Microfluidic perfusion shows intersarcomere dynamics within single skeletal muscle myofibrils

Significance

The sarcomere contains a variety of molecules responsible for force generation in striated muscles. During muscle contraction, many sarcomeres work cooperatively to produce force. The mechanisms behind the interaction among sarcomeres during muscle activation have puzzled scientists for decades. To investigate intersarcomere dynamics, we used microfluidic perfusions to activate a single sarcomere within isolated myofibrils. Using computational sarcomere tracking, we observed that the contraction of one sarcomere affects other sarcomeres in series. Studying the interactions between sarcomeres is crucial, because sarcomere nonuniformity has been long associated with several phenomena in muscle contraction that cannot be easily understood.

Abstract

The sarcomere is the smallest functional unit of myofibrils in striated muscles. Sarcomeres are connected in series through a network of elastic and structural proteins. During myofibril activation, sarcomeres develop forces that are regulated through complex dynamics among their structures. The mechanisms that regulate intersarcomere dynamics are unclear, which limits our understanding of fundamental muscle features. Such dynamics are associated with the loss in forces caused by mechanical instability encountered in muscle diseases and cardiomyopathy and may underlie potential target treatments for such conditions. In this study, we developed a microfluidic perfusion system to control one sarcomere within a myofibril, while measuring the individual behavior of all sarcomeres. We found that the force from one sarcomere leads to adjustments of adjacent sarcomeres in a mechanism that is dependent on the sarcomere length and the myofibril stiffness. We concluded that the cooperative work of the contractile and the elastic elements within a myofibril rules the intersarcomere dynamics, with important consequences for muscle contraction.

The smallest contractile unit of animal striated muscles is the sarcomere, which is formed from a bipolar array of thick and thin filaments composed mostly of myosin and actin proteins, respectively. The cyclic interaction between myosin and actin driven by ATP hydrolysis drives sarcomere shortening and ultimately, produces force (1, 2). In addition, the sarcomeres are structurally interconnected through the Z disks to form myofibrils (1, 3). Therefore, individual sarcomeres are continuously interacting with each other. The sarcomeres contain titin, an elastic protein that spans the half-sarcomere (4, 5). Titin molecules link all of the different areas of a single sarcomere as well as adjoining sarcomeres, creating an elastic network throughout the length of a myofibril (6, 7). Because the sarcomeres are connected in series in a myofibril, changes in the length of one sarcomere on activation may affect the length of adjacent sarcomeres. Such phenomenon is hereupon referred to as intersarcomere dynamics, which may affect force in ways that are difficult to predict based solely on the sliding filament theory.

The classic force–sarcomere length (FSL) relationship is widely used to predict force from the overlap between thick and thin filaments in a sarcomere during Ca²⁺ activation, because different sarcomere lengths (SLs) lead to different degrees of filament overlap. However, the presence of intersarcomere dynamics and nonuniformity of SLs (8) provide additional complexity to the system during myofibril activation. It has been known that the lengths of different sarcomeres change and differ significantly during activation, with consequences for force production. Studies investigating spontaneous oscillatory contractions (9) and the residual force enhancement observed after myofibrils are stretched during activation (10) suggest that changes in individual SLs are the result of links between the contractile apparatus and intermediate filaments composed mostly of titin molecules. Accordingly, sarcomere nonuniformity during activation may lead to the extension of some sarcomeres with the consequent engagement of titin molecules for passive force production, which enables the myofibrils to stabilize in a given activation condition. Because of technical limitations, the mechanisms governing the interaction of sarcomeres in a myofibril and its consequences for force production remain unclear (11).

In this study, we tested the hypotheses that the mechanical work of one sarcomere effectively communicates with other sarcomeres in series through the passive work of titin and that myofibril mechanics are largely governed by intersarcomere dynamics. To test these hypotheses, we used microfluidic perfusions to locally control one sarcomere or a predetermined group of sarcomeres within an isolated myofibril. In this way, we could manipulate the activation and relaxation of a target sarcomere while measuring the behavior of the other sarcomeres in a myofibril. Our data show that intersarcomere dynamics are regulated through a mechanism that combines the work of the contractile apparatus and intermediate filament systems along myofibrils.

Results

Force Produced by Myofibrils After Point Activation of One Sarcomere.

We tested isolated single sarcomeres and groups of sarcomeres within a rabbit myofibril in three different ranges of initial sarcomere length (SL_i), which were chosen so as to induce different initial passive tension: 2.4–2.65 μm (very short; called here “slack”), 2.65–2.9 μm (short), and >2.9 μm (long). A local flow of activation solution, which surrounded ∼1 μm of the preparation, resulted in the contraction of one sarcomere, whereas the other sarcomeres in series were maintained in a relaxed state (Fig. 1A and Movies S1 and S2). The striation pattern of the nonactivated sarcomeres remained clear over the repeated activation/relaxation cycles of the target sarcomeres. The isometric forces produced by isolated single sarcomeres (Fig. 1B) were between ∼10 and 60 nN/μm² within the range previously published in the literature (12).

Fig. 1.

Experimental system used to control myofibril subareas and force measured by precalibrated flexible needles in response to the activation. (A, Upper) Scheme of the experimental system showing the microfluidic perfusion tip (blue), which is built to be smaller than the sarcomere A-band length. Microperfusion was controlled by a pressure system that allowed local flow of solutions (black dashed arrow). The red dashed arrows represent the flow from the regular perfusion system coming from a double-barreled pipette, which allows rapid changes of solutions. (A, Lower) A typical myofibril suspended between two flexible needles. The contrast and brightness of the image were adjusted to improve visibility and clarity. Because the experiments were performed using phase contrast microscopy, some areas around the needles appear brighter than other areas in the myofibrils. (Scale bar: 5 μm.) (B) Force produced by experiments with single sarcomeres (colored circles at 1 in x axis) and experiments in which activation of one sarcomere was performed within myofibrils with different numbers of sarcomeres (colored circles at 5–40 on the x axis) at three different SL_i: slack (n = 34; red), short (n = 73; green) and long (n = 71; blue) lengths. All data were fit using a second-order polynomial. (C) Model simulation of the experiments shown in B, showing the final force produced by activation of a single sarcomere as a function of the number of adjacent inactive sarcomeres. SL_i was set at 2.5, 2.8, and 3.15 μm. (D) Average SL_i and SL_f of the target sarcomere for the preparations tested at slack, short, and long SL_i. (E) Typical traces obtained from a myofibril tested at different SLs. (F) Simulation of the first seconds of force development after activation of a single sarcomere adjacent to 10 inactive sarcomeres. Error bars represent SEM. ***P < 0.001.

