The asynchronous growth and movement reconstruction of the early molting animals

Epithelium is one of the basic types of animal tissue, and forms tissue boundaries that act as physical barriers to separate adjacent cell clusters. However, tissue boundaries at cellular resolutions can hardly be found in the fossil record. Here we focus on the growth and movement patterns of early Ecdysozoans by quantifying cell-level forces in the epithelium of two worms from the early Cambrian and Ordovician period. The arrangement of the epithelium cells (that do not necessarily represent biological cells) separating the body rings of these early Ecdysozoans indicates precise morphological patterning at the cellular level was established in the early Cambrian. The force distribution patterns on the body ring further suggest that the boundary cells helped maintain a pressure gradient between the rings, consistent with a role in movement. Finally, the active tension eld of the worms plates throughout their ontogeny, and steady state of their epithelium cells, indicate these molting animals employed an asynchronous growth pattern in their epithelium. plates separated by tiny linear boundary cells; H, 6 sides polygons, some of which elongated along AP axis. Abbreviation: bc: boundary cell; p: plate; po:


Introduction
Growth and movement are two basic proprieties of animals. The growth patterns of a living organism can be reconstructed by analyzing the mechanical forces underlying its development [1]. Peristaltic movement is widely employed by the worms living near sediment/water (air). Worms using peristaltic movement have an epithelial system that displays a tension -compression rhythm [2] with relatively high potential energy. In contrast, when in a steady state and not involved in movement, epithelial cell clusters minimize their potential energy [3].
In a physical perspective, the forms of living beings are created by cell movements. Recent studies quantifying forces in cell proliferation, sorting and other developmental processes, showed that physical forces also contribute to maintain boundaries [4][5][6]. The mechanical properties of cell lattices have been quantitatively described [7]. Most of the cell boundaries are relatively straight. Comparatively, the leaf epidermal cells with puzzles and pavements of the cell boundary increase the contact area of the neighboring cells and strengthen the structural integrity of the epithelium. The pavement cell form corresponds to higher grade anatomical structures and recently pavement cells have been found in the 535 ma worms fossil cuticles [8].
In a larger scale, segments can be regarded as periodically organized cell clusters. The segment number varies considerably among species, ranging from six in some frogs to several hundred in snakes. It is known that physical cues, like mechanical stretching, can induce the formation of additional somites in the vertebrate embryo [9]. Similarly, some larval worms will add from 80 to more than 300 rings during development [10]. The maintenance of straight and sharp boundaries of the segment is crucial for subsequent patterning events.
Segmentation step wisely evolves in organ systems. Epithelium derives from ectoderm and it can segment normally without the mesoderm [11], suggesting epithelium segmentation is regulated independently from mesodermal segmentation [12]. Segmentation may have evolved to improve locomotion in arthropods, annelids and chordates [13]. The Cycloneuralians display epithelial segmentation and remarkable biodiversity in the Cambrian-Ordovician period [14][15][16].

Material And Methods
In this study, the de nition of the cell includes, but is not restricted to, the biological cell. Two new species of the stem group Cycloneuralia of the early Paleozoic period were reported. Both fossils' surface displays ne polygonal structures on the scale of biological cells. Here we use the light microscope Leica 205C and scanning electron microscope to photograph the specimens.
The vertex model was employed to describe cell clusters states within the epithelium of the worms. In the vertex model, the epithelial shape is represented by a set of vertices that mark the common point of three or more neighboring cells. It was initially used to study the packing of bubbles in foams, then adapted to study the 2D packing and rearrangement of apical cell surfaces in the planar epithelium [17].

Image segmentation
We use the watershed algorithm [18] of Image J to segment the cells. Initial scanning electron microscope (SEM) images of the worm fossils were smoothened to reduce the noise and facilitate the cell boundary segmentation.

