# The physical basis of sarcomere self-assembly

Francine Kolley-Köchel, Frank Schnorrer, Benjamin M Friedrich

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Francine Kolley-Köchel, Frank Schnorrer, Benjamin M Friedrich. The physical basis of sarcomere self-assembly. Biophysics Reviews, 2025, 6 (4), 10.1063/5.0281811. hal-05514851

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# The physical basis of sarcomere self-assembly

Francine Kolley-Köchel ; Frank Schnorrer ; Benjamin M. Friedrich

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# The physical basis of sarcomere self-assembly

Cite as: Biophysics Rev. 6, 041305 (2025); doi: 10.1063/5.0281811

Submitted: 21 May 2025 · Accepted: 24 November 2025 ·

Published Online: 17 December 2025

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Francine Kolley-Köchel,¹,²,³ ID Frank Schnorrer,⁴,⁵,⁶ ID and Benjamin M. Friedrich¹,⁸,⁹ ID

## AFFILIATIONS

¹Cluster of Excellence Physics of Life, TU Dresden, Dresden, Germany

²Faculty of Informatics/Mathematics, Technische Universität Freiberg, Freiberg, Germany

³Faculty of Informatics/Mathematics, Hochschule für Technik und Wirtschaft Dresden, Dresden, Germany

⁴Aix Marseille University, CNRS, IBDM, Turing Centre for Living Systems, Marseille, France

a) Authors to whom correspondence should be addressed: frank.schnorrer@univ-amu.fr and benjamin.m.friedrich@tu-dresden.de

## ABSTRACT

Voluntary movement and heartbeat in animals are powered by the contraction of periodically patterned acto-myosin bundles, called myofibrils, which are present inside striated skeletal and cardiac muscle cells. Myofibrils are “active cytoskeletal crystals” that span across the long muscle cells with hundreds of stereotyped, micrometer-sized sarcomere units repeated in series. Despite enormous progress in understanding the molecular composition and structure of sarcomeres, we still know little about the physical mechanisms that underlie sarcomere assembly during development. In this review, we critically discuss different hypotheses on the biophysical mechanisms of myofibrillogenesis. We describe how periodic myofibrils originate from mixed-polarity acto-myosin bundles that resemble unstriated stress fibers. These bundles undergo a transition from nematic (parallel) to smectic (layered) order, thereby establishing a state of higher molecular order, with alternating localization of myosin and actin crosslinkers. This order transition from a spatially homogeneous to a periodic pattern occurs simultaneously across the long myofibrils and is likely coordinated by mechanical tension. We provide an overview of previous theoretical models of sarcomere assembly. In light of recent experimental advances, we propose a new model in which muscle-specific myosin motor filaments, actin crosslinkers, and titin interact in a feedback loop that establishes an initial periodic pattern of proteins bound to a mixed-polarity actin filament bundle. This initial periodic pattern guides subsequent remodeling and results in a polarity sorting of the actin filaments, remodeling the nematic (mixed polarity) actin filament bundle into a smectic ordered chain of mechanically connected actin filament stacks with alternating polarity. This new model integrates previously contradictory ideas, such as the prominent pre-myofibril hypothesis, the stitching model, and the concept of tension-driven sarcomere self-organization.

© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0281811

## TABLE OF CONTENTS

I. A CYTOSKELETAL SOFT-MATTER CRYSTAL 1

II. HISTORIC MYOFIBRILLOGENESIS MODELS 3

A. The pre-myofibril model 3

B. Stitching model: I-Z-I bodies as building blocks 4

III. THE INSECT FLIGHT MUSCLE AS MODEL SYSTEM - THE ROLE OF TENSION 4

IV. MYOFIBRILLOGENESIS AS SELF-ORGANIZED PATTERN FORMATION 5

V. STRIATED STRESS FIBERS: SIMILAR BUT DIFFERENT? 6

VI. PREVIOUS MATHEMATICAL MODELS 7
A. Periodic myosin patterns by stress-polarity coupling 7

B. Motor-induced polarity sorting of actin patterns 7

C. Sarcomeric pattern formation by actin polymerization forces 7

D. Pattern formation by elastic interactions 7

VII. A NEW MODEL OF SARCOMERE SELF-ASSEMBLY BY A NEMATIC-TO-SMECTIC ORDER TRANSITION 9

A. Model I: Sarcomeric pattern formation driven by nonlocal interactions 9

B. Model II: Sarcomeric pattern formation driven by tension-responsive catch bonds 9

C. Polarity sorting of actin 11

VIII. SARCOMERE ADDITION BY SARCOMERE DIVISION 11

IX. OUTLOOK 12
# I. A CYTOSKELETAL SOFT-MATTER CRYSTAL

Striated muscles power all voluntary and many involuntary movements in animals, including walking, swimming, flying, as well as heartbeat (Lemke and Schnorrer, 2017; Alberts et al., 2002).

Muscles comprise about 30%-40% of total body weight in adult humans (Frontera and Ochala, 2015). Striated muscles are composed of elongated, parallel aligned muscle fiber cells, which are connected at their ends to the skeleton via tendons (Zelzer et al., 2014; Schnorrer and Dickson, 2004). Muscle fibers are multi-nucleated cells (syncytia) (Kim et al., 2015) that can measure from several millimeters to tens of centimeters in length in humans (Frontera and Ochala, 2015; Lemke and Schnorrer, 2017). Inside each muscle fiber, periodically patterned acto-myosin bundles, termed myofibrils, span its entire length. Regulated contraction of the individual acto-myosin units, called sarcomeres, results in muscle fiber shortening and skeletal movement (van Leeuwenhoek, 1682; Huxley and Niedergerke, 1954; Huxley and Hanson, 1954; Llewellyn et al., 2008; Lemke and Schnorrer, 2017; and Luis and Schnorrer, 2021).

Each micrometer-sized sarcomere contains parallel, polarity- sorted actin filaments, which are crosslinked by α-actinin and other actin crosslinkers at their structural plus-ends (barbed ends) located at the so-called Z-disc at the boundaries of each sarcomere (see Fig. 1). Thus, all the minus-ends (pointed ends) of the actin filaments point away from the Z-discs. Long muscle-specific bipolar myosin filaments are positioned in the center of each sarcomere, forming the so-called A-band. The A-band partially overlaps with the actin filaments point- ing away from the Z-discs. Actin and myosin filaments are linked by the “giant elastic spring” protein titin, which spans across half the sarcomere from the Z-disc to the middle of the myosin filaments, called the M-band. Additionally, sarcomeres contain 20-30 accessory structural proteins, including troponins and tropomyosin (Clark et al., 2002; Lange et al., 2006).

The periodic patterns of the sarcomere components represent a state of smectic (layered or periodic) order along the length of

myofibrils. Additionally, within the A-bands of each myofibril, the actin and myosin filaments form a triangular double lattice of almost crystalline regularity (transverse to the myofibrillar axis) (Millman, 1998; Wang and Raunser, 2023), resulting in characteristic X-ray dif- fraction patterns (Iwamoto et al., 2002; Dickinson et al., 2005).

Myofibrils and sarcomeres form during muscle development in a process called myofibrillogenesis. The almost crystalline nature of sar- comeres highlights myofibrillogenesis as an extreme example of cyto- skeletal pattern formation that builds an active “soft-matter crystal.” How this process works on the molecular scale and which physical mechanisms are involved is not well understood.

Understanding the mechanisms of sarcomere assembly is impor- tant, as defects in sarcomere assembly often result in severe (cardio-) myopathies. While individuals with a complete knockout of an essen- tial sarcomeric protein are usually not viable (Clark et al., 2002; Frey et al., 2012), an amino acid point mutation, a truncation, or a reduc- tion in the expression level of a sarcomere protein can result in seem- ingly regular myofibrillogenesis, yet high susceptibility to muscle fatigue or adult cardiomyopathies (Ahmad et al., 2005; Yotti et al., 2019). Understanding how sarcomeres assemble can thus provide a basis for a better molecular explanation of such (cardio-)myopathies.

