Are cell jamming and unjamming essential in tissue development?

Abstract

The last decade has seen a surge of evidence supporting the existence of the transition of the multicellular tissue from a collective material phase that is regarded as being jammed to a collective material phase that is regarded as being unjammed. The jammed phase is solid-like and effectively ‘frozen’, and therefore is associated with tissue homeostasis, rigidity, and mechanical stability. The unjammed phase, by contrast, is fluid-like and effectively ‘melted’, and therefore is associated with mechanical fluidity, plasticity and malleability that are required in dynamic multicellular processes that sculpt organ microstructure. Such multicellular sculpturing, for example, occurs during embryogenesis, growth and remodeling. Although unjamming and jamming events in the multi-cellular collective are reminiscent of those that occur in the inert granular collective, such as grain in a hopper that can flow or clog, the analogy is instructive but limited, and the implications for cell biology remain unclear. Here we ask, are the cellular jamming transition and its inverse —the unjamming transition— mere epiphenomena? That is, are they dispensable downstream events that accompany but neither cause nor quench these core multicellular processes? Drawing from selected examples in developmental biology, here we suggest the hypothesis that, to the contrary, the graded departure from a jammed phase enables controlled degrees of malleability as might be required in developmental dynamics. We further suggest that the coordinated approach to a jammed phase progressively slows those dynamics and ultimately enables long-term mechanical stability as might be required in the mature homeostatic multicellular tissue.

1. Introduction

Accumulating evidence now shows that the onset of multicellular collective motion and mechanical malleability within a tissue is often accompanied by the phenomenon termed cell unjamming (Atia et al., 2018; Garcia et al., 2015; Malinverno et al., 2017; Mongera et al., 2018; Palamidessi et al., 2019; Park et al., 2015, 2016). In a broader context, the concepts of jamming and unjamming are illustrated by familiar inert multi-component particulate systems such as sand in a pile or grain in a hopper (Aste and Di Matteo, 2008; Edwards and Oakeshott, 1989; Liu and Nagel, 1998). In some circumstances these inert systems can unjam and flow while in others they become jammed, stuck, and static. Analogous behavior has been observed in the collective migration of confluent epithelial cells in vitro (Fig. 1), which are immobile in some circumstances but can also exhibit swirling motions that arise in cooperative multi-cellular packs and clusters (Farhadifar et al., 2007; Holmes, 1914; Park et al., 2015). In these collective systems, whether inanimate or living, constituent particles can interact with nearest neighbors, and these mechanical interactions can ramify through the system. The collective as a whole can then exhibit a transition from a fluid-like and malleable unjammed phase —one that is suitable for sculpting of tissue microstructure, as in branching morphogenesis for example— to a solid-like and frozen jammed phase that is suitable for maintaining that microstructure.

Fig. 1.

Primary human bronchial epithelial cells in air-liquid interface culture showing maximum intensity of immuno-fluorescent projections of the tight junction protein ZO-1. Left: The jammed epithelial cell layer is non-migratory and shows variable cobblestone cell shapes characteristic of mature epithelial layers (Gibson et al., 2006). Right: The unjammed layer is migratory, with cell shapes that become systematically more elongated, more variable, and spatially more correlated (Atia et al., 2018; Mitchel et al., 2020; Park et al., 2015). Images courtesy of Jennifer Mitchel.

Cell jamming and unjamming have been implicated in wound healing and cancer cell migration and invasion (Ilina et al., 2020; Kim et al., 2020) but here we focus on the role of jamming and unjamming in development (Atia et al., 2018; Goodwin and Nelson, 2020; Mongera et al., 2018; Spurlin et al., 2019). The first suggestion of the existence cellular jamming and unjamming in any biological system came from traction force data measured in the advancing confluent epithelial monolayer (Trepat et al., 2009), and the presence of jamming in collective cellular systems was rigorously confirmed some time later (Park et al., 2015). Table 1 highlights some of the notable advances in understanding of the role of cell jamming and fluidization in development. In gastrulation of the developing fruit fly embryo, for example, ventral furrow formation is marked by a statistical distribution of cell shapes that is a signature of unjamming of the multicellular collective (Atia et al., 2018; Bi et al., 2014, 2015; Park et al., 2015; Schotz et al., 2013). In the developing chicken embryo, dynamics of injected beads show a solid-like to fluid-like unjamming transition in lung mesenchymal tissues, thus enabling epithelial growth and airway branching (Spurlin et al., 2019). In body axis elongation of the developing zebrafish embryo, clever microinjection of deformable ferro-fluid droplets has established evidence of a jamming-induced gradient in yield stress that provides spatially graded mechanical malleability to the presomitic mesoderm (Mongera et al., 2018). In the developing zebrafish blastoderm, a small but critical change in adhesion-dependent cell connectivity causes tissue viscosity to change by more than an order of magnitude (Petridou et al., 2021).

