Mechanisms of Sarcomere Assembly in Muscle Cells Inferred from Sequential Ordering of Myofibril Components

Voluntary movement in animals is driven by the contraction of myofibrils in striated muscle cells, which are linear chains of regular cytoskeletal units termed sarcomeres. While the ordered structure of mature sarcomeres, key to muscle contraction, is well established, the physical mechanism governing sarcomere assembly is still under debate. Here we put forward a theory of sarcomere self-assembly based on data. We measured the sequential ordering of sarcomere components in developing Drosophila flight muscles, using a novel tracking-free algorithm. We find that myosin molecular motors, $\alpha$-actinin cross-linkers, and the titin homologue Sallimus form periodic patterns before actin filaments become polarity sorted. Based on these, we propose that myosin, Sallimus, and sarcomere Z-disk proteins including $\alpha$-actinin dynamically bind and unbind to an unordered bundle of actin to establish an initial periodic pattern. Periodicity of actin filaments is established only later. Our model proposes that nonlocal interactions between spatially extended myosin and titin/Sallimus containing complexes, and possibly tension-dependent feedback mediated by an $\alpha$-actinin catch bond, drive this ordering process. We probe this hypothesis using mathematical models and derive predictive conditions for sarcomere pattern formation to guide future experiments.

Figure 1

(a) Myofibrillogenesis represents a pattern formation problem: how do initially stress-fiber-like bundles of parallel actin filaments (red) with homogeneous distribution of myosin (blue) and Z-disk proteins (green) rearrange into periodic sarcomeric patterns? In mature myofibrils, actin filaments form polarity-sorted domains, with their plus ends cross-linked at the Z-disk rich in $\alpha$-actinin, which marks the boundary of the sarcomere. Bipolar myosin filaments in the middle of each sarcomere are cross-linked by myomesin/Obscurin (dark blue) and anchored to the Z-disks by titin/Sallimus (yellow). (b) Images of Drosophila flight muscle at $32\mathrm{h}$ and $48\mathrm{h}$ APF showing tropomodulin (Tmod), which specifically binds to actin filaments minus ends (pointed end), using an endogenous GFP-Tmod line [76, 77]. Tmod is detectable at $32\mathrm{h}$ APF, but does not display periodic patterns yet. At $48\mathrm{h}$ APF, periodic patterns of Tmod indicate polarity sorting of actin filaments, delineating the boundaries of the H-zone. Scale bar $10\mu \mathrm{m}$.

Figure 2

(a) Multichannel images of Drosophila flight muscle at $22\mathrm{h}$ to $32\mathrm{h}$ after puparium formation (APF) with actin (magenta), myosin (blue), titin/Sallimus (yellow), and myosin-Sallimus merge. Scale bar $5\mu \mathrm{m}$. (b) Tracking-free algorithm to compute correlation functions along local bundle axis. After preprocessing, a field of local nematic directors is determined (middle). Line scans along these nematic directions enable to compute mean correlation functions (right). (c) Autocorrelation functions (ACFs) for actin (red), myosin (blue), Sallimus (yellow), and $\alpha$-actinin (green) at selected time points. A monotonically decreasing ACF indicates a random distribution of proteins, while a peak (arrow) reveals periodic patterns with wavelength given by peak position. (d) Cross-correlation function (CCF) between myosin and Sallimus [green, mean $\pm \mathrm{s}$.e.m. (dashed), $\pm \mathrm{s}$.d. (shaded)]. A positive peak at nonzero $\mathrm{\Delta }x$ indicates a localization of the two proteins at a characteristic distance, while a negative dip at $\mathrm{\Delta }x=0$ indicates a local exclusion. (e) Proposed model of nonlocal interactions between myosin and Z-disk proteins driving pattern formation. Lateral interactions between bipolar myosin filaments and cross-linkers favor autocatalytic attachment. Lateral interactions between bipolar myosin filaments favor autocatalytic binding of myosin to the actin bundle. Likewise, interactions between Z-disk proteins favor autocatalytic binding of Z-disk proteins. Steric repulsion by Z-disk proteins impedes myosin binding to the actin bundle, causing a negative feedback. Finally, myosin recruits Sallimus, which recruits Z-disk proteins such as $\alpha$-actinin. This positive feedback is nonlocal, here modeled by an interaction kernel ${\chi }_m$ with mean interaction distance $l_m/2+l_s$ set by the length $l_m$ of myosin and $l_s$ of the giant protein Sallimus.

