Tensile Force Induced Cytoskeletal Reorganization: Mechanics Before Chemistry

Understanding cellular remodeling in response to mechanical stimuli is a critical step in elucidating mechano-activation of biochemical signaling pathways. Experimental evidence indicates that external stress-induced subcellular adaptation is accomplished through dynamic cytoskeletal reorganization. To study the interactions between subcellular structures involved in transducing mechanical signals, we combined experimental and computational simulations to evaluate real-time mechanical adaptation of the actin cytoskeletal network. Actin cytoskeleton was imaged at the same time as an external tensile force was applied to live vascular smooth muscle cells using a fibronectin-functionalized atomic force microscope probe. In addition, we performed computational simulations of active cytoskeletal networks under a tensile external force. The experimental data and simulation results suggest that mechanical structural adaptation occurs before chemical adaptation during filament bundle formation: actin filaments first align in the direction of the external force, initializing anisotropic filament orientations, then the chemical evolution of the network follows the anisotropic structures to further develop the bundle-like geometry. This finding presents an alternative, novel explanation for the stress fiber formation and provides new insight into the mechanism of mechanotransduction. Author Summary Remodeling the cytoskeletal network in response to external force is key to mechanosensing and locomotion. Despite much focus on cytoskeletal remodeling in recent years, a comprehensive understanding of actin remodeling in real-time in cells under mechanical stimuli is still lacking. We integrated stress-induced 3D actin imaging and 3D computational simulations of actin cytoskeleton to study how the actin cytoskeleton form bundles and how these bundles evolve over time upon external tensile stress. We found a rapid actin alignment and a slower bundle evolution leading to denser bundles. Based on these results, we propose a “mechanics before chemistry” model of actin cytoskeleton remodeling under external force.


Introduction
Cells adapt to local mechanical stresses by converting mechanical stimuli into biochemical activities that alter the cellular structure-function relationship and lead to specific responses (1)(2)(3).
Cellular response to mechanical stimulation is a balance between contractile elements of the cytoskeleton, matrix stiffness, and cell-matrix adhesions (4). Although cellular mechanotransduction has been an active field of research for a number of years, the process by which transduction of external mechanical signals across the cellular cytoplasm induces cytoskeletal remodeling is not well understood. The most important question in the field of mechanobiology is 'how do cells sense and integrate mechanical forces at the molecular level to produce coordinated responses necessary to make decisions that change their homeostatic state?' Vascular smooth muscle cells (VSMCs) provide an excellent model system to study the mechanotransduction process. The mechanism by which VSMCs sense and adapt to external mechanical forces that result in cytoskeletal remodeling (6)(7)(8) is critical in understanding arterial disease pathology. In vivo, they sense and respond to mechanical forces generated by pulsatile blood pressure changes by altering signal transduction pathways to induce remodeling of their cytoskeleton and adhesions (5,6). Thus, VSMCs residing in the vessel wall are subjected to axial stress and circumferential stretch (7)(8)(9). While circumferential stretch is well accepted as an important mechanical stressor (10,11), the axial stress in the vessel wall, which can be considered as tensile force applied to cells, has been less studied (12). Moreover, VSMC cytoskeletal network response to tensile force is not well-understood (13,14).
