Gerbal Fabien, Wang Yuan
Laboratoire Matière et Systèmes Complexes UMR 7057 (CNRS) and Université Denis Diderot-Sorbonne Paris Cité, 75013 Paris, France;
Université Pierre et Marie Curie-Paris 6, Sorbonne Universités, 75252 Paris Cedex 05, France.
Proc Natl Acad Sci U S A. 2017 Mar 7;114(10):2456-2461. doi: 10.1073/pnas.1608697114. Epub 2017 Feb 22.
The rigidity of numerous biological filaments and crafted microrods has been conveniently deduced from the analysis of their thermal fluctuations. However, the difficulty of measuring nanometric displacements with an optical microscope has so far limited such studies to sufficiently flexible rods, of which the persistence length ([Formula: see text]) rarely exceeds 1 m at room temperature. Here, we demonstrate the possibility to probe 10-fold stiffer rods by a combination of superresolutive optical methods and a statistical analysis of the data based on a recent theoretical model that predicts the amplitude of the fluctuations at any location of the rod [Benetatos P, Frey E (2003) 67(5):051108]. Using this approach, we report measures of [Formula: see text] up to 0.5 km. We obtained these measurements on recently designed superparamagnetic [Formula: see text]40-[Formula: see text]m-long microrods containing iron-oxide nanoparticles connected by a polymer mesh. Using their magnetic properties, we provide an alternative proof of validity of these thermal measurements: For each individual studied rod, we performed a second measure of its rigidity by deflecting it with a uniform magnetic field. The agreement between the thermal and the magnetoelastic measures was realized with more than a decade of values of [Formula: see text] from 5.1 m to 129 m, corresponding to a bending modulus ranging from 2.2 to 54 (×[Formula: see text] Jm). Despite the apparent homogeneity of the analyzed microrods, their Young modulus follows a broad distribution from 1.9 MPa to 59 MPa and up to 200 MPa, depending on the size of the nanoparticles.
许多生物细丝和人造微棒的刚性已通过对其热涨落的分析方便地推导出来。然而，用光学显微镜测量纳米级位移的困难迄今将此类研究限制在足够灵活的棒上，在室温下其持久长度（[公式：见原文]）很少超过1米。在这里，我们展示了通过超分辨光学方法与基于最近预测棒在任何位置涨落幅度的理论模型进行数据统计分析相结合来探测刚度高10倍的棒的可能性[贝内塔托斯P，弗雷E（2003年）67(5):051108]。使用这种方法，我们报告了高达0.5千米的[公式：见原文]测量值。我们在最近设计的超顺磁性40 - [公式：见原文]米长的微棒上获得了这些测量值，这些微棒包含通过聚合物网连接的氧化铁纳米颗粒。利用它们的磁性，我们为这些热测量的有效性提供了另一种证明：对于每个单独研究的棒，我们通过用均匀磁场使其偏转来对其刚度进行第二次测量。在5.1米至129米的[公式：见原文]值范围内，热测量和磁弹性测量之间的一致性在十多年的时间里得以实现，对应于2.2至54（×[公式：见原文]焦耳米）的弯曲模量。尽管所分析的微棒表面上是均匀的，但它们的杨氏模量根据纳米颗粒的大小从1.9兆帕到59兆帕以及高达200兆帕呈现出广泛的分布。
