The organization of muscle is the product of functional adaptation over several length scales spanning from the sarcomere to the muscle bundle. One possible strategy for solving this multiscale coupling problem is to physically constrain the muscle cells in microenvironments that potentiate the organization of their intracellular space. We hypothesized that boundary conditions in the extracellular space potentiate the organization of cytoskeletal scaffolds for directed sarcomeregenesis. We developed a quantitative model of how the cytoskeleton of neonatal rat ventricular myocytes organizes with respect to geometric cues in the extracellular matrix. Numerical results and in vitro assays to control myocyte shape indicated that distinct cytoskeletal architectures arise from two temporally-ordered, organizational processes: the interaction between actin fibers, premyofibrils and focal adhesions, as well as cooperative alignment and parallel bundling of nascent myofibrils. Our results suggest that a hierarchy of mechanisms regulate the self-organization of the contractile cytoskeleton and that a positive feedback loop is responsible for initiating the break in symmetry, potentiated by extracellular boundary conditions, is required to polarize the contractile cytoskeleton.
During biological development, evolving forms are marked by distinct functionalities. An interesting example is the organization of myofibrils in striated muscle cells. As the myocyte matures, the myofibrils are rearranged from an irregularly dispersed pattern into tightly organized bundles spanning the length, rather than the width, of the cell [1]. Although assembly of the myofibril from its molecular constituents has been extensively investigated [2], [3], [4], how myofibrils build this specialized architecture and its functional consequences remains unanswered. This is important because changes in muscle structure accompany not only morphogenesis, but also pathogenesis [5], [6]. Myofibrils mature in a force-dependent manner [7], [8], [9], suggesting that the contractility of a cell may play an important role in polarizing the myofibrillar network. This has been shown in nonmuscle cells where the cytoskeletal architecture within a geometrically-defined microcompartment becomes polarized with increasing tractional forces [10], [11]. Thus, we hypothesized that geometric cues in the extracellular matrix (ECM) can organize the intracellular architecture and potentiate directed myofibrillogenesis. Because of the difficulty in identifying de novo sarcomeres in primary harvest muscle cells in culture, one strategy for studying myofibrillogenesis is to coax the disassembly and reassembly of myofibrils by forcing myocytes to assume shapes that are not commonly observed in vivo using engineered substrates in vitro [10], [11]. To guide these experiments, we developed a computational model of myofibrillar patterning to show the sensitivity of the intracellular architecture to the extracellular space. With these tools, we sought to understand the critical events in the global assembly and organization of the contractile apparatus in cardiac myocytes. By comparing experimental results with our computational model, we were able to elucidate the role of maturing myofibrils, their parallel coupling, and their functional attachment to the focal adhesion assembly and how these processes are guided spatially by the boundary conditions imposed on the cell. After determining the roles of these parameters in myofibrillogenesis, we then expanded our model to test the functional implications of these architectures. We developed a novel method for micropatterning on soft substrates and were able to engineer myocyte shape on substrates that would allow us to measure the contractility of these artificial shapes and compare them with the model results. Together, these results suggest that the self-assembly and -organization of the contractile apparatus is facilitated by a symmetry-breaking event that is potentiated by either a geometric cue in the extracellular space or a random event in the intracellular space.
