The nature of the helix–random coil transition of biological macromolecules attached to a surface

The effect of the presence of a surface on the helix–random coil transition is investigated. It is found that a grand canonical ensemble formation used previously to solve exactly the problem of a polymer between two plates can be used to solve approximately the problem of DNA near a plane surface. The formalism is applied to the homogeneous perfect‐matching model of infinite molecular weight. A crucial part of the calculation for double‐stranded molecules involves the evaluation of the entropy of the loops connecting the helical portions of the double‐stranded chains. One obtains as a measure of the configurational freedom of a loop Asi/jc where c has the following values: for a loop connecting two helical regions both off the surface c = 3/2; for a loop connecting a helical region on the surface to a helical region off the surface c = 5/2; for a loop connecting helixes both on the surface c = 4. Corresponding values for an n‐stranded molecule are c = (3n − 3)/2, c = (4n − 3)/2, c = (5n − 2)/2. In all cases, the effect of the surface is to sharpen the transition. In the case of double‐stranded molecules, the transition becomes first order. We take the view that self‐assembly of biological macromolecules can be considered as a sharp thermodynamic phase transition. Thus, the above systems become models of self‐assembling systems. They are also relevant to the problem of surface‐induced enzymatic activity.