Table 1.

Milestones: fluidization and unjamming transitions in development.

Year	Ref.	Animal model	Key point
2010	(Bénazéraf et al., 2010)	Chicken	Raised the hypothesis that anteroposterior (AP) body axis elongation is an emergent tissue property that arises due to collective cell motion in the presomitic mesoderm (PSM).
2013	(Lawton et al., 2013)	Zebrafish	Identified transitions in tissue fluidity during tailbud elongation. Suggested that hindered collective cellular motion may cause a ‘traffic jam’ in the posterior tailbud and lead to a contorted trunk.
2014	(David et al., 2014)	Xenopus	In a variety of different regions in the gastrula, cell-cell adhesion and tissue viscosity are positively proportional and, together, limit the rate of multicellular rearrangements and motion.
2018	(Barriga et al., 2018)	Xenopus	Underlying the cephalic neural crest, the head mesoderm goes through a tissue level stiffening transition which promotes EMT-mediated collective migration of crest cells.
	(Atia et al., 2018)	Drosophila	Unjamming transition imposes a specific statistical distribution that governs cell shape in both inert systems, and during collective cellular migration in the formation of the ventral furrow.
	(Mongera et al., 2018)	Zebrafish	Rapid fluctuation of cells in the mesodermal progenitor zone (MPZ), coupled with a cell-cell adhesion gradient, promotes an unjamming transition which decreases a tissue-level yield stress and underlies body axis elongation.
2019	(Petridou et al., 2019)	Zebrafish	A drop in the tissue-level viscosity in the blastoderm suggests that a fluidization process permits the spreading of the epithelial enveloping layer (i.e. doming) and the initiation of cellular intercalations.
	(Iyer et al., 2019)	Drosophila	Increased E-cadherin turnover, in response to mechanical stress in the wing epithelium, induces cell rearrangements and promotes a viscous behavior.
	(Spurlin et al., 2019)	Chicken	Adjacent to the tip of the branching epithelium in the avian lung is an unjammed mesenchymal tissue, through which the branch tip can expand and eventually bifurcate.
2020	(Saadaoui et al., 2020)	Quail	Due to cell division events, the embryonic epithelium transition s to a fluid-like state thus enabling large-scale tensile forces to induce multicellular flows governing the formation of the primitive streak.
	(Wang et al., 2020)	Drosophila	Cell shape, together with the degree of alignment between cells, predict the onset of cell rearrangements in the converging and extending germband epithelium.
	(Jain et al., 2020)	Tribolium	During epiboly, tensile forces from actomyosin cable contribute to the fluidization of the leading edge in the spreading epithelium.
2021	(Petridou et al., 2021)	Zebrafish	Random division events in the blastoderm lead to a small but critical change in cell-cell connectivity, which in turn causes tissue-level rigidity to transition abruptly.
	(Kim et al., 2021)	Zebrafish	Aided by a generalized vertex model that accounts for both confluent and sub-confluent regimes, it is shown that cell-cell contact length fluctuations actively drive tissue fluidization.

Here, we use these and other examples drawn from developmental biology to identify gaps of knowledge relevant for understanding the question of the fundamental contribution, if any, of cell jamming and unjamming to core biological processes that are essential for development of multicellular life. We conclude with open questions concerning energy metabolism and associated evolutionary pressures that might have given rise to cellular jamming and unjamming. Here we offer no good answers to these questions. Instead, we argue for their importance.

2. What is cell jamming? Why do cells jam and unjam?

The answers to these particular questions are simple in outline but complicated in scientific details. Using nomenclature given in the glossary, we start with the simple outline.