Cell mechanical analysis
The processed images were load in the CellFIT to reconstruct the force eld of the cell cluster [19]. Cell boundaries were generated from uniformly spaced mesh points at each edge in order to obtain ideal triplet approach angles for calculating forces. A cell is not represented by a polygon, but by a polyarc.
The key equation of CellFIT is for any particular triplet junction to be in equilibrium, the adjacent cell edges satisfy the force balance equation: where the unit vectors r mnA are constructed tangent to the limiting angle at which the membrane along the boundary between cells m and n approaches the triple junction and pointing away from the junction, and the summation is carried out over all edges that connect to the triple junction. The γ mn values are the corresponding unknown membrane tensions [19].
The Laplace's equation is used to solve the pressures elds of the system, Δp is the pressure difference between cells. γ is the parameter of the surface tension. R is the radius of curvature of the cells. Base on these equations [19], the tension and pressures elds of the study area of the cell clusters were solved by CellFIT . Remarks: Convergent evolution likely forces several clades to fall into a close morpho space. The inter plate polygons have been found in the phosphatized epithelial fragments of Hadimopanella in which named the micro plates and the boundary cells were previously named "inter annular furrows" [20,21]. These structures have received less attention than the plate. The small specimens have a relatively narrow inter plate space, while the space extends in the larger specimens ( Figure S1). The specimen series is interpreted as a developmental sequence of the J. rosettea. New inter plate cell lattices emerge ( Figure S1). The developmental patterns are widely recorded in other early Cycloneuralia [22].
Etymology. The generic name derives from the the Meitan formation, the strata that the fossil been found. Species name after elegance.
Locality and horizon. The specimen was collected from the lower mudstone of the Meitan Formation, Early Ordovician (Florian), Guiyang city, South China.
Dignosis for genus and species. The body of the worm is made up of rings. Each ring boundary is de ned by annular furrows (Figure 1f,g; 4c,d). The annular furrows consist of rectanglar polygons. The platelets are distributed along the two sides of a row of rectangle polygons. The surface of the epidermis dominated by 6 sided cell lattices (Figure 1f). The aspect ratio of the plate range is from 1 -2 ,and the apexes of the plates range from 1 to 3 (Figure 1g).
Remarks: The ornaments of the epidermis of the Ordovician worms [23] occupied a much wider morphospace than that of their Cambrian counterparts. Meitis elegans gen. et sp. nov. share similarities with the plate outline of the 495-Myr-old Palaeoscolex piscafumm and Gnmoscolex herodes from the lower Ordovician strata. All of them have distinct boundary zone of the rings [24,25]. However, the plate apexes and distribution pattern of these species are remarkably different [24,25]

(b) Growth and movement pattern reconstruction
The study used a quantitative approach to understand the growth pattern of the epidermal cell grade structures of the worms by analysizing the force uctuation landscapes of the cell clusters [26]. Growth and movement processes potentially affect the tension and pressure eld of the cells. The tension eld was treated as the proxy for the growth rate within a ring [26,27] (Figure 2). The platelets and plates were regarded as a developmental continuum in the case of the early worms (Figure 1g; Figure 2b-d). The developing plate was interpreted as a hot spot of the tension eld (Figure 2b-d). Conversely, the cell polygons re ect the relaxed network con guration (Figure 2e,f), and represent the steady state of the epithelial system of the early molting animals [3].
The tension is unequally distributed around the worms' plates (Figure 2b-d) similar to the mitosis loop [28] of the epidermal cells, with the new cells proliferating from the hot spot where a relatively high tension value is recorded (Figure 2a) [28]. While the plate is not a mitosis loop, and does not necessary represent a single cell, , the nonequilibrium tension elds of the plates suggest they are in an active state.
More broadly, the asymmetric distributions of the tension eld are found within the mesh like plates of the Microdictyon (Figure 3) [29]. Under the assumption that tension correlates positively to the growth rate, the results suggest allometric growth of the early worm's epithelial elements.
The pressures are unequally distributed on the two sides of the BCs (Figure 4b, d), suggesting the boundary cell prevents pressure transmission to the region's base on the 2D lattices analysis (Figure 4e).
The cells density of BCs region is higher than that of the surrounding cells which resistance to nonequivalent stress eld and the tissue under pressure tends towards a uniform cell organization (BCs) [30].

