Book of Abstracts: Albany 2007
June 19-23 2007
Calculation of DNA-ligand Binding Characterized by the Infinite Radius of Interactions of Adsorbed Ligands
Adsorption of ligands on DNA has been considered using our modification of the Zasedatelev, Gursky, Volkenshtein, and Nechipurenko method (hereinafter the ZGVN method). It is supposed in their model that each ligand covers several neighboring binding centers (m) and interacts with its nearest two neighbors along a DNA chain if the distance to them (i) is less than V binding centers (0≤i<V). If the distance (i) is greater than or equal V, then the free energy of interaction between ligands (εi) is taken to be zero (ai=exp[(-εi/(RT)]=1 for i≥V). In our model, the energy εi is taken arbitrarily for any i. We have found that characteristics of ligand binding to the infinite chain can be represented in a simple form using two infinite series S1 and S2:
Dmitri Y. Lando*
Institute of Bioorganic Chemistry
In the expressions, the parameter P is taken arbitrarily from the interval 0≤P<1, after that series S1 and S2 are calculated using Eqs. [1a], [1b], then the molar concentration of free ligands Co is found from Eq. [1c]. The number of ligands per bp c and the number of distances between ligands of i binding centers per bp zi corresponding to this Co are calculated using Eqs. [1d], [1e]. In the expressions, g is the number of base pairs per binding center; K the ligand-DNA binding constant; ai=exp[(-εi/(RT)] the factor of interaction of a ligand with its nearest right neighbor located at a distance of i binding centers. P=1 corresponds to free DNA without ligands: S1=∞, S2=∞, S1/S2=0, Co=0, c=0; zi=0 (for i=0, ∞). P=0 corresponds to DNA fully covered with ligands without free binding centers between them: S1=ao, S2=0, Co=∞, c=(g·m)-1; zo=(g·m)-1; zi=0 (for i=1, ∞). The infinite series S1 and S2 can be easily reduced to the finite ones if the energy of ligand-ligand interaction is independent of distance i for i≥V, i.e., ai=aV for i≥V.
By comparison of results of calculation for the infinite chain (the modified ZGVN method) and the finite one (matrix formalism), we have demonstrated that the additional parameter P is equal to the number of binding centers that locate out of blocks of interacting ligands divided by the sum of this quantity and the number of regions formed by binding centers located out of the blocks.
As an example of the application of the modified ZGVN method, calculation has been carried out for repulsive long-range interaction between neighboring DNA bound ligands, which strengthens with the distance. Such interactions arise, for example, if ligands are crosslinking agents that form loops in a single stranded polynucleotides or partially melted DNA. It is known that, for loops in partially melted DNA, ai∼(1+i)-α where α=1.5-2.25. We have shown that, for such crosslinking ligands, a plot c/Co versus c (Scatchard curve) tends to zero at c→0 in contrast to non-cooperative binding and contact cooperativity characterized by c/Co that tends to the binding constant K at c→0.
The work was supported in part by the Fund of Fundamental Investigations of the Republic of Belarus (grants X06R-102 and B06M-127).