At all SL_i tested, the targeted sarcomere could overcome the overall myofibril passive tension. As long as there was overlap between the thick and thin filaments (SL up to ∼3.6 μm), all sarcomeres reached a similar final sarcomere length (SL_f) on activation (Fig. S1B and Movie S3). The force produced by an isolated sarcomere was higher than the force produced by one target sarcomere that was activated within a myofibril (Fig. 1B). Furthermore, when we compared preparations with the same number of sarcomeres in series, the force was higher at longer SL_i, suggesting a SL dependence for the force development (Fig. 1 B and E). For the same SL_i group, force transmitted to the precalibrated needles decreased with increasing numbers of sarcomeres in series. These results were reproduced in our mechanical model, in which the elements that compose a myofibril are modeled as either linear or nonlinear spring elements. We initiated the model calculations using the same average SL_i that we used for the experiments with the myofibrils. When we activated one sarcomere, the force developed by a myofibril decreased nonlinearly as a function of the number of adjacent inactive sarcomeres and was higher at longer SL_i (Fig. 1 C and F). At the end of the contraction, the forces developed in the model were also similar to the experimental forces.

Fig. S1.

SL analysis. (A) Gray intensity profile along the long axis of a myofibril before and after activation of one sarcomere within the myofibril. SLs were measured using the distance between two Z disks. (B) Changes in SL of the three different groups tested. Circles, squares, and triangles represent long, short, and slack groups, respectively. Gray symbols represent the ±1 sarcomeres. Black diamonds represent the activated sarcomeres from the different myofibrils. Change in length was fit using linear regression (r² = 0.7733). (C) Histograms of the changes in length of nonactivated sarcomeres. Comparing with control (SL measured during relaxing conditions of two random frames at least 5 s apart), the nonactivated sarcomeres stretch in response to the activation of one sarcomere within the myofibril.

In our system, the measured force is a function of the displacement and stiffness of the microneedles used during mechanical testing. Thus, assuming that the stiffness of sarcomeres within a single myofibril is similar, our data suggest that the measured force is dependent on the magnitude of shortening of the target sarcomere, which is greater at longer SL_i (Fig. 1D) (P < 0.001). The force sensed by the precalibrated needles results from the active and the passive forces components in the myofibrils. Based on the characteristics of titin, it is likely that, at the beginning of activation, individual sarcomere shortening results in an increased strain over the titin molecules of the nonactivated sarcomeres. Because passive force develops in a nonlinear manner (13), contractions starting at longer SL_i will lead to a greater force development than contractions produced at shorter lengths (for a given change in length). Furthermore, the higher passive tension may cause the activated sarcomere to cease shortening at slightly longer SL_f. Although our data show a lack of statistical difference (Fig. 1C) in the range of SL_f below 2.00 µm, there is a steep region of the ascending limb of the FSL relation, and thus, even very small differences in SL_f (that we may have failed to detect) may strongly affect the force. We observed that ≥40 sarcomeres in a myofibril can adjust their length after a point activation, a result that was confirmed with our mechanical model.

Nonactivated Sarcomeres Adjust Their Lengths After Target Activation of One Sarcomere.

To evaluate (i) how an activated target sarcomere dynamically interacts with adjacent sarcomeres and (ii) how the passive forces in adjacent sarcomeres are adjusted along the myofibril, we measured the SLs (SLs; Z disk to Z disk distances) (Fig. S1A) and tracked the A-band displacements of all sarcomeres in response to the activation of a sarcomere in the center of the myofibril (Fig. 2 A and B). After activation, the SL_fs were not different among nonactivated sarcomeres (Fig. 2C); all of these sarcomeres responded by slightly stretching (Fig. 2D and Fig. S1) (i.e., there is a mechanical linkage among the sarcomeres). To further investigate the processes leading to these SL adjustments, we tracked the A bands of the myofibrils (Fig. 2B and Fig. S2). The absolute displacement of the A bands was larger in nonactivated sarcomeres located closer to the activation point than in sarcomeres located farther from the activation point. The absolute A-band displacement was dependent on SL_i and therefore, the initial passive tension of myofibrils (Fig. 2B). When the A-band displacements were normalized, this dependence of SL_i was not observed (Fig. S3A). These experimental results were well-captured in our mechanical model, which shows a decrease in the displacement of A bands when they are located in sarcomeres away from the activated sarcomere (Fig. S3B).

Fig. 2.

Response of sarcomeres after point activation. (A, Upper) A typical view of a myofibril (100× magnification) before, during, and after point activation. For clarity, the side to the right of the activated sarcomere is defined as the positive side, whereas the side to the left of the activated sarcomere is defined as the negative side. Vertical arrows represent the direction of the solution flow (red arrows indicate the large flow; the black arrow indicates the flow delivered via microperfusion). When the microperfusion flow is applied to the target sarcomere, it contracts and produces force. (A, Lower) A-band tracking used for data analysis. Each white circle represents one A band tracked, and each color overlapping the A bands represents the displacement (x, y coordinates for every frame). (Scale bar: 5 μm.) (B) Absolute displacement of A bands in the myofibrils after activation of one sarcomere. The activated sarcomere is represented at the center [slack (n = 31), short (n = 47), and long (n = 67) lengths] of the figure (dotted line). The A bands of the adjacent sarcomeres are displaced toward the activated sarcomere. Activation of the target sarcomere creates a quasisymmetrical displacement of the nonactivated sarcomeres in the plus and minus sides. (C) SL changes after activation of one sarcomere. Starting from different SL_i (circles), the final SL_f (diamonds) of the nonactivated sarcomeres do not change substantially after activation. (D) Histogram showing the change in SL (ΔSL) of the nonactivated sarcomeres caused by point activation of one sarcomere. The orange bars represent control measurements that we performed by taking two images from the same myofibril in a relaxed state (∼5 s apart). The continuous line shows the Gaussian fit for these control experiments. The dotted line shows the Gaussian fit when three experimental groups are merged into the same analysis. Note that the cure is slightly skewed to the right, suggesting a small stretch of the nonactivated sarcomeres. (E) A-band displacements of myofibrils tested in three conditions: long SL_i (3–3.3 μm; n = 26), long SL_i in rigor solution (n = 26), and very long SL_i (3.35 to ∼3.6 μm; n = 22). Error bars represent SEM. Act., activation.