To address how application of external tensile stress induces adaptive cellular remodeling, we combined imaging techniques with simultaneous mechanical stimulation of single cells using fibronectin-functionalized atomic force microscope (AFM) probes (15). In anchorage-dependent cells, external mechanical forces are imposed on a pre-existing balanced force equilibrium generated by cytoskeletal tension (16)(17)(18). Thus, forces acting on a cell will induce cytoskeleton deformation throughout the cell. Our previous experiments on VSMCs suggested that cellular adaptation to the applied tensile force is a characteristic of the integrated cell system as a whole (19). We found that mechanical stimulation increases the total intensity and alignment of bundled actin filaments. Here, we build upon these results, and ask how tensile force induces cytoskeletal remodeling and the active formation of actin bundles.
Actin cytoskeleton consists of semi-flexible actin filaments, myosin motors, and crosslinking proteins. During the adaptation process, the actin cytoskeleton remodels to better sustain the external load in two ways (20)(21)(22). On the one hand, actomyosin networks crosslinked by a-actinin and other crosslinking proteins are able to adapt external forces via fast mechanical response; the mechanical stress relaxation occurs on the timescale of seconds (23)(24)(25)(26). On the other hand, cytoskeletal reactions, such as myosin activation, continuously convert biochemical energy into mechanical force; remodeling of the actin networks takes place on the time scale of minutes (27)(28)(29). As a result of myosin dominant mechanochemical dynamics, actin networks tend to contract (30,31). For convenience, we called this process slower chemical response in contrast to the faster mechanical response. Observation of actin filament microstructure changes under these two mechanisms requires super-resolution and ultra-fast imaging, which is not achievable using our present experimental methods. Prior computational models have investigated actin bundles generation and remodeling due to slower biochemical reactions (32)(33)(34)(35)(36), but how external stimuli induce the active formation of actin bundles is still poorly understood.
To better understand the detailed spatiotemporal dynamics of cytoskeletal reorganization upon the external mechanical loading, we simulated the mechanical and chemical dynamics of the actin cytoskeleton using the MEDYAN (MEchanochemical DYnamics of Active Network) package (37). In our simulations, we model the active cytoskeletal networks using polymer mechanics of semi-flexible filaments, crosslinking proteins, and motor proteins. A stochastic reaction-diffusion scheme was used to simulate biochemical reactions, including myosin activation, crosslinking proteins binding, and actin filament assembly. Additionally, we applied tensile external force to the actin network to mimic the AFM mechanical stimulation experiments. In these simulations, a few filaments anchored to a pseudo-AFM probe were initialized in addition to a free filament pool.
The external force was applied via moving the pseudo-AFM probe, and the amplitude of z-axis displacement directly determined the magnitude of the force. In highly crosslinked actomyosin networks, the external force exerted on a small fraction of filaments would transmit to the entire filament network that changes its homeostatic state in microseconds (38): this will be considered as the fast mechanical response. After each tensile force was applied, the system was allowed to evolve for minutes, such that we can study how the actin network transforms under the slower chemical response.
In the present work, to investigate the detailed spatiotemporal cytoskeletal remodeling during tensile mechanical loading, we integrated experimental and modeling approaches. Both experiments and simulations suggest that the external tensile force applied on actin networks quickly induces alignment of actin filaments along the direction of force, and this directional alignment is independent of longer timescale biochemical responses. We also observed filament bundle formation as a result of external tensile force; however, the bundle development relies on both the faster mechanical response and the slower chemical response. We hypothesized that the cellular cytoskeletal adaptation to external mechanical forces and filament bundle formation follows a "mechanics before chemistry" process.