Our theoretical approach focuses on the interaction between the myofibril and the ECM, as well as adjacent myofibrils (Fig. 1). Inherent to our model are two key assumptions: 1) the force that the myofibrillar bundle exerts on the substrate is fiber length-dependent [12] and 2) adjacent myofibrils affect each other to facilitate lateral coupling, which is akin to them exerting torque on each other. We have modeled only the maturation of cytoskeletal structural elements responsible for contraction and integrin binding to the ECM. We define these components using coarse-grained variables that are experimentally observable. This eliminates the computational complexity required to model detailed molecular interactions and the effect of different protein isoforms. The nomenclature for the immature and mature versions of the myofibril vary with different qualitative models (reviewed by Sanger and colleagues [2]). Here we refer to the immature state as the premyofibril, and the quasi-mature state as the nascent myofibril [1], [13]. Our mathematical approach differs from others [14], [15] in that we incorporate focal adhesion (FA) kinetics, mutual alignment of adjacent contractile fibers, and the dependence of contractile forces on fiber length [16]. The variables used in our approach are: (1) the density of bound and unbound integrin, and, respectively; with the bound integrins connected to premyofibrils and nascent myofibrils labeled as and, respectively; (2) the net force exerted on the bound integrin, ; (3) the local density, , orientation, , and the orientational order parameter, , of the premyofibril network and the nascent myofibril network; and (4) the resultant 2D stress field exerted by the cell on the substrate, T. Previously, we reported [17] that when cardiac myocytes are constrained on 2D islands, their vertical dimension, orthogonal to the plane of the culture surface, is uncontrolled. In that study, we reported that myofibrils are predominantly located under the nucleus, in a plane parallel to the culture surface. However, as that study also showed, several layers of myofibrils may be present, and the nucleus and microtubule organizing center may represent an obstacle to a symmetrical array of myofibrils in the thicker regions of the cell. Our model and analysis is restricted to the 2D intracellular plane closest to the culture surface. Instead of solving the steady state for all of the variables, we numerically simulated their spatiotemporal profiles. This allows us to trace the effect of local symmetry-breaking events such as the mutual alignment of fibers on myofibrillar patterning, which cannot be easily predicted by conventional steady-state analysis. The local symmetry-breaking event may result from a static cue or a transient perturbation. In our simulation, we began with randomly distributed densities of the unbound integrin, unless fitting parameters, in which case we examined several sets of initial conditions. The unbound integrin can initially become bound through a random process, with the rate proportional to its local concentration. The fraction of bound integrins connected to the fibrils is modeled as an adsorption process, and is calculated using the Langmuir isotherm. The force exerted between FAs is assumed to be proportional to the product of fiber connections at each site [16]. The net force at a local FA is computed by integrating the tension contributed by all connected contractile elements (Fig. 1A). The net force governs the growth rate of local FAs, which in turn modulates the premyofibril network [18], [19]. The assembly of FAs and the bundling of its associated fibers is coupled by a positive feedback loop via forces exerted on the FA [16], [18]. As a consequence of the positive feedback, when the net force on a FA is not zero, both the FA and its associated fibers are structurally reinforced (Fig. 1B–D) [20]. If the net force is zero, the bound integrins will disassemble at each time step and disassociate the attached fibers (Fig. 1E–G) [18], [21]. As time lapses, the premyofibrils are converted to the nascent myofibrils. The local orientation of the nascent myofibril is primarily determined by the antecedent premyofibril network, but also can be modulated by adjacent myofibrils due to their lateral coupling [1], [22]. In some cell shapes, polarization of the myofibrillar array can only be achieved by the lateral alignment of adjacent myofibrils, which occurs at a much slower time scale than that of fiber assembly [1], [22]. The effect of the lateral coupling is modeled as a biasing potential field that distributes the free integrins, such that the nascent myofibrils are moved towards each other through the course of normal integrin recycling. To visualize the amount of parallel, or