Cellular Microbiaxial Stretching to Measure a Single-Cell Strain Energy Density Function

A Graphical Approach to Visualize and Interpret Biochemically Coupled Biomechanical Models

The last decade has seen the emergence of progressively more complex mechanobiological models, often coupling biochemical and biomechanical components. The complexity of these models makes interpretation difficult, and although computational tools can solve model equations, there is considerable potential value in a simple method to explore the interplay between different model components. Pump and system performance curves, long utilized in centrifugal pump selection and design, inspire the development of a graphical technique to depict visually the performance of biochemically-coupled mechanical models. Our approach is based on a biochemical performance curve (analogous to the classical pump curve) and a biomechanical performance curve (analogous to the system curve). Upon construction of the two curves, their intersection, or lack thereof, describes the coupled model's equilibrium state(s). One can also observe graphically how an applied perturbation shifts one or both curves, and thus how the other component will respond, without rerunning the full model. While the upfront cost of generating the performance curve graphic varies with the efficiency of the model components, the easily interpretable visual depiction of what would otherwise be nonintuitive model behavior is valuable. Herein, we outline how performance curves can be constructed and interpreted for biochemically-coupled biomechanical models and apply the technique to two independent models in the cardiovascular space. The performance curve approach can illustrate and help identify weaknesses in model construction, inform user-applied perturbations and fitting procedures to generate intended behaviors, and improve the efficiency of the model generation and application process.

A computational bridge between traction force microscopy and tissue contraction

Arterial wall active mechanics are driven by resident smooth muscle cells, which respond to biological, chemical, and mechanical stimuli and activate their cytoskeletal machinery to generate contractile stresses. The cellular mechanoresponse is sensitive to environmental perturbations, often leading to maladaptation and disease progression. When investigated at the single cell scale, however, these perturbations do not consistently result in phenotypes observed at the tissue scale. Here, a multiscale model is introduced that translates microscale contractility signaling into a macroscale, tissue-level response. The microscale framework incorporates a biochemical signaling network along with characterization of fiber networks that govern the anisotropic mechanics of vascular tissue. By incorporating both biochemical and mechanical components, the model is more flexible and more broadly applicable to physiological and pathological conditions. The model can be applied to both cell and tissue scale systems, allowing for the analysis of in vitro, traction force microscopy and ex vivo, isometric contraction experiments in parallel. When applied to aortic explant rings and isolated smooth muscle cells, the model predicts that active contractility is not a function of stretch at intermediate strain. The model also successfully predicts cell-scale and tissue-scale contractility and matches experimentally observed behaviors, including the hypercontractile phenotype caused by chronic hyperglycemia. The connection of the microscale framework to the macroscale through the multiscale model presents a framework that can translate the wealth of information already collected at the cell scale to tissue scale phenotypes, potentially easing the development of smooth muscle cell-targeting therapeutics.

Stiffness sensing by smooth muscle cells: Continuum mechanics modeling of the acto-myosin role

Aortic smooth muscle cells (SMCs) play a vital role in maintaining homeostasis in the aorta by sensing and responding to mechanical stimuli. However, the mechanisms that underlie the ability of SMCs to sense and respond to stiffness change in their environment are still partially unclear. In this study, we focus on the role of acto-myosin contractility in stiffness sensing and introduce a novel continuum mechanics approach based on the principles of thermal strains. Each stress fiber satisfies a universal stress-strain relationship driven by a Young's modulus, a contraction coefficient scaling the fictitious thermal strain, a maximum contraction stress and a softening parameter describing the sliding effects between actin and myosin filaments. To account for the inherent variability of cellular responses, large populations of SMCs are modeled with the finite-element method, each cell having a random number and a random arrangement of stress fibers. Moreover, the level of myosin activation in each stress fiber satisfies a Weibull probability density function. Model predictions are compared to traction force measurements on different SMC lineages. It is demonstrated that the model not only predicts well the effects of substrate stiffness on cellular traction, but it can also successfully approximate the statistical variations of cellular tractions induced by intercellular variability. Finally, stresses in the nuclear envelope and in the nucleus are computed with the model, showing that the variations of cytoskeletal forces induced by substrate stiffness directly induce deformations of the nucleus which can potentially alter gene expression. The predictability of the model combined to its relative simplicity are promising assets for further investigation of stiffness sensing in 3D environments. Eventually, this could contribute to decipher the effects of mechanosensitivity impairment, which are known to be at the root of aortic aneurysms.