2.1. Crowding in particulate versus confluent systems

The behavior of cells migrating within a disordered (amorphous) multicellular tissue is in many ways analogous to the behavior of familiar disordered particulate systems such as coffee beans flowing in a chute at the market, sand grains poured onto the apex of a sand pile, passengers disembarking from a crowded trolley car, or automobiles travelling in traffic. In such particulate systems, when the number density of respective particles is sufficiently small the particle motions are unconstrained by mechanical interactions with immediate neighbors. In the presence of a driving force, such as gravitational or autonomous propulsive forces for example, the collective in each instance can therefore flow like a fluid. But as system density is progressively increased particle-particle interactions grow in number and progressively constrain the range of possible motions (Liu and Nagel, 1998). Each additional particle-particle contact removes one or more degrees of freedom from the system (Lawson-Keister and Manning, 2021). As a result, overall system dynamics progressively slow, where this slowing as particle density increases is a hallmark of the jamming transition.

The topology of cells in a confluent layer is in many ways different, yet a similar slowing of dynamics in cellular systems occurs nonetheless. Chief among these differences is that the confluent tissue by definition has no available free space, and in that sense is already maximally crowded and particle-particle contacts (i.e., cell-cell contacts) are already maximized. Whereas a particulate material under this circumstance of no available free space would necessarily be jammed, a confluent cellular system —depending upon the factors described below— could be either jammed or unjammed (Fig. 2). Because cells are both deformable and propulsive, the cellular collective —even when fully confluent— can retain sufficient internal degrees of freedom for cells to flow collectively and for microstructures to dynamically rearrange locally (Bi et al., 2015, 2016).

Fig. 2.

Different types of percolation transitions can occur in model cellular networks. In a confluent cell layer with heterogeneous cell stiffness, it is possible to observe networks of rigid cells (top row, rigid cells in red) and networks of cells exerting forces on their neighbors (bottom row, boundaries under tension in bold). The fraction of rigid cells at which contact percolation occurs versus the fraction at which system-spanning networks of tension emerge are different, with contact percolation (top right) occurring at a much higher fraction of rigid cells than tension percolation (bottom middle). Adapted from Li et al. (2019).

2.2. Short-range particle caging begets long-range force transmission

The slowing of dynamics in a granular system approaching jamming is a system-scale view. But it is also useful to consider dynamics at the micro-scale. As the degrees of freedom in a system become progressively fewer, each particle (or cell) can then become constrained in a small region of space, trapped by its neighbors, caged with no possibility of escape. This trapping occurs when the exchange of positions between neighboring particles (cells) is impeded by an energy barrier. When the self-propulsive force generated by a cell is too weak to overcome such an energy barrier, for example, the cell becomes effectively trapped.

Trapping of this kind ramifies. The motions of one particle become blocked by its neighbors, which in turn are blocked by their neighbors, and so on. Mechanical forces then become transmitted in chains which ramify from particle-to-particle through the system, sometimes to great distances. In doing so immobile clusters grow and —above some critical condition— such clusters become large enough to span the entire system. As such, internal degrees of freedom vanish and, as a result, particles can no longer flow collectively or rearrange their positions mutually, and a finite fraction of the system becomes frozen and rigid in a process known as rigidity percolation (Fig. 2) (Cates et al., 1998; Keys et al., 2007; O’Hern et al., 2001; Petridou et al., 2021).

As such, rigidity percolation versus jamming are understood to be opposite sides of the same coin (Ghosh et al., 2014; Li et al., 2019; Trappe et al., 2001). In the disordered particulate system, jamming invariably entails rigidity percolation. And rigidity percolation, in turn, is an indispensable hallmark of jamming. In the living multicellular system, remarkably, rigidity percolation in the developing zebrafish blastoderm (Petridou et al., 2021) is closely similar to that observed in suspensions of weakly attractive inert colloidal particles (Trappe et al., 2001). In the living zebrafish blastoderm and the inanimate attractive colloid alike, as packing fraction approaches a critical value, particle-particle connectivity on the microscale changes smoothly but overall system rigidity on the macroscale diverges so sharply as to be approximated sometimes as being virtually a discontinuous transition (Fig. 3). Indeed, a wide variety of collective systems —including granular, colloidal, molecular, and cellular— are now known to exhibit transitions between fluid-like versus solid-like phases attributable solely to rigidity percolation and associated kinetic arrest of jammed particles. The key idea is that jamming, once it occurs, precludes the collective system from further exploration of its local configuration space.

