence of wall binding by ligand, or variable point density, or non-Gaussian noise, or the occurrence of another mode of binding distinct from the models of McGhee and von Hippel. Each of these will introduce additional error, possibly biased error, in the parameters estimated; however, this does not obviate our conclusion. Even under these ideal circumstances there are serious limitations that must be considered when fitting neighbor exclusion model data. The direct fitting of absorbance data [to Eq. (2) or functions that incorporate other parameters] will also be sensitive to these considerations.