Despite enormous progress in unveiling the molecular composi- tion and structure of sarcomeres, including the molecular mechanisms of sarcomere contraction (Wang and Raunser, 2023), we still know lit- tle about the physical mechanisms that underlie sarcomere assembly during myofibrillogenesis. A key question is how the first periodic pat- terns of sarcomere proteins are established. A remarkable conundrum is that the plus-end directed molecular motor muscle myosin II is not localized near the plus-end of actin filaments in mature sarcomeres. The latter would be expected and was indeed observed after mixing actin and myosin filaments with ATP *in vitro* (Wollrab et al., 2019) or in fibroblasts under non-physiological conditions (Verkhovsky et al., 1997). Instead, yet unknown mechanisms ensure that during sarco- mere assembly, myosin becomes localized in between two polar actin

<figure><img src="image_10.png" /><figcaption>**FIG. 1.** Sketch of a sarcomere (here for insect muscle). In mature myofibrils, the Z-discs (green), containing α-actinin, mark the boundary of each sarcomere. Structurally polar actin filaments (red) are cross-linked with their plus-ends at the Z-discs (green), while their minus-ends are facing toward the center of the sarcomere. Bipolar myosin filaments (blue) are located at the center of each sarcomere. These motor filaments are connected to the Z-disc by the “giant protein” titin (orange) that spans from the Z-disc to the M- band in human and from the Z-disc to the beginning of the myosin filaments in insects (as shown in this scheme; the *Drosophila* l-band titin homologue is called Sallimus). At the M-band, in the middle of the sarcomere, myosin filaments are crosslinked by myomesin in vertebrates or obscurin in insects (dark blue). The region comprising myosin is referred to as A (anisotropic)-band, while the complementary myosin-free region is called the I (isotropic)-band. The latter region contains those parts of actin filaments that do not interdigitate with myosin. [This terminology dates back to early polarized light microscopy studies, in which the different bands display distinct optical properties (Huxley, 1956)]. The stereotypic architecture of sarcomeres is key to their function: upon activation by calcium, the plus-end directed myosin motor heads, on both sides of the bipolar fil- aments, pull the actin filaments toward the center of the sarcomere. Thus, during sarcomere contraction the I-bands shorten, while the A-band length remains constant, with the acto-myosin overlap increasing (sliding hypothesis) and the sarcomere length shortening (Huxley and Niedergerke, 1954; Huxley and Hanson, 1954).</figcaption></figure>
filament stacks with myosin stacks overlapping with the minus ends of actin filaments (see Fig. 1). Finally, myofibrils contain sarcomeres of a stereotypic length, including a precise length of the actin and myosin filaments. This sets them apart from seemingly similar patterns of striated acto-myosin stress fibers in non-muscle cells, with alternating localization of myosin and actin crosslinkers. Mechanisms of length control must operate during myofibrillogenesis, relying on the muscle-specific giant protein titin (Linke, 2018), acting as a sarcomere ruler protein (Tskhovrebova and Trinick, 2017).

In this review, we aim to summarize the current knowledge on putative mechanisms of myofibril self-assembly, accessible to biologists and biological physicists alike.

## II. HISTORIC MYOFIBRILLOGENESIS MODELS

### A. The pre-myofibril model

Sanger proposed a model of myofibrillogenesis (Rhee et al., 1994), in which stress-fiber like acto-myosin bundles with a periodic localization of non-muscle myosin II, called pre-myofibrils, serve as templates for myofibrils (Sanger et al., 2002; Sanger et al., 2006; Sanger et al., 2010; and Dabiri et al., 1997) [see Fig. 2(a)]. This pre-myofibril hypothesis remains subject to debate. To structure a discussion, we divide the pre-myofibril model into three sub-hypotheses:

(i) The pre-myofibril model proposed that myofibrillogenesis commences from initially unstriated acto-myosin bundles, which share similarities to stress-fibers in non-muscle cells.

Periodic sarcomeric patterns emerge in these unstriated acto-myosin bundles, establishing a so-called “pre-myofibril”.

(ii) The early periodic patterns of the pre-myofibrils comprise an alternating localization of Z-disc proteins, such as α-actinin, and non-muscle myosin. Only subsequently, this non-muscle myosin is replaced by muscle-specific myosin, marking the transition from pre-myofibrils to nascent myofibrils.

(iii) Titin becomes incorporated into these structures only after the earliest periodic patterns had already formed.

There is now increasing evidence supporting sub-hypothesis (i): myofibrils originate from stress-fiber like, initially unstriated acto-myosin bundles, as also seen in *Drosophila* and cultured cardiomyocytes (Weitkunat et al., 2017; Fenix et al., 2018; and Kolley et al., 2024).

However, sub-hypothesis (ii), whether the first periodic patterns are formed by non-muscle myosin, and whether these are precursors for periodic muscle-myosin patterns and titin, remains open. Initial work found no evidence for periodic patterns of non-muscle myosin in the developing chicken heart (Ehler et al., 1999) [as opposed to cultured cardiomyocytes used in (Rhee et al., 1994)]. More recent work verified the presence of non-muscle myosin mini-filaments in acto-myosin bundles or possibly assembling myofibrils in human induced pluripotent stem cell (iPSC) derived cardiomyocytes; however, a rather irregular pattern of non-muscle myosin was found (Fenix et al., 2018). siRNA-induced knock-down of non-muscle myosin IIA and IIB did

<figure><img src="image_11.png" /><figcaption>**FIG. 2.** Schematics of two historic models of myofibrillogenesis. (a) In the pre-myofibril model (Rhee et al., 1994; Sanger et al., 2002), a stress fiber-like bundle of parallel actin filaments with a periodic pattern of non-muscle myosin, called the pre-myofibril, serves as myofibril template. Upon maturation, non-muscle myosin (purple) becomes replaced by muscle-specific myosin (blue) and only then titin (orange) is recruited. (b) In the stitching model, so-called I-Z-I bodies, consisting of polarity-sorted cross-linked actin filaments (red), and stacks of myosin filaments (blue) assemble independently and become “stitched together” to subsequently form myofibrils.</figcaption></figure>
result in a sarcomere phenotype by one group (Fenix et al., 2018); however, this phenotype was not reproduced by CRISPR induced knock-out of non-muscle myosin IIA and IIB by others (Chopra et al., 2018). Myhre and Pilgrim (2012) proposed stabilization of early non-myosin patterns by chaperons.

Hence, it is clear that non-muscle myosin filaments are present in acto-myosin bundles, but whether these serve as direct templates for muscle myosin remains open. Since non-muscle myosin cannot bind to titin, it would be unclear how it should be arranged at regular distances on the actin bundles.

Similarly, sub-hypothesis (iii) on the late incorporation of titin may not hold true at least in some systems (Hill et al., 1986).

In *Drosophila*, the titin homologue Sallimus is present as early as the first periodic muscle myosin patterns (Weitkunat et al., 2014; Kolley et al., 2024). No periodic patterns of myosin or other sarcomere components are formed after knock-down of Sallimus (Loreau et al., 2023) or its splicing variant Kettin (Rui et al., 2010). Sallimus is the I-band domain homolog of mammalian titin, while Projectin is the A-band domain homolog. In stem cell-derived cardiomyocytes, deletion of the A-band domain of titin suppressed sarcomere formation (Musa et al., 2006; Zaunbrecher et al., 2019), suggesting an essential role of titin-myosin interactions for sarcomere assembly; similar observations were made in zebrafish (Zou et al., 2015). In contrast, a partial deletion of the I-band domain caused only a mild phenotype (Zou et al., 2015). Together, these reports suggest that titin-muscle myosin interactions are needed to produce the highly regular periodic pattern of muscle myosin in myofibrils.

One key question left open by the pre-myofibril model is how the initial periodic patterns of non-muscle myosin would be established.

## B. Stitching model: I-Z-I bodies as building blocks

A second historic model of sarcomere assembly is the so-called “stitching model” by Holtzer et al. (1997), named as such by Sanger et al. (2006), based on early observations in cardiac muscle cells (Lu et al., 1992) and later skeletal muscle (Holtzer et al., 1997). The stitching model proposes that I-Z-I bodies, which consist of cross-linked actin filament stacks, assemble on their own and independently from myosin filaments and myosin filament stacks. Only later, these two building blocks then become stitched together to form periodic myofibrils. For this, titin binds with its N-terminus to the I-Z-I bodies and then recruits myosin filaments at its C-terminus [Fig. 2(b)]. In contrast to the pre-myofibril model, non-muscle myosin would not be required, at least it would not form a periodic pattern (Holtzer et al., 1997; Sanger et al., 2006). Indeed, both free-floating I-Z-I bodies and muscle myosin stacks were observed in taxol-treated myogenic cells (Holtzer et al., 1997); similar latent protein complexes were observed in mutants for key sarcomeric proteins, which do not assemble sarcomeres (Rui et al., 2010). Stacks of non-muscle myosin were observed in fibroblasts (Hu et al., 2017). Recent *in vitro* experiments demonstrated the formation of Z-bodies as punctate aggregates, which adhere to actin filaments, reminiscent of liquid-liquid phase separation of Z-disc proteins and wetting of actin filaments by these phase-separated droplets (Sponga et al., 2021), suggesting a physical mechanism for the assembly of I-Z-I bodies.

However, it is not clear how large supra-molecular complexes such as I-Z-I bodies move in the crowded environment of a muscle cell. On a historical note, the stitching model seems to contradict previous work by the same group, which rather proposed a transition from stress fibers to nascent and then to mature myofibrils (Dlugosz et al., 1984). During this transition, periodic patterns of titin and muscle myosin appear simultaneously (Hill et al., 1986). It is possible that the formation of I-Z-I bodies and myosin stacks observed later in atypical conditions rather reflect a “dead end” of self-organized pattern formation of myofibrillogenesis, resulting from an intrinsic tendency of components to form self-aggregates by cooperative binding to themselves. This interpretation was explored in a recent mathematical model of sarcomeric pattern formation (Kolley et al., 2024), see Sec. VII A.