Actin cytoskeleton reorganization of live VSMCs under mechanical stimulation reveals two types of responses
Live VSMCs were subjected to the mechanical loading delivered by the AFM probe at the apical cell surface (Figure 1a). Vertical forces (along the z-axis) applied through a fibronectin (FN) functionalized probe induces cytoskeletal remodeling by pulling on cortical actin through a FNintegrin-actin linkage (9,19). Cell responses to the probe displacement over time were recorded using spinning-disk confocal microscopy. The reconstructed 3D-images of the actin cytoskeleton were used to segment actin bundles in 3D (Figures 1b & 1c). We used these 3D bundles to calculate an average fiber alignment index in the direction of the pulling force. The alignment index is   Interestingly, pulling on only a small fraction of AFM-attached filaments is sufficient to alter the actin filament structure of the entire network. After 900s and five AFM probe pulling steps, each with d=500 nm, the actin networks reorganized into a bundle ( Figure 3a, and Video 1), which is approximately 2 µm long and around 500 nm thick under Case i pulling pattern (red line in Figure   2b). These actin bundles have mixed filament polarity, i.e., plus ends or minus ends of filaments are randomly distributed ( Figure S1 in Supporting Information), implying that they are closer to stress fibers rather than unipolar actin filaments in filopodia (21,39). In contrast, actin networks On the other hand, the directional alignment barely changes at long timescale in all step size patterns. Since the long timescale response is regulated by slower chemical evolutions, we hypothesize that filaments directionally aligned in response to tensile force is primarily due to fast mechanical adaptation.  F-actin distribution further showed that the tensile AFM pulling immediately stretches the actin fiber network along the direction of pulling force (Figures 5a-c), leading to a wider distribution.
As a result, the standard deviations (s) of these distributions increased right after pulling ( Figure   5e). When we measure the radius of gyration (Rg) to quantify the cluster size of actin networks, we also find instantaneous jumps similar to those in the filament alignment and accumulation results (Figure 5f). These instant stretches eventually shape actin networks into the thinner bundles.
Furthermore, these actin bundles maintain their geometric structures at a longer timescale. The F-actin distribution of bundle networks shifts slightly towards the force direction after 150 seconds of chemical evolution (Figure 5a and 5d), but the shape and the standard deviation from the mean, s, remain almost the same (Figure 5e). In addition, the contraction rate, measured as Rg change speed, is much slower than that for the cluster networks under no AFM pulling (Figures 5g). These observations are consistent with the slower F-actin accumulation rate in the bundle region, as shown in Figure 4b, suggesting that the bundle structure is more stable than the cluster induced by myosin. These results are also in agreement with the fact that the actin bundle can preserve its shape and would not contract into clusters under myosin driven contractility at long timescale. To explore this hypothesis, we developed a new capability in the MEDYAN software that mimics the conditions of our AFM experiments. Our simulation results reveal that tensile force triggers a rapid mechanical adaptation of actin networks that forces filaments to align along the pulling direction and encourages actin bundle (stress fiber) formation. We also found that slower biochemical evolution is essential to the formation of stress fibers, which requires integration of actin networks through a-actinin crosslinking followed by myosin activation and eventual further actin recruitment to the stress fiber. Moreover, we found that actin bundles generated in our simulations are stable since they contract much slower than networks free of external force.
Thus, our simulations agree with the experiments, supporting a "mechanics before chemistry" hypothesis as an alternative, novel explanation regarding how active cytoskeletal networks adapt to external mechanical stimuli in real-time. In the control case of actin networks without external forces, primarily driven by myosin motors, actin network contraction does not have a bias towards a specific direction, leading to an isotopically collapse into globular clusters (Figure 6a). The external tensile force first stretches the actin cytoskeletal network, forcing filaments to align, as a rapid mechanical response, which initializes anisotropic bundle-like structures. Longer time scale chemical processes further stabilize the bundle structures that can preserve the anisotropy ( Figure   6b). As a result, the contractility generated by subsequent chemical evolution follows the anisotropic distribution, which strengthens actin bundles by recruiting more actin filaments while maintaining the bundle shape. triggering signaling pathways (40,41). Moreover, responses to mechanical forces induced by changes in substrate stiffness will further trigger the adaptation of their cytoskeletal network in less than 100 ms (42), proposing a 'mechanics first' mechanism of cellular response that supports our hypothesis. Thus, when the cell experiences an external force, the cytoskeletal adaptation will