lateral, coupling of the fibers, we define a variable, ψ, which varies from zero for no local coupling, to unity for the maximal local coupling. The model' s calculations are ordered as depicted in Fig. 1H. To fit the parameters of the computational model, we chose an uncommon cell shape, a stair-shaped myocyte, that we could model computationally in silico and repeatably in vitro with cell engineering techniques (Fig. S1). The parameters were fit on a variety of initial conditions (Fig. S2) such that the steady state results were the same for each. In Fig. 2A we show the temporal results for an initial condition with a random distribution of free integrins. Initially, there are no fibers in the cell, as no integrins are bound (Fig. 2A). The geometrical symmetry of the stair-shape cell potentiates the initial appearance of fibers predominantly along the diagonal. As the fibers form, the fiber density is mostly uniform throughout the cell, as evident from the line segment thickness (Fig. 2A). When the nascent myofibrils form and begin to laterally couple, they are distributed diffusely within the cell (Fig. 2A). As time progresses, the positive feedback increases, i. e. greater number of fibers produces a greater force which drives the clustering of bound integrins and fibers. As a result, the myofibrils achieve a distribution very similar to the steady state (Fig. 2A). For the rest of the simulation the nascent myofibrils mutually align and exhibit greater degrees of parallel coupling (Fig. 2A). Myocytes were cultured on stair-step shaped islands for three days and then stained against actin filaments (Fig. 2B). At equilibrium, most nascent myofibrils are coupled and aligned with the major diagonal, as shown experimentally in Fig. 2B and in simulation (Fig. 2A). The parallel coupling of the nascent myofibrils emerges later in the simulation, as suggested by previous reports [1], [21], [22], [23]. In summary, the simulated dynamics visualized for nascent myofibril bundling and realignment show that well-aligned myofibrils first occurred in the center of the cell, followed the longest diagonal, and recruited additional adjacent fibers to form a bundled, parallel arrangement. To test our hypothesis, we examined the sensitivity of myocytes and our model to various cellular boundary conditions. We reasoned that when myocytes are constrained by a heterogeneous boundary curvature, triangles (Fig. 3A) and squares (Fig. 3F), the distinct geometrical cues at the cell boundaries would potentiate unique cytoskeletal architectures, but when cells are constrained by a homogeneous boundary curvature, a circle (Fig. 3K), there is no external cue to break the symmetry of the isotropic network. Thus, we examined two cases of the cell with heterogeneous curvature at the periphery: the square shaped cell, where the longest axes are on the diagonal, and the equilateral triangle shaped cell, where the long axes are along the cell periphery. We also tested cells with homogeneous boundary curvature: the circular shaped cell, in which no major axis is defined. To ensure that the observations resulted from geometric considerations alone, we used the same parameter values from the previous simulations. Fluorescent staining of actin filaments in myocytes cultured on square and triangular ECM islands for 72 hrs revealed that polymerized actin fibers were densely arranged along the longest axes (Fig. 3). The fibers are regularly punctuated along their length, indicating the presence of sarcomeres (Fig. 3B, G). At steady state, modeled triangular and square cells displayed the same cytoskeletal arrangement as the in vitro results, with enhanced parallel bundling occurring along the longest axis of these cells (Fig. 3C, H). Fluorescent staining of vinculin revealed elongated FAs in the corners of the square and triangular cells that were oriented in parallel with their attached myofibrils (Fig. 3D, I). Numerical results revealed the same accumulation pattern of FAs, as indicated by the density of bound integrin located in the corners (Fig. 3E, J). The dynamics of the simulation results are depicted in Fig. 3C, E, H, and J and Video S1, S2, S3, and S4. As previously observed in the simulation shown in Fig. 2, the predominant orientation of the premyofibrils occurs quickly and the parallel bundling increased with time to further stabilize the myofibrillar architecture with respect to the geometric cues in the ECM. These data suggest that FAs localize and mature at the corners because the premyofibrils that align along the longest axes of the cell are the strongest by virtue of their greater propensity for parallel bundling and binding myosin motors [24], [25]. In contrast, myocytes cultured on circular ECM islands (Fig. 3K) for the same period