## III. THE INSECT FLIGHT MUSCLE AS MODEL SYSTEM - THE ROLE OF TENSION

Historically, myofibrillogenesis has been largely investigated in cell culture either using primary myocytes or cardiomyocytes isolated from chicken or quail (Dabiri et al., 1997; Wang et al., 2005) or using a rhabdomyosarcoma cell line (Holtzer et al., 1997) as this allowed transfection and easier imaging. However, *in vitro*, the myotubes are mainly attaching homogeneously to their underlying substrate, instead of to defined tendon cells at the two long ends of the myotube only. Hence, studying myofibrillogenesis in a mechanically native environment requires an *in vivo* system, which is compatible with live imaging. This was made possible by imaging myofibrillogenesis of the *Drosophila* flight muscles during the pupal stage. Flight muscles are large cells; each cell contains many hundred nuclei and about 2000 individual myofibrils (Spletter et al., 2018; Pal et al., 2025). Using life imaging, our group found that after myotube-tendon attachment, all 2000 myofibrils assemble at the same time, each containing about 100 periodic sarcomeres (Weitkunat et al., 2014; Spletter et al., 2018). The surprise was that the periodic patterns of myosin and the fly titin homolog Sallimus (Sls) become visible in all the myofibrils simultaneously, suggesting a coordinated self-organization of a sarcomeric pattern (Fig. 3). What could drive and coordinate this self-organization? We found that before the periodicity becomes detectable, mechanical tension in the flight muscles is strongly built-up along the long axis of the myotube, reaching from one tendon attachment site to the other (Fig. 3). Then, the initially unpatterned actomyosin bundles transition into individual periodic myofibrils, each of which spans across the entire length of the myotube. This converts the non-periodic myotube to a periodic muscle fiber (Fig. 3). Strikingly, if the buildup of tension is compromised by reducing tendon attachment or by acute laser surgery, the formation of long periodic myofibrils is inhibited. This coined the hypothesis of tension-driven myofibril self-organization (Weitkunat et al., 2014). An important benefit of the tension model is that the exact number of periodic sarcomeres that fit per myofibril to span across the length of the entire muscle fiber will be self-determined by the tension build up. Only with the correct number of sarcomere units, the correct tension levels can be reached (Fig. 3). Later, when the muscles grow in length, new sarcomeres are added to each of the already assembled myofibrils (Spletter et al., 2018; Rodier et al., 2025) (see also Sec. VIII).

After the initial proposal of the tension-driven myofibril self-organization in flight muscles, we showed that this mechanism is also conserved in other *Drosophila* muscle types that contain a cross-striated organization of their myofibrils (Weitkunat et al., 2017), as
<figure><img src="image_12.png" /><figcaption>**FIG. 3.** Tension-driven sarcomere self-organization. Top: early acto-myosin bundles only contain actin and non-muscle myosin. Tension is relatively low. Middle: muscle myosin and titin expression begins. Both are initially located in non-periodic patterns. Tension is increasing and a first pattern assembles. Bottom: tension is high, and a mature periodic pattern has been established (Weitkunat et al., 2014; Lemke and Schnorrer, 2017).</figcaption></figure>

well as in human iPSC-derived muscle fibers that are grown on Matrigel substrate (Mao et al., 2022). Thus, mechanical tension appears as a key coordinator during the early sarcomere self-organization process that acts like a molecular compass to orient and sort the individual protein components (Lemke and Schnorrer, 2017). The important remaining open question is how does tension sort and order the individual protein components?

## IV. MYOFIBRILLOGENESIS AS SELF-ORGANIZED PATTERN FORMATION

From a physics perspective, myofibrillogenesis is a multi-step pattern formation process. The most disordered state of the actin cytoskeleton would be an isotropic network without preferential alignment of actin (or myosin) filaments, as observed at the actin cortex of various non-muscle cells, see Fig. 4(a). In such networks, neither positional nor orientational order is present (i.e., there is no regular spacing of filaments and the orientation of filaments is random).

In contrast to isotropic actin networks, cellular stress fibers and the stress fiber-like actin filament bundles present in myotubes (the precursors of myofibrils) display nematic order. This means actin filaments are preferentially aligned along a common axis, i.e., there is orientational order. The polarity of the actin filaments in these bundles is mixed, i.e., the orientation of plus- and minus-ends is random at any position. In myotubes, actin filaments align with the long axis of these elongated cells, along which tension is built-up after myotubes attach to tendons or an extracellular substrate (Weitkunat et al., 2014; Mao et al., 2022). This defines the axis of the nematic order.

The term nematic order originates from the theory of liquid-crystals, in which it describes a phase with orientational but no positional order (de Gennes and Prost, 1993; Chaikin et al., 1995). In contrast, smectic order can be considered as a refined state of nematic order, in which molecules additionally acquire a layered arrangement, and thus, if the spacing between the layers is regular, form a periodic pattern. In physics terms, layered smectic order breaks continuous translational symmetry in the direction perpendicular to the layers. Applied to a sarcomere, smectic order requires an approximately constant length of each filament type. In mature myofibrils, actin filaments are additionally sorted such that actin filament stacks face each other with opposite polarities [see Fig. 4(a)]. This is achieved by cross-linking them with actin filaments of opposite polarity at the Z-disc (see Fig. 1).

A crystal, finally, is the most regular form of matter, in which molecules adopt perfectly regular positions (and thus continuous translational symmetry is broken in all directions). Crystals are perfectly periodic, displaying long-range order.

Using this terminology, unstriated stress fibers and the yet unpatterned precursors of myofibrils represent a state of nematic order. During myofibrillogenesis, these precursors undergo a nematic-to-smectic order transition, to establish an approximately periodic pattern, which subsequently becomes increasingly regular, changing from a state of low periodic order to a state of high periodic order with a well-defined sarcomere length [see Fig. 4(b)].

The establishment of the initial nematic order of the actin filament bundles in myotubes may occur by similar mechanisms as the assembly of stress fibers in non-muscle cells including actin polymerization from
<figure><img src="image_13.png" /><figcaption>**FIG. 4.** Types of order. (a) From left to right: an isotropic network is characterized by lack of a preferred orientation, here shown for actin filaments (red). For a high nematic order, the orientations of actin filaments are parallel, yet the structural polarity of the filaments (marked by barbed plus-end and pointed minus-end) randomly points in both directions. For smectic order, filaments adopt a layered organization; thus, there is positional order along the bundle axis, yet no positional order within the individual layers. A crystal is characterized by both orientational order and fixed positions. (b) In an actin filament bundle, such as an individual myofibril containing myosin (blue) and actin crosslinkers (green), an initial pattern of low periodic order (lacking a fixed repeat length-scale and thus long-range order) transitions to a pattern with high periodic order, as observed in mature myofibrils. In mature myofibrils with high periodic order, additionally, actin filament stacks alternate their polarity at the Z-discs.</figcaption></figure>

adhesion points, followed by annealing as discussed in (Hotulainen and Lappalainen, 2006; Tojkander et al., 2011; and Burridge and Guilluy, 2016). Nematic alignment coincides with a strong up-regulation of mechanical tension in these bundles, generated by non-muscle myosin II, while the actin filaments become nematically aligned (Loison et al., 2018). Additionally, alignment of actin filaments by actin crosslinkers, by myosin forces (Walcott and Sun, 2010), by depletion forces (Hošek and Tang, 2004), by protein condensates (Walker et al., 2025), or entropy-driven Onsager alignment (Coppin and Leavis, 1992; Furukawa et al., 1993) may contribute to the establishment of nematic order.

In the following Secs. VI and VII, we discuss putative physical mechanisms that could establish the first periodic patterns of sarcomere proteins. Once a pattern with detectable periodicity is established, it guides the periodic localization of additional sarcomeric proteins by localized recruitment. It is conceivable that the actin filaments within the myofibrils change dynamically, with sorting, selective anchoring, and localized nucleation guided by the initial periodic pattern, to establish the highly ordered pattern of mature sarcomeres. Thus, patterns of low periodicity would continuously mature to the highly periodic sarcomere patterns. In parallel, thin myofibrils can grow radially in diameter by recruitment of additional protein components (Spletter et al., 2018; Pal et al., 2025), similar to epitaxy. Finally, neighboring myofibrils align in registry with each other in most muscle types, forming the typical cross-striated pattern of muscle fibers (Friedrich et al., 2011; Weitkunat et al., 2017).

Hence, myofibrillogenesis is a multi-step process, with the assembly of an initial periodic pattern being only the first step. We hypothesize consecutive steps involve both self-assembly and self-organization processes.