Fig. S2.

Real time A-band displacement tracking of two different myofibrils. (A) Single activation of one sarcomere within the myofibril (red) and passive response of the other sarcomeres A bands. (B) Eight cycles of activation and relaxation of the same sarcomere within a myofibril (red).

Fig. S3.

Supporting data for Fig. 2. (A) Normalized data showing that the damping behavior does not differ among different groups of myofibrils. B, Upper shows the simulation of the displacement of A bands as a function of sarcomere position after activation of a single sarcomere. Notice that the displacement of the A band of the activated sarcomere is zero. In the model, there are 10 inactive sarcomeres adjacent to the activated sarcomere. B, Lower shows overlay of plus or minus sides in the myofibrils, showing the symmetry of displacement on both sides (displacement was significantly different among all groups; P < 0.0001). (C) Simulation results for the final SL achieved by a single activated sarcomere within a myofibril as a function of detector stiffness. There are 10 inactive sarcomeres adjacent to the activated sarcomere. (D) Simulation results for the final force measured for a myofibril, in which a single sarcomere is activated and all other sarcomeres are in rigor. There are 10 inactive sarcomeres adjacent to the activated sarcomere. Act., activation.

It has been shown that the elastic network of intermediate filaments can link all force-bearing structures of the sarcomere (14). This mechanism is mainly governed by titin molecules, which are the proteins responsible for passive force development in myofibrils. During our experiments, the local increase in Ca²⁺ leads the target sarcomere to contract and stretch the adjacent sarcomeres, likely enhancing the strain over titin filaments. This strain is passively transmitted across the myofibril via the intermediate filament system, affecting several sarcomeres in series.

To further test the myofibril adjustment to local activation, we repeated the previous experiments using inflexible needles, so that the total length of the myofibrils would not change significantly as a result of activation, removing partially the effects of end compliance. Myofibrils were tested at long SL_i (2.9–3.3 μm), very long SL_i (3.4–3.6 μm), and long SL_i in rigor solution (i.e., in the absence of ATP and Ca²⁺), a condition that substantially increases the stiffness of the preparation, because it induces a large number of cross-bridges. For all of these conditions, myofibrils remained able to contract in response to the point activation, suggesting that sarcomeres in series can adapt their lengths in response to a local increase in Ca²⁺ concentration without significant changes in total myofibril length (Fig. 2E). There was some shortening observed at each end of the myofibrils as indicated by A-band displacements. However, our mathematical model that incorporates the end compliances was able to predict sarcomere contraction and shortening even with probes of very high stiffness and myofibrils in rigor state (Fig. S3 C and D), strengthening the interpretation that intersarcomere dynamics are not necessarily dependent on changes in total myofibril length.

Half-Sarcomeres Are Displaced During Activation.

During the experiments described above, we noticed a small displacement of the target A band in the activated sarcomere, which may have been caused by half-sarcomere nonuniformity during activation. Moreover, previous studies have suggested that the stabilization of the A band in the center of sarcomeres during muscle contraction is regulated by titin (15, 16). Consequently, we evaluated A-band displacements in sarcomeres by changing the position of the point activation to measure how it affected intersarcomere dynamics. Point activation with the microperfusion system placed at the Z disk led to the activation of two adjoining half-sarcomeres, because two A bands were collapsed together at the end of the activation (Movie S4).

Fig. 3B shows that activation of two half-sarcomeres led to a relatively large displacement from the zero position of at least one of the A bands compared with one target sarcomere activation. However, in this situation, the adjoining sarcomeres displaced less than in conditions where one entire sarcomere was activated. This change in position of the thick filament has been seen before at the beginning of myofibril contraction and is attributed to half-sarcomere mechanics (17), leading us to investigate how the myofibril responds to point activation of just one half-sarcomere. We hypothesized that the asymmetrical behavior results from differential half-sarcomere mechanics. We tested this hypothesis by activating half-sarcomeres using micropipettes with diameters of 0.5 μm to reach a small flow area (Movie S5). A-band tracking showed that one side of the myofibril was displaced more than the other side (Fig. 3C). Surprisingly, the side that was displaced more was not always the one adjacent to the activated half-sarcomere. Instead, two behaviors were observed: either (i) the A band did not move (and the Z disk was pulled toward the A band) or (ii) the A band was displaced toward the Z disk (Fig. 3D), explaining the asymmetry observed when two half-sarcomeres are activated together. For simplicity, we will consider one sarcomere that has one half-sarcomere activated. If the A band is displaced from its zero position toward the Z disk of this half-sarcomere, it drags the other half-sarcomere (Fig. 3D, blue). If the A band does not change its position, it pulls the Z disk and the half-sarcomeres (Fig. 3D, orange). In practice, both situations happen in our experiments. Note that these movements do not result in differential SL_f between the two sides of the myofibril.

Fig. 3.

Half-sarcomere activation. A, Left shows a sarcomere in three different conditions: (Top) before point activation, (Middle) half-sarcomere activated at the positive side, and (Bottom) half-sarcomere activated at the negative side. A, Top Right shows two half-sarcomeres activated together. A, Middle Right shows the start of the activation; note that one half-sarcomere was contracted. A, Bottom Right shows that, after the second half-sarcomere was contracted, both half-sarcomeres come close together. (Scale bar: 5 μm.) (B) A-band displacement of all sarcomeres in a myofibril in response to activation of two half-sarcomeres by targeting the microperfusion flow to a Z disk (n = 30). (C) A-band displacement in response to activation of one half-sarcomere (n = 37). (D) Response of adjacent sarcomeres to the activation of one half-sarcomere (Z-disk displacement, n = 20; A-band displacement, n = 17). The data were adjusted based on the A-band displacement (displacements of the target A band were significantly different; P < 0.0001). The diagrams display the behavior observed by the A bands. Error bars represent SEM. *P < 0.05; **P < 0.01; ***P < 0.001. Act., activation.