of time have random myofibrillar architectures (Fig. 3L) [26], which is recapitulated in the model (Fig. 3M). Without an external cue to break the geometric symmetry, computer simulations suggest that myofibrillar polarity will emerge after a longer period of time, (almost five times as long as other shapes). Transient multi-pole patterns develop within cellular microcompartments (Video S5) and at equilibrium there is local bundling and nascent myofibril formation, but no overall cell organization (Fig. 3M, Video S5). In vitro, vinculin stains irregularly around the myocyte perimeter (Fig. 3N). In silico, after a similarly prolonged simulation, FAs appear as opposing bands along the cell periphery (Fig. 3O, Video S6). It is important to note that this patterning is due to a random, intercellular, symmetry-breaking event and that while the model will always converge, circular cells both in silico and in vitro, after 2–3 days in culture, often display irrepeatable cytoskeletal structures. Together, the simulation and experimental results summarized in Fig. 3 suggest that the orientation of the premyofibrillar network is regulated by ECM cues. These cues promote stabilization of the network and FAs, facilitating parallel bundling of the nascent myofibrils. Furthermore, our model predicted that the polarized myofibrillar network has a preference to align along the longest axis of cells. Proper functioning of myocytes requires the correct myofibrillar configuration for coordinated contraction [5]. To correlate myofibrillar structure with contractile function, we investigated the spatial patterning of sarcomeric proteins and conducted traction force microscopy on the cultured myocytes. Fluorescent micrographs of myocytes immunostained against sarcomeric α-actinin revealed distinct myofibrillar patterning on ECM islands of heterogeneous boundary curvature (Fig. 4A, F). The sarcomeric Z-lines register in the internal angles of the corners of both the square and triangle and are perpendicular to the orientation of the actin fibers. To measure myocyte contractile stresses, we engineered ECM islands on soft substrates. When freshly harvested myocytes are cultured on these substrates, they remodel to assume the shape of the island in the same manner as they do on rigid substrates (Fig. 4B, G). Unlike myocytes cultured on the rigid substrates, myocytes on soft substrates do not contract isometrically and can be observed to shorten as in traditional assays of single myocyte contractility (Fig. 4C, H, Video S7 and S8). To visualize substrate deformation due to myocyte contraction, fluorescent beads were embedded in the substrate and bead movement was detected using high speed fluorescence microscopy. The nominal stress field exerted on the substrate due to systolic contraction, with the resting myocyte position defined as the reference state, was calculated from substrate deformation with the known substrate mechanical properties and assuming that the substrate is linearly elastic. In the videos (Videos S9 and S10), the substrate displacement vectors, as depicted by the white arrows, are directed inward during systole, indicating that the substrate is pulled towards the center of the myocyte by the shortening FA-anchored myofibrils. During diastole, they reversed direction as the elastic recoil of the myocyte pushed the substrate back to the rest position. The myocytes generate a unique contractile footprint that mimics the position of the FAs depicted in Fig. 3, with the highest systolic stresses exerted on the substrate at the corners of the myocyte (Fig. 4D, I). Note that even though the model does not differentiate between systolic and diastolic stresses, the experimental substrate stress field pattern matches the simulated results (Fig. 4E, J). In myocytes of homogeneous boundary curvature, the myofibrillar patterns are not reproducible. However, structural coordination of the myofibrils on a preferential axis was observed, as evidenced by the well-demarcated Z-lines that continuously traversed the 1 to 7 o' clock axis in the circular myocyte shown in Fig. 4K. Similarly, the circular shaped myocytes cultured on soft substrates appear to shorten concentrically during contraction (Fig. 4L, M, Video S11), where a principal axis of shortening is apparent at peak systole but does not occur with the same spatial regularity of the square and triangular cells (Fig. 4N, Video S12), consistent with previous findings with nonmuscle cells [10]. Our model predicted a similar contractile signature (Fig. 4O), with the peak stresses coincident with the location of the widest FA bands observed in Fig. 3O. Thus, these data suggest that muscle cells depend on extracellular spatial cues to efficiently and functionally organize the myofibrils