Discussion
asynchronous growth pattern Some clades (tardigrata, onychophora etc.) employed an incomplete molting pattern. Hard epidermal derivatives (jaws, claws, dorsal spines etc.) have a cone-in-cone construction [31]. The desynchronization of molting ensures stiffness of these functional elements (feeding, climbing and protection etc.) throughout the lifetime of the organisms. This system tends to relax to the minimum energy state in the plate-free region of the ring (Figure 2e,f). The developing plates formed like volcanic islands interspersed among the inactive epithelial ocean. Thus, we suggest the early worms employed an asynchronous growth pattern in their epithelium. Simulation experiments reveals the cell types with lower tension will envelop the cell clusters with higher cortical tension [32].
The epithelial sheet are three dimensional (3D) in reality, and 3D-preserved specimens [14] (Figure 4g; S1 b,c,f) show the boundary region of the worms is slightly curved. The annuli/furrow patterns are widely observed in worm-like animals. Previous work shows differential tension drives epithelial cell ingression [33]. Our results show the consequence of the ingression: The boundary cells prevent pressure transmission to the adjustment region, establishing pressure gradients beween the rings (Figure 4), which is the basis of peristaltic movement. The pressure eld was used as a proxy to re ect the movement state of individual rings.

Topological structure proprieties and development
The cuticle of the worm is stiff [14], however, the cells underneath the cuticle have relatively lower Yong's modulus [34] and are condensable during the movement of the worm. The puzzle type cell boundaries have multiple re -entrant angles (Figure 1d). The negative poisson's ratio structure [35] would increase the shear modulus [35] of the cell lattices. Thus, the Cambrian worm epithelium is more resistant to the shear force, and the shape of a cell within tissues can re ect the history of physical signals it encounters [36]. In the contract and elongation stage of the ring (Figure 4f), the big octagon cells have an opposite deformation direction to the small quadrangle cells [37], the anisotropy deformation forces may affect the distribution of cell proliferation events [38] within cell clusters.
The morphology of cells across boundary zones switches dramatically, indicating the fates of the cell-like structures are precisely determined. The energy -consuming mechanisms govern cell shape. The 4 -8 cell lattices consist of puzzle type cells with negative Poisson's ratio, the structures display hystersis response to strong compression or elongation on the lattices [37]. Both the foam and puzzle type membranes are employed by modern cells [39]. The foam type cell predominate, ensuring exibility during bending and facilitating a wide range of reshaping and rearrangement behaviors that are crucial to development and movement of the animals.
The developmental sequence of Jinia suggests the process by which the worms' rings elongate ( Figure  S1). On a larger scale, Jinia body elongation should start in the embryonic stages. If we treat Markuelia [40] as a model for the late embryonic stage of Cycloneuralia, we nd each ring is approximately 20 micrometers in width which would occupy only two rows of cells [40]. Annelid segments can form from single-cell-wide precursors [9], and daughter cells emerge during the process of ring elongation ( Figure   S1e-g). The rosette pattern is treated as an intermediate phase of the elongation process [41]. The boundary cells constrain the cell ow within each ring, which may explain the rosette pattern formed near the boundary of the ring. Moreover, the boundary cells may promote the uid-to-solid jamming transition underlies body axis elongation [42].
The study demonstrates the establishment of precise tissue boundary formation of early molting animals through the Cambrian -Early Ordovician period. The subdivision of the elongating body axis into repeated units is employed by dozens of phyla [43]. This framework restricts cell proliferation and force transmission within a segment, laying the foundation for functional differentiation among and within each unit of the animals body.

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