Sarcomeres and Myofibrils May Produce Different Forces.

Sarcomeres comprising a myofibril have a similar structure and cross-section. Thus, if all sarcomeres were able to reach the same SL_f, they should hypothetically produce similar active forces. To test this hypothesis, we point-activated all sarcomeres within a myofibril (one at a time) and used the average displacement of the ±1 and ±2 A bands in relation to the target sarcomere to estimate the individual sarcomere forces. Although an indirect measurement of the force in this situation, this procedure was based on our observation that the displacement of the A bands surrounding an activated sarcomere is very similar to the displacement of the needles when we activated one sarcomere (mechanically isolated from the myofibril). In general, we found forces varying from 8 to 45 nN/μm² when comparing all sarcomeres tested in different myofibrils (merged data in Fig. 4A), similar to the forces produced by isolated sarcomeres (dotted line in Fig. 1A). We observed a small range of forces among the different sarcomeres within a single myofibril caused by small variations in SL_i (Fig. 4A). When myofibrils were analyzed individually, it was possible to observe differences in forces produced by sarcomeres in some myofibrils. These differences are likely related to different changes in length caused by nonuniform SL_i or SL_f.

Fig. 4.

Force of several sarcomeres within a myofibril and full activation of myofibrils with different numbers of sarcomeres in series. The average displacement of ±1 and ±2 sarcomeres was multiplied by the needle’s stiffness to estimate the force of the majority of sarcomeres in a myofibril. (A) Blue box and whiskers plots represent the 25th percentile, the median (line), and the 75th percentile of different myofibrils, and the error bars show the minimum and maximum values. The dots represent the force produced by sarcomeres within one myofibril. The dotted line shows the average force considering all sarcomeres tested. The plot in Right merges the force of all preparations. (B) Isometric force of myofibrils ranging from 4 to 48 sarcomeres in series compared with forces produced by one sarcomere. (C) Force normalized by the number of sarcomeres in series in a myofibril. (D) Relationship between the shortening magnitude during myofibril contraction and the number of sarcomeres in series in a myofibril. (E) FSL relationship produced during full activation of isolated myofibrils (n = 12). The force was normalized by the highest value for a given myofibril. Data were fit using a third-order polynomial regression (r² = 0.83). The blue area represents the plateau of the FSL relationship. The green and yellow areas represent the ascending and descending limbs of the FSL relationship, respectively. Note that the green area covers lengths in which filament overlap is between 70 and 90% of the optimum overlap. The dotted line was created based on theoretical predictions (20) and previous experimental data (18). (F) Average SL_f of all myofibrils plotted as a function of the number of sarcomeres and the amount (percentage) of optimum overlap between myosin and actin filaments according to the FSL relationship (n = 95). (G) Length of all sarcomeres (excluding the ones at the edges) of 10 randomly chosen myofibrils that contracted to an SL_f within the plateau regions (blue) of the FSL relationship. Green and yellow areas represent the ascending and descending limbs of the FSL, respectively. Note that the green area covers lengths in which filament overlap is 70–90% of the optimum. Gray box and whiskers plots represent a different myofibril with the 25th percentile, the median (line), and the 75th percentile; error bars show the minimum and maximum values.

According to our data, sarcomeres reach similar SL_f when point-activated, but this activation affects other sarcomeres in series. Therefore, during full myofibril activation, the dynamic work of sarcomeres in series and the differences in SL_i among sarcomeres may influence how a myofibril develops force to reach a steady state. In such a state, myofibril internal motion is close to equilibrium. If, during myofibril activation, every sarcomere shortened to the same SL_f, the force would be a function of the number of sarcomeres in series and the SL_i of each sarcomere. We, therefore, tested the hypothesis that a greater number of sarcomeres in series allows a greater shortening magnitude and hence, higher forces. We performed full activation of myofibrils with different numbers of sarcomeres in series at an SL_i of ∼2.8 μm. We first activated myofibrils with ∼25 sarcomeres, and after the first activation, we reduced the number of sarcomeres in series in the preparation by one-half by positioning the holding needle close to the center of the myofibril. We found that myofibrils with a greater number of sarcomeres produced higher forces, regardless of the average SL_f (Fig. S4 A and D). These results may be attributed to cumulative shortening when more sarcomeres are activated (i.e., a greater shortening of the myofibril may be possible when more sarcomeres are activated) (Fig. S4 B and C).

Fig. S4.

Full myofibril activation before (long; n = 6) and after (short; n = 6) the removal of one-half of the initial number of sarcomeres composing the myofibril (n = 6). (A) Mean maximal specific force. (B) Mean shortening magnitude (μm). (C) Mean initial myofibril length (μm). (D) Mean sarcomere length. Error bars represent SEM. *P < 0.05; **P < 0.01; ***P < 0.001.

To further test our hypothesis that more sarcomeres in series allow for a greater shortening and to remove the potential confounding effect of myofibril damage during manipulation, we measured the forces produced by the first contraction of 95 myofibrils and compared them with single sarcomeres. We confirmed that myofibrils with more sarcomeres in series shortened more than myofibrils with fewer sarcomeres and produced higher forces (Fig. 4 B and D). However, the increase in force in longer myofibrils was not linearly related to the number of sarcomeres in series (Fig. 4B). When the force was normalized by the number of sarcomeres in the myofibrils, they produced less force per sarcomere than single sarcomeres (Fig. 4C).

To evaluate whether the final SL reached during the contractions was in the zone where maximal force is produced, we performed separate experiments to derive an FSL relation for the myofibrils used in this study (Movie S6). We observed an FSL relation similar to that reported previously in other preparations (18), with a plateau between SL_fs of ∼2.1 and 2.7 μm (Fig. 4E). Based on these measurements, we evaluated if the SL_f of the myofibrils reached optimal filament overlap. In fact, the majority of the myofibrils contracted to the plateau of the FSL relationship or in an area within 70% of the optimum filament overlap (Fig. 4E). There were some sarcomeres in these myofibrils that reached a length longer than those at the plateau of the FSL, likely because of an increased SL nonuniformity (Fig. 4F). Based on these findings, we decided to test the hypothesis that a larger degree of nonuniformity in SLs along the descending limb of the FSL leads to a decrease in the total force produced by the myofibrils.