and contracion. We hypothized that a hierarchy of mechanisms may be responsible for myofibrillar organization. We reasoned that our model would allow us to determine which of the two model features, the fiber length-force dependence and parallel coupling of fibers, was dominant in organizing the myofibrillar architecture. We also reasoned that the nature of the cell boundaries may determine the sensitivity of the cell to these two mechanisms. To test this hypothesis, we ran simulations where these two features were either on, or turned off, within the cell. In the staire-shaped cell, we ran simulations where: 1) there is no mutual alignment mechanism but fiber contractility is fiber length-dependent (L = ON, τ = OFF, refer to Eq. (1) & (4) ); 2) the fiber contractility is not myofibril length-dependent but there is mutual alignment of fibers (L = OFF, τ = ON); and 3) there is neither fiber force-length dependence nor any mutual alignment of fibers (L = OFF, τ = OFF). In simulations where the nascent myofibrils have fiber force-length dependence, fibers will predominantly organize along the major diagonal (Fig. 5A) as shown experimentally (Fig. 2B), however, when there is no fiber force-length dependence, fiber bundles follow both the long and short diagonals (Fig. 5B). We compared the mean degree of parallel coupling as a function of time for all conditions (Fig. 5C). This analysis reveals that the force-fiber length dependence is an essential contributor to the emergence of an organized equilibrium in the myofibrillar network. In these simulations, the absence of the force-length dependence potentiated a less organized nascent myofibril network, whereas mutual alignment of nascent myofibrils enhanced parallel coupling. Eliminating the mutual alignment alone (grey dot-dashed line), produces a minor effect in the stair cell as shown in the inset of Fig. 5C, however, previous reports suggest that the effect of mutual fiber alignment is seen at longer time scales [1], [21], [22], [23]. We asked how mutual fiber alignment would effect myofibrillar organization in the circular cell, whose homogeneous boundary curvature requires an internal, random symmetry break to achieve equilibrium. By eliminating the ability of fibers to cooperatively align in circular cells (grey-empty circle line Fig. 5C), we show that the increase in parallel fiber coupling is solely depended on the ability of the nascent myofibrils to mutually align. The importance of mutual alignment is illustrated by contrasting the steady state fiber organization in circle cell with mutual alignment (Fig. 5D) and no mutual alignment (Fig. 5E). In the case of no mutual fiber alignment the fibers in the circular cell remain randomly organized, which is contradicted by experimental results (Fig. 3L and Fig. 4N). In summary, our data suggests that the fiber length-force dependence is necessary to reproduce myofibrillogenesis in all cell shapes, while the importance of mutual fiber alignment effect increases in cells with homogenous boundary conditions.
Muscle morphogenesis is a hierarchal, self-organizing process spanning from nanometer scale conformational changes in proteins to bundled fibers sometimes a meter in length. We reasoned that boundary constraints are a physical signal that is conserved over all of these length scales and spatially organizes this broad range of coupled structures. Based on previous experimental evidence [17], [26], [27], [28], we hypothesized that geometric cues in the extracellular space help organize the assembly of the contractile apparatus in the cytoplasm and developed computational and experimental models to recapitulate these events. We report that distinct cytoskeletal architectures arise from two temporally-ordered, organizational processes: the cooperative interaction between premyofibrils and focal adhesions, as well as the mutual alignment and parallel bundling of nascent myofibrils. Our model assumes that the assembly of FAs and the parallel bundling of actin based fibers is coupled by a positive feedback loop and that the growing force on the FA potentiates its structural reinforcement, as suggested by previous experimental work [7], [8], [9]. By modeling the amount of bound and unbound integrin and by marking the maturation of the premyofibril to a nascent myofibril simply by increased contractility, we are able to predict the organization of the contractile apparatus in cardiac myocytes cultured on engineered substrates in a computationally efficient manner. To achieve this efficiency, we ignore the details of the molecular constituents of the assembly of myofibrils [2], [3], [4]. However, we were able to account for all the dominant factors in a course grained manner as indicated by the match between all our models