von Hansen Yann, Mehlich Alexander, Pelz Benjamin, Rief Matthias, Netz Roland R
Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany.
Rev Sci Instrum. 2012 Sep;83(9):095116. doi: 10.1063/1.4753917.
The thermal fluctuations of micron-sized beads in dual trap optical tweezer experiments contain complete dynamic information about the viscoelastic properties of the embedding medium and-if present-macromolecular constructs connecting the two beads. To quantitatively interpret the spectral properties of the measured signals, a detailed understanding of the instrumental characteristics is required. To this end, we present a theoretical description of the signal processing in a typical dual trap optical tweezer experiment accounting for polarization crosstalk and instrumental noise and discuss the effect of finite statistics. To infer the unknown parameters from experimental data, a maximum likelihood method based on the statistical properties of the stochastic signals is derived. In a first step, the method can be used for calibration purposes: We propose a scheme involving three consecutive measurements (both traps empty, first one occupied and second empty, and vice versa), by which all instrumental and physical parameters of the setup are determined. We test our approach for a simple model system, namely a pair of unconnected, but hydrodynamically interacting spheres. The comparison to theoretical predictions based on instantaneous as well as retarded hydrodynamics emphasizes the importance of hydrodynamic retardation effects due to vorticity diffusion in the fluid. For more complex experimental scenarios, where macromolecular constructs are tethered between the two beads, the same maximum likelihood method in conjunction with dynamic deconvolution theory will in a second step allow one to determine the viscoelastic properties of the tethered element connecting the two beads.
在双阱光镊实验中，微米级珠子的热涨落包含了关于包埋介质粘弹性特性以及（如果存在的话）连接两个珠子的大分子结构的完整动态信息。为了定量解释测量信号的光谱特性，需要详细了解仪器特性。为此，我们给出了一个典型双阱光镊实验中信号处理的理论描述，该描述考虑了偏振串扰和仪器噪声，并讨论了有限统计的影响。为了从实验数据中推断未知参数，我们推导了一种基于随机信号统计特性的最大似然方法。第一步，该方法可用于校准目的：我们提出了一个涉及三次连续测量的方案（两个阱都为空、第一个阱被占据且第二个阱为空、反之亦然），通过该方案可以确定装置的所有仪器和物理参数。我们针对一个简单的模型系统，即一对未连接但存在流体动力学相互作用的球体，测试了我们的方法。与基于瞬时以及延迟流体动力学的理论预测进行比较，突出了流体中涡度扩散导致的流体动力学延迟效应的重要性。对于更复杂的实验场景，即两个珠子之间连接有大分子结构的情况，第二步中，同样的最大似然方法结合动态反卷积理论将能够确定连接两个珠子的连接元件的粘弹性特性。