Induced Nonuniformity/Deactivation Reduces Total Myofibril Force.

Over the years, SL nonuniformity has been observed to happen naturally during muscle contraction. To test how nonuniformity of SLs affects the final force reached by the myofibrils, we used the microperfusion system to induce nonuniformity in activated myofibrils. We performed five different sets of experiments. First, we measured the myofibril force when three to five sarcomeres were activated before full myofibril activation (preactivation group) and compared the results with those of regular full activation (control) (Movie S7). Two segments of the same myofibril were tested for preactivation. The protocol consisted of three cycles of full myofibril activation followed by two cycles of preactivation and a control contraction. When preactivated, the myofibril generated a small increase in force before a larger increase caused by full activation (dashed square in Fig. 5A). Interestingly, we did not observe significant differences in the final forces measured, showing that initial nonuniformities did not affect force development (Fig. 5A). Second, in another series of experiments, nonuniformity was induced either after contraction or before activation by using a low-Ca²⁺ solution to relax one sarcomere in a fully activated myofibril (Movie S8). We noticed a sudden reduction in the total myofibril force (Fig. 5B) that was reversed after removal of the microperfusion pipette. We then repeated this experiment but used a high-Ca²⁺ solution with 40 mM 2,3-butanedione monoxime (BDM), which led to a similar reduction in force (Fig. 5C). A reduction in the total myofibril force was also observed by delaying the activation of a small portion of the myofibril (approximately one sarcomere) during a contraction (Fig. 5D). For all of these situations, the target sarcomere was able to contract, although both sides of the myofibril were inducing sarcomere stretching. This finding suggests that one sarcomere is able to pull several activated sarcomeres and produce a force that is close to its maximum level.

Fig. 5.

Controlling nonuniformity. (A) Preactivation of a short area of the myofibril does not affect the total force. A subarea of the myofibril was activated before full activation using microperfusion. In a typical experiment, the first contraction induced full myofibril contraction, and the second contraction was induced after preactivation. The increase in force caused by preactivation is shown in the dashed square. Note that the total forces were similar in both contractions. (B) One sarcomere is deactivated during full myofibril contraction using relaxing solution (pCa²⁺ 9.0) within the microperfusion system (n = 21). (C) The same protocol used in A, but this time, the solution (pCa²⁺ 4.5) used to deactivate the sarcomere contained 40 mM BDM (n = 8). (D) A small area of a myofibril was kept relaxed, whereas the rest of the myofibril was activated and contracted (n = 12). (E, Left) Myofibril force before and after one A-band extraction using high-strength ionic solution in the microperfusion system (n = 15). E, Right show typical experimental traces. (F) Extraction of one A band had a smaller effect or a lack of effect in longer myofibrils. We performed additional A-band extractions in three myofibrils (with 31, 33, and 36 sarcomeres), which reduced the force significantly. The straight line represents the normalized isometric force before A-band extraction. Error bars represent SEM. **P < 0.01; ***P < 0.001.

Finally, we used a high-strength ionic solution that depletes the preparation from thick myosin filaments (19) (Movie S9). Extraction of the A band results in a sarcomere with only the intermediate filaments that is able to communicate with other sarcomeres through passive forces. However, A-band extraction may also lead to more compliant titin because of the loss of the interaction between titin and myosin filaments. We compared forces developed by the myofibrils before and after the extraction of the A band of one sarcomere. We found a significant reduction in the isometric force compared with experiments in which the A band was intact (Fig. 5E), supporting the idea that the number of sarcomeres is an important factor for total force development. The extraction of one A band had a smaller effect on the total force in myofibrils with a large number of sarcomeres than in myofibrils with a small number of sarcomeres (Fig. 5F). In longer myofibrils, force dropped after the additional extraction of A bands. We performed a few experiments in which we applied a small stretch after extraction of the A band from myofibrils to evaluate if force could be recovered back to the original values. However, the force remained lower than it was before extraction of the A band (Fig. S5 and Movie S10).

Fig. S5.

Sarcomere extraction followed by stretch. Raw data of two different myofibrils that had a control contraction followed by sarcomere extraction. (A) Myofibril was stretched by 1 μm per extracted sarcomere (Movie S10). (B) Myofibril was stretched by 2 μm per extracted sarcomere. Notice that the force cannot be recovered by stretching the myofibril.

Overall, our data suggest that, during muscle contraction and force development, events that create nonuniform distribution of SL along myofibrils have an impact on the final force that they produce.

Discussion

In this study, we assessed intersarcomere dynamics in isolated myofibrils using microfluidic perfusion, a technique that allows the point activation of one (half-) sarcomere within a myofibril while measuring the response of all other sarcomeres. We triggered cross-bridge formation and contraction of target sarcomeres by locally increasing the Ca²⁺ concentration. We showed that the shortening of an activated sarcomere leads to an internal regulation in the remaining sarcomeres in the myofibril through passive forces. This result shows that intersarcomere dynamics arise from the cooperative work of the contractile and elastic systems, enabling the action of one sarcomere to be transmitted to the others.

We found that single sarcomeres are able to contract as long as there is myofilament overlap (20), reaching similar SL_f independent of the SL_i (with small differences when SL_i is ∼3.6 μm). This behavior is not observed during full myofibril activation (Figs. 1D and 4G), where the SL_f is highly nonuniform during activation (17). Although passive and active forces have been investigated separately (21, 22), we showed that the passive force component is responsible for the interaction of sarcomeres in series, facilitating the transmission of the force of one sarcomere to others.

Recent studies have shown that titin controls important aspects of thick filament structure, playing an important role in muscle activation (23, 24). In the future, it will be important to consider how the activation of one sarcomere may be sensed by a thick filament from the neighboring sarcomeres. Moreover, it has been suggested that titin can assist muscle contraction at physiological SLs using the stored elastic energy from unfolded Ig domains (25). The importance of the elastic system was shown in our experiments, in which a few sarcomeres were activated before full myofibril activation (Fig. 5A). There was not a difference in force compared with myofibrils that were not preactivated, showing that the passive force components hold the nonactivated area of the myofibril at the optimum length for contraction.