and experiments. By experimenting with our assumptions in silico and comparing them to data from in vitro experiments, our results suggest that the force that the myofibrillar bundle exerts on the substrate is fiber length-dependant [10], [11], [12] and that the adjacent myofibrils exert “torque” on one another to facilitate coupling [24], are necessary to describe how these myocytes build and organize their internal cytoskeleton relative to extracellular cues. Our computationally efficient model recapitulates the elegant protein choreography of the sarcomere assembly, where an ensemble of proteins assembles repetitively along the length of the actin fiber template. Several models of cell cytoskeleton assembly and mechanics have been reported and it is worthwhile to compare and contrast the efforts [14], [15], [29]. Our model is similar to the model by Novak and colleagues [16] in that we have used reaction kinetics to simulate the dynamic self-assembly and – organization of the cytoskeleton. These approaches differ from that of Deshpande, et al [14], [15], [16] who report a solid mechanics model and Pazek and colleagues [14], [15], [29] who use a mechanochemical model. All four of these models simulate the bound and free states of integrins in some form and also model the increasing stabilization, or maturation, of focal adhesions with increases in exerted force. The Despande and Pazek models offer detailed mechanical analysis of the cell-substrate interface, whereas our model, like the Novak model, does not. While the Pazek, et al. , model does not recapitulate stress fibers, our model, like the Novak and Deshpande models, does. Our model accounts for the specialized case of the maturing striated muscle cell by mimicking the transition of a premyofibril to the nascent myofibril, modeled by an increased ability to generate tension. The Hammer and Novak models omit the fiber length-force assumption that is critical to our model' s ability to recapitulate our experimental data. Similarly, the Desphande and Novak models explicitly do not account for mutual alignment of fibers, whereas ours does. Our model, like the Desphande et al. and Pazek models, calculates the load exerted on the substrate by the contracting cell, where the Desphande and Pazek models offer detailed descriptions of the solid mechanics at this interface. Both our model and that by Novak et al. , are similar to larger scale models of myofibril adaptation in the left ventricle [30], in the assumption that there is a network of fibers where all integrins are connected to all other integrins. Each model, including the one reported herein, varies in approach and further work is required to test all of these models against experimental data as we have attempted. We were able to reproduce the results shown by Novak et al. , [16], who predicted that with no fiber tension-length dependence, and homogeneous boundary conditions the FAs would aggregate to the perimeter. However, as our in vitro work shows even with a homogeneous boundary condition, i. e. the circular cell, there occurs a symmetry break, therefore it is necessary to introduce fiber tension-length dependance and mutual alignment of fibers for in silico experiments. We can also utilize the model to explore the effect of cell boundary curvature, cell aspect ratios and combinations of multiple cells on the myofibril distribution, as well as the relative importance of mutual fiber alignment in three dimensions. Additionally, it will be possible to integrate our model with adhesion dynamics models using the same methods as Paszek et al. , to explore integrin clustering with contractile cells on substrates with different material properties [29]. This combination of a mechanical model with our myofibrillogenesis model could also allow for simulations of the rearrangement of the extracellular matrix by contractile cells. In summary, our study suggests that hierarchal organization of muscle requires localized cues that guide myofibrillogenesis. Specifically, a local symmetry break is required to potentiate the assembly and organization of FA and actin complexes that are the template for myofibrillar organization. Such cytoskeletal symmetry-breaking has also been widely observed in other important biological behaviors such as cellular migration [11], cellular division [31], and formation of tissue sheets [32]. The symmetry-breaking can arise from a static, external cue, such as a geometric feature in the boundary conditions imposed on the cell, or from a dynamic internal cue, such as a local overlapping of long fibers. The multiple time scales of these interacting events suggest a hierarchy of post-translational, self-organizational processes that are required for coupling cellular form and function.