In physical terms, self-assembly describes physical processes at equilibrium, in which building blocks acquire precise geometric arrangements, which are energetically favorable to an extent that exceeds entropy, an example being crystallization. The related concept of self-organization is a non-equilibrium process that requires active processes that dissipate energy to establish a large-scale organization from local interactions (Turing, 1952; Cross and Greenside, 2009). In biological terms, self-organization needs to be fueled by ATP, whereas self-assembly does not require energy input and can occur spontaneously in a cell when a protein exceeds a certain concentration and assembly starts.

Myofibrillogenesis likely combines both processes. The proteins making up a sarcomere have specific binding sites, guiding their self-assembly. The tension-driven self-organization of myofibrils hints at the importance of active forces generated by myosin motors to coordinate the assembly across the entire myofibril length. Motor-deficient myosin rods achieve a high nematic actin filament ordering but fail to establish a regular periodic pattern (Loison et al., 2018).

## V. STRIATED STRESS FIBERS: SIMILAR BUT DIFFERENT?

Historically, stress fibers in non-muscle cells were often compared to early stage acto-myosin bundles in muscle fibers (Dlugosz et al., 1984). Unstriated stress fibers resemble precursors of myofibrils, characterized by nematically ordered actin filaments and irregular patterns of non-muscle myosin and α-actinin (Lazarides and Weber, 1974; Weber and Groeschel-Stewart, 1974; and Lazarides and Burridge, 1975). Intriguingly, stress fibers in non-muscle cells can become striated and occasionally display a more regular, alternating pattern of non-muscle myosin mini-filaments and actin crosslinkers along the bundle axis (Langanger et al., 1986; Hotulainen and Lappalainen, 2006; Peterson et al., 2004; Hu et al., 2017; and Hu et al., 2019). Similar periodic patterns were observed in the contractile ring, forming at the cleavage furrow in dividing cells (Fenix et al., 2016; Wollrab et al., 2016). In some cases, periodic actin patterns were documented (Hu et al., 2017). Thus, non-muscle myosin, actin crosslinkers, and actin can in principle form periodic patterns in non-muscle cells.

In contrast to mature myofibrils with their well-defined sarcomere size, these striated stress fibers display only low periodic order with quite variable spacing (Livne and Geiger, 2016; Stachowiak et al., 2012). Furthermore, the non-muscle myosin mini-filaments are very short (about 300 nm) and hence do not resemble the 1.6-µm-long myosin filaments of mammalian sarcomeres (Hu et al., 2017; Dasbiswas et al., 2018). A second key difference between myofibrils and striated stress fibers is the lack of titin, which is essential for the formation of periodic patterns in myofibrils (Rui et al., 2010; Loreau et al., 2023), but is absent in striated stress fibers. While the physical mechanisms that establish periodic patterns in striated stress fibers may thus be different from those of myofibrillogenesis, certain aspects of the initial filament sorting might be shared. We therefore review
proposed models for the formation of a periodic pattern in stress fibers.

In striated stress fibers, the alternating pattern between aggregates of non-muscle myosin and α-actinin was proposed to result from a tendency of myosin to assemble into myosin stacks, combined with (indirect) interactions between myosin and α-actinin (Hu et al., 2019). The formation of non-muscle myosin stacks in stress fibers (Hu et al., 2017; Jiu et al., 2019; and Hu et al., 2019) starts with the formation of small myosin puncta and their fusion into larger puncta. Remarkably, single myosin filaments were observed to translocate along the actin bundle, and to become captured upon passing an existing myosin punctum (Hu et al., 2017). Thus, a myosin stack can grow in size, despite the absence of a cross-linker like myomesin or obscurin that binds to the center of muscle myosin filaments in muscles. A similar mechanism of myosin stack concatenation was observed in the assembly of the contractile ring in dividing cells (Fenix et al., 2016). Additionally, myosin filaments promote the assembly of additional myosin filaments, possibly by templated nucleation (Beach et al., 2017; Quintanilla et al., 2024).

A mathematical model by Stachowiak et al. (2012) suggests a mechanism for the formation of myosin puncta based on the active motion of myosin along actin filaments. In this model, a small local variation in net actin polarity causes myosin motors to move in the direction set by the dominant local actin polarity, until these myosins reach a position where the net actin polarity is zero. There, the myosin motors accumulate. This simple mechanism predicts a highly variable distribution for the spacing between myosin puncta. Specifically, the model predicts a power-law distribution for the distances between myosin puncta (with exponent -3/2, which follows from a stochastic model that describes the net actin filament polarity as a diffusive jump process along the actin bundle axis). This power-law distribution was indeed observed in *in vitro* experiments (Stachowiak et al., 2012). The resultant broad distribution for the distances between myosin puncta reflects a pattern of low periodic order, in contrast to the high periodic order in myofibrils of muscle cells.

Thus, simple feedback mechanisms can amplify fluctuations in an initially disordered system and establish periodic patterns with low periodicity in a process of self-organization.

# VI. PREVIOUS MATHEMATICAL MODELS

To theoretically propose possible biophysical mechanisms of sarcomere assembly, mathematical models have been developed in the past. We review four mathematical models that address the spontaneous formation of periodic patterns in acto-myosin bundles, applicable to either striated stress fibers or myofibrils. The first three models assume that actin filaments become polarity-sorted at the first stage of periodic pattern formation.

## A. Periodic myosin patterns by stress-polarity coupling

Inspired by the spontaneous formation of periodic patterns of myosin in striated stress fibers, Yoshinaga et al. (2010) proposed a one-dimensional mean-field model of a bundle of polar actin filaments with initially random polarity, with possibly position-dependent active stress generated by the interaction between polar actin filaments and myosin motors [Fig. 5(a)]. A generic coupling between actin polarity and active stress was shown to be sufficient to drive the formation of periodic patterns of actin polarity with characteristic wavelength. The

model of Yoshinaga et al. (2010) assigned an important role to mechanical tension for sarcomeric pattern formation, consistent with a notion of tension-driven myofibrillogenesis put forward by Weitkunat et al. (2017). However, the model stipulates that polarity-sorted periodic patterns of actin filaments and periodic myosin patterns form simultaneously. This is at odds with a recent quantification of early periodic patterns of sarcomere components in the insect flight muscle by Kolley et al. (2024), which showed that α-actinin, myosin and Sallimus/titin form sarcomeric patterns first, while the actin filaments become polarity sorted only hours later.

## B. Motor-induced polarity sorting of actin patterns

Zemel et al. proposed a model for the establishment of polarity-sorted actin patterns by molecular motors (Zemel and Mogilner, 2008; Zemel and Mogilner, 2009) [Fig. 5(b)]. In agent-based simulations, molecular motors were assumed to cross-link neighboring actin filaments and slide these relative to each other. Both unipolar and bipolar motors could establish patterns of polarity-sorted actin domains, starting from a homogeneous initial state with random polarity. Thus, myosin as a plus-end directed, bipolar motor could induce polarity-sorted actin patterns. Indeed, a similar motor-induced sliding of actin filaments was proposed to account for semi-periodic myosin patterns in the cytokinetic ring of dividing cells (Wollrab et al., 2016). However, the mechanism proposed by Zemel et al. cannot explain the assembly of sarcomeres. The mechanism predicts final patterns, in which myosin would be localized near the plus-ends of actin filaments, i.e., opposite to its observed localization in sarcomeres. This argues against motor-induced sliding as a myofibrillogenesis mechanism.

## C. Sarcomeric pattern formation by actin polymerization forces

A third model of sarcomeric pattern formation based on actin treadmilling was proposed by Friedrich et al. (2012) [Fig. 5(c)]. They proposed a mechanism by which Z-disc proteins cross-link actin filaments at their plus-ends, while still allowing for polymerization at the plus-end. Indeed, such plus-end tracking crosslinker had been described previously (Zigmond et al., 2003) and suggested to transmit actin polymerization forces (Laurent et al., 1999). In the model, these active polymerization forces cause an apparently stochastic motion of small clusters of crosslinked actin filaments, which coalesce to form larger clusters. Myosin motor filaments bind to actin in a polarity-specific manner and exert an opposing force. This eventually halts actin cluster coalescence and results in the establishment of periodic sarcomeric patterns. Active myosin forces slow down this pattern formation process, which is predicted to fail for myosin forces above a critical value. Yet, while some actin polymerization at the plus-end has been observed in developing myofibrils, actin polymerization forces may be too weak to drive filament sorting (Littlefield et al., 2001).

