Tensile force-induced cytoskeletal remodeling: Mechanics before chemistry.

Understanding cellular remodeling in response to mechanical stimuli is a critical step in elucidating mechanical 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 data 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. Moreover, we performed computational simulations of active cytoskeletal networks under an external tensile 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 by initializing anisotropic filament orientations, then the chemical evolution of the network follows the anisotropic structures to further develop the bundle-like geometry. Our findings present an alternative two-step explanation for the formation of actin bundles due to mechanical stimulation and provide new insights into the mechanism of mechanotransduction.

Introduction

Cells adapt to local mechanical stresses by converting mechanical stimuli into chemical activities that alter the cellular structure-function relationship and lead to specific responses [1-3]. Cellular response to mechanical stimulation is a balance between contractile elements of the cytoskeleton, cell-matrix adhesions, and extracellular matrix [4]. Although cellular mechano-transduction 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 induce 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 (6–8) is critical for understanding arterial disease pathology. In vivo, they sense and respond to mechanical forces generated by pulsatile blood pressure changes through alteration of signal transduction pathways to induce remodeling of their cytoskeleton and adhesions [5, 6]. Thus, VSMCs residing in the vessel wall are mainly subjected to circumferential stretch and axial stress [7-9]. Circumferential stretch generated by the pulsatile blood flow exerts dynamical mechanical stimulation on the vessel wall in a direction perpendicular to the direction of blood flow. This is a well-recognized mechanical stressor and its biomechanical effects were well studied [10, 11]. Axial stress in the vessel wall arises from longitudinal loading along the vessel length [12]. Even though axial stress (i.e., tensile force) has been known as an important mechanical stressor of the vessel wall for a long time [13, 14] and a fundamental contributor to vessel wall homeostasis (12), less attention was given to studying its biomechanical effects at the cellular level.

In anchorage-dependent cells, external mechanical forces are imposed on a pre-existing balanced force equilibrium generated by cytoskeletal tension [15-17]. Thus, forces acting on a cell will induce cytoskeleton deformation throughout the cell, such that the actin cytoskeleton remodels to better sustain the external load. Actin cytoskeleton consists of semi-flexible actin filaments, myosin motors, and crosslinking proteins. It has been proposed that de novo actin polymerization is critical for actin fiber formation in migrating cells [18], while the aggregation of existing actin filament fragments is most likely for stationary cells in a static environment [19]. Mechanical stimulation of stationary VSMCs in tissue represents an intermediate state, in which cells must dynamically adapt to their native, mechanically active environment. It is not known which mechanism is favored in this normal functional homeostatic state. Moreover, research has shown that cells adapt to external force by activating mechanically-sensitive signaling pathways that involve conformational changes of proteins at cell-matrix adhesions (e.g., integrins, vinculin, talin, etc), and promote actin filament polymerization [20].

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 [21]. To address how application of external tensile force induces actin cytoskeleton remodeling, we combined imaging techniques with simultaneous mechanical stimulation of single cells using fibronectin-functionalized atomic force microscope (AFM) probes [22]. Thus, we found that mechanical stimulation not only increases alignment of actin filaments, but also induces actin bundling measured by increased fluorescence intensity of F-actin [23].

Here, we build upon these experimental results and investigate the biomechanical effects of axial stress at cellular level using computational modeling, by asking how tensile force induces actin cytoskeleton adaptive remodeling? During the adaptation process, the actin cytoskeleton remodels to better sustain the external load [24-26]. Thus, actomyosin networks crosslinked by α-actinin and other crosslinking proteins are able to adapt to external forces via fast mechanical response, in which stress relaxation occurs on the timescale of seconds [27-30]. However, cytoskeletal reactions, such as actin (de)polymerization or myosin II activation that continuously converts chemical energy into mechanical force, remodel the actomyosin networks on a slower pace, on a time scale of minutes [31-33]. As a result of myosin dominant mechanochemical dynamics, actomyosin networks tend to contract [34, 35]. Prior computational models have investigated remodeling of the actin cytoskeleton due to slower chemical reactions [36-40], however, how external mechanical stimuli induce the active formation of actin bundles is still poorly understood.

To better understand the detailed spatiotemporal dynamics of cytoskeletal reorganization due to external mechanical loading, we simulated the mechanical and chemical dynamics of the actin cytoskeleton using the MEDYAN (MEchanochemical DYnamics of Active Network) software [41]. 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 chemical reactions, including myosin activation, crosslinking protein binding, and actin filament assembly. Additionally, we have applied external tensile forces to the actin network to mimic the AFM mechanical stimulation in the experiments. In these systems, a few filaments were initially anchored to a simulated AFM probe, in addition to a free filament pool. The external force was applied by moving the simulated AFM probe upward, by increasing the amplitude of z-axis displacement. In highly crosslinked actomyosin networks, the external force exerted on a small fraction of filaments would transmit to the entire system that changes their homeostatic state in microseconds [42]; 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 were able to study how the actin network adapts under a slower chemical response.

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 chemical response. In addition, the formation of actin bundles as a result of external tensile force relies on both the faster mechanical response and the slower chemical response. We hypothesized that cellular cytoskeletal adaptation to external tensile forces and formation of actin bundles follows a “mechanics before chemistry” process.

Results

Actin cytoskeleton reorganization in live VSMCs under mechanical stimulation reveals a two-step adaptive response

Live VSMCs expressing mRFP1-actin-7 were subjected to the mechanical loading delivered by the AFM probe at the apical cell surface (Fig 1A). Vertical forces (along the z-axis) applied through a fibronectin (FN) functionalized probe induced cytoskeletal remodeling by pulling on cortical actin through a FN-integrin-actin linkage [9, 21]. Cell responses to the probe displacement over time were recorded using spinning-disk confocal microscopy (S1 Video). The reconstructed 3D-images of the actin cytoskeleton were used to segment actin bundles in 3D (Fig 1B and 1C). We used these 3D bundles to calculate an average fiber alignment index in the direction of the pulling force. The alignment index is defined as the average of cos(θ), where θ is the acute angle between each filament segment and the direction of the force (Z-axis) (Eq 1 in Methods). With a value between 0 and 1, the alignment index equals to 1 for perfect alignment with the Z-axis, and 0 for alignment perpendicular to the Z-axis. The alignment index increases right after the application of an external force, but levels off (Fig 1E) upon larger pulling forces. Note that the small alignment index value is due to the cell aspect since the VSMCs lay flat on the substrate, and the majority of the filaments were perpendicular to the Z-axis. In addition, the normalized fluorescence intensity of actin filaments increased steadily as the AFM displacement continued (Fig 1F). These experimental results show a force-induced actin cytoskeleton remodeling via the directional alignment and actin fiber bundling.