Figure 3

Pattern formation by nonlocal interactions. (a) Agent-based simulations of mathematical model I as proposed in Fig. 2, simulated in one space dimension, visualized in two space dimensions, for different simulation times ($t=0,2,100$) with myosin (blue) and Z-disk protein (green) bound to a scaffold of parallel, infinitely long actin filaments (shown schematically, red). (b) Corresponding concentration profiles at $t=0,2,100$ for myosin (blue) and Z-disk protein (green). (c) Autocorrelation functions (ACFs) at $t=0,2,100$ for myosin concentration. The ACF for $t=0$ fluctuates around zero, reflecting the initially random distribution of myosin. The ACF for $t=2$ exhibits a Fourier peak with amplitude $A$, indicative of a periodic pattern. (d) Quality factor $Q=-\pi /ln\left(A\right)$ of periodic patterns determined from the amplitude $A$ of the Fourier peak in the ACF of myosin concentration as function of time $t$ for different values of total myosin density $\lambda$ ($\mathrm{mean}\pm \mathrm{s}$.e.m., $n=10$ simulation runs). (e) Example concentration profile for different values of $\lambda$, corresponding to different steady-state values of the quality factor $Q$. A mean-field model was used for the limit $\lambda \to \infty$. (f) Phase diagram showing regimes of stable patten formation as function of the strength $\alpha$ of nonlocal interactions between myosin and Z-disk proteins, and the diffusion coefficient $D$ of bound myosin filaments. (g) Analytical solution from linear stability analysis in the limit $D=0$ reveals three different regimes as function of the autocatalytic feedback strengths $\mu$ and $\zeta$. (h) Memo of interaction scheme highlighting parameters $\alpha$, $\mu$, $\zeta$ of Eqs. (1) and (2). Parameters (a–c): $\lambda =5000/L_{\mathrm{sys}}$. For detailed list of model parameters, see Table S1 in the SM [39].

Figure 4

Pattern formation by tension-responsive catch bonds. (a) Tension-driven myofibrillogenesis: Bipolar myosin filaments can attach to polar actin filaments in different configurations labeled $m_{+}$, $m_{-}$, and $m_2$ distinguished in Eqs. (5) and (6). Single-bound myosin with concentrations $m_{\pm }\left(x\right)$ are attached to actin filaments of only one polarity (referred to as $+$ and $-$, respectively), and move towards the respective plus end with velocity $\mp v_0$. Double-bound myosin filaments with concentration $m_2\left(x\right)$ are attached simultaneously to actin filaments of opposite polarity, and thus do not move, but generate active tension $\sigma \left(x\right)$. The Z-disk protein $\alpha$-actinin is a catch-bond, i.e., its unbinding rate from actin decreases with increased tension. Together, this defines a second nonlocal interaction from myosin to Z-disk proteins. (b) Snapshots of agent-based simulations of the mathematical model II at different simulation times ($t=0,2,100$). Simulations of model II in Eqs. (5, 6, 7) were performed in one space dimension, and visualized in two dimensions for clarity with double-bound myosin (blue), Z-disk protein (green), and polar actin filaments (red). (c) Corresponding concentration profiles $m_2\left(x\right)$ and $z\left(x\right)$ at time points $t=0$, 2, 100 for double-bound myosin (blue) and Z-disk protein (green). (d) Corresponding ACFs for these concentration profiles. (e) Quality factor $Q$ characterizing the regularity of periodic myosin patterns as function of time $t$ for different values of the number-density parameter $\lambda$ scaling small-number fluctuations ($\mathrm{mean}\pm \mathrm{s}$.e.m., $n=10$ simulation runs). (f) Phase diagram showing regimes of stable patten formation as function of the relative length $l_a/l_m$ of actin filaments, and the effective diffusion coefficient $D$ of myosin filaments with ${\omega }^{*}=\omega \left(m_2^{*}\right)$. Parameters (b)–(d): $\lambda =5000/L_{\mathrm{sys}}$. For detailed list of model parameters, see Table S2 in the SM [39].