Sculpting tissues by phase transitions

Abstract

Biological systems display a rich phenomenology of states that resemble the physical states of matter - solid, liquid and gas. These phases result from the interactions between the microscopic constituent components - the cells - that manifest in macroscopic properties such as fluidity, rigidity and resistance to changes in shape and volume. Looked at from such a perspective, phase transitions from a rigid to a flowing state or vice versa define much of what happens in many biological processes especially during early development and diseases such as cancer. Additionally, collectively moving confluent cells can also lead to kinematic phase transitions in biological systems similar to multi-particle systems where the particles can interact and show sub-populations characterised by specific velocities. In this Perspective we discuss the similarities and limitations of the analogy between biological and inert physical systems both from theoretical perspective as well as experimental evidence in biological systems. In understanding such transitions, it is crucial to acknowledge that the macroscopic properties of biological materials and their modifications result from the complex interplay between the microscopic properties of cells including growth or death, neighbour interactions and secretion of matrix, phenomena unique to biological systems. Detecting phase transitions in vivo is technically difficult. We present emerging approaches that address this challenge and may guide our understanding of the organization and macroscopic behaviour of biological tissues.

Fig. 1. Rich phenomenology of states of matter displayed by biological materials.

Similar to physical matter, biological materials display both fluid-like and solid-like properties at the population level, resulting from the interaction of cells with their neighbors and the extracellular media. State of tissue can be gas-like (e.g., mesenchymal cells in chick embryos, adapted from ref. with permission from Nature), liquid-like (e.g., epithelial tissue during gastrulation in Drosophila, adapted from ref. with permission from Nature Cell Biology) or solid-like (e.g., bones, cartilage, tree barks).

Fig. 2. Jamming transition in biological materials.

A Physical systems under the influence of external conditions such as temperature, pressure, or density can undergo flowing to rigid phase transitions known as jamming, without the spontaneous emergence of long-range order. An analogous phase diagram in biological systems has three control parameters: active fluctuations, supracellular stress, and volume fraction (adapted from ref. with permission from Nature). B During axial elongation in zebrafish, cells leaving the mesodermal progenitor zone (MPZ, blue) to mature into presomitic mesoderm (PSM, orange) undergo a jamming transition. Within MPZ high cell–cell contact length fluctuations (high effective temperature) and more extracellular space renders the tissue fluid-like, as compared to the PSM where cell rearrangements and cell mixing is halted due to smaller extracellular spaces and low cell–cell contact fluctuations (low effective temperature). This jamming of the tissue acts as a rigid support biasing tissue expansion (elongation) toward the posterior direction (adapted from refs. ^, with permission from Nature and Nature Physics). C Progressive accumulation of F-actin and myosin II at the posterior boundary of younger somites leads to a local increase in tension fluctuations that transiently fluidizes the tissue for remodeling. Once somites are physically pinched off due to this boundary tension increase and fluidization, tissue returns to its rigid state maintaining the shape of somites (adapted from ref. ).

Fig. 3. Phase transitions resulting from changes in cellular motility.

A In chick presomitic mesoderm (PSM), mesenchymal cells display Brownian motion relative to the underlying extracellular matrix, such that the overall tissue has a fluid-like behavior. They undergo gradual “solidification” as they move from posterior to anterior under the influence of Fgf (adapted from ref. with permission from Nature). B Active cellular rearrangements, due to myosin-dependent junction remodeling, during germband elongation of the Drosophila embryo render the tissue fluid-like due to neighbor exchanges (adapted from ref. with permission from Nature Cell Biology). On the contrary, an elastic deformation keeps the same configuration between neighbors. C, D Kinetic phase transition of motile cells marks the emergence of self-ordered motion in systems of self-propelled particles. Within a collection of motile cells, each cell can change its direction of motion ($\overrightarrow{\mathit{\nu }}$), with some perturbation ($\overrightarrow{\mathit{\eta }}$ denoted by green shade) depending upon the average direction of motion in its neighborhood (denoted by blue circle). This leads to progressively increasing correlation of velocities as a function of density and noise the particles move with, resulting in a novel phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry (adapted from refs. ^, with permission from Physical Review Letters and Physical Review E).