## D. Pattern formation by elastic interactions

A biophysical model proposed how several, already striated acto-myosin bundles can interact and thereby align their periodic patterns in registry, thus extending the periodic pattern in lateral direction [Fig. 5(d)] (Friedrich et al., 2011; Dasbiswas et al., 2018; and Dasbiswas et al., 2019). In this coarse-grained model, myosin motors exert active forces, which can be idealized as force dipoles that interact
<figure><img src="image_14.png" /><figcaption>**FIG. 5.** Mathematical models for the formation of periodic patterns in acto-myosin bundles. (a) Yoshinaga et al. (2010) considered a generic coupling between actin polarity and myosin-generated tension, which establishes periodic patterns. (b) Zemel and Mogilner (2009) showed how molecular motors can establish polarity-sorted patterns of cytoskeletal filaments by sliding neighboring filaments. Yet, applied to myofibrillogenesis this model would predict a wrong localization of myosin at actin plus-ends. (c) Friedrich et al. (2012) proposed that actin polarization forces could drive the coalescence of crosslinked actin clusters, which likewise establishes periodic sarcomeric patterns. All three models assume that actin filaments become polarity-sorted at the first stage of periodic pattern formation, which is inconsistent with some experimental observations (Kolley et al., 2024). (d) A model by Dasbiswas et al. (2018) considered elastic interactions between acto-myosin force dipoles, which can establish inter-fiber registry of striated acto-myosin fibers, thus promoting the formation of myosin stacks.</figcaption></figure>
in an elastic medium. This interaction induces relative motion of the periodic patterns, e.g., by force-dependent actin polymerization (Dasbiswas et al., 2019). Such feedback mechanisms could contribute to myosin stack assembly.

None of the above models had incorporated a role for titin, despite the fact that titin is essential for sarcomere formation. Furthermore, the biophysical mechanism by which mechanical tension guides sarcomere assembly is not modeled explicitly. Finally, the first three models predict early polarity sorting of actin filaments, while the last model already assumed an initial periodic pattern.

## VII. A NEW MODEL OF SARCOMERE SELF-ASSEMBLY BY A NEMATIC-TO-SMECTIC ORDER TRANSITION

The mathematical models in the preceding Sec. VI had assumed that actin filaments become polarity sorted as the first step in sarcomeric pattern formation (Yoshinaga et al., 2010; Zemel and Mogilner, 2009; and Friedrich et al., 2012). A recent quantitative analysis of developing myofibrils in *Drosophila* flight muscle instead suggests that myosin, α-actinin and titin/Sallimus form periodic patterns first, before periodic patterns of actin become detectable (Kolley et al., 2024). This revised notion that myosin and Z-proteins establish periodic pattern first, while actin filaments follows later, is consistent with earlier, more qualitative reports (Tokuyasu and Maher, 1987; Ono, 2010), as well as with the relative late appearance of periodic patterns of the plus-end capping protein CapZ (Wang et al., 2005) and the minus-end actin capping protein Tropomodulin (Kolley et al., 2024). This observation forms the basis of two mathematical models that propose self-organized periodic pattern formation by mutual interactions between myosin and Z-proteins that bind to a scaffold of actin filaments with nematic but not yet smectic order.

### A. Model I: Sarcomeric pattern formation driven by nonlocal interactions

We recently proposed a minimal-model of myofibrillogenesis, assuming interactions between myosin and Z-disc proteins, which are mediated by the giant protein titin/Sallimus (Kolley et al., 2024). We show that periodic sarcomeric patterns form spontaneously, even for a finite number of interacting molecules subject to small-number fluctuations. This model can be summarized as follows [Fig. 6(a)]:

(i) Myosin and Z-disc proteins are assumed to bind and unbind to a scaffold of nematically aligned actin filaments with (initially) random polarity. This idea builds on the experimental observation that myosin and Z-disc proteins form periodic patterns first, while actin filaments become polarity sorting only later.

(ii) Both myosin filaments and Z-disc proteins exhibit autocatalytic attachment in the model, motivated by the experimental observation of spontaneously forming myosin stacks (Hu et al., 2017), and Z-disc protein aggregates (Sponga et al., 2021). Steric hindrance between Z-disc proteins and spatially extended myosin filaments gives rise to negative feedback by which any local increase in Z-disc protein concentration subdues the recruitment of myosin in that location. Conversely, binding of titin to myosin at its C-terminus and recruiting Z-disc proteins such as α-actinin at its N-terminus, gives rise to positive feedback, which is described as a non-local interaction [Fig. 6(a)].

(iii) In simulations based on these modeling assumptions, myosin and Z-disc proteins form spontaneous periodic sarcomeric patterns.

(iv) A non-local interaction length-scale, set by the length of titin and myosin, sets the wavelength of emergent patterns, and thus the sarcomere size.

(v) Pattern formation is not driven by a diffusion-driven Turing instability, but instead by a different self-organization process that depends on the assumed non-local interaction between extended myosin filaments, titin and Z-disc proteins.

We predict critical numbers of sarcomere components necessary for the formation of periodic patterns. The model includes a role for titin and hence can predict the formation of sarcomeres of given length depending on the choice of the titin length. Assuming a shorter length of titin results in shorter sarcomeres in simulations, consistent with previous experiments with genetically engineered titin (Tskhovrebova and Trinick, 2003; Brynnel et al., 2018; Granzier et al., 2014; and Loreau et al., 2025).

### B. Model II: Sarcomeric pattern formation driven by tension-responsive catch bonds

Previous experiments suggest that mechanical tension plays an important role during sarcomeric pattern formation (Weitkunat et al., 2014; Lemke and Schnorrer, 2017; Weitkunat et al., 2017; Chopra et al., 2018; and Mao et al., 2022). The appearance of the first periodic patterns coincides with the upregulation of tension (Weitkunat et al., 2014), suggesting that the increase in tension may act as a trigger for sarcomeric pattern formation, which could explain the almost simultaneous start of sarcomere formation along the entire length of myofibrils observed in some systems (Weitkunat et al., 2014; Weitkunat et al., 2017; Chopra et al., 2018; Fenix et al., 2018; and Mao et al., 2022). Consistent with this, no long periodic myofibrils form if muscle-tendon attachments are weakened (Weitkunat et al., 2014).

Intriguingly, Z-disc proteins such as α-actinin were demonstrated to behave as tension-responsive catch bonds in both the actin cortex of HeLa cells (Hosseini et al., 2020; Ruffine et al., 2023) and in reconstituted actin networks (Mulla et al., 2022). In contrast to normal slip bonds, the average lifetime of a bond between a catch-bond actin crosslinker and actin filaments increases with force (presumably as a result of cryptic binding sites that become exposed under force), up to a critical piconewton force (Mulla et al., 2022), beyond which bond lifetimes decrease again (Marshall et al., 2003).

Motivated by these two observations, we formulated a second minimal model of myofibrillogenesis (Kolley et al., 2024). In this model, spatial inhomogeneities in myosin concentration cause similar spatial inhomogeneities in mechanical tension. This local tension is assumed to stabilize actin-bound Z-disc proteins. This results in a feedback interaction from myosin to Z-disc proteins [Fig. 6(b)], similar to the non-local interactions proposed in the above model I.

This model II likewise generates stable sarcomeric patterns with alternating localization of myosin and Z-disc proteins, yet it is less robust to small-number fluctuations (Kolley et al., 2024). We argue that myofibrillogenesis could possibly be described by a combination of both models. Future experiments, i.e., a partial knockdown of myosin, Z-disc proteins and length variation of titin, can test these models.

The new theoretical model retains one central idea from the previous pre-myofibril hypothesis, namely, that myofibrils originate from
<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /><figcaption>**FIG. 6.** Mathematical models for periodic patterns of myosin and Z-disc proteins in unstriated actin bundles. (a) Model I assumed that myosin and Z-disc proteins bind and unbind to a bundle of parallel actin filaments, which serves as a passive scaffold (Kolley et al., 2024). Autocatalytic attachment of myosin and Z-disc proteins, together with steric hindrance of spatially extended molecules and a non-local positive feedback mediated by binding of titin, establishes spontaneous periodic patterns, characterized by an alternating localization of myosin and Z-disc proteins along the actin filament bundle. Bottom: stills from agent-based simulations (myosin: blue, Z-disc proteins: green, actin filaments: red). (b) Model II proposed that Z-disc proteins behave as effective catch-bonds whose binding is stabilized by tension. Myosin-generated local tension forces stabilize Z-disc proteins accordingly in a position-dependent manner, again resulting in sarcomeric patterns. Adapted from Kolley et al., PRX Life 2, 013002 (2024). Copyright 2024 authors, licensed under a Creative Commons Attribution (CC BY) license.</figcaption></figure>
stress-fiber-like unstriated acto-myosin bundles that undergo a nematic-to-smectic order transition. It combines this idea with the concept of tension-driven self-organization of myofibrillogenesis, and suggests a molecular mechanism. The proposed mechanism of self-organization requires autocatalytic assembly of Z-disc proteins to actin filaments, as well as of myosin filaments to themselves. These feedback mechanisms may have caused the observed formation of isolated I-Z-I bodies and myosin stacks in unphysiological conditions that motivated the previous stitching model (Holtzer et al., 1997; Hu et al., 2017; Rui et al., 2010; Sponga et al., 2021; and Lu et al., 1992). Importantly, once a first periodic pattern with alternating localization of myosin and Z-disc proteins is established, it can guide subsequent sarcomere maturation (irrespective of whether the first pattern comprises non-muscle myosin as proposed by Sanger or not). Unlike other previously proposed mathematical models (Yoshinaga et al., 2010; Zemel and Mogilner, 2008; Zemel and Mogilner, 2009; and Friedrich et al., 2012), the new model does not assume that actin filaments become polarity sorted as first step of sarcomere assembly, consistent with our observations in the insect flight muscle (Kolley et al., 2024).