Cellular Microbiaxial Stretching Assay for Measurement and Characterization of the Anisotropic Mechanical Properties of Micropatterned Cells

Characterizing the mechanical properties of single cells is important for developing descriptive models of tissue mechanics and improving the understanding of mechanically driven cell processes. Standard methods for measuring single-cell mechanical properties typically provide isotropic mechanical descriptions. However, many cells exhibit specialized geometries in vivo, with anisotropic cytoskeletal architectures reflective of their function, and are exposed to dynamic multiaxial loads, raising the need for more complete descriptions of their anisotropic mechanical properties under complex deformations. Here, we describe the cellular microbiaxial stretching (CμBS) assay in which controlled deformations are applied to micropatterned cells while simultaneously measuring cell stress. CμBS utilizes a set of linear actuators to apply tensile or compressive, short- or long-term deformations to cells micropatterned on a fluorescent bead-doped polyacrylamide gel. Using traction force microscopy principles and the known geometry of the cell and the mechanical properties of the underlying gel, we calculate the stress within the cell to formulate stress-strain curves that can be further used to create mechanical descriptions of the cells, such as strain energy density functions. © 2022 Wiley Periodicals LLC. Basic Protocol 1: Assembly of CμBS stretching constructs Basic Protocol 2: Polymerization of micropatterned, bead-doped polyacrylamide gel on an elastomer membrane Support Protocol: Cell culture and seeding onto CμBS constructs Basic Protocol 3: Implementing CμBS stretching protocols and traction force microscopy Basic Protocol 4: Data analysis and cell stress measurements.

AFM Stiffness Mapping in Human Aortic Smooth Muscle Cells

Aortic Smooth Muscle Cells (SMCs) play a vital role in maintaining mechanical homeostasis in the aorta. We recently found that SMCs of aneurysmal aortas apply larger traction forces than SMCs of healthy aortas. This result was explained by the significant increase of hypertrophic SMCs abundance in aneurysms. In the present study, we investigate whether the cytoskeleton stiffness of SMCs may also be altered in aneurysmal aortas. For that, we use Atomic Force Microscopy (AFM) nanoindentation with a specific mode that allows subcellular-resolution mapping of the local stiffness across a specified region of interest of the cell. Aortic SMCs from a commercial human lineage (AoSMCs, Lonza) and primary aneurysmal SMCs (AnevSMCs) are cultured in conditions promoting the development of their contractile apparatus, and seeded on hydrogels with stiffness properties of 12kPa and 25kPa. Results show that all SMC exhibit globally a lognormal stiffness distribution, with medians in the range 10-30 kPa. The mean of stiffness distributions is slightly higher in aneurysmal SMCs than in healthy cells (16 kPa versus 12 kPa) but the differences are not statistically significant due to the large dispersion of AFM nanoindentation stiffness. We conclude that the possible alterations previously found in aneurysmal SMCs do not affect significantly the AFM nanoindentation stiffness of their cytoskeleton.

Orientation of neurites influences severity of mechanically induced tau pathology

Chronic traumatic encephalopathy is a neurodegenerative disease associated with repeated traumatic brain injury (TBI). Chronic traumatic encephalopathy is a tauopathy, in which cognitive decline is accompanied by the accumulation of neurofibrillary tangles of the protein tau in patients' brains. We recently found that mechanical force alone can induce tau mislocalization to dendritic spines and loss of synaptic function in in vitro neuronal cultures with random cell organization. However, in the brain, neurons are highly aligned, so here we aimed to determine how neuronal organization influences early-stage tauopathy caused by mechanical injury. Using microfabricated cell culture constructs to control the growth of neurites and an in vitro simulated TBI device to apply controlled mechanical deformation, we found that neuronal orientation with respect to the direction of a uniaxial high-strain-rate stretch injury influences the degree of tau pathology in injured neurons. We found that a mechanical stretch applied parallel to the neurite alignment induces greater mislocalization of tau proteins to dendritic spines than does a stretch with the same strain applied perpendicular to the neurites. Synaptic function, characterized by the amplitude of miniature excitatory postsynaptic currents, was similarly decreased in neurons with neurites aligned parallel to stretch, whereas in neurons aligned perpendicular to stretch, it had little to no functional loss. Experimental injury parameters (strain, strain rate, direction of stretch) were combined with a standard viscoelastic solid model to show that in our in vitro model, neurite work density during stretch correlates with tau mislocalization. These findings suggest that in a TBI, the magnitude of brain deformation is not wholly predictive of neurodegenerative consequences of TBI but that deformation relative to local neuronal architecture and the neurite mechanical energy during injury are better metrics for predicting trauma-induced tauopathy.