Fig. 4. Phase transitions resulting from dynamic modulation of cellular contacts.

A, B A balance between cortical tension and strength of cell–cell adhesion in non-motile cells can lead to solid–fluid transition in a density-independent manner. The control parameter (shape index s₀) determines the probability of local cellular rearrangements. In an epithelium, the shape index corresponding to those for regular hexagons (3.72) marks the loss of stability and the rigidity transition occurs at a value of shape index that corresponds to regular pentagons (3.81, adapted from ref. with permission from Physical Review X). C Cell divisions can lead to fluidization of tissues due to the loss of cell–cell contacts during mitotic cell rounding. In early zebrafish embryos (4 h post fertilization), cells in the blastoderm center undergo mitosis showing a decrease in cell–cell contact length and increase in interstitial gaps thereby leading to a temporary decrease in tissue viscosity and fluid-like behavior. However, the cells at the margin, do not show fluidization due to noncanonical Wnt signaling that strengthens cell–cell contacts (adapted from ref. with permission from The Embo Journal). D Loss of cells in densely packed tissue (due to cell death or delamination) can lead to loss of cell–cell junctions and reduction in tissue viscosity and leading to fluid-like behavior (adapted from ref. with permission from Nature). E Pulsed contractions of cells due to actomyosin contractility (such as ones seen in early mouse embryos at the eight-cell stage) when suppressed in tissues, due to cell–cell contacts, result in forces at the long timescale and increase the overall mechanical integrity of the tissue (adapted from ref. with permission from Nature Cell Biology). F Changes in adhesion-dependent cell connectivity (such as ones in zebrafish blastoderm) around a critical value can lead to rigidity phase transition as predicted by percolation theory. The sudden disappearance of giant rigid clusters (red) below a critical value of cell connectivity can lead to an abrupt decrease in tissue viscosity making the tissue more fluid-like (adapted from ref. with permission from Cell). Dashed vertical lines (purple) in the graphs in C–F denote critical points (in relevant parameter space) where phase transitions occur.

Fig. 5. Rheological measurements (contact-based methods) to detect phase transitions in situ.

A The class of microscopic techniques aim to probe rheology at the cellular scale where the measurements typically require a mechanical apparatus or the insertion of force probes and the determination of force-deformation curves. B Mesoscopic rheological measurements aim to measure supracellular properties relying on the same principle of utilizing a force-deformation curve but induce deformation at the multicellular level.

Fig. 6. Kinematic measurements (non-contact methods) to detect phase transitions in situ.

A, B Velocity measurements can be done either based on the movement of a collection of particles (global flow patterns) by particle image velocimetry or related techniques (A) or the movement of individual particles through segmentation and tracking (B). C Higher-order measures on velocity such as spatial cross-correlation and temporal autocorrelation allow inference of relaxation times and correlation lengths for collective cell movement respectively, both of which are useful to detect phase (jamming) transitions in cell monolayers (adapted from refs. ^, with permission from the Proceedings of the National Academy of Sciences of the United States of America and Soft Matter). D Root-mean-square displacement can be inferred from individual tracks of the particles (cells) and can be used to infer caged vs uncaged dynamics. E Higher-order measures can be made on cell–cell contact length (l) in a segmented image: spatial cross-correlation of cell–cell contact lengths separated by a distance r or temporal autocorrelation of cell–cell contact length are useful to detect the amount of “jiggling” characteristic of phase (jamming) transition (adapted from ref. with permission from Nature).

Fig. 7. Changes to tissue stiffness resulting from changes in cellular composition and extracellular environments.

A, B Amount of water present in plant cells, builds up the turgor pressure (A), and drives local morphogenesis and overall integrity and rigidity of the tissue, such as the growth of the pollen tube in flowers (B, adapted from ref. with permission from the Annals of Botany). C ECM components such as fibronectin fibrils delimit tissue boundaries, such as between neural/mesoderm interface in developing Xenopus embryos (adapted from ref. with permission from Developmental Dynamics).