Fig 1

Response of VSMC to external pulling force.

(a) Schematic of a VSMC mechanically stimulated with a FN functionalized AFM probe and simultaneously imaged by spinning-disk confocal microscopy. (b-c) Fluorescence images of VSMC expressing mRFP1-actin-7 (left) and the 3D reconstructed image of the representative segmentation of actin filament bundles (right) for before (b) the AFM probe displacement at time 0 min, and after (c) the AFM probe displacement at time 68 min. Scale bar: 20 μm. Left panels used with permission from JOVE [21]. (d) The scheduled pulling force in three phases: small, intermediate and large forces. (e) The alignment index for the actin filament bundles increased rapidly as small force was applied, but slowed down as the force increased. (f) The normalized intensity for mRFP1-actin-7 increased steadily through all force ranges. Blue lines: piece-wise linear fit for forces below 0.5 nN and ≥0.5 nN.

Rapid formation of actin bundles in response to tensile force in MEDYAN simulations

To understand the molecular mechanisms of the actin cytoskeleton reorganization under tensile force application using the AFM probes, we designed computational simulations of actin networks with external tensile force using MEDYAN software. We generated 300 free filaments in a 3×3×1.25 μm3 simulation box, initially as a random network, and another 30 filaments attached to an AFM probe located at the center of the upper boundary of the simulation box. The number of filaments attached to the AFM-probe was chosen based on the reported number of filaments in actin bundles [19]. The simulation box contained 20 μM of actin, 2 μM of non-muscle myosin II (NMII), and 2 μM of α-actinin crosslinkers. The simulated AFM probe was displaced by a distance d, every 150 seconds. Each pull (Z-axis tensile force application) created a 250 nm or 500 nm step displacement of the simulated-AFM probe, generating tensile force on the filaments attached to the probe via stiff harmonic springs (Fig 2A). The amplitude of step displacement size d is linearly proportional to the pulling force of the AFM probe. Chemical interactions, including filaments treadmilling, myosin activation, and α-actinin crosslinking, took place throughout the simulations. We varied the pulling patterns (Fig 2B) to simulate the different pulling forces in the experiment (Fig 1D).

Fig 2

(a) A sketch of the simulation setup. The simulation box is 3 μm in x and y directions, and the initial height (z-direction) is 1.25 μm. The simulation box contains 300 free actin filaments, as well as diffusible G-actin, myosin, and α-actinin linkers. A semi-spherical AFM probe is located at the upper boundary, and 30 filaments are attached to the probe via stiff harmonic springs. At the beginning of simulations, all filaments are 0.108 μm long (containing 40 actin subunits). The input G-actin concentration is much higher than the equilibrium concentration, making actin filaments rapidly elongate. An average length of 0.8 μm is achieved and maintained after around 40s of simulation. (b) Simulated AFM-probe position, equivalent to the height of upper boundary, as a function of time for Cases i-iii. The control case (Case iv) is without AFM probe and without filament attachment, with only the upper boundary moving in the same way as in Case i to avoid potential boundary effects.

Interestingly, pulling on only a small fraction of filaments attached to the AFM-prove 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 (case i), the actin networks reorganized into a bundle (Fig 3A and S2 Video), which is approximately 2 μm long and around 500 nm thick. These actin bundles have mixed filament polarity, i.e., plus ends or minus ends of filaments are randomly distributed (S1 Fig in Supporting Information). In contrast, actin networks free of external force geometrically collapsed into a globular cluster-like structure (Fig 3B and S3 Video), as a result of contractility driven by myosin motors and crosslinkers. Reducing the step size d in Cases ii and iii creates an intermediate geometry between the bundle and cluster (S2 Fig). If the step size is further reduced to 0, but the 30 filaments are maintained attached to the simulated AFM probe, the geometry would be similar to the cluster (S3 Fig). Moreover, if we release the filaments from the simulated AFM probe after bundle formation, then actin bundles would also tend to collapse into globular clusters (S4 Video).

Fig 3

(a-b) Representative snapshots of (a) bundle-like actin networks under Case i pulling condition at time t = 900 s, and (b) cluster-like actin networks without external force at time t = 900 s. Actin filaments, myosin motors, and crosslinkers are shown in red, blue, and green cylinders, respectively. The gray sphere in (a) represents the AFM probe. (c) Filament alignment index along the Z-axis for 500 nm step size (red, Case i), mixed step sizes (250 nm for the first three pulling events and 500 nm for the last two, blue), 250 nm step size (purple, Case ii) and no AFM-probe pulling (green, Case iii). α-actinin linker:actin is 0.1 and myosin:actin is 0.005 in all simulations. Error bars represent the standard deviation from the mean in 5–10 simulation replicates.

The actin bundle formation was also regulated by the number of actin filaments attached to the AFM-probe. When too few filaments were attached to the AFM probe, the pulling force was insufficient to generate a bundle (S4A Fig). In some of the simulations, after pulling, the actin filaments that were attached to the AFM-probe would disconnect completely from the free actin filament pool. For the myosin motor and α-actinin concentrations used in our simulations, we found that about 20 actin filaments need to be attached to the probe for actin bundle formation. On the other hand, increasing the number of AFM-probe attached filaments lowered the density of the free filaments. As a consequence, most free filaments could only collapse into small globular clusters locally and were unable to join the actin bundle formed by the filaments attached to the AFM-probe (S4B Fig).

Tensile force induces actin alignment in MEDYAN simulations

To investigate actin filament alignment during actin bundle formation, we calculated the alignment index cos(θ) as described in the experimental section. The alignment index increases immediately after each of the AFM-probe pulling events in all three pulling patterns tested (Fig 3C, Case i-iii). In the simulation, mechanical equilibration is instant, therefore these rapid jumps suggest very strong mechanical responses. Moreover, the directional filament alignment is regulated by the magnitude of the external tensile force, since reducing the pulling step size amplitude (compared to Cases ii and iii) results in a weaker alignment response. 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 the directional alignment of actin filaments in response to tensile force is primarily due to fast mechanical adaptation.