Architecture-Dependent Mechano-Adaptation in Single Vascular Smooth Muscle Cells

Arteries grow and remodel following mechanical perturbation. Vascular smooth muscle cells (VSMCs) within the artery undergo hyperplasia, hypertrophy, or change their contractility following sustained changes in loading. Experimental evidence in vivo and in vitro suggests that VSMCs grow and remodel to maintain a constant transmural stress, or "target" stress. This behavior is often described using a stress-dependent finite growth framework. Typically, computational models of arterial growth and remodeling account for VSMC behavior in a constrained mixture formulation that incorporates behavior of each component of the artery. However, these models do not account for differential VSMC architecture observed in situ, which may significantly influence growth and remodeling behavior. Here, we used cellular microbiaxial stretching (CμBS) to characterize how VSMCs with different cytoskeletal architectures respond to a sustained step change in strain. We find that VSMC F-actin architecture becomes more aligned following stretch and retains this alignment after 24 h. Further, we find that VSMC stress magnitude depends on cellular architecture. Qualitatively, however, stress behavior following stretch is consistent across cell architectures-stress increases following stretch and returns to prestretch magnitudes after 24 h. Finally, we formulated an architecture-dependent targeted growth law that accounts for experimentally measured cytoskeletal alignment and attributes stress evolution to individual fiber growth and find that this model robustly captures long-term stress evolution in single VSMCs. These results suggest that VSMC mechano-adaptation depends on cellular architecture, which has implications for growth and remodeling in regions of arteries with differential architecture, such as at bifurcations.

Regulation of SMC traction forces in human aortic thoracic aneurysms

Smooth muscle cells (SMCs) usually express a contractile phenotype in the healthy aorta. However, aortic SMCs have the ability to undergo profound changes in phenotype in response to changes in their extracellular environment, as occurs in ascending thoracic aortic aneurysms (ATAA). Accordingly, there is a pressing need to quantify the mechanobiological effects of these changes at single cell level. To address this need, we applied Traction Force Microscopy (TFM) on 759 cells coming from three primary healthy (AoPrim) human SMC lineages and three primary aneurysmal (AnevPrim) human SMC lineages, from age and gender matched donors. We measured the basal traction forces applied by each of these cells onto compliant hydrogels of different stiffness (4, 8, 12, 25 kPa). Although the range of force generation by SMCs suggested some heterogeneity, we observed that: 1. the traction forces were significantly larger on substrates of larger stiffness; 2. traction forces in AnevPrim were significantly higher than in AoPrim cells. We modelled computationally the dynamic force generation process in SMCs using the motor-clutch model and found that it accounts well for the stiffness-dependent traction forces. The existence of larger traction forces in the AnevPrim SMCs were related to the larger size of cells in these lineages. We conclude that phenotype changes occurring in ATAA, which were previously known to reduce the expression of elongated and contractile SMCs (rendering SMCs less responsive to vasoactive agents), tend also to induce stronger SMCs. Future work aims at understanding the causes of this alteration process in aortic aneurysms.

