Photoelastic Gel Microscopy (PGM): towards beacon-free direct imaging of cellular traction forces

在过去的二十年中，已经表明机械力在决定细胞过程中起着至关重要的作用-无论是在生理还是病理条件下-这导致了机械生物学的新兴领域[1]。已经证明，细胞以双向方式与其环境机械地相互作用，其中它们能够施加力，并且以类似的方式破译机械线索，例如体积刚度、刚度的时空变化、应力松弛、纳米形貌或剪切力的存在[2]。虽然控制这种双向相互作用的确切分子途径尚不清楚，但已知细胞内和细胞外间室之间的力的机械交换通过局灶性粘连发生。这些是超分子复合物，通常面积为几平方微米，通过大量蛋白质桥接细胞内和细胞外环境[3]。因此，细胞能够拉动周围环境-通过细胞内通过众所周知的肌动蛋白-肌球蛋白收缩机制产生的力-并通过粘着斑向外传递。然后细胞感觉到周围的机械反应，这是内源性的（即细胞外基质或ECM）或人造的（例如水凝胶）通过相同的转导机制，这反过来又可以引起和影响大量的细胞过程[1]。因此，为了充分利用机械生物学在诊断应用中的潜力，越来越需要能够以高精度和可再现性揭示和测量低至极限水平的力的专用工具。在这种情况下，细胞施加在其基质上的收缩力是特别感兴趣的-导致通常称为牵引力的收缩应力。已知这些力在生理条件下强烈参与组织和器官三维组织的发育和建立[4]。相反，观察牵引力的生理模式的损伤，可能是推断异常病理学（例如癌症）的发作的一种方式，已知异常病理学与细胞的机械行为的变化相关，细胞从其原始位置分离、挤出、侵入并最终呈现不同的三维组织，即转移[5，6].尽管揭示机械生物学丰富意义的途径仍处于起步阶段，但在生物医学研究的背景下已经迈出了第一步，解决了单细胞水平上牵引力的组织，并评估了特定事件-无论是生物化学，遗传的或机械的-反过来影响这种模式。最常见的方法是测量细胞-基质界面处的细胞力。自15年前首次出现以来，该领域发展迅速，导致了现在被称为牵引力显微镜（TFM）[7，8]。最常见的TFM方法是将细胞接种在含有参考荧光珠的已知硬度的基底（水凝胶）上。当细胞在基质上施加牵引力时，这些珠子的位移被光学监测，并且所施加的力从位移中恢复。力的间接测量需要基底的机械响应的本构模型和其物理性质的精确知识。这一点用线弹性弹簧的例子很容易理解，其本构模型由胡克定律（F = k（x-x 0））给出，其中F是力，k是弹簧的刚度，x-x 0是弹簧相对于其参考位置x 0的位移。如果不测量x（及其参考状态x 0），不知道k和整体本构律，原则上就不能得到力[7，8]。值得注意的是，这不是一个triv

Over the last two decades, it has been shown that mechanical forces play a crucial role in determining cellularprocesses - both in physiological and pathological conditions - which led to the emerging field of mechanobiology[1]. It has been demonstrated that cells mechanically interact with their environment in a bidirectional fashion,where they are able to exert forces and, in like manner, decipher mechanical cues, such as bulk stiffness, spatiotemporal changes in stiffness, stress relaxation, nanotopography or the presence of shear forces [2]. Whereasthe exact molecular pathways governing this bidirectional interplay remain unclear, the mechanical exchange offorces between the intracellular and extracellular compartments is known to occur via focal adhesions. Theseare supramolecular complexes, often of several square micrometres in area, bridging the intracellular and extracellular environments through a multitude of proteins [3]. As a result, cells are able to pull on their surroundingenvironment - via forces that are intracellularly generated through the well known mechanism of acto-myosincontractility - and transduced externally via focal adhesions. Cells then sense the mechanical response of theirsurrounding, being endogenous (i.e. the Extracellular Matrix or ECM) or man-made (e.g. hydrogels) via thesame transducing machinery, which, in turn, can give rise and influence a large number of cellular processes [1].As a consequence, in order to fully exploit the potential of mechanobiology for diagnostic applications, there isan increasing need for specialised tools providing the ability to reveal and measure forces down to the singlecell level with high accuracy and reproducibility.In this context, the contractile forces that cells exert on their substrate are of particular interest - resultingin contractile stresses commonly referred to as traction forces. These forces have been known to stronglyparticipate in the development and establishment of the three-dimensional organisation of tissues and organs inphysiological conditions [4]. Conversely, looking at the impairment of the physiological pattern of traction forces,might be a way to infer about the onset of an aberrant pathology, such as a cancer, known to be associated toa change in the mechanical behaviour of cells, which detach from their original location, extrude, invade andfinally assume a different three dimensional organisation, the metastasis [5, 6].Whereas the path to disclose the wealth of implications of mechanobiology is still in its infancy, the firststeps have been taken in the context of biomedical research addressing the organisation of traction forces at thelevel of the single cell, and evaluating how specific events - either biochemical, genetic or mechanical - in turninfluence this pattern. The most common approach is to measure cellular forces at the cell-matrix interface.This field has grown rapidly since it first emerged 15 years ago, leading to what is now known as Traction ForceMicroscopy (TFM) [7, 8]. The most common TFM approach is to seed cells on a substrate of known stiffness(a hydrogel) containing reference fluorescent beads. As cells apply tractions on the substrate, the displacementof such beads is optically monitored and the exerted forces retrieved from the displacement. The indirectmeasurement of forces requires both a constitutive model of the substrate's mechanical response and preciseknowledge of its physical properties. This is easily understood with the example of a linear elastic spring, whoseconstitutive model is given by Hooke's law (F = k(x - x0)), where F is the force, k is the spring's stiffnessand x - x0 is the spring's displacement with respect to its reference position, x0. Without a measurement ofx (and its reference state x0), knowledge of k and the overall constitutive law, the force, in principle, cannotbe retrieved [7, 8]. Notably, this is not a triv