Two-step development of actin bundles depends on both faster mechanical alignment and slower chemical response

To further analyze the formation and evolution of actin bundles, we next defined a cylinder-shaped boundary under the AFM probe (500 nm in diameter). More than 80% of the total F-actin accumulated within this boundary towards the end of simulations under the Case i pulling condition, suggesting that monitoring F-actin accumulation in the bundle region provides a simple but robust way to quantify the bundle development process. We observed instant F-actin accumulation after each pulling event (Fig 4A), while reducing step size hindered the accumulation (S2A Fig). Similar to the directional alignment, these results suggest that actin bundle development relies on the fast, mechanical response.

Fig 4

(a) The F-actin fraction in the bundle region as a function of time for actin networks under 500 nm displacement steps (red, Case i) and actin networks free of external force (green, Case iv). The bundle region is defined as the volume under the simulated AFM probe, which is a cylindrical region of 500 nm in diameter and the height of the simulation box. The box size varies over time based on the position of the AFM probe. Insert shows a 2D illustration of the bundle region. (b) The rate of F-actin accumulation in the bundle region from simulations with the AFM probe pulling force (red, Case i) and without AFM probe pulling- force (green, control Case iv). The recruitment rates are calculated by linear-fitting of the data points every 50 seconds. Shaded colors and error bars are the standard deviations of 10 replica simulations for Case i and 5 replicas for Case iv, respectively.

Surprisingly, the accumulation of actin filaments into the bundle kept increasing steadily between pulling events, suggesting that slower chemical dynamics contribute to bundle development as a result of the adaptation to force. To capture the long timescale of F-actin recruitment, we calculated the F-actin recruitment rate in the defined bundle region (Fig 4B). The control case without external pulling (Case iv, green line) shows the chemically driven F-actin recruitment, as a result of myosin and α-actinin induced contractility and bundling, respectively. Similarly, the recruitment rate of F-actin during the intervals between pulling (Case i, red line) is always positive, showing net recruitment of F-actin. The rate of F-actin recruitment for bundling is lower than that for actin clustering into globular foci in the control case.

To further explore the significance of chemical evolution of bundle development, we tested three different conditions with “insufficient” chemical evolution. First, we reduced the myosin concentration from 2 μM to 0.4 μM. Without sufficient myosin, the network was unable to generate enough contractility of the actomyosin network, leading to high actin filament dispersion (S5 Video). Second, by reducing α-actinin crosslinker concentration from 2 μM to 0.4 μM, the F-actin network could not form properly (S6 Video). Although myosin motors still generated contractility, the actin fiber network is fragmented as disconnected actin foci. Lastly, we shorten the time between each pulling from 150 seconds to 10 seconds. Only a small fraction of actin filaments bundled together and followed the upward movement of the simulated AFM probe, disconnecting from the rest of the filaments (S7 Video).

F-actin distribution further showed that the tensile force application using AFM-probe immediately stretches the actin fiber network along the direction of force (Fig 5A–5C), leading to a wider distribution. As a result, the standard deviations (σ) of these distributions increased right after pulling (Fig 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 recruitment results (Fig 5F). These instant stretches eventually shape actin networks into thinner actin bundles. Furthermore, these actin bundles maintain their geometric structures at a longer timescale. The F-actin distribution of actin bundle networks shifts slightly towards the force direction after 150 seconds of chemical evolution (Fig 5A), but the shape and the standard deviation from the mean, σ, remain almost the same (Fig 5D and 5E). In addition, the contraction rate, measured as the rate of Rg change (), is much slower than that for the actin globular clusters in the control case without force application (Fig 5G). These observations are consistent with the slower F-actin accumulation rate in the bundle region, as shown in Fig 4B, suggesting that the actin bundle structure is more stable than the actin cluster. 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 longer timescale.

Fig 5

(a) F-actin distribution along the force direction (Z-axis) of the most representative trajectory before the 4th pulling at t = 600 s (blue), after the 4th pulling at t = 601 s (orange), and after the long-timescale chemical evolution at t = 750 s (yellow). (b-d) Corresponding simulation snapshots before pulling, after pulling, and after chemical evolution, respectively. (e) Standard deviations (σ) of the F-actin distribution along the force direction before pulling (blue), after pulling (orange), and after 150 s of chemical evolution (yellow) at the third, fourth, and fifth pulling events. σ are averaged over 10 duplicated trajectories, and error bars represent the standard errors. (f) The radius of gyration, Rg and (g) the rate of Rg change, , of actin networks in Case i with 500 nm pulling (red) and in Case iv without pulling (green). Shaded colors and error bars are the standard deviations of 10 duplicated trajectories for Case i and 5 duplicated trajectories for Case iv.

Discussions

Mechanotransduction is the process by which cells convert mechanical stimuli into biochemical activity. A key aspect of the mechanotransduction is that cells remodel their cytoskeleton in response to mechanical stimuli. To study external force-induced adaption of the actin cytoskeleton, AFM was used to apply external, tensile forces on single cells adherent on a substrate. Cell responses measured through probe displacement over time are directly dependent on the intrinsic contractility that modulates the function of the actomyosin apparatus. The observed rapid rise in actin fiber alignment upon tensile force stimulation contrasts with the continuous growth of actin fluorescence intensity, leading to our hypothesis of ‘mechanics before chemistry’: fast mechanical stimulation-induced actin bundle alignment, followed by a slower chemical driven process to stabilize the actin bundle structure.

To explore this hypothesis, we developed a new feature in the MEDYAN software that mimics the conditions of our AFM mechanical stimulation experiments. Our simulation results reveal that tensile force triggers a rapid mechanical adaptation of actin networks that induces actin filament to align along the direction of force application, and promotes actin bundle formation. We also found that slower chemical evolution is essential to the formation of actin bundle, which requires the integration of actin networks through α-actinin crosslinking followed by myosin activation and eventual further actin recruitment to the bundle. 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 two-step explanation regarding how active cytoskeletal networks adapt to external mechanical stimuli in real-time. In the control case of actin networks without external forces, actomyosin network contraction does not have a bias towards a specific direction, leading to an isotopic collapse into globular actin clusters (Fig 6A). The external tensile force first stretches the actin cytoskeletal network, forcing filaments to align, as a rapid mechanical response, which initializes anisotropic actin bundle-like structures. Longer time scale chemical processes further stabilize the actin bundle structures that can preserve the anisotropy (Fig 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.

