End-to-surface reaction dynamics of a single surface-attached DNA or polypeptide

The dynamics of surface-attached polymers play a key role in the operation of a number of biological sensors, yet its current understanding is rather limited. Here we use computer simulations to study the dynamics of a reaction between the free end of a polymer chain and a surface, to which its other end has been attached. We consider two limiting cases, the diffusion-controlled limit, where the reaction is accomplished whenever the free chain end diffuses to within a specified distance from the surface, and the reaction-controlled limit, where slow, intrinsic reaction kinetics rather than diffusion of the chain is rate limiting. In the diffusion-controlled limit, we find that the overall rate scales as N(-b), where N is the number of monomers in the chain and b approximately = 2.2 for excluded volume chains. This value of the scaling exponent b is close to that derived from a simple approximate theory treating the dynamics of the chain end relative to the surface as one-dimensional diffusion in an effective potential. In the reaction-controlled limit, the value of the scaling exponent b is close to 1. We compare our findings with those for the related (and better studied) problem of end-to-end reactions within an unconstrained polymer chain and discuss their implications for electrochemical DNA sensors.