All experiments were conducted in accordance with the guidelines of the Institutional Animal Care and Use Committee of Harvard University. Trypsinized ventricular tissue isolated from 2-day old neonatal Sprague Dawley rats (Charles River Laboratories, Wilmington, MA) was serially dissociated into single cells by treating the ventricular tissue 4 times with a 0. 1% solution of collagenase type II (Worthington Biochemical, Lakewood, NJ) for 2 minutes at 37°C. The myocyte fraction was purified and pre-plating the cells twice for 45 minutes each time. Purified myocytes were plated onto micropatterned substrates prepared as described below at a density of 100,000 cells per coverslip and kept in culture at 37°C with a 5% CO2 atmosphere. The culture medium was M199 (Invitrogen, Carlsbad, CA) base supplemented with 10% heat-inactivated Fetal Bovine Serum, 10 mM HEPES, 20 mM glucose, 2mM L-glutamine, 1. 5µM vitamin B-12, and 50 U/ml penicillin. The medium was changed 24 hours after plating to remove unattached and dead cells and every 48 hours afterwards. After 72 hours in culture, most cardiac myocytes beat spontaneously and were used either for immunostaining or traction force measurements. Micropatterned substrates containing square, triangular, or circular adhesive islands were prepared for immunostaining and traction force microscopy, as follows. For immunostaining, the substrates were micropatterned using a microcontact printing procedure similar to that described by Tan et al. [35]. Micropatterned substrates for traction force experiments were created by adapting the published techniques [10], [36]. Briefly, a thin layer of 10% by weight poly-N-iso- propylacrylamide (PIPAAM) prepared in 1-butanol was spin coated on a silicon wafer (Fig. S1a). A 50∶75 µm layer of photoresist (SU-8, MichroChem Corp, Newton, MA) was spin-coated on top of the PIPAAM (Fig. S1b), UV light treated through a photolithographic mask (Fig. S1c), and developed to obtain a complementary master that contained holes with the same size and shape as the desired adhesive islands (Fig. S1d). The master was immersed in ice water to dissolve the PIPAAM and the photoresist membrane was released from the wafer (Fig. S1e). Polyacrylamide gels (0. 1% bis and 5% acrylamide; 90 µm thick) containing 1∶500 volume of carboxylate-modified fluorescence latex beads (0. 2 µm Fluospheres, Molecular Probes, Eugene, OR) were fabricated on 25 mm coverslips. The Young' s modulus of the gel was estimated to be ∼3 KPa using atomic force microscopy as described previously [37]. The photoresist membrane was placed on the surface of the gel and 1 mM sulfo-SANPAH (sulfosuccinimidyl- 6-4-azido-2-nitrophenylamino-hexanoate; Pierce, Rockford, IL) in 50 mM HEPES was added through the holes in the photoresist membrane. The whole system was then placed under vacuum for 3 minutes to ensure that the sulfo-SANPAH reached the gel surface. The surface of the gel that contacted with the sulfo-SANPAH was photoactivated by UV light exposure (Fig. S1f). After excess sulfo-SANPAH was removed, fibronectin (FN) 100 µg/mL was added to the membrane and the gel was placed under vacuum for another 3 minutes to remove bubbles from the holes (Fig. S1g). The FN was allowed to react with the photoactivated gel for at least 4 hours at 37°C to create FN-coated adhesive islands. Excess FN was washed away with PBS. After removal of the photoresist membrane, the gel was immediately used for cell plating (Fig. S1h). In vitro studies show that the maturation of sarcomere can be determined by measuring the distance between two adjacent α-actinin rich spots that are supposed to be the precursors of the Z-band [13]. A 2–2. 5 µm spacing between the sarcomeric α-actinin rich spots indicates a matured sarcomere [2]. We used a fast Fourier transform (FFT) to calculate the spacing of sarcomeric -actinin rich spots in Fig. 4A, F, K. An intensity profile of the sarcomeric α-actinin stains was chosen along myofibrils spanning the long axis of the cells. The profile was then detrended, weighted with a Hamming window and transformed into the spatial frequency domain by FFT. The spatial frequency at peak power of the first-order harmonic in the spatial frequency domain was identified and converted into the spatial domain to yield the sarcomere length. The results reveal that the sarcomere lengths are 2. 4±0. 1 µm, 2. 2±0. 1 µm, and 2. 4±0. 