### C. Polarity sorting of actin

Quantitative analysis of emergent periodic patterns of different sarcomere components suggest that actin filaments establish periodic patterns of polarity-sorted domains only after myosin and Z-disc proteins established periodic patterns with alternating localization (see Sec. VII A) (Kolley et al., 2024).

We hypothesize that these periodic myosin/Z-disc protein patterns may then orchestrate the remodeling of the initially mixed-polarity actin filament bundle by two different mechanisms. First, the Z-disc comprises actin nucleators such as formin, which may nucleate new actin filaments with correct sarcomeric polarity, while other, not anchored actin filaments would disassemble. Similarly, preferential actin nucleation from the minus-ends by myosin was proposed (Chereau et al., 2008). Both scenarios would establish polarity-sorted domains of actin filaments with minus-ends facing the A-band.

Second, active myosin forces could stabilize actin filaments that are correctly anchored at a Z-disc. Actin filaments in ectopic positions, however, would be prone to buckle in response to myosin forces (Lenz et al., 2012; Murrell and Gardel, 2012; and Soares E Silva et al., 2011), which should accelerate their depolymerization. This mechanism would be consistent with observed accelerated actin turn-over in the presence of myosin activity (Skwarek-Maruszewska et al., 2009; Aratyn-Schaus et al., 2011; and Haviv et al., 2008). Additionally, myosin forces or actin treadmilling could move these actin filaments out of the bundle, where these would depolymerize. These mechanisms would likewise establish a polarity-sorting of the actin filaments.

Intriguingly, FRAP experiments indicated two distinct actin populations with different turn-over kinetics (Hotulainen and Lappalainen, 2006), which may reflect these two populations of anchored and free actin filaments, respectively.

One key feature of sarcomeres is that actin filaments are polar and anchored at the Z-disc. Additionally, Z-disc proteins anchor the N-terminal end of polar oriented titin molecules. Since titin's C-terminal end interacts with myosin filament components, both in mammalian and in insect sarcomeres (see Fig. 1), it is conceivable that titin plays a key role to anchor the position of correctly ordered actin-Z-disc-actin bodies (called I-Z-I bodies in the stitching model) by binding to myosin

filaments at both far ends of these complexes. Thus, correctly positioned actin filaments will be stabilized, which also ensures the correct interaction of the actin filaments with the myosin filaments. This will allow the buildup of high mechanical tension, which was observed to increase during myofibrillogenesis both in insect and mammalian muscle (Weitkunat et al., 2014; Mao et al., 2022).

Sarcomere formation and maturation require fine-tuned interactions between actin filaments and muscle myosin. For example, deregulated acto-myosin interactions caused by a loss of troponin complex members result in sarcomere defects (Sehnert et al., 2002; Nishii et al., 2008), or even failure of sarcomere assembly (Nongthomba et al., 2004; Ferrante et al., 2011).

Sarcomere maturation further requires a precise regulation of the length of actin filaments. Simple mechanisms of length control, such as actin severing proteins that bind in a length-dependent manner, can explain a unimodular distribution of actin filament length, with a characteristic mean length; however, the predicted distributions would be broad, with coefficient of variation of at least 0.5 (Friedrich et al., 2012). Developmental data from maturing *Drosophila* flight muscle show a decrease in the coefficient of variation of sarcomere length, from 0.19 at 32h APF (after puparium formation) to 0.04 at 48h APF (Rodier et al., 2025) and further refinement in mature sarcomeres (Spleiter et al., 2018). This shows that sarcomere length becomes increasingly regular with time and likely actin filament length becomes very precise too. Thus, the remodeling of the actin filament bundle during sarcomere maturation is likely accompanied by a refined regulation of actin filament length.

Actin capping proteins regulate actin polymerization dynamics [Tropomodulin at minus-ends, CapZ at plus-ends (Clark et al., 2002; Gokhin et al., 2015)]. If such capping proteins are recruited in a pre-established periodic pattern, they could stabilize actin filaments with correct polarity and fine-tune actin length at the same time. Importantly, the giant proteins titin and in particular, nebulin, the latter extending from the Z-disc almost to the end of the actin filaments in mammalian sarcomeres, were suggested to serve as molecular rulers, either by stabilizing actin filaments directly, or indirectly by recruiting actin capping proteins to specific locations, though details are not well understood (Castillo et al., 2009; Pappas et al., 2010; Bennett et al., 2020; and Wang et al., 2022).

In contrast, insect sarcomeres do not house a long nebulin protein and actin filament length strongly depends on the muscle type. A recent model for actin filament regulation suggests that actin filament (and sarcomere) length in insects is regulated by a combination of the I-band titin isoform expression, which regulates the length of the I-band, and the rate of spontaneous contractions during development, which regulates the length of the actin-myosin overlap and hence the length of the actin and myosin filaments in insect muscle types (Loreau et al., 2025). Therefore, actin filament length control is a multi-step process, with only coarse length control before the formation of periodic sarcomeric patterns, followed by fine-tuning of actin filament length by localized capping proteins, molecular rulers and regulated contractions, which is only possible once periodic patterns are established.

### VIII. SARCOMERE ADDITION BY SARCOMERE DIVISION

After the initial periodic sarcomere pattern has been established along myofibrils, muscle fibers and their myofibrils often continue to
grow in length, because the animal skeleton to which the muscles are attached grows (Heallen et al., 2020; Kardon, 2011; Luis and Schnorrer, 2021; Kaya-Copur et al., 2021; Orfanos et al., 2015; Spletter et al., 2018; and Rodier et al., 2025). As sarcomeres maintain their stereotypic micrometer size, the number of sarcomeres in each myofibril must increase accordingly (Spletter et al., 2018; Rodier et al., 2025). This requires the insertion of new sarcomeres into a myofibril that is firmly attached to tendons at both terminal ends and already under mechanical tension (Weitkunat et al., 2017). Sarcomere addition thus represents a nontrivial problem, as any opening of the myofibril could cause its rupture and subsequent disassembly, as indeed observed in laser microsurgery experiments (Mao et al., 2022). Former electron microscopy studies discussed addition of new sarcomeres at the terminal ends (Dix and Eisenberg, 1990; Williams and Goldspink, 1973; Balakrishnan et al., 2020; and Ganassi et al., 2020), yet without providing direct evidence.

Recent live imaging of growing *Drosophila* muscles showed that sarcomeres are added all along the length of a myofibril (Rodier et al., 2024), whereas sarcomere addition exclusively at the terminal ends was not found. Quantitative image registration combined with live imaging demonstrated that a “mother sarcomere” divides along the myofibril tension axis by splitting its A-band myosin stack, with some bipolar myosin filaments moving left, others moving right, resulting in two myosin stacks of reduced size, which are subsequently pulled apart on a timescale of tens of minutes to eventually form two “daughter” sarcomeres. Each daughter inherits about half of the original myosin stack of the mother sarcomere. Together with each myosin stack fragment, Z-disc components including the I-band titin Sallimus are pulled out of each of the two flanking Z-discs as two clusters that eventually merge to give rise to a new Z-disc that links the two daughter sarcomeres. FRAP experiments indicated that new sarcomere proteins are recruited during the process to refill the protein content of the daughter sarcomeres reaching standard sarcomere levels (Rodier et al., 2025). Thus, the increased tension, produced by the growing skeleton, will trigger sarcomere divisions, which in turn will lower the tension and adapt the sarcomere number to maintain the correct steady-state sarcomere length for the respective muscle type in insects.

Sarcomere divisions were found in the *Drosophila* flight muscle, which shares a number of similarities with cardiomyocytes. Flight muscles are stiff, perform oscillatory contractions, and contain a short I-band titin version, as cardiomyocytes do. Sarcomere divisions were also observed in *Drosophila* larval muscles (Rodier et al., 2025), which resemble mammalian skeletal muscle. The proposed division mechanism is further consistent with electron microscopy studies of growing crab muscle (Jahromi and Charlton, 1979). Does a similar mechanism also apply in vertebrates? An important difference in mammalian muscle is that titin interacts very tightly with the myosin filaments in the A-band (Tamborrini et al., 2023) and is strongly bound to the M-band crosslinker myomesin (Gautel, 2011; Young et al., 2001), a protein not present in insects. As the tension-induced division mechanism proposes the weakest bond to initiate the division, sarcomere division in mammalian muscle might be initiated by a tension-induced splitting of one Z-disc rather than the M-band. Indeed such a Z-division mechanism throughout the muscle fiber has recently been suggested by monitoring incorporation of new proteins after mechanical exercise induced longitudinal muscle growth (Hibbert et al., 2025). These new data are consistent with earlier observations that indirectly

supported that muscle growth and repair of mature muscle likely involve sarcomere addition (Lynn and Morgan, 1994; Yu et al., 2004; and Yang et al., 2016), reviewed in (Jorgenson et al., 2020).