Our microfluidic perfusion system allowed the control of a long known phenomenon of muscle contraction, the nonuniform lengths of sarcomeres during activation (26, 27). From the proposal of the sliding filament theory (1, 2), nonuniform behavior of sarcomeres and its effects in force production during contraction have puzzled scientists. We found that, in short myofibrils, enabling the relaxation of one sarcomere either during or before contraction leads to a reduction in the total force (Fig. 5 B–D). This result can be explained by the reduction in the total shortening caused by the relaxed sarcomeres. The same reduction was observed when we extracted the A bands from myofibrils (Fig. 5E). However, this reduction in force was attenuated in myofibrils with more sarcomeres in series (Fig. 5F). It is possible that the lack of one sarcomere was compensated for by an increase in shortening of other sarcomeres. Such a mechanism may have important implications, because the structure of the muscle cell may be designed to balance the presence of weaker or damaged sarcomeres along the myofiber.

This study uses a microfluidic perfusion to show the importance of intersarcomere dynamics and the cooperative work of the contractile and elastic proteins in the myofibril, opening possibilities for new venues of investigation in muscle biophysics.

Methods

Experimental Solutions and Experimental System.

Myofibril preparation and imaging (SI Text) were done as described before (28). The protocol was approved by the McGill University Animal Care Committee and complied with the guidelines of the Canadian Council on Animal Care. Rigor solution was 50 mM Tris, 100 mM KCl, 4 mM MgCl₂, and 10 mM EGTA, pH 7.0. Relaxing solution was 70 mM KCl, 20 mM imidazole, 5 mM MgCl₂, 5 mM ATP, 14.5 mM creatine phosphate, 7 mM EGTA, and pCa²⁺ (equal to –log[Ca²⁺]) 9.0, pH 7.0. Activation solution was 50 mM KCl, 20 mM imidazole, 5 mM MgCl₂, 5 mM ATP, 14.5 mM creatine phosphate, 7.2 mM EGTA, and pCa²⁺ 4.5, pH 7.0. We used two precalibrated needles to pierce the myofibrils parallel to the Z disks (28). The stiffness of all needles (43.40 ± 0.76 nN/μm) was measured using the same atomic force cantilever. All procedures were imaged using a Hamamatsu Orca-ER digital camera. Movies were recorded at 43.3 frames per 1 s. Myofibrils were pierced and lifted from the coverslip, and the SL_i was adjusted. Sarcomeres within myofibrils were point-perfused by a microperfusion system, in which glass micropipettes filled with the desired solution were controlled by a pressure system and micromanipulators (NT88-V3; Nikon). To avoid diffusion of the microperfusion solution to undesired areas, myofibrils were constantly perfused by a larger perfusion flow that controlled the remaining sarcomeres in the preparation. Micropipettes and needles were pulled using a capillary puller (Kopf Model 720; David Kopf Instruments). Micropipette tip diameter was adjusted to 1 μm or less (<0.5 μm for half-sarcomeres) to keep it smaller than the sarcomere A bands. All experimental procedures were recorded and analyzed using the TrackMate plugin for ImageJ software (NIH). Absolute sarcomere displacement was defined as the difference between the zero position (relaxed state) and the position of the tracked A band during the experiment. The experiments comparing the active force development of myofibrils before and after reduction in the number of sarcomeres in series were performed using atomic force microscopy as previously described (28). Because the forces produced by myofibrils are proportional to their cross-sectional areas and because we wanted to compare different conditions irrespective of this variable, all measured forces were normalized and reported in units of stress, assuming a circular geometry for the myofibril (nanonewtons per micrometer²).

Statistical Analyses.

We used a two-way ANOVA for repeated measures to compare displacement of A bands. For nonuniformity experiments, we used one-way ANOVA for repeated measures. We used a Student–Newman–Keuls test when significant changes were observed. A level of significance of P ≤ 0.05 was set for all analyses. Values are presented as means ± SEM.

Mechanical Model.

We developed a mechanical model of a half-myofibril to better interpret our experimental data (SI Text, Figs. S6–S8, Table S1, and Movie S11) using the framework of Campbell (29).

Fig. S6.

Mechanical model for a single activated half-sarcomere in series with N inactive sarcomeres and a probe. The nonlinear passive element is represented by a black spring, the probe is represented by an orange spring, and an elastic cross-bridge linkage is represented by a red spring.

Fig. S8.

Displacement of the boundaries of the half-sarcomeres that result when the system returns to mechanical equilibrium.

Table S1.

Constants associated with the chemomechanical cycle of a cross-bridge and the mechanical properties of the elastic elements within each half-sarcomere and the probe

Parameter	Value
$k_{cb}$	$0.0016\hspace{0.17em}\text{N/m}$
$k_{probe}$	0.043 N/m
A	10−12 m2
$\sigma$	7,000 N/m2
$x_{offset}$	1,130 nm
$L$	125 nm
$k_1$	20 s−1
$k_{-1}$	0.2 s−1
$k_2^o$	50 s−1
${\delta }_2$	0.1 nm
$k_{-2}^o$	0.5 s−1
${\delta }_{-2}$	0.5 nm
$k_3^o$	37.5 s−1
${\delta }_3$	0.5 nm
$k_{-3}^o$	0.375 s−1
${\delta }_{-3}$	−0.1 nm

SI Text

Modeling Activation of a Single Sarcomere Within the Myofibril.

In our half-myofibril, there are N inactive half-sarcomeres (or N/2 sarcomeres) adjacent to our activated half-sarcomere. For each time interval ($\mathrm{\Delta }t=5\hspace{0.17em}\text{ms}$), we go through the following process.

