Cell stiffness measurements have led to insights into various physiological and pathological processes1,2. Although many cellular behaviors are influenced by intracellular mechanical forces3–6 that also alter the material properties of the cell, the precise mechanistic relationship between intracellular forces and cell stiffness remains unclear. Here we develop a high spatial resolution cell mechanical imaging platform that reveals the existence of nanoscale stiffness patterns that are governed by intracellular forces. Based on these findings, we develop and validate a cellular mechanical model that quantitatively relates cell stiffness to intracellular forces. This allows us to determine the magnitude of tension within actin bundles, cell cortex, and plasma membrane from the cell stiffness patterns across individual cells. These results expand our knowledge on the mechanical interaction between cells and their environments and offer an alternative approach to determine physiologically-relevant intracellular forces from high-resolution cell stiffness images.

Highlights d Flexible nanopipettes are minimally invasive intracellular nanoelectrodes d Quantum-dot coatings enable two-photon visualization of flexible nanopipettes d Two-photon targeted recordings from both somata and dendrites in vivo d PV + interneurons go into depolarization block during seizure spread in vivo

Cells sense the rigidity of their environment through localized pinching, which occurs when myosin molecular motors generate contractions within actin filaments anchoring the cell to its surroundings. We present high-resolution experiments performed on these elementary contractile units in cells. Our experimental results challenge the current understanding of molecular motor force generation. Surprisingly, bipolar myosin filaments generate much larger forces per motor than measured in single molecule experiments. Further, contraction to a fixed distance, followed by relaxation at the same rate, is observed over a wide range of matrix rigidities. Lastly, step-wise displacements of the matrix contacts are apparent during both contraction and relaxation. Building upon a generic two-state model of molecular motor collections, we interpret these unexpected observations as spontaneously emerging features of a collective motor behavior. Our approach explains why, in the cellular context, collections of resilient and slow motors contract in a stepwise fashion while collections of weak and fast motors do not. We thus rationalize the specificity of motor contractions implied in rigidity sensing compared to previous in vitro observations.

Different types of cells, i.e. from different tissues, typically look quite different from each other. Even when cultured on two-dimensional surfaces like glass slides or tissue culture polystyrene under identical conditions, cells adopt different shapes. These shapes are in general functions of the cytoskeletal properties of those cells, itself a subset of what we call the ''state'' of the cell. Moreover the changes in cell shape upon perturbation of the surface or of the cells themselves should reflect their intrinsic cellular properties, i.e. the cell state. Significant evidence has accumulated that changes in shape can also alter cellular properties, at least for some cells. Our experiments suggest that for Mesenchymal Stem Cells (MSCs), shape perturbations have consequences for their differentiation into osteoblasts. Thus shape seemed linked to fate. These statements beg the question: is it possible to use cell shape to assess cell state? For example can we back-calculate the cytoskeletal properties of the cell from the way it looks on surfaces? This question becomes all the more interesting for cancer cells since cancer cells are known to have altered mechanical properties compared to normal cells, and invasive cancer cells appear to have altered mechanical properties compared to noninvasive cancer cells. In this work we present a combination of experiments and statistical data analysis to try to begin to understand how cell shapes are affected by changes in surface properties or by perturbations of the cytoskeleton. We use fluorescent imaging to obtain the two-dimensional profile of cells and novel Third Harmonic Generation methods to obtain threedimensional images on cells on substrates. We use these experiments to infer how the cell shape of cancer cells could be associated with their invasive properties. We discuss some rudimentary mathematical models based on these results.

Synapses play a critical role in neural circuits, and they are potential sites for learning and memory. Maintenance of synaptic adhesion is critical for neural circuit function, however, biophysical mechanisms that help maintain synaptic adhesion are not clear. Studies with various cell types demonstrated the important role of stiffness in cellular adhesions. Although synaptic stiffness could also play a role in synaptic adhesion, stiffnesses of synapses are difficult to characterize due to their small size and challenges in verifying synapse identity and function. To address these challenges, we have developed an experimental platform that combines atomic force microscopy, fluorescence microscopy, and transmission electron microscopy. Here, using this platform, we report that functional, mature, excitatory synapses had an average elastic modulus of approximately 200 kPa, two orders of magnitude larger than that of the brain tissue, suggesting stiffness might have a role in synapse function. Similar to various functional and anatomical features of neural circuits, synaptic stiffness had a lognormal-like distribution, hinting a possible regulation of stiffness by processes involved in neural circuit function. In further support of this possibility, we observed that synaptic stiffness was correlated with spine size, a quantity known to correlate with synaptic strength. Using established stages of the long-term potentiation timeline and theoretical models of adhesion cluster dynamics, we developed a biophysical model of the synapse that not only explains extreme stiffness of synapses, their statistical distribution, and correlation with spine size, but also offers an explanation to how early biomolecular and structural changes during functional potentiation could lead to strengthening of synaptic adhesion. According to this model, synaptic stiffness serves as an indispensable physical messenger, feeding information back to synaptic adhesion molecules to facilitate maintenance of synaptic adhesion.