Department of Chemistry and Biochemistry and Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA.
J Phys Chem B. 2010 Mar 11;114(9):3321-9. doi: 10.1021/jp910669d.
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.
表面附着聚合物的动力学在许多生物传感器的运作中起着关键作用，但目前对此的理解相当有限。在这里，我们使用计算机模拟来研究聚合物链自由端与表面之间的反应动力学，其另一端已附着在表面上。我们考虑了两种极限情况，即扩散控制极限，只要自由链端扩散到离表面指定距离内，反应就会完成，以及反应控制极限，其中缓慢的固有反应动力学而不是链的扩散是限速的。在扩散控制极限下，我们发现总速率与 N(-b)成正比，其中 N 是链中的单体数，b 约为 2.2 对于排斥体积链。该标度指数 b 的值接近从简单的近似理论中得出的数值，该理论将链末端相对于表面的动力学处理为有效势中的一维扩散。在反应控制极限下，b 的标度指数值接近 1。我们将我们的发现与未受约束聚合物链内端到端反应的相关（且研究得更好）问题的发现进行了比较，并讨论了它们对电化学 DNA 传感器的影响。
