Ray Chad, Brown Jason R, Akhremitchev Boris B
Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.
J Phys Chem B. 2007 Mar 1;111(8):1963-74. doi: 10.1021/jp065530h. Epub 2007 Feb 7.
Single-molecule force spectroscopy has become a valuable tool for the investigation of intermolecular energy landscapes for a wide range of molecular associations. Atomic force microscopy (AFM) is often used as an experimental technique in these measurements, and the Bell-Evans model is commonly used in the statistical analysis of rupture forces. Most applications of the Bell-Evans model consider a constant loading rate of force applied to the intermolecular bond. The data analysis is often inconsistent because either the probe velocity or the apparent loading rate is being used as an independent parameter. These approaches provide different results when used in AFM-based experiments. Significant variations in results arise from the relative stiffness of the AFM force sensor in comparison with the stiffness of polymeric tethers that link the molecules under study to the solid surfaces. An analytical model presented here accounts for the systematic errors in force-spectroscopy parameters arising from the nonlinear loading induced by polymer tethers. The presented analytical model is based on the Bell-Evans model of the kinetics of forced dissociation and on the asymptotic models of tether stretching. The two most common data reduction procedures are analyzed, and analytical expressions for the systematic errors are provided. The model shows that the barrier width is underestimated and that the dissociation rate is significantly overestimated when force-spectroscopy data are analyzed without taking into account the elasticity of the polymeric tether. Systematic error estimates for asymptotic freely jointed chain and wormlike chain polymer models are given for comparison. The analytical model based on the asymptotic freely jointed chain stretching is employed to analyze and correct the results of the double-tether force-spectroscopy experiments of disjoining "hydrophobic bonds" between individual hexadecane molecules that are covalently tethered via poly(ethylene glycol) linkers of different lengths to the substrates and to the AFM probes. Application of the correction algorithm decreases the spread of the data from the mean value, which is particularly important for measurements of the dissociation rate, and increases the barrier width to 0.43 nm, which might be indicative of the theoretically predicted hydrophobic dewetting.
单分子力谱已成为研究广泛分子缔合的分子间能量景观的重要工具。原子力显微镜（AFM）常被用作这些测量中的实验技术，而贝尔 - 埃文斯模型通常用于断裂力的统计分析。贝尔 - 埃文斯模型的大多数应用都考虑作用于分子间键的力的恒定加载速率。由于将探针速度或表观加载速率用作独立参数，数据分析往往不一致。这些方法在基于AFM的实验中使用时会产生不同的结果。与将研究中的分子连接到固体表面的聚合物系链的刚度相比，AFM力传感器的相对刚度会导致结果出现显著差异。本文提出的一个分析模型考虑了由聚合物系链引起的非线性加载导致的力谱参数的系统误差。所提出的分析模型基于强迫解离动力学的贝尔 - 埃文斯模型和系链拉伸的渐近模型。分析了两种最常见的数据简化程序，并给出了系统误差的解析表达式。该模型表明，在分析力谱数据时，如果不考虑聚合物系链的弹性，势垒宽度会被低估，解离速率会被显著高估。给出了渐近自由连接链和蠕虫状链聚合物模型的系统误差估计值以供比较。基于渐近自由连接链拉伸的分析模型被用于分析和校正通过不同长度的聚乙二醇连接子共价连接到基底和AFM探针上的单个十六烷分子之间“疏水键”解离的双系链力谱实验结果。校正算法的应用减少了数据相对于平均值的离散度，这对于解离速率的测量尤为重要，并将势垒宽度增加到0.43 nm，这可能表明了理论预测的疏水去湿现象。