(i) To determine the number of motors that can interact with the thin filament in the activated half-sarcomere, we calculate the overlap of the thick and thin filaments:

$$x_{overlap}=l_{thin}+l_{thick}-x_{hs,active},$$ [S1]

where all lengths are defined in Fig. S6. The number of myosin heads per unit cross-sectional area in a single half-sarcomere framework is $N_o=1.15\times {10}^{17}{\hspace{0.17em}\text{m}}^{-2}$, and the cross-sectional area of the myofibril is $A={10}^{-12}{\hspace{0.17em}\text{m}}^2$. Thus, the number of motors that can engage with the thin filament is calculated as

$$\begin{array}{c}{N}_{motors}=A{N}_o\left(\frac{x_{overlap}}{x_{max,overlap}}\right)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{x}_{overlap}<x_{max,overlap}\\ \begin{array}{c}{N}_{motors}=A{N}_o\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}{x}_{overlap}>x_{max,overlap},\end{array}\end{array}$$ [S2]

where

$$x_{max,overlap}=l_{thick}-l_{bare}=735\hspace{0.17em}\text{nm}.$$ [S3]

(ii) We next model the cross-bridges as they cycle through the chemomechanical cycle described in Fig. S7 and then calculate the resultant forces that change the length of the half-sarcomere. However, because $N_{motors}$ is such a large number, modeling every motor is time-intensive. To speed up the simulation, we thus model the cycle for $N_{motors}/100$ cross-bridges. After calculating the resultant net force, we multiply this value by 100 to determine the total force exerted on the half-sarcomere.

Fig. S7.

Chemomechanical cycle for an individual cross-bridge in the activated sarcomere.

We go through each of the $N_{motors}/100$ cross-bridges one at a time using a random number generator to determine whether they will transition to a new state. For a motor starting at state i (i = 1, 2, or 3), the random number generator selects a number $n_{rand}$ between 0 and 1, and a decision is made based on the following rules:

$$\begin{array}{l}\text{if}\hspace{0.17em}{\mathit{n}}_{\mathit{rand}}<{\mathit{p}}_{forward},\text{the}\hspace{0.17em}\text{motor}\hspace{0.17em}\text{transitions}\hspace{0.17em}\text{to}\hspace{0.17em}\text{the}\hspace{0.17em}\text{state}\hspace{0.17em}i+1\\ \text{if}\hspace{0.17em}{\mathit{p}}_{\mathit{forward}}<n_{rand}<p_{forward}+p_{backward},\text{the}\hspace{0.17em}\text{motor}\hspace{0.17em}\text{transitions}\hspace{0.17em}\text{to}\hspace{0.17em}\text{the}\hspace{0.17em}\text{state}\hspace{0.17em}i-1\\ \text{if}\hspace{0.17em}{\mathit{n}}_{\mathit{rand}}>p_{forward}+p_{backward},\text{the}\hspace{0.17em}\text{motor}\hspace{0.17em}\text{remains}\hspace{0.17em}\text{in}\hspace{0.17em}\text{state}\hspace{0.17em}i,\end{array}$$ [S4]

where

$$p_{forward}=k_{i}dt$$

$$p_{backward}=k_{-i}dt,$$ [S5]

where all rate constants are given by Eqs. S18–S20. For each motor, we also define a term ${\epsilon }_n$ describing the extension of the nth elastic cross-bridge linkage away from its equilibrium position. For a motor in state 1, $\epsilon$ is zero. For a motor that has just entered state 2 or 3 from state 1, $\epsilon$ is also zero. For a motor that transitions from state 2 to 3, $\epsilon$ changes from its current value ${\epsilon }_n$ to ${\epsilon }_n-10\hspace{0.17em}\text{nm}$ (indicating a power stroke of magnitude $10\hspace{0.17em}\text{nm}$). For a motor that transitions from state 3 to 2, $\epsilon$ changes from its current value to ${\epsilon }_n+10\hspace{0.17em}\text{nm}$ (indicating a reversal of the power stroke).

(iii) We next allow our system to return to mechanical equilibrium by moving the boundaries of each half-sarcomere (defined in Fig. S8).

We solve for the value of $\mathrm{\Delta }{y}_{active}$ that brings the system to equilibrium by finding the value for which all forces cancel out at the interface between the activated and the Nth inactive half-sarcomere. In other words, we solve for the value of $\mathrm{\Delta }{y}_{active}$ that satisfies the equilibrium condition

$$F_{active}+F_{inactive}+100{\displaystyle \sum _{n=1}^{\frac{N_{motor}}{100}}}{F}_{cross-bridge}=0,$$ [S6]

where the individual terms in this relation are given by

$$F_{cross-bridge}={\mathrm{\Gamma }}_n{k}_{cb}\left({\epsilon }_n+\mathrm{\Delta }{y}_{active}\right),$$ [S7]

$$\begin{array}{l}{\mathrm{\Gamma }}_n=1\hspace{0.17em}\text{if}\hspace{0.17em}\text{the}\hspace{0.17em}n\text{th}\hspace{0.17em}\text{motor}\hspace{0.17em}\text{is}\hspace{0.17em}\text{in}\hspace{0.17em}\text{state}\hspace{0.17em}2\hspace{0.17em}\text{or}\hspace{0.17em}3\\ {\mathrm{\Gamma }}_n=0\hspace{0.17em}\text{if}\hspace{0.17em}\text{the}\hspace{0.17em}n\text{th}\hspace{0.17em}\text{motor}\hspace{0.17em}\text{is}\hspace{0.17em}\text{in}\hspace{0.17em}\text{state}\hspace{0.17em}1\end{array}$$ [S8]

$$F_{active}=-\sigma A\hspace{0.17em}\text{exp}\left(\frac{\left(x_{hs,active}-\mathrm{\Delta }{y}_{active}\right)-x_{offset}}{L}\right)$$ [S9]

$$F_{inactive}=\sigma A\hspace{0.17em}\text{exp}\left(\frac{\left(x_{hs,inactive}+\mathrm{\Delta }{y}_{inactive}\right)-x_{offset}}{L}\right),$$ [S10]

where we have used the mechanical model described by Eq. S17, and $x_{hs,active}$ and $x_{hs,inactive}$ are the lengths of the active and inactive half-sarcomeres, respectively, and $\mathrm{\Delta }{y}_{inactive}$ is the change in the length of an inactive half-sarcomere.

