Sarcomeric Pattern Formation by Actin Cluster Coalescence

Citation: Friedrich BM, Fischer-Friedrich E, Gov NS, Safran SA ( Sarcomeric Pattern Formation by Actin Cluster Coalescence Benjamin M. Friedrich 0 Elisabeth Fischer-Friedrich 0 Nir S. Gov 0 Samuel A. Safran 0 Shoichiro Ono, Emory University, United States of America 0 1 Department of Materials and Interfaces, Weizmann Institute of Science , Rehovot , Israel , 2 Max Planck Institute for the Physics of Complex Systems , Dresden, Germany , 3 Department of Chemical Physics, Weizmann Institute of Science , Rehovot , Israel Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells. - Funding: This work was supported by the German Academic Exchange Service (BMF), a Minerva post-doctoral fellowship (EFF), the Israel Science Foundation (SAS), and the historic generosity of the Perlman Family Foundation. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. The intriguing striations of muscles were first observed more than a century ago [1]. All skeletal and cardiac muscle cells develop striated acto-myosin bundles of striking regularity termed mature myofibrils, which are characterized by a periodic localization of myosin II filaments alternating with crosslinking regions rich in a-actinin [2]. An analogous, though less regular, arrangement of actin and myosin filaments can be found in adherent, non-muscle cells that express striated stress fibers [3,4]. Some developing muscle cells contain similar striated stress-fiber like acto-myosin bundles termed premyofibrils and nascent myofibrils [57] that have been proposed to represent intermediate structures for the formation of mature myofibrils [8]. Figure 1 depicts the periodic structure of mature myofibrils. Periodically spaced crosslinking regions termed Z-bodies or Z-bands delineate 1mm-wide sarcomeric regions that comprise actin filaments of organized polarity and crosslinking myosin filaments in the sarcomere midzone. How are these surprisingly regular structures assembled? Numerous proteins involved in myofibrillogenesis have been identified together with their critical role in several muscle diseases [9]. However, the mechanistic basis for sarcomere selfassembly and the establishment of striated order remains elusive. There is evidence that striated fibers are preceded by unstriated fibers, which lack apparent sarcomeric localization of myosin and crosslinkers. Nascent striations first become visible as agglomerations of the actin crosslinker a-actinin, which then grow and change position to establish a regular, periodic spacing [10]. The formation of these early, unstriated bundles requires the parallel alignment of actin filaments, their mutual crosslinking as well as some means to control bundle thickness. Initial bundle formation depends on actin crosslinking, and possibly Onsager nematic alignment and depletion attractions of entropic origin [11,12], or kinetic effects due to polar actin flow [13]. The thickness of such actin bundles might be kinetically controlled [14]; additionally, geometric frustration effects due to the chirality of actin filaments have been proposed to set bundle thickness [1517]. Here, we focus on the stage of development in which there is already a preformed, unstriated bundle of finite thickness and present a mechanism to explain the subsequent emergence of initial sarcomeric order within this unstriated bundle. In muscle cells, subsequent myofibrillar maturation processes, not modeled here, and fine-tuning of actin filament length, e.g. by nebulin [18,19], drive the transition to final crystalline order. So far, a number of sarcomeric scaffolding proteins such as titin, N-RAP, and WASP have been identified [1823] and it is highly probable that these scaffolding proteins help to enhance and maintain striated order. However, it is unclear if these scaffolding proteins are able to establish initial striated order in the first place. To do this, these proteins would have to align in a periodic manner on a super-micrometer length-scale by some yet unknown mechanism. Additionally, it is unclear how myosin filaments, which normally walk towards actin plus-ends, become localized near actin minus-ends during myofibril assembly. Here, we ask if physical interactions of actin and myosin filaments, as well as crosslinkers are sufficient to induce initial striated order in filament bundles. Such a mechanism could be generic and could also apply to the formation of striations in acto-myosin stress fibers in Muscle contraction driving voluntary movements and the beating of the heart relies on the contraction of highly regular bundles of actin and myosin filaments, which share a periodic, sarcomeric pattern. We know little about the mechanisms by which these biological crystals are assembled and it is a general question how order on a scale of 100 micrometers can emerge from the interactions of micrometer-sized building blocks, such as actin and myosin filaments. In our paper, we consider a computational model for a bundle of actin filaments and discuss physical mechanisms by which periodic order emerges spontaneously. Mutual crosslinking of actin filaments results in the formation and coalescence of growing actin clusters. Active elongation and shrinkage dynamics of actin filaments generates polymerization forces and causes local actin flow that can act like a conveyor belt to sort myosin filaments in place. non-muscle cells. We show that the combination of treadmilling actin filaments and processive, plus-end tracking crosslinkers suffices to account for the self-organization of striated order and the localization of myosin filaments. Some examples of plus-end tracking crosslinkers such as formins and VASP are known in the biological literature [24,25]. We emphasize th (...truncated)