Fig 6

Motor-driven chemical evolution generates contractility that induces the geometric collapse of the actin network.

In random networks without external forces, the geometric collapse would be isotropic, causing filaments to cluster into globular foci (a). However, the external tensile force induces filament directional alignment and favors anisotropic chemical evolution, resulting in filament bundling (b).

Actin cytoskeleton plays a crucial role in maintaining cellular shape and supporting force transmission to and from extracellular substrates. Numerous studies have demonstrated the direct coupling between mechanical forces and chemical signaling. Mechanical stretch alters the conformation of integrins [43] such that their cytoplasmic β-tails provide binding sites for focal adhesion proteins (43) and further induce assembly of an adhesion complex at the site of force application [44, 45]. This process is followed by actin stress fiber remodeling, which is necessary to redistribute physical forces needed for cell contraction and to enable cell adaptation to the extracellular microenvironment [46, 47]. Moreover, sensing of substrate stiffness via integrins further triggers the adaptation of cellular cytoskeleton in less than 100 ms [48], proposing a ‘mechanics first’ mechanism of cellular response that supports our hypothesis. Thus, when the cell experiences an external force, the cytoskeletal adaptation will first elicit the actin fiber rearrangements (mechanical) before spending ATP to initiate the chemical reactions (chemical).

In summary, we integrated in vitro cellular biophysical experiments with in silico modeling to investigate the effects of external load on the actin cytoskeleton network. Our experimental data and modeling results suggest that under tensile force actin filaments align first, and then contractility induced by chemical evolution takes place to further restructure the cytoskeleton. The mechanical stimulation of stationary cells (in vitro or in tissue) represents an intermediary state of dynamic adaptation to stress of stationary cells placed in a mechanically active environment (i.e., vessel wall). Thus, our results suggest that in this intermediate cellular state, short timescale mechanical structural adaptation operates before chemical evolution necessary to further remodel the actin network. This study lays the groundwork for further studies related to predicting cellular adaptation to mechanical stimulation, which will be important for understanding diseases that involve changes of cellular stiffness, e.g., in cancer, hypertension and aging.

Methods

Experimental methods

Vascular smooth muscle cell cultures and transient transfections

VSMC were previously isolated from rat cremaster arterioles [49] and handled as previously described [23]. Briefly, cells were cultured in a smooth muscle cell culture media containing Dulbecco’s Modified Eagle Medium (DMEM) supplemented with 10% fetal bovine serum (FBS), 10 mM HEPES (Sigma, St. Louis, MO), 2 mM L-glutamine, 1 mM sodium pyruvate, 100 U/ml penicillin, 100 μg/ml streptomycin and 0.25 μg/ml amphotericin B. Cells were trypsinized and transient transfections were performed according to manufacturer’s protocol by using the Nucleofector apparatus (Lonza, formerly Amaxa Biosystems, Gaithersburg, MD) with Nucleofector kit VPI-1004. Then, cells expressing mRFP1-actin-7 were plated on 60 mm MatTek glass bottom dishes (Ashland, MA, USA) in phenol-red free cell culture media, and incubated overnight in 5% CO2 at 37 oC. The plasmid mRFP1-Actin-7 was a gift from Michael Davidson (Florida State University, Tallahassee, FL). Unless otherwise specified, all reagents were purchased from Invitrogen (Carlsbad, CA, USA).

Vascular smooth muscle cell imaging

The integrated microscope system used for these studies was described in detail (45). Briefly, the system was constructed using an inverted Olympus IX-81 microscope (Olympus Corp., NY). An atomic force microscope (XZ Hybrid Head, Bruker Instruments, Santa Barbara, CA) was set on top of the inverted microscope and a Yokogawa CSU 22 spinning-disk confocal attachment was added to the left imaging port of the microscope. This combination of techniques enabled mechanical stimulation of live cells and simultaneous visualization of molecular dynamic events at the subcellular level in real-time. A PLAN APO TIRF 60x oil 1.45 NA objective lens (Olympus Corp., NY) was used for imaging live cells expressing fluorescent protein constructs excited by a Stabilite 2018 RM laser (Spectra Physics/Newport, Mountain View, CA) using a dual 488/568 nm bandpass filter from Chroma Technology (Brattleboro, Vermont). Confocal images were acquired as 3D stacks of 20 planes at a 0.25 μm step size with an exposure time of 100 ms using a QuantEM 512SC camera (Roper Scientific Photometrics, Tuscon, Arizona). The fluorescence imaging was controlled by Slidebook software (Intelligent Imaging Innovations, Denver, CO).

AFM mechanical stimulation of VSMCs

Tensile stress was applied to live VSMCs using an atomic force microscope probe with a 2 μm glass bead functionalized with fibronectin (Novascan Technologies, IA, USA) [9]. Formation of a functional linkage between the fibronectin on the AFM probe and cortical cytoskeleton via integrins enabled mechanical stimulation of the cell through the application of tensile forces. A mechanical stimulation experiment consists of four segments of force application. First, the probe is brought in contact with the cell for 20min to allow the formation of a functional adhesion through recruitment of integrins and focal adhesion proteins. During this time, the probe rest on the cell surface, and no tensile force is applied. The second step consists of the application of small tensile forces (i.e., mechanical stimulations of 0.2–0.4 nN) to further reinforce the adhesion by enhancing protein recruitment at the respective site. Then, the mechanical stimulation of the cell with low (~0.5 nN) and high (~1 nN) magnitude forces consisted of controlled upward movement of the cantilever in discrete steps at every 3–5 minute intervals. The same force regime mechanical stimulation was applied for 20–25 minutes each, while the actin cytoskeleton was imaged by spinning-disk confocal microscopy after each force application [9]. The AFM data were acquired using NanoScope 6.14R1 software (Veeco Instruments, Santa Barbara, CA) and were processed off-line in MATLAB (Mathworks) and Excel (Microsoft).