Fig. 3.

As the number of cell-cell-contacts on the microscale varies smoothly tissue viscosity on the macroscale changes rather sharply. In subconfluent systems, the critical number of contacts sets the criterion for rigidity percolation and the jamming/unjamming transition. Adapted from Petridou and Heisenberg (2019).

In connection with rigidity percolation, cell populations during embryogenesis are often heterogeneous, in which case both cell sorting and cell mixing processes come into play. But how cell sorting and mixing are impacted not only by the classical notion of differential adhesion, but also by cell jamming/unjamming and associated rigidity percolation, remains unclear (Amack and Manning, 2012; Bazellières et al., 2017; Brodland, 2002; Foty and Steinberg, 2005; Heine et al., 2021; Pawlizak et al., 2015).

2.3. Thermal agitation? Or athermal agitation

Despite the force of gravity, beans in the chute can clog. Grains in the sand pile can organize into a stable non-zero slope —the so-called angle of repose. Passengers in the trolley car can become trapped, and traffic flow on the highway can come to a standstill. But if one tilts the sand pile sufficiently, bangs on the chute hard enough, or pushes forcefully toward the trolley exit, collective flow can become reinitiated (Liu and Nagel, 1998). With automobiles in traffic being the exception, the systems described above have in common that a sufficiently large perturbing stress —exceeding the yield stress— can restore flow. Similarly, cellular propulsive forces can overcome local yield stresses to unjam a cellular collective (Bi et al., 2016).

These are all examples wherein energy barriers far exceed available thermal energy, k_BT, where k_B is the Boltzmann constant and T is thermodynamic temperature. When thermal energy is insufficient to overcome energy barriers, such systems are often referred to as being “athermal”. Just as each grain of sand in a sand pile is much too large to be moved by k_BT, and hence is athermal, so too each cell within a confluent tissue. Nevertheless, it can be fruitful in some cases to imagine larger non-thermal mechanisms of local agitation —whether through the stochastic action of molecular motors, propulsive forces, or other factors— as acting as an “effective temperature” (Bi et al., 2016; Fabry et al., 2001; Hakim and Silberzan, 2017). Sufficiently large random agitation can locally unjam the cellular system, and thus allow cells to overcome energy barriers and thereby exchange neighbors. The distinction between thermal versus athermal systems brings us to the issue of the glass transition.

2.4. Jamming transition? Or glass transition?

The concepts of degrees of freedom, crowding, percolation, and agitation complete the simple outline. But a word of clarification is in order concerning what is to the physicist, if not the biologist, a nontrivial aspect of nomenclature. Material transitions of multicellular systems have come to be called jamming and unjamming transitions even when this terminology, formally speaking, is imprecise. When the competition between energy barriers on the one hand and agitation energy on the other sets the transition from fluid-like to solid-like behavior, such a transition is more properly called a ‘glass transition’ (Angelini et al., 2011; Angell, 1995; Berthier et al., 2019; Fabry et al., 2001). Generally speaking, the agitation can be external and non-thermal, such as in the case of pounding on a chute, or internal and thermal as in the glass transition of biopolymers (Angell, 1995). As noted above, still another instance of non-thermal internal agitation is the propulsive cellular force generated by precession of molecular motors (Angelini et al., 2011; Guo et al., 2014; Kim et al., 2013, 2020). By contrast with the glass transition, the jamming transition in the strict sense of the term does not depend upon agitation, whether thermal or otherwise. Rather, the jamming transition depends solely upon geometrical factors, and formally thus represents a zero-activity (i.e., zero agitation) limit (Atkinson et al., 2014; Berthier et al., 2019; Parisi and Zamponi, 2010). But because the word ‘jamming’ is more easily grasped, it has come into common usage notwithstanding that agitation of one form or another, and at one level or another, in cell biology is virtually ever-present (Berthier et al., 2019; Guo et al., 2014; Tjhung and Berthier, 2020).