Combining Eqs. S6–S10 leaves us with two unknowns: $\mathrm{\Delta }{y}_{active}$ and $\mathrm{\Delta }{y}_{inactive}$. However, we can relate these two terms using the following argument. Because the force along the length of the myofibril is the same at every point when the system returns to equilibrium, the interface between the probe and the first inactivate half-sarcomere (Fig. S8) moves by a distance

$$\mathrm{\Delta }{y}_1=\frac{F_{active}}{k_{probe}}.$$ [S11]

As a result of this change in the length of the probe, the length of the entire myofibril changes by $\mathrm{\Delta }{y}_1$. At the same time, the length of the region of the myofibril occupied by the N inactive half-sarcomeres has also changed because of the change in length of the active sarcomere ($\mathrm{\Delta }{y}_{active}$). Because all inactive half-sarcomeres are at the same length at equilibrium, the change in lengths of the active and inactive sarcomeres are linked through the relation

$$\mathrm{\Delta }{y}_{inactive}=\frac{\mathrm{\Delta }{y}_{active}-\mathrm{\Delta }{y}_1}{N}.$$ [S12]

Combining Eqs. S11 and S12 yields the relation

$$\mathrm{\Delta }{y}_{inactive}=\frac{\mathrm{\Delta }{y}_{active}-\frac{F_{active}}{k_{probe}}}{N},$$ [S13]

where $F_{active}$ is given by Eq. S9.

We can thus plug Eq. S13 into Eq. S10 and Eqs. S7–S10 into Eq. S6, yielding an equilibrium condition relation that depends only on the single unknown, $\mathrm{\Delta }{y}_{active}$. We then use Matlab to find the value of $\mathrm{\Delta }{y}_{active}$ that satisfies this relation.

We use this value of $\mathrm{\Delta }{y}_{active}$ to adjust the appropriate values in our model. In other words, we make the following changes to our system:

$$x_{hs,active}\hspace{0.17em}\to x_{hs,active}-\mathrm{\Delta }{y}_{active}$$ [S14]

$$x_{hs,inactive}\to x_{hs,inactive}+\mathrm{\Delta }{y}_{inactive}$$ [S15]

$${\epsilon }_i\to {\epsilon }_i+\mathrm{\Delta }{y}_{active}.$$ [S16]

We repeat steps i–iii for each successive time interval. Because our simulation does not incorporate a mechanism that explains why the contraction of the active half-sarcomere stops at a half-sarcomere length of ∼0.75 μm (likely because the actin filament enters the bare zone and crosses to the other half-sarcomere), we simply stop the simulation when this value of $x_{hs,active}$ is reached.

Mechanical Model of Myofibril.

We modeled a half-myofibril that consists of numerous adjacent half-sarcomeres linked in series (Fig. S6). Every half-sarcomere contains a nonlinear passive component, representing structural molecules with the sarcomere, such as titin. A single half-sarcomere at the end of the half-myofibril is activated and thus, also contains cross-bridge linkages, each of which is in parallel with the other cross-bridges and the passive element. At the other end of the myofibril is an additional elastic element representing the probe.

The force generated by stretching the passive element within each half-sarcomere is given by the relation

$$F\left(x_{hs}\right)=\sigma A\hspace{0.17em}\text{exp}\left(\frac{x_{hs}-x_{offset}}{L}\right),$$ [S17]

where $x_{hs}$ is the length of the half-sarcomere, $A$ is the cross-sectional area of the myofibril, $\sigma$ is the stress at $x_{hs}=x_{offset}$, and L defines the curvature of the passive length–tension relationship.

Model of Cross-Bridges in Activated Sarcomeres.

Individual cross-bridges within the activated sarcomere pass through a kinetic cycle shown in Fig. S7. The motor can be in one of three states: (i) detached from actin in a prestroke state, (ii) attached to actin in a prestroke state, and (iii) attached to actin in a poststroke state. The power stroke occurs as the motors transitions from state 2 to state 3.

Both $k_1$ and $k_{-1}$ are force-independent rates, and all other rates exhibit force dependence. Specifically, rates $k_2$ and $k_{-3}$ are described by the relation

$$k_i=k_i^o\text{exp}\left(\frac{F{\delta }_i}{k_{B}T}\right),$$ [S18]

where $F$ is the magnitude of the force on the cross-bridge. A positive force is defined as a force that is directed in the same direction as the power stroke (i.e., a force that assists the power stroke); ${\delta }_2$ and ${\delta }_{-3}$ are positive and negative, respectively, to indicate that a positive force accelerates $k_2$ and slows $k_{-3}$.

The rates of detachment from actin are given by

$$k_{-2}=k_{-2}^o\text{exp}\left(\frac{\left|F\right|{\delta }_i}{k_{B}T}\right)$$ [S19]

and

$$k_3=k_3^o\text{exp}\left(\frac{F{\delta }_i}{k_{B}T}\right).$$ [S20]

The absolute value in Eq. S19 indicates that the force dependence of this rate is independent of the direction of the applied force. We originally modeled both rates this way but were unable to get the model to emulate the data unless $k_3$ exhibited the asymmetric force dependence described by Eq. S20.

The values for all constants used in the model are found in Table S1.

Myofibril Preparations.

Small muscle bundles from rabbit psoas were dissected, rinsed in rigor solution, and tied to wooden sticks. The samples were stored in rigor solution:glycerol (50:50) solution for 15 h at −20 °C and then transferred to fresh rigor solution:glycerol (50:50) solution containing a mixture of protease inhibitors (Roche Diagnostics) for at least 7 d before experiments. On the day of the experiment, small muscle pieces were cut and defrosted in rigor solution at 4 °C for 1 h. These pieces were then homogenized in rigor solution. The homogenate was transferred to an experimental temperature-controlled bath (10 °C), where rigor solution was slowly replaced by relaxing solution. Myofibrils were imaged with a phase contrast inverted microscope (Eclipse TE2000-U). Under high magnification (Plan Fluor 100 oil objective plus 1.5× built-in microscope magnification used for shorter myofibrils), the contrast between the dark A bands and the light I bands provided a dark–light intensity pattern representing the striation pattern produced by the sarcomeres, which enabled the measurement of SL during the experiments. Myofibrils were chosen for mechanical measurement based on their striation patterns. Myofibril contraction was induced using an activation solution.