## IX. OUTLOOK

While the fundamental structure and contraction mechanism of sarcomeres was identified more than 70 years ago (Huxley and Niedergerke, 1954; Huxley and Hanson, 1954), the biophysical mechanisms of sarcomerogenesis remain surprisingly under-researched. The development of *in vivo* live imaging of sarcomere assembly together with quantitative image analysis established the basis for a unifying theoretical model that combined the previous pre-myofibril hypothesis with the tension-driven self-organization of myofibrillogenesis.

The next steps for the experimentalists will be to test the theoretical predictions of this model. It needs to be tested how the assembly dynamics changes when the sarcomere protein concentration is modified. Theory would predict a gradual reduction in periodic order for a partial knockdown of sarcomere proteins, with a failure of sarcomere assembly below a critical protein concentration. Another open question is the distribution of actin filament lengths and polarity, which theory predicts to change as a function of time during myofibrillogenesis.

It will be interesting to quantify at which stage titin adapts its extended confirmation. Does the extension of titin depend on the assembly of early sarcomeres, which may stretch titin? Further, are active myosin forces needed to generate the initial periodic pattern, or only to refine and mature the pattern? Sarcomere protein turnover experiments can test the theory prediction whether early periodic patterns represent a slowly evolving dynamic steady-state, which becomes more static upon maturation. The dynamics of topological defects in the sarcomere pattern should likewise inform about the dynamic processes underlying self-organized sarcomere assembly. Genetically tractable systems like *Drosophila*, in combination with iPSC derived mammalian systems, which allow high-resolution imaging, should enable these tests of the theoretical model and further provide more quantitative data on sarcomere protein dynamics to feed future model improvements.

The models of sarcomere assembly and sarcomere addition discussed in Secs. VII and VIII are based on recent observations in *Drosophila*. Given that the structure and molecular architecture of sarcomeres are highly conserved across the animal kingdom, these models are likely to apply in a similar form to vertebrate muscle, albeit with some differences. Such differences may include the debated role of non-muscle myosin and the contribution of distinct titin domains to the establishment of early periodic patterns, as well as force-dependent mechanisms regulating actin and myosin filament length. The mechanism of sarcomere addition by sarcomere division described in *Drosophila* also applies to vertebrates, though initiated by a Z-disc split rather than an A-band split. Finally, the stoichiometry between sarcomeric proteins differs across species.

Thus, open questions include mapping out commonalities and differences in physical self-assembly mechanisms between different muscle types, as well as between striated muscle fibers and cardiomyocytes, and, at the most extreme level of disparity, between myofibrils and striated stress fibers in non-muscle cells. Combining complementary approaches including cell culture systems (to target cell-type specific differences and disease-related phenotypes), invertebrate model organisms such as *Drosophila* (to harness genetic tractability and advanced *in vivo* imaging, ensuring proper muscle-tendon
attachments), and vertebrate systems (for physiological relevance) promise an integrated understanding of sarcomere self-assembly. With the recent advances in imaging and controlled genetic perturbations, identifying the physical mechanisms of sarcomere assembly may be within reach, yet will require a concerted effort that combines experiment, quantitative data and image analysis, with mathematical modeling.

## ACKNOWLEDGMENTS

We thank Clara Sidor for insightful discussion and generation of biological data of myofibril assembly that inspired some of the presented models. F.S. and B.M.F. acknowledge financial support from the Human Frontiers Science Program (HFSP, Grant No. RGP0052). F.S. acknowledges support from the Centre National de la Recherche Scientifique (CNRS), the European Research Council under the European Union's Horizon 2020 Programme (ERC-2019-SyG 856118), the excellence initiative Aix-Marseille University A*MIDEX (ANR-11-IDEX-0001-02), the France-BioImaging National Research Infrastructure (ANR-10-INBS-04-01), and by funding from France 2030, the French Government program managed by the French National Research Agency (ANR-16-CONV-0001) and from the Excellence Initiative of Aix-Marseille University, A*MIDEX (Turing

Centre for Living Systems). B.M.F. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy, EXC-2068-390729961, as well as through a Heisenberg grant (421143374) and a project grant (555765544) of the DFG.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Francine Kolley-Köchel:** Writing – original draft (equal); Writing – review & editing (equal). **Frank Schnorrer:** Funding acquisition (equal); Writing – original draft (equal); Writing – review & editing (equal). **Benjamin M. Friedrich:** Conceptualization (equal); Funding acquisition (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

## DATA AVAILABILITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

## SARCOMERE COMPONENTS

**Myofibrils**—highly regular acto-myosin bundles in skeletal and heart muscle cells that span the entire length of the muscle cell. Each myofibril is a linear chain of micrometer-sized contractile sub-units, called sarcomeres.

**Sarcomere**—smallest periodic unit of myofibrils with conserved characteristic architecture comprising actin and myosin filaments, Z-disc proteins, titin and numerous accessory proteins. Parallel actin filaments are anchored at their structural plus-ends in a dedicated structure termed the Z-disc, which is rich in actin crosslinkers, and delineates the boundaries of each sarcomere. Bipolar myosin filaments are positioned in the center of the sarcomere. The giant protein titin links actin and myosin filaments together (the I-band titin in *Drosophila* is called Sallimus).

**Actin filaments**—polymers polymerized from monomeric actin with typically a micrometer length in mature sarcomeres. Actin filaments are structurally polar, with their structural plus-ends (barbed ends) anchored at the Z-disc, and their minus-ends (pointed ends) facing the center of a sarcomere. Actin filaments inside sarcomeres are also called thin filaments (due to their appearance in electron microscopy) and are decorated with additional proteins such as nebulin.

**Myosin filaments**—bipolar motor filaments of micrometer length located in the center of a sarcomere. Myosin filaments are polymerized from myosin heavy chains, regulatory light chains and essential light chains. They are also called thick filaments and contain other accessory proteins like myosin binding protein C. Myosin filaments possess motor head domains at both ends that interact with actin filaments. Upon activation, these motor heads induce plus-end directed sliding, which shortens the sarcomeres in length and thus causes muscle contraction.

**Z-disc**—marks the boundary of a sarcomere and contains numerous actin cross-linking proteins, the most prominent being α-actinin. The Z-disc anchors the plus-ends of structurally polar actin filaments and the N-terminus of the giant protein titin.

**Titin**—a giant protein, whose I-band part serves as an entropic spring that links actin and myosin filaments, by spanning over half the length of the sarcomere. In insects, titin is replaced by the homologues Sallimus and Projectin.

Based on their appearance in electron microscopy, traditionally different, partially overlapping zones of sarcomeres are distinguished:

**A-band**—“anisotropic band”, sarcomere zone containing the aligned, parallel myosin filaments at the center of a sarcomere. The length of the A-band length remains constant when the sarcomere contracts.

**M-band**—narrow zone in the center of the A-band containing myosin filament crosslinkers but no myosin motor heads.

**I-band**—“Isotropic band”, sarcomere zone of actin filaments not interdigitated with myosin filaments (spanning two adjacent sarcomeres across the shared Z-disc). The length of the I-band reduces when the sarcomere contracts.

**H-zone**—sarcomere zone free of actin filaments in the center of the sarcomere. The H-zone shortens in length when the sarcomere contracts.
## MECHANISM OF MUSCLE CONTRACTION

The physical mechanism underlying muscle contraction was identified in the 1950s (Huxley and Niedergerke, 1954; Huxley and Hanson, 1954). The “sliding filament theory” was based on the experimental observation that the I-band and H-zone shorten in length during muscle contraction, while the length of the A-band remains constant [see Fig. 1(b)]. This observation is explained by the relative sliding of myosin motor heads of the bipolar myosin filaments toward the respective plus-ends of the actin filaments on both sides of the sarcomere. Thus, the actin filaments are pulled closer to the center of the sarcomere, and the sarcomere contracts. The simultaneous contraction of all sarcomeres in every muscle fiber of a muscle causes a macroscopic muscle contraction.