Investigation of Pathophysiological Aspects of Aortic Growth, Remodeling, and Failure Using a Discrete-Fiber Microstructural Model

Aortic aneurysms are inherently unpredictable. One can never be sure whether any given aneurysm may rupture or dissect. Clinically, the criteria for surgical intervention are based on size and growth rate, but it remains difficult to identify a high-risk aneurysm, which may require intervention before the cutoff criteria, versus an aneurysm than can be treated safely by more conservative measures. In this work, we created a computational microstructural model of a medial lamellar unit (MLU) incorporating (1) growth and remodeling laws applied directly to discrete, individual fibers, (2) separate but interacting fiber networks for collagen, elastin, and smooth muscle, (3) active and passive smooth-muscle cell mechanics, and (4) failure mechanics for all three fiber types. The MLU model was then used to study different pathologies and microstructural anomalies that may play a role in vascular growth and failure. Our model recapitulated many aspects of arterial remodeling under hypertension with no underlying genetic syndrome including remodeling dynamics, tissue mechanics, and failure. Syndromic effects (smooth muscle cell (SMC) dysfunction or elastin fragmentation) drastically changed the simulated remodeling process, tissue behavior, and tissue strength. Different underlying pathologies were able to produce similarly dilatated vessels with different failure properties, providing a partial explanation for the imperfect nature of aneurysm size as a predictor of outcome.

The Protein Mat(ters)-Revealing the Biologically Relevant Mechanical Contribution of Collagen- and Fibronectin-Coated Micropatterns

Understanding cell-material interactions requires accurate characterization of the substrate mechanics, which are generally measured by indentation-type atomic force microscopy. To facilitate cell-substrate interaction, model extracellular matrix coatings are used although their tensile mechanical properties are generally unknown. In this study, beyond standard compressive stiffness estimation, we performed a novel tensile mechanical characterization of collagen- and fibronectin-micropatterned polyacrylamide hydrogels. We further demonstrate the impact of the protein mat on the tensile stiffness characterization of adherent cells. To our knowledge, our study is the first to uncover direction-dependent mechanical behavior of the protein coatings and to demonstrate that it affects cellular response relative to substrate mechanics.

Bimodal sensing of guidance cues in mechanically distinct microenvironments

Contact guidance due to extracellular matrix architecture is a key regulator of carcinoma invasion and metastasis, yet our understanding of how cells sense guidance cues is limited. Here, using a platform with variable stiffness that facilitates uniaxial or biaxial matrix cues, or competing E-cadherin adhesions, we demonstrate distinct mechanoresponsive behavior. Through disruption of traction forces, we observe a profound phenotypic shift towards a mode of dendritic protrusion and identify bimodal processes that govern guidance sensing. In contractile cells, guidance sensing is strongly dependent on formins and FAK signaling and can be perturbed by disrupting microtubule dynamics, while low traction conditions initiate fluidic-like dendritic protrusions that are dependent on Arp2/3. Concomitant disruption of these bimodal mechanisms completely abrogates the contact guidance response. Thus, guidance sensing in carcinoma cells depends on both environment architecture and mechanical properties and targeting the bimodal responses may provide a rational strategy for disrupting metastatic behavior.

Invasive cells respond to contact guidance cues during migration. Here, using micro- and nanopatterning with different ligands and varying stiffness, the authors find that cells can make cellular protrusions through both contractility-dependent and contractility-independent means.

Architecture-Dependent Anisotropic Hysteresis in Smooth Muscle Cells

Cells within mechanically dynamic tissues like arteries are exposed to ever-changing forces and deformations. In some pathologies, like aneurysms, complex loads may alter how cells transduce forces, driving maladaptive growth and remodeling. Here, we aimed to determine the dynamic mechanical properties of vascular smooth muscle cells (VSMCs) under biaxial load. Using cellular micro-biaxial stretching microscopy, we measured the large-strain anisotropic stress-strain hysteresis of VSMCs and found that hysteresis is strongly dependent on load orientation and actin organization. Most notably, under some cyclic loads, we found that VSMCs with elongated in-vivo-like architectures display a hysteresis loop that is reverse to what is traditionally measured in polymers, with unloading stresses greater than loading stresses. This reverse hysteresis could not be replicated using a quasilinear viscoelasticity model, but we developed a Hill-type active fiber model that can describe the experimentally observed hysteresis. These results suggest that cells in highly organized tissues, like arteries, can have strongly anisotropic responses to complex loads, which could have important implications in understanding pathological mechanotransduction.