Three-dimensional image analysis

For each raw three-dimensional (3D) image volume at a specific time point, imaging data in z-direction were interpolated by linear interpolation to generate a new sequence. Spatial sizes of a voxel in three dimensions were not all equal, i.e., Δx = Δy = 0.178 μm, and Δz = 0.25 μm. The resulting image sequences were imported to Imaris (v.9.3.0, Oxford Instruments, Inc.) for Automatic Tracing analysis. The coordinates of branch points from the tracing analysis was exported and saved. The 3D coordinates of all paired points that are 10 points apart along a given trace were used to compute the alignment index: where Δx, Δy, Δz are differences of the paired points in x, y, and z direction, respectively. The resulting set of measurements along each trace were 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 measurements from all traces at a given time point were further averaged.

Simulation methods

A computational model for mechanochemical dynamics of active networks (MEDYAN) [41] was used to simulate the actin cytoskeletal network with an external tensile (i.e., z-axis) force. In this model, actin filaments are treated as “cylinders” connected into chains. 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 (NMII) [50]. Crosslinking proteins are also modeled as harmonic springs with an equilibrium length for α-actinin (30–40 nm) [51]. 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 [52, 53]. Simulation parameters and other model details can be found in Supplementary Information and a previous publication [41].

We initialized a 3×3×1.25 μm3 simulation volume with a 250 nm radius semi-spherical AFM probe that was 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 simulated AFM probe attachment are allowed to polymerize and depolymerize on either the plus end or the minus end. To appropriately transmit the external force generated by probe displacement to the actin network, additional 30 seed filaments were initialized with their minus-end attached to the simulated AFM probe via stiff harmonic springs (Fig 2A). These filaments are allowed to polymerize and depolymerize at the plus end. Myosin II concentration is 2 μM (equivalent to 0.1 μM NMII mini-filament) and α-actinin concentration is 2 μM, based on their concentrations reported in Dictyostelium discoideum [54-56]. We use a concentration of 20 μM for actin, which is consistent with the physiological concentration of actin [57, 58]. The concentrations of actin, motors, and crosslinkers in the computational model were also used in prior computational modeling works [39, 41]. Based on an earlier work using MEDYAN, these concentrations are adequate for filament bundle to maintain their structure [39]. 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 [59], seed filaments would grow rapidly and reach an average F-actin length of ~0.8 μm in a few seconds of simulation. Myosin motors and α-actinin crosslinkers were added after 5 seconds of simulation. The addition of myosin and α-actinin linkers connect the free filament pool to the filaments attached to the probe.

The external tensile force from the AFM probe was implemented as follows. The network was allowed to evolve for 150 s before the AFM probe vertical displacement (i.e., tensile force on z-axis). Each probe displacement created a 250 nm or 500 nm step displacement of the AFM probe, applying tensile force to the AFM probe-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 were able to treat the network change before and after displacement as a fast, mechanical response that is independent of chemistry. Networks were allowed to evolve for another 150 s before the next probe pulling step (Fig 2B). During the 150 s period, cytoskeletal network remodeling was chemically dominated by filament treadmilling, myosin activation, and α-actinin linker binding and unbinding. Since the time interval between two displacement steps is much longer than the pulling time (1 s), we define the network evolution during each 150 s as the long timescale chemical response. We applied the AFM-probe pulling 5 times, for a total of 900 seconds, during each simulation. Table 1 lists all the modeling parameters.

Table 1

Parameters for the simulations.

Reaction rates (unit of s-1)	Value (reference)
Actin diffusion	80 [41]
α-actinin diffusion	8 [41]
Non-muscle myosin II (NMII) mini-filament diffusion	0.8 [41]
Actin polymerization at plus end	0.151 [60]
Actin polymerization at minus end	0.017 [60]
Actin depolymerization at plus end	1.4 [60]
Actin depolymerization at minus end	0.8 [60]
NMII head binding	0.2 [61]
NMII mini-filament unbinding under no external load	0.2
α-actinin binding	0.009 [62]
α-actinin unbinding under no external load	0.3 [62]
Mechanical parameters
Parameters	Value
Length of cylindrical actin filament segment	108 nm [63]
Actin filament bending energy	672.5 pNαnm [63]
Actin filament stretching constant	100 pN/nm [41]
Actin filament excluded volume repulsion constant	100000 pN/nm [41]
NMII head stretching constant	2.5 pN/nm [64]
α-actinin stretching constant	8 pN/nm [65]
Boundary repulsion energy	41 pN·nm [66]
Boundary repulsion screening length	2.7 nm [66]
Mechanochemical parameters
Force Parameters	Value
Unbinding force of NMII head	12.6 pN [67]
Stall force of NMII head	15 pN [41]
Characteristic unbinding force of α-actinin	17.2 pN [68]
Characteristic polymerization force of actin filaments	1.5 pN [69]

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-probe attached filaments. 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 to avoid any problems due to the boundary effects.

(a) The probability distribution of filament polarity alignment index for bundle-like networks under pulling condition Case i. Data are taken from t = 751s–900s out of 5 duplicated trajectories. (b) The polarity alignment index is defined as cos′θ, where θ′ 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 that the generated actin bundles have mixed polarity.

(TIF)

Click here for additional data file.

(a) F-actin radial distribution after the last pulling event (t = 751 - 900s) under pulling condition Case i-iv. (b) Representative snapshots at t = 900s for each case.

(TIF)

Click here for additional data file.

(a) Representative snapshot of actin network with a static AFM probe at t = 700 s. The height of AFM probe is fixed at 1750 nm. (b) Representative snapshot of actin network with no pulling force (control case iv). (c) The alignment index for static AFM-probe (red) and no force condition (green). Error bars represent the standard deviation from the mean from 5 replicate simulations.

(TIF)

Click here for additional data file.

(a) Representative snapshot of actin network with 5 filaments attached to the AFM probe, after the fifth pulling event (d = 500 nm). (b) Representative snapshot of actin network with 60 filaments attached to the AFM probe, after the fourth pulling event (d = 500 nm). Actin filaments, myosin motors, and crosslinkers are shown in red, blue, and green cylinders, respectively. The gray sphere represents the AFM probe.

(TIF)

Click here for additional data file.

Movies of VSMC expressing mRFP1-actin-7 (red) under AFM pulling, used with permission from JOVE [21].

(MP4)

Click here for additional data file.

Actin filament bundle formation under tensile force induced by a simulated AFM-probe with step size d = 500nm (Case i pulling condition).

The network contains 330 filaments with 30 filaments attached to the simulated AFM-probe. The gray sphere represents the simulated AFM probe, and red, blue, and green cylinders represent the actin filaments, crosslinkers, and myosin motor mini filaments, respectively. Cactin = 20 μM, Cmyosin = 2 μM, and Ccrosslinkers = 2 μM.

(MP4)

Click here for additional data file.

Actin network geometrically contracts into cluster-like structure without external force.

The network also contains 330 filaments, and no filaments are attached to the simulated AFM probe. Red, blue, and green cylinders represent the actin filaments, crosslinkers, and myosin, respectively. Cactin = 20 μM, Cmyosin = 2 μM, and Ccrosslinkers = 2 μM.

(MP4)

Click here for additional data file.

Actin network evolution showing AFM-probe detachment at 600 s.

The pulling pattern is Case i (d = 500nm) at t = 150 s, 300 s, and 450 s. The 30 filaments attached to the AFM-probe were anchored to the probe until t = 600 s. At t = 601 s, the filaments detached from the probe. The gray sphere represents the simulated AFM probe, and red, blue, and green cylinders represent the actin filaments, crosslinkers, and myosin motor mini filaments, respectively. Cactin = 20 μM, Cmyosin = 2 μM, and Ccrosslinkers = 2 μM.

(MP4)

Click here for additional data file.

Actin network evolution under Case i pulling condition (d = 500nm), but myosin concentration is reduced to 0.4 μM.

Under this condition, the network does not contract, and the majority of the network remains random throughout the simulation. The gray sphere represents the simulated AFM probe, and red, blue, and green cylinders represent the actin filaments, crosslinkers, and myosin, respectively. Cactin = 20 μM, and Ccrosslinkers = 2 μM.

(MP4)

Click here for additional data file.

Actin network evolution under Case i pulling condition (d = 500nm) with lower crosslinker concentration (Ccrosslinkers = 0.4 μM).

Although the network still contracts, the filaments attached to the AFM probe disconnected from the free actin filament pool after ~ 300s. Eventually, the networks become a small filament bundle attached to the AFM probe at the top of the network and a disconnected larger cluster at the bottom. The gray sphere represents the simulated AFM probe, and red, blue, and green cylinders represent the actin filaments, crosslinkers, and myosin, respectively. Cactin = 20 μM, and Cmyosin = 2 μM.

(MP4)

Click here for additional data file.

Actin network evolution under d = 500 nm tensile displacement size with the time interval between two displacements reduced from 150s to 10s.

The network is first allowed to evolve for 160s before the first pulling event. The video shows the trajectory between 130 ~ 198s with four pulling events in total. The gray sphere represents the simulated AFM-probe, and red, blue, and green cylinders represent the actin filaments, crosslinkers, and myosin, respectively. Cactin = 20 μM, Cmyosin = 2 μM, and Ccrosslinkers = 2 μM.

(MP4)

Click here for additional data file.

3 Mar 2020

Dear Dr. Jiang,

Thank you very much for submitting your manuscript "Tensile Force Induced Cytoskeletal Reorganization: Mechanics Before Chemistry" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

Important additional instructions are given below your reviewer comments.

Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Jeffrey J. Saucerman

Associate Editor

PLOS Computational Biology

Daniel Beard

Deputy Editor

PLOS Computational Biology

***********************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: This manuscript presents important and interesting findings from molecular simulations and experiments about dynamic remodeling of actin network under the influence of external force. Both experiments and simulations demonstrated fast actin alignment to external force followed by slow myosin-mediated stabilization of the bundled actin network, termed as “mechanics before chemistry” by the authors. The videos of the simulated dynamic remodeling of actin networks under various conditions are particularly enlightening. Findings from this work has strong implications for mechano-transduction and stress fiber formation in cells. The paper is clearly written.

I have the following comments/questions about the manuscript.

1.Comparing the default case and the case with 10 s between pulling, it seems like a proper balance between the pulling rate and the biochemical relaxation rate is important for maintaining a continuous actin bundle. Is dynamic pulling necessary though? Could the actin network remodeling be induced just by geometry? For example, if the AFM probe is initially placed 2500 nm away from the initial random actin network and stay there, would an actin bundle similar to that in case iv form?

2.Seems like Case iv without pulling was simulated without the 30 AFM-attached actin filaments. Addition of the AFM-attached filaments alone (without pulling) should induce actin alignment, which explains why in Fig.3c case i-iii has slightly higher alignment index than case iv without pulling in the first 150 seconds. This effect is very weak though, probably because the AFM probe is initially right on top of the initial random actin network. Related to the question above, if the AFM probe is initially set farther away from the initial actin network, would the above effect become stronger?

3.“With a value between 0 and 1, the alignment index equals to 1 for perfect alignment with the Z-axis, 0.5 for completely random, and 0 for alignment perpendicular to the Z-axis.” According to the definition of the alignment index, average of cos(theta), completely random directions of actin between 0 and pi/2 should give an alignment index of 2/pi = 0.64. Why would it be 0.5 in this case? It is also noted that in Fig. 3c, case iv, the alignment index initializes around 0.5 and gradually drops to around 0.4. Why would the index drop to 0.4 for globular actin cluster?

Typos found:

1.“The alignment index increases immediately after each of the AFM pulling events in all three pulling patterns tested (Figure 4c, Case i-iii).” Should be Figure 3c.

2.“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.” Case i-iii move in different ways. Case iv should move up in the same way as for Cases i, as stated in the caption of Fig. 2b.

