Morphogenetic Roles of Hydrostatic Pressure in Animal Development.

During organismal development, organs and systems are built following a genetic blueprint that produces structures capable of performing specific physiological functions. Interestingly, we have learned that the physiological activities of developing tissues also contribute to their own morphogenesis. Specifically, physiological activities such as fluid secretion and cell contractility generate hydrostatic pressure that can act as a morphogenetic force. Here, we first review the role of hydrostatic pressure in tube formation during animal development and discuss mathematical models of lumen formation. We then illustrate specific roles of the notochord as a hydrostatic scaffold in anterior-posterior axis development in chordates. Finally, we cover some examples of how fluid flows influence morphogenetic processes in other developmental contexts. Understanding how fluid forces act during development will be key for uncovering the self-organizing principles that control morphogenesis.

Notochord segmentation in zebrafish controlled by iterative mechanical signaling.

In bony fishes, patterning of the vertebral column, or spine, is guided by a metameric blueprint established in the notochord sheath. Notochord segmentation begins days after somitogenesis concludes and can occur in its absence. However, somite patterning defects lead to imprecise notochord segmentation, suggesting that these processes are linked. Here, we identify that interactions between the notochord and the axial musculature ensure precise spatiotemporal segmentation of the zebrafish spine. We demonstrate that myoseptum-notochord linkages drive notochord segment initiation by locally deforming the notochord extracellular matrix and recruiting focal adhesion machinery at these contact points. Irregular somite patterning alters this mechanical signaling, causing non-sequential and dysmorphic notochord segmentation, leading to altered spine development. Using a model that captures myoseptum-notochord interactions, we find that a fixed spatial interval is critical for driving sequential segment initiation. Thus, mechanical coupling of axial tissues facilitates spatiotemporal spine patterning.

Axial segmentation by iterative mechanical signaling.

In bony fishes, formation of the vertebral column, or spine, is guided by a metameric blueprint established in the epithelial sheath of the notochord. Generation of the notochord template begins days after somitogenesis and even occurs in the absence of somite segmentation. However, patterning defects in the somites lead to imprecise notochord segmentation, suggesting these processes are linked. Here, we reveal that spatial coordination between the notochord and the axial musculature is necessary to ensure segmentation of the zebrafish spine both in time and space. We find that the connective tissues that anchor the axial skeletal musculature, known as the myosepta in zebrafish, transmit spatial patterning cues necessary to initiate notochord segment formation, a critical pre-patterning step in spine morphogenesis. When an irregular pattern of muscle segments and myosepta interact with the notochord sheath, segments form non-sequentially, initiate at atypical locations, and eventually display altered morphology later in development. We determine that locations of myoseptum-notochord connections are hubs for mechanical signal transmission, which are characterized by localized sites of deformation of the extracellular matrix (ECM) layer encasing the notochord. The notochord sheath responds to the external mechanical changes by locally augmenting focal adhesion machinery to define the initiation site for segmentation. Using a coarse-grained mathematical model that captures the spatial patterns of myoseptum-notochord interactions, we find that a fixed-length scale of external cues is critical for driving sequential segment patterning in the notochord. Together, this work identifies a robust segmentation mechanism that hinges upon mechanical coupling of adjacent tissues to control patterning dynamics.

Universality classes of absorbing phase transitions in generic branching-annihilating particle systems with nearest-neighbor bias.

We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one-dimensional ring, where the walkers hop to their nearest neighbor with a bias ε. For ε=0, three universality classes-directed percolation (DP), parity-conserving (PC), and pair contact process with diffusion (PCPD)-are typically observed in such systems. We find that the introduction of ε does not change the DP universality class but alters the other two universality classes. For nonzero ε, the PCPD class crosses over to DP, and the PC class changes to a new universality class.

Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with generic particle nonconservation.

We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state-the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between the above phases are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

Phase coexistence and spatial correlations in reconstituting k-mer models.

In reconstituting k-mer models, extended objects that occupy several sites on a one-dimensional lattice undergo directed or undirected diffusion, and reconstitute-when in contact-by transferring a single monomer unit from one k-mer to the other; the rates depend on the size of participating k-mers. This polydispersed system has two conserved quantities, the number of k-mers and the packing fraction. We provide a matrix product method to write the steady state of this model and to calculate the spatial correlation functions analytically. We show that for a constant reconstitution rate, the spatial correlation exhibits damped oscillations in some density regions separated, from other regions with exponential decay, by a disorder surface. In a specific limit, this constant-rate reconstitution model is equivalent to a single dimer model and exhibits a phase coexistence similar to the one observed earlier in totally asymmetric simple exclusion process on a ring with a defect.