Isotropic clustering
Anisotropic Bundling first elicit the actin fiber rearrangements (mechanical) before spending ATP to initiate the biochemical reactions (chemical).
In summary, we integrated in vitro and in silico modeling to investigate the effects of external load on the cytoskeleton network. Both experimental and simulation results suggest that tensile stress aligns the fibers along the direction of the external stress, before biochemical evolution to further remodel the network. This result suggests the short timescale mechanical structural adaptation operates before slower biochemical processes, which can have important implications to mechano-signal transduction.

Vascular smooth muscle cell culture and transient transfections
VSMC were previously isolated from rat cremaster arterioles (43) and handled as previously

Vascular smooth muscle cell imaging
The integrated microscope system used for these studies was described in detail (45). Briefly, where ∆ , ∆ , ∆ are differences of the paired points in x, y, and z direction, respectively. The resulting set of measurements along each trace was averaged as an estimate for the angle between each trace and the z-axis. As an aggregated measure for trace angles at each time point, angle measures from all traces at a given time point were further averaged.

Simulation Methods
A computational model for mechanochemical dynamics of active networks (MEDYAN) (37) was used to simulate the actin cytoskeletal network with an external pulling force. In this model, actin filaments are considered as connected "cylinders" with strong axial stretching stiffness. The cylinder itself is unbendable, and the radial deformation of filaments is realized by bending between two neighboring connected cylinders. Each cylinder consists of up to 40 actin monomers, where a full cylinder is 108 nm long and has 4 possible binding sites for myosin motors and crosslinkers. Myosin motors are modeled as harmonic springs that can walk towards filament plus end with equilibrium length from 175 nm to 225 nm based on the non-muscle myosin II.
Crosslinking proteins are also modeled as harmonic springs with an equilibrium length for aactinin (30-40 nm). The main chemical events we considered in this work include filament polymerization and depolymerization, binding and unbinding of myosin and crosslinker, and myosin activation. These reactions are mechanochemically sensitive and are modeled by an efficient Next Reaction Method based on the Gillespie algorithm (46,47). Simulation parameters and other model details can be found in Supplementary Information and a previous publication (37).
We initialized a 3×3×1.25 µm 3 simulation volume with a 250 nm semi-spherical AFM tip that attached to the upper boundary. At time 0 sec, 300 seed filaments, each with 40 monomers, were randomly created in the network, defined as the free filament pool. These filaments free from AFM attachment are allowed to polymerize and depolymerize on either the plus end or the minus end.
To appropriately transmit the external force generated by AFM displacement to the actin network, another 30 seed filaments with their minus-end attached to the AFM tip via stiff harmonic springs were initialized (Figure 2a). Only plus ends of these filaments are allowing to polymerize and depolymerize. At the start of simulations, free G-actin was added to the network to ensure the total actin concentration is 20 µM. Since the concentration is much larger than the critical concentration (48), seed filaments would grow rapidly and reach an average F-actin length of ~0.8 µm in a few seconds of simulation. 0.1 µM myosin motors and 2 µM a-actinin crosslinkers were added after 5 seconds of simulation. The addition of myosin and a-actinin linkers connect the free filament pool to AFM-attached filaments while generating contractility to allow the network to self-construct.
The external tensile force from the AFM tip was implemented as follows. The network was allowed to evolve for 150 seconds before AFM probe vertical displacement (i.e., vertical pulling).
Each probe displacement created a 250 nm or 500 nm step displacement of the AFM tips, generating tensile force to AFM-attached filaments via stiff harmonic springs. To ensure the energy was properly minimized, each displacement step was broken up into 100 sub-steps (2.5 nm or 5 nm displacement per 0.01 s). Networks were mechanically equilibrated after each sub-step, and displacement would create additional simulation space by raising the upper boundary. Since all AFM probe displacements were finished in 1s and each mechanical minimization was instant in the simulation, we are able to treat the network change before and after displacement as a fast mechanical response that is independent of biochemistry. Networks were allowed to evolve for another 150 seconds before the next AFM displacement step (Fig. 2b). During the 150 second period, cytoskeletal network remodeling was biochemically dominated by filament treadmilling, myosin activation, and a-actinin linker binding and unbinding. Since the time interval between two displacement steps is much longer than the pulling time (1 second), we define the network evolution during each 150 seconds as the long timescale biochemical response. We applied the tensile AFM step displacement 5 times during each simulation, taking 900 seconds of simulation time in total.
The present work tested four different tensile force conditions. For convenience, we labeled them as Case i-iv in decreasing order of displacement sizes (Fig. 2b). In Case i, a constant 500 nm step size was applied. This step size exerted an instantaneous force on the AFM attached filaments twice higher than the 250 nm step size. In Case ii, we used mixed step sizes: in the first three pulling events, each step generates 250 nm displacement, and in the last two pulling events, each step generates 500 nm displacement. In Case iii, we reduced the displacement size to constant 250 nm, implying a weaker external force. In the last case, we did not apply any external force to the network, hence, all 330 filaments were in the free filament pool. However, the upper boundary in Case iv would still move up in the same way as for Cases i-iii to avoid any influences from the boundary effects.

Acknowledgements
This work was supported, in part, by Public Health Service grants R01CA201340 and 1R01EY028450 from the NIH/NCI and NIH/NEI, respectively (to Y.J.), K25CA181503 and U01CA242936 from NIH/NCI (to JK), National Science Foundation grant CHE-1800418 (to GP). The experimental work was supported by NSF CAREER 0747334 award to AT.
Supplementary Figure   Figure S1. (a) The probability distribution of filament polarity alignment index for bundle-like networks under pulling condition Case i. Data are taken from 751s~900s out of 5 duplicated trajectories. (b) The polarity alignment index is defined as cos H , where H is the angle between a filament vector and the force direction. The filament vector (red arrow) in this case, considers the polarity of plus end and minus end. (a-b) The distribution spreads across [-1,1], suggesting actin bundles generated in this work is similar to stress fiber with mixed polarity. For a filopodia-like bundle, where actin fibers have the same polarity, the alignment index should have a single peak at either 1 or -1. ii. iii.
iv. a b