2.5. Rigidity changes: discrete or continuous? Rapid or slow?

As a fluid-like collective system approaches a solid-like glassy phase its internal microstructure fails to crystalize. Instead, microstructure remains all the time amorphous as dynamics progressively slow. Mechanical properties change smoothly and continuously, not discontinuously as in crystallization. For example, transitions between fluid-like and solid-like phases are sometimes determined by the competition between agitation versus the strength of binding interactions between neighboring particles. Similarly, the fine balance between solid-like versus fluid-like behavior was recently used to describe flowing tissues during development (Betz, 2021; Stooke-Vaughan and Campàs, 2018). In general, the transition from fluid-like to solid-like behavior of a glassy material is defined by a dramatic but smooth increase in the relaxation time of stresses and marked slowdown of local particle rearrangements (Angell, 1995; Berthier and Biroli, 2011). But because glasses exhibit no discrete transition, a glassy system can be said to be more solid-like or fluid-like but not definitively a solid or a fluid. In the context of biological tissues, similar to non-biological glassy systems, the time-scale of the dynamics of rearrangements determine how we characterize the “phase” of matter, as either unjammed and fluid-like or jammed and solid-like.

2.6. Active versus passive glasses

In multi-cellular tissues the rearrangements among neighboring cells are typically disordered. These rearrangements tend to occur when mechanical forces associated with cell motility or other active ATP-dependent processes allow cells to break adhesion bonds with neighbors and form new bonds with new neighbors. Acting as an “effective temperature,” these active forces agitate the tissue and tend to promote system fluidity (Hakim and Silberzan, 2017), but are impeded not only by cell stiffness but also by the adhesion energy and friction conferred by cell-cell and cell-substrate adhesive bonds, which tend to slow the dynamics and thus promote solidity (Garcia et al., 2015). For these reasons, dynamics involving active forces have been recently investigated as models for “active-glasses” (Janssen, 2019; Nandi et al., 2018).

In addition to the effects of propulsive forces associated with cell motility, other active processes that can agitate and therefore fluidize the cellular collective include pulsatile contractions, cell division and apoptosis (Farhadifar et al., 2007; Krajnc et al., 2018; Martin et al., 2009; Ranft et al., 2010; Rossen et al., 2014).

2.7. Parsing the complexities

Relevant factors controlling jamming behavior are diverse. In addition to percolation and agitation, as described above, other factors include cytoskeletal deformability, cortical tension, cell-cell adhesion, friction, confinement, proliferation, apoptosis, system dimensionality (2D vs 3D), surface curvature, and the magnitude, persistence and cooperativity of autonomous cellular propulsive forces (Farhadifar et al., 2007; Ilina et al., 2020; Petridou et al., 2021). Important as well are imposed tissue stretch, as occurs during breathing (Park et al., 2015; Trepat et al., 2007), and, potentially, the innate pulsed contractions of a supracellular actin-myosin network that accompany apical constriction of the Drosophila embryo during morphogenesis (Martin et al., 2009). As such, there are multiple distinct mechanisms that can impact fluidization or solidification of the cellular collective. Because the terms jamming and unjamming have been invoked to describe all of them, it often remains unclear which particular mechanisms might dominate the jamming phenomenon in any given situation (Lawson-Keister and Manning, 2021). To capture these complexities, several proposals have been advanced to describe a phase diagram for cell jamming (Chiang and Marenduzzo, 2016; Ilina et al., 2020; Lawson-Keister and Manning, 2021; Sadati et al., 2013).

In the face of this remarkable diversity, theoretical physicists have developed tools for thought that reveal an equally remarkable understanding of these factors, oftentimes under one unifying umbrella. Computational models have shown than many of the factors described above may enter the problem in remarkably simplifying combinations. For example, vertex-type models which operate at constant cell density show that cell deformability, cell cortical tension and, cell-cell adhesion combine to determine a master parameter —the so-called preferred cell perimeter or, equivalently, a target shape index (Bi et al., 2014, 2015, 2016; Giavazzi et al., 2018; Park et al., 2015). Whether in the 2D or the 3D collective, it is a fixed critical value of this shape index that determines whether the collective is solid-like and jammed or fluid-like and unjammed (Bi et al., 2016; Park