Reviewer #2: In their manuscript, Li and Ni et al. investigate a fundamental question in the cellular mechanotransduction field: how do cells sense and react to externally applied mechanical stimuli? To do this, they combine experiments performed in living cells with computational modeling performed in silico to investigate the ability of the actin cytoskeleton within a cell to dynamically respond to tensile external force. Specifically, their experiments consisted of imaging and quantifying the reorganization of the actin cytoskeleton within living vascular smooth muscle cells (VSMCs) expressing mRFP1-tagged actin as an external tensile force was applied to the their apical plasma membrane via a fibronectin-functionalized atomic force microscopy (AFM) probe. They then used computational modeling to simulate the mechanical structural adaptation of active actin cytoskeleton networks in response to externally applied tensile force in a manner similar to their AFM-based VSMC experiments. Based on the results of their experiments and modeling, the authors conclude that mechanical structural adaptation occurs before chemical adaptation during actin bundle formation. Basically, Li and Ni propose that actin filaments first align in the direction of the externally applied tensile force, which results in their anisotropic orientation followed by the chemical evolution of the actin network into a dense bundle-like geometry. They call this a “mechanics before chemistry” model of actin cytoskeleton remodeling in response to externally applied force. While I feel that this manuscript tackles an important and timely question in the field of cellular mechanobiology, I have several major and minor issues that I strongly feel that the authors need to address before I can recommend this work for publication at PLoS Computational Biology. In addition, there were several grammatical/writing issues that I would like the authors to address. These issues are all described below.

Major Issues:

1)The authors need to do a better job of motivating their work. Why is it important that they “ask how tensile force induces cytoskeletal remodeling and the active formation of actin bundles” in VSMCs?

2)Where is the AFM probe placed on the apical surface of the VSMCs? Is it placed in the same relative position? Is it place on or away from the nucleus? More information is needed.

3)The authors need to explain why they chose the specific concentrations of the molecules included in their computational models. What are the references that these concentrations were pulled from and in which cell types?

4)Why were only 30 filaments attached to the AFM tip in the simulations shown in Fig. 2? What happens if the number of attached filaments is increased or decreased? Are the filaments always attached to the AFM tip or do the have a dissociation constant?

5)The simulation described in Fig. 2A does not seem to be physiologically relevant to the AFM experiments performed on live VSMCs shown in Fig. 1. I say this because the authors are measuring the axial displacement of fluorescently labeled pre-assembled actin stress fibers caused by the pulling of an AFM tip on the apical surface of a VSMC, while the simulations are pulling on an active network of actin filaments that evolves over the time that tensile force is applied to the network. In addition, the geometry of the stress fibers in the VSMCs is quite noticeably different from the geometry of the simulated AFM experiments. Were the authors to have measured the accumulation of an active cytoskeletal network underneath the adhered AFM as it was pulled away from the apical VSMC plasma membrane, the simulations presented in this work would be more directly comparable.

6)I cannot agree with the authors’ description of their simulated active actin networks under tension as being stress fiber-like. While the simulated networks and stress fibers both have mixed filament polarity, the architecture of these two actin structures are quite different. The architecture of a stress fiber is reminiscent of a contractile sarcomere in muscle, which are “blocks of actin filaments of alternating polarity and bands of interdigitating non-muscle myosin” (Pellegrin and Mellor, 2007 J Cell Science). Pellegrin and Mellor go on to say, “the structure (i.e. sarcomere /stress fiber) is held together by α-actinin and also crosslinked by non-muscle myosin”. In contrast, the authors’ simulated active actin networks more closely resemble the actin “comet tails” responsible for the intracellular movement of endosomes, some bacteria (i.e. Listeria monocytogenes and Rockettsia conorii), and some viruses (i.e. Vaccinia and Baculoviruses) (Welch and Way, 2013 Cell Host Microbe; Fehrenbacher et al., 2003 J Exp Biol). Given this disconnect between the VSMC experiments and the simulations, I find it difficult to see how the in silico modeling complements or illuminates the in vitro cellular experiments presented in this work.

7)I would very much like to seem movies of the AFM experiments performed on VSMCs expressing the so-called actin-mRFP1 construct (see Minor Issue #5 below).

8)In lines 5-6 of the 2nd paragraph of the “Two-step development of actin bundles relies on both faster mechanical alignment and slower chemical stabilization” section of the Results, the authors state, “The control case without external pulling (iv, green line) shows the biochemically driven F-actin accumulation, as a result of myosin-induced contractility”. Why do they authors think that this is all due to myosin-induced contractility and not also due to alpha-actinin-induced bundling and/or actin polymerization?

9)Why do the authors only include “4 possible binding sites for myosin motors and crosslinkers” for a 40 subunit 108 nm long cylinder of an actin filament? This is a gross underestimation, as a myosin-II motor can interact with each actin subunit in a filament. Therefore, I would assume that there were 40 myosin-binding sites per actin filament cylinder. What happens if the number of binding sites were increased in the computational models?

10)I would recommend that the authors tone down their conclusion that their “mechanics before chemistry” hypothesis is novel. It is well known in mechanobiology that the timescales of mechanotransduction range from milliseconds to seconds for the stretching of mechanosensor proteins to the polymerization of actin, respectively.

Minor Issues:

1)In the legend of Fig. 2, the authors need to state how long the 300 free actin filaments are that are in their simulations.

2)In the 5th line of the 4th paragraph of the Discussion, the authors might elaborate on which specific signaling pathways might be triggered by stretching focal adhesion proteins.

3)In the last paragraph of the Discussion, the authors state, “we integrated in vitro and in silico modeling”. However, I do not understand what is meant by “in vitro modeling” in this statement. It seems to me that the authors integrated cellular biophysical experiments with in silico modeling instead.

4)In the last sentence of the Discussion, the authors state, “This result suggests….which can have important implications to mechano-signal transduction. Perhaps they might provide some examples of such “important implications”? This would give the reader a sense of where the authors plan on going next with this line of research.

5)The authors state that they are expressing an actin-mRFP construct that they received from the late Michael Davidson in VSMCs to visualize the actin cytoskeleton. However, a quick search of Michael’s fluorescent protein construct collection for a red actin construct suitable for mammalian expression revealed that he had a construct named “mRFP1-actin-7”, not one named “actin-mRFP”. Therefore, the authors should change all mentions of “actin-mRFP” to “mRFP1-actin-7”. This change is important for others to be able to reproduce the authors’ results. Moreover, the way that the authors write “actin-mRFP” suggests that the mRFP is fused to the C-terminus of actin, which is not correct.

6)In the Materials and Methods, the authors cite direct their readers to reference #45 for detailed information regarding the “integrated microscope system” used in this manuscript. While I understand that they do not want to have to go into all of the details of their previously described imaging system, I do feel that they need to at least provide their readers with the following information:

a.The name of the microscope company that the base of the microscope was built on.

b.The numerical aperture value for their 60x objective and the name of the microscope company that manufactured it.

c.The cameras used and the companies that made them.

d.The light source (I assume that they are lasers, but which ones and from where?).

e.The information about the excitation and emission filters used.

f.The software used to drive the imaging system.