2 µm for the cell in Fig. 4A, F, K, respectively, indicating that they are mature sarcomeres. Coverslips containing the beating myocytes were removed from the incubator, mounted onto a custom-made microscope stage containing a bath chamber, and continuously perfused with 37°C normal Tyrode' s solution (1. 192 g of HEPES, 0. 901 g of glucose, 0. 265 g of CaCl2,0. 203 g of MgCl2,0. 403 g of KCl, 7. 889 g of NaCl and 0. 040 g of NaH2PO4 per liter of deionized water, reagents from Sigma, St. Louis, MO). Fluorescence images of gels containing fluorescent beads immediately beneath the contracting myocytes were taken at 28. 1 Hz. The duration of image acquisition was long enough to include at least two complete cycles of contraction-relaxation of individual myocytes. Consecutive images were paired and the prior image was used as a reference to measure the change of the position of the fluorescence beads using the algorithm described previously [38]. This yielded the discretized displacement field between two consecutive frames. The calculated displacements were summed up for a whole systolic cycle to determine the overall 2D displacement field. The systolic traction field was calculated from the displacement field by adapting the algorithm previously developed [39], [40]. This algorithm solved the inverse of the Boussinesq solution from the displacement field on the surface of an elastic halfspace to obtain the traction field when the mechanical properties of the gel are known. The Poisson ratio of the gel was assumed to be close to 0. 5 [10]. The interior of the cell was subdivided into 4×4 µm2 squares to approximate the discretized localization of contractile forces. The ability of a particular solved traction field to explain the observed displacements was estimated with statistics. In addition to a zero-order Tikhonov regularization, a constraint that the forces should not become exceedingly large was used to minimize and stabilize the solution [40]. The L-curve criterion, as previously described [40], was used to determine the optimal balance between the data agreement and the regularization. Cardiac myocytes stained for actin (Alexa 488 Phalloidin, Molecular Probes), vinculin (clone hVIN-1, Sigma), and sarcomeric α-actinin (clone EA-53, Sigma) were fixed in 4% PFA with 0. 01% Triton X-100 in PBS buffer at 37°C for 15 minutes and equilibrated to room temperature during incubation. Secondary staining was performed using tetramethylrhodamine- conjugated goat anti-mouse IgG (Alexa Fluor 594, Molecular Probes), and nuclei were visualized by staining with 4′, 6′-diamidino-2- phenylindole hydrochloride (DAPI, Molecular Probes). All fluorescence and traction force microscopy was conducted with a Leica DMI 6000B microscope, using a 63× plan-apochromat objective. For traction force experiments, images were collected with a Cascade 512b enhanced CCD camera, while immunofluorescence images were collected with a CoolSnap HQ CCD camera (both from Roper Scientific, Tucson, AZ) controlled by IPLab Spectrum (BD Biosciences/Scanalytics, Rockville, MD).
How muscle is organized impacts its function. However, understanding how muscle organizes is challenging, as the process occurs over several length scales. We approach this multiscale coupling problem by constraining the overall shapes of muscle cells to indirectly control the organization of their intracellular space. We hypothesized the cellular boundary conditions direct the organization of cytoskeletal scaffolds. We developed a model of how the cytoskeleton of cardiomyocytes organizes with respect to boundary cues. Our computational and experimental results to control myocyte shape indicated that distinct muscle architectures arise from two main organizational mechanisms: the interaction between actin fibers, premyofibrils and focal adhesions, as well as cooperative alignment and parallel bundling of more mature myofibrils. We show that a hierarchy of processes regulate the self-organization of cardiomyocytes. Our results suggest that a symmetry break, due to the boundary conditions imposed on the cell, is responsible for polarization of the contractile cytoskeletal organization.
physiology/cardiovascular physiology and circulation
mathematics
physiology/pattern formation
biophysics/experimental biophysical methods
physiology/muscle and connective tissue
cell biology/cell adhesion
cell biology/extra-cellular matrix
physiology/morphogenesis and cell biology
biophysics/cell signaling and trafficking structures
cell biology/cytoskeleton
Self-Organization of Muscle Cell Structure and Function