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Intracellular forces from stiffness

A high-spatial-resolution force microscopy method combined with a model of cellular mechanics quantifies intracellular forces from nanoscale stiffness patterns at the cell membrane.

Mechanobiology aims to understand how mechanical forces determine biological interactions and processes. The mechanical properties of cells are crucial regulators of several cellular functions, from signalling to cell division. They are also used as markers of disease1,2. At the single-cell level, mechanical forces are generated by a complex machinery that involves a variety of proteins (for example, receptors, molecular motors) and cytoskeletal filaments, resulting in nanoscale force distributions whose origin and properties are difficult to characterize3. Now, writing in Nature Materials, Ozgur Sahin and colleagues4 describe a method to determine the intracellular tension of an actin bundle anchored beneath the plasma membrane from spatially resolved cell stiffness maps obtained by a force microscope. The same approach is also applied to measure the cortex and plasma membrane tensions.

In recent years a wave of contributions have proposed novel experimental and theoretical approaches to generate high-resolution maps of mechanical properties of living cells5,6,7,8,9. Most of these methods are based on atomic force microscopy (AFM) and are used to determine the stiffness of living cells under different physiological or pathological conditions. Stiffness is an elastic material property that has units of force divided by distance. It is determined from the force exerted on a cell as a function of the tip distance (force–distance curve). AFM enables the determination of force–distance curves as a function of the tip lateral position on the cell surface, which can be used to build cellular stiffness maps. Until now, the interpretation of stiffness values in terms of the mechanical properties (for example, Young’s modulus) of the cell structure, such as the actin bundles, cell cortex, plasma membrane or nucleus, required the use of contact mechanical models. Typically, these models consider the cell as a semi-infinite, elastic and isotropic system, and also require knowledge of the tip’s geometry. Those approximations make it difficult to establish a direct relationship between the spatial variation observed in the stiffness maps with the intracellular forces determining the local cell mechanics.

Sahin and colleagues adapted a T-shaped cantilever for cell stiffness imaging, which was mounted in a multi-frequency AFM. This approach enables the acquisition of force–distance curves with low cellular indentations (down to 20 nm) and force noise (less than 10 pN) in several types of living cells. From these data, high-spatial-resolution cellular stiffness maps can be generated. Such maps provide two main observables, the stiffness and curvature radius of the peripheral actin bundles. To demonstrate the relationship between the stiffness of a filament and its tension, the authors developed a cell mechanical model where an actin bundle anchored at its ends to focal adhesions (Fig. 1a) is considered as a cylindrical beam resting on an elastic mattress (the cytoplasm) (Fig. 1b). An external force applied to the beam like the one exerted by the tip (Fig. 1b) will cause a deformation of the beam. The reaction force of the beam could have two different origins, one arising from the tension along the beam and another imposed by the beam-bending modulus. Those contributions are characterized by different relationships between the stiffness and the curvature radius of the beam. The authors use AFM images of living cells to measure the curvature radius of different actin bundles and study their dependence on the bundle stiffness. They find that the bundle curvature radius is proportional to the square of the bundle stiffness. This relationship can only be explained if the reaction force is dominated by the tension of the bundle. A relevant consequence of this result is that the curvature radius of a bundle is proportional to its tension, indicating that nanoscale cellular stiffness can be quantitatively linked to intracellular forces.

Fig. 1: Cellular mechanical model for intracellular forces determination from stiffness measurements.

a, Forces operating on an actin bundle underneath the cell surface. A curved actin bundle stretched between focal adhesions has a tension T (red arrows), imposing an outer force towards the plasma membrane (orange arrows). From the tension on a bundle at the cell edge and its curvature radius (R), it is possible to determine the plasma membrane tension. b, Two-dimensional illustration of the actin bundle, plasma membrane, cortex and cytoplasm mechanical model under the action of an AFM tip (blue). The green layer represents the plasma membrane and the cortex. The springs simulate the response of the cytoplasm. The red arrows are the direction of the tension of the actin bundle. The force applied by the tip induces a deformation on the plasma membrane and cell cortex and a reaction force from the bundle. By measuring local stiffness with AFM it is possible to determine the tension on the bundle using a. Adapted from ref. 4, Springer Nature Ltd.

Altogether, the authors demonstrate that the tension of actin bundles, cell cortex and plasma membrane can be determined from cell stiffness measurements if these have enough spatial resolution. These findings represent a significant advancement in the characterization of the local mechanical response of cells for two reasons. First, the measurement on an acting bundle is linked in a specific manner with the intracellular forces between the bundle and the rest of the cell. Second, the cellular pre-stress could change as the cell experiences a metabolic process and thus this approach could be applied to follow quantitatively dynamic processes. The quantitative accuracy, spatial resolution and directness of the AFM-based approach reported by Sahin and colleagues in determining intracellular forces in living cells will accelerate our understanding of how internal forces contribute for cellular activity.


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Correspondence to Ricardo Garcia.

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Garcia, R. Intracellular forces from stiffness. Nat. Mater. 18, 1037–1038 (2019).

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