7)What was the concentration of fibronectin used to coat the AFM probe?

8)In the “Simulation Methods” section of the Methods, I do not understand what the authors mean by the phrase “strong axial stretching stiffness”.

9)In the “Simulations Methods” section of the Methods, the authors need a reference for the following statements:

a.“Myosin motors are modeled as harmonic springs…pm the non-muscle myosin II”.

b.“Crosslinking proteins are also modeled as harmonic springs…(30-40 nm)”.

Writing Suggestions:

1)In the 3rd line of the 2nd paragraph of the Introduction, the authors state, “is critical in understanding”. They should change the “is” to a “for”.

2)In the 6th line of the 4th paragraph of the Introduction, the authors should change “myosin activation” to ”myosin-II activation”.

3)In the 1st line of the 5th paragraph of the Introduction, the authors should remove the “the” following “upon”.

4)In the 3rd line of the 5th paragraph of the Introduction, the authors should insert the word “software” following “Network)”.

5)In the heading of the 1st section of the Results, the authors should change the “of” before “live” to “in”.

6)In the 1st line of the 2nd paragraph of the “Two-step development of actin bundles relies on both faster mechanical alignment and slower chemical stabilization” section of the Results, the authors need to change “filament” to “filaments” and “keeps” to “kept”.

7)In the 3rd line of the 2nd paragraph of the “Two-step development of actin bundles relies on both faster mechanical alignment and slower chemical stabilization” section of the Results, the authors need to change “calculate” to “calculated”.

8)In the 5th line of the 3rd paragraph of the Discussion, the authors should change “isotropically” to “isotropic”.

9)In the 2nd line of the last paragraph of the Discussion, the authors should insert “actin” before “cytoskeleton”.

10)In the last sentence of the Discussion, the authors should change the “to” to a “for”.

11)In the 2nd to last sentence of the “Experimental Methods” section of the Methods, the authors should change the “of” before “Michael” to “from”.

12)In the “AFM mechanical stimulation to VSMCs” section of the Methods, the authors should make the following changes:

a.Change the “to” before “VSMCs” to “of” in the heading of this section.

b.Change the two “consists in” to “consists of”.

13)In the “Three-dimensional image analysis” section of the Methods, the authors should make the following change:

a.In the penultimate sentence before the Alignment Index equation, the word “was” needs to be changed to “were”.

14)In the “Simulations Methods” section of the Methods, the authors need to make the following changes:

a.In the 2nd paragraph, the “allowing” found in the sentence that begins with “Only plus ends of these filaments” needs to be changed to “allowed”.

b.In the 3rd paragraph, the “tips” in the sentence that begins with “Each probe displacement” needs to be changed to “tip” and the “generating” needs to be changed to “applying”.

c.In the 3rd paragraph, the “are” in the sentence that begins with “Since all AFM” needs to be changed to “were”.

15)In the legend of Fig. 1, the authors need to delete the “were” from the description of panel (a).

16)In the legend of Fig. S1, the “is” in the sentence that begins with “The distribution spreads” needs to be changed to “are” and ”a” needs to be inserted before “stress”. In addition, a reference for this statement needs to be provided.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: Yes

Reviewer #2: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Figure Files:

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, . PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email us at .

Data Requirements:

Please note that, as a condition of publication, PLOS' data policy requires that you make available all data used to draw the conclusions outlined in your manuscript. Data must be deposited in an appropriate repository, included within the body of the manuscript, or uploaded as supporting information. This includes all numerical values that were used to generate graphs, histograms etc.. For an example in PLOS Biology see here: http://www.plosbiology.org/article/info%3Adoi%2F10.1371%2Fjournal.pbio.1001908#s5.

Reproducibility:

To enhance the reproducibility of your results, PLOS recommends that you deposit laboratory protocols in protocols.io, where a protocol can be assigned its own identifier (DOI) such that it can be cited independently in the future. For instructions, please see

15 Apr 2020

Submitted filename: ExternalForce_Rebuttal_Final.docx

Click here for additional data file.

21 Apr 2020

Dear Dr. Jiang,

We are pleased to inform you that your manuscript 'Tensile Force-Induced Cytoskeletal Remodeling: Mechanics Before Chemistry' has been provisionally accepted for publication in PLOS Computational Biology.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow up email. A member of our team will be in touch with a set of requests.

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

Should you, your institution's press office or the journal office choose to press release your paper, you will automatically be opted out of early publication. We ask that you notify us now if you or your institution is planning to press release the article. All press must be co-ordinated with PLOS.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Computational Biology.

Best regards,

Jeffrey J. Saucerman

Associate Editor

PLOS Computational Biology

Daniel Beard

Deputy Editor

PLOS Computational Biology

***********************************************************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: The authors have fully addressed all my comments.

Reviewer #2: I thank the authors for having addressed all of my concerns, especially for improving the clarity of their manuscript. I feel that the manuscript is acceptable for publication.

**********

Have all data underlying the figures and results presented in the manuscript been provided?

Large-scale datasets should be made available via a public repository as described in the PLOS Computational Biology data availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.

Reviewer #1: None

Reviewer #2: Yes

**********

PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

3 Jun 2020

PCOMPBIOL-D-20-00147R1

Tensile Force-Induced Cytoskeletal Remodeling: Mechanics Before Chemistry

Dear Dr Jiang,

I am pleased to inform you that your manuscript has been formally accepted for publication in PLOS Computational Biology. Your manuscript is now with our production department and you will be notified of the publication date in due course.

The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. Please note that major changes, or those which affect the scientific understanding of the work, will likely cause delays to the publication date of your manuscript.

Soon after your final files are uploaded, unless you have opted out, the early version of your manuscript will be published online. The date of the early version will be your article's publication date. The final article will be published to the same URL, and all versions of the paper will be accessible to readers.

Thank you again for supporting PLOS Computational Biology and open-access publishing. We are looking forward to publishing your work!

With kind regards,

Laura Mallard

PLOS Computational Biology | Carlyle House, Carlyle Road, Cambridge CB4 3DN | United Kingdom ploscompbiol@plos.org | Phone +44 (0) 1223-442824 | ploscompbiol.org | @PLOSCompBiol