This mechanism prompts precise control of myosin motor activity. In a nutshell, in a relaxed muscle fiber, tropomyosin decorates the myosin binding site on the actin filaments and thereby blocks the cross-bridge between myosin motor heads and the actin filaments (Lynn and Taylor, 1971; Neupane et al., 2019; Howard, 2001; and Alberts et al., 2002). To trigger contraction, a nerve impulse, activating the muscle cells, causes the release of $Ca^{2+}$ from internal stores (Endo, 1977). These calcium ions bind to the troponin complex, which changes conformation and moves tropomyosin to a different position on the actin filaments. This exposes the binding sites for the myosin motor heads, which can now perform a power-stroke and pull the actin filaments toward the center of the sarcomere. The energy for myosin's power-stroke is provided by the hydrolysis of adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and phosphate (Pi). In relaxed muscle, the majority of myosin motor heads is stuck in a high-energy state in their chemico-mechanical cycle: after hydrolysis of one ATP molecule, yet ADP and Pi remain bound, a substantial part of the chemical energy is stored in elastic strain of the motor head. When this pre-strained myosin head binds to actin, a conformational change of myosin is induced, triggering the powerstroke and thus progression of the myosin motor head in its chemo-mechanical cycle. During the powerstroke, the elastic energy of the myosin head is released to perform work by relative sliding of myosin and actin [up to 50 zJ (Howard, 2001)]. After the power-stroke, each myosin head is in a low-energy state, releases the ADP, and needs to bind a new ATP molecule to detach from the actin filament. Hydrolysis of ATP renders the motor head ready for its next powerstroke.

## APPENDIX A: BIOPHYSICAL PARAMETERS OF SARCOMERE ASSEMBLY

*Sarcomere length.* Sarcomere length varies across different muscle types, yet is tightly regulated in a given muscle type; in humans it is about 2 µm in relaxed cardiac and 3 µm in relaxed skeletal muscles (Llewellyn et al., 2008). In *Drosophila* flight muscles, sarcomeres measure 3.4 µm in length, while relaxed larval muscle sarcomeres are 8.5 µm long (Loreau et al., 2025).

*Filament lengths.* A myosin length of 1.6 µm was measured in vertebrates, containing about 300 muscle myosin II hexamers with a total of 600 motor heads (Davis, 1988). In contrast, in cultured fibroblasts, striated stress fibers contain myosin filaments with only 10–30 non-muscle myosin hexamers of a typical length of 200–300 nm per filament (Quintanilla et al., 2024; Billington et al., 2013; Niederman and Pollard, 1975; and Ricketson et al., 2010). The length of actin filaments depends on muscle type, with typical lengths of 1.0–1.4 µm in vertebrate skeletal muscle (Gokhin and Fowler, 2013).

*Numbers of components.* The number of myosin filaments in the cross section of developing myofibrils can be as low as 35–50, counted from electron microscopy images (Loison et al., 2018). Assuming a 3:1 stoichiometry of actin filaments to myosin filaments in the insect flight muscle (Millman, 1998), this number would correspond to 100–150 actin filaments per myofibrillar cross section. The actin:myosin stoichiometry can be different in other muscle types, e.g., 2:1 in vertebrate skeletal muscle (Tamborrini et al., 2023). A 6:1 stoichiometry has been proposed for titin to myosin filaments (Tamborrini et al., 2023). In mature myofibrils, the cross-sectional area density of myosin filaments ranges from 250 to $700 \mu m^{-2}$ in different muscle types (inferred from the lattice spacing of their triangular lattice) (Millman, 1998). As the diameter of

myofibrils increases during myofibrillogenesis (Spletter et al., 2018), the number of filaments per cross section should likewise increase.

*Active myosin forces.* Energetics and mechanics of the power-stroke of myosin heads during contraction of mature myofibrils is discussed, e.g., in (Howard, 2001), from which we quote maximal sliding speeds of 6 µm/s, maximal drag-stroke distances of up to 3.5 nm and up to 50% efficiency of converting chemical energy released by ATP hydrolysis into mechanical work. Each myosin motor head can generate a maximal force of 1 pN, though at a low duty ratio < 0.1 (Uyeda et al., 1990; Howard, 2001). The persistence length of actin filaments was estimated as 20 µm (Gittes et al., 1993), which corresponds to a critical buckling force of 1 pN for an actin filament of 1 µm length; such forces are likely reached and exceeded during actin filament remodeling as hypothesized in Fig. 7.

*Protein turnover.* FRAP experiments quantified the turn-over of sarcomeric proteins during myofibrillogenesis. For actin, FRAP revealed two distinct actin populations with fast turn-over (≈ 1 min, 25%) and slow turn-over (>30 min, 75%) in beating cardiomyocytes (Skwarek-Maruszewska et al., 2009). For titin, turn-over times of several hours were measured in cultured mouse myocytes (da Silva Lopes et al., 2011), while turn-over times > 30 min were determined for titin/Sallimus in mature *Drosophila* larval muscle (Loreau et al., 2023). FRAP experiments on stress fibers indicated turn-over rates of $0.5 \min^{-1}$ for actin and $3 \min^{-1}$ for $\alpha$-actinin (Hotulainen and Lappalainen, 2006).

*Force-dependent detachment of actin crosslinkers.* Rupture forces to break bonds between actin and muscle $\alpha$-actinin were previously measured using optical traps, with typical rupture forces in the range 20–80 pN and bond lifetimes of several seconds under constant load (Miyata et al., 1996; Ferrer et al., 2008). In HeLa cells, the residence time of bound $\alpha$-actinin-4 at the actin cortex increased by a factor of 2–3 with increasing tension (Hosseini et al., 2020). Measured changes
<figure><img src="image_17.png" /><figcaption>FIG. 7. Possible mechanisms for the polarity sorting of actin filaments. A periodic pattern of myosin (blue) and actin cross-linking proteins (green) attached to an initially unstrat-ated bundle of parallel actin filaments (red) can remodel this actin filament bundle by different mechanisms, including de-novo nucleation of actin filaments with correct polarity at Z-discs (green), localized recruitment of actin capping proteins, expulsion by treadmilling, buckling-induced depolarization of ectopic actin filaments by active myosin forces, and stabilization of actin filaments with correct polarity by myosin-generated tension. The resulting regular actin-myosin pattern is able to generate high tension along the myofi-bril axis (see text for details).</figcaption></figure>

of cortical tension on the order of $\gamma \approx 1$ nN/µm (Hosseini et al., 2020) were estimated to correspond to a molecular force of 10 pN (Kolley et al., 2024). This order-of-magnitude estimate is consistent with the pico-Newton forces required to induce a change in bond lifetime in single-molecule experiments (Mulla et al., 2022).

APPENDIX B: IMAGE ANALYSIS TOOLS

Quantitative analysis of myofibrillogenesis requires software tools to trace myofibrils and detect nascent sarcomeres. We list a selection of tools that can be useful for this purpose.

*Tools to quantify cardiomyocyte contractions.* SarcTrack (Matlab) was developed to track hundreds of fluorescently-tagged sarcomeres in 2D video microscopy data of beating cardiomyocytes to estimate contraction and relaxation parameters, even if sarco-meres are not well aligned, by fitting a collection of wavelets representing a pair of neighboring Z-discs with variable orientation (Toepfer et al., 2019). Other tools to quantify cardiomyocyte con-tractions from 2D video microscopy data include SarcOptiM (ImageJ plugin) using Fourier analysis (Pasqualin et al., 2016), MUSCLEMOTION (ImageJ plugin) using frame differences (Sala et al., 2018), or SarcGraph (Python), which tracks Z-discs (Zhao et al., 2021).

*Tools to quantify sarcomere length and morphometrics.* SarcApp (Python) employed deep learning-based segmentation (using a U-net architecture) to segment Z-lines and M-bands in static 2D multi-channel fluorescence images, which enables compu-tation of morphometric features (Neininger-Castro et al., 2023). SarcAsM (Python) uses a similar U-net architecture to track Z-discs in 2D fluorescence microscopy movies, including quantification of sarcomere contractions using a user-friendly API (Haerttter et al., 2024). PatternJ (ImageJ plugin) allows computing statistical features and average profiles in regular one-dimensional structures (Baheux Blin et al., 2024). Other tools to quantify sarcomere lengths and myofibril width in static 2D images include MyofibrilJ (ImageJ plu-gin) (Spletter et al., 2018), ZlineDetection (Python) (Morris et al., 2020), or the Individual Myofibril Analyzer (IMA; Python) (Görög et al., 2025). The SarcOmere Texture Analysis (SOTA) algorithm (Matlab) estimates spacing and regularity of Z-disc stripe patterns from Haralick correlations (Sutcliffe et al., 2018), which was later extended and ported to Python (Stein et al., 2022).

*Sarcomere detection in 3D.* A multi-step feature-detection algo-rithm (Matlab) was used to detect ten thousand sarcomeres in 3D multi-channel fluorescence microscopy images of the insect flight muscle at 36h and 40h APF (Rodier et al., 2025).

*Quantification of early patterns.* An algorithm to analyze early stages of myofibrillogenesis (Matlab) computes correlation func-tions of fluorescence intensity of sarcomeric proteins by averaging local correlation functions computed along short segments parallel to the local myofibril direction, without the need to trace individual myofibrils (Mao et al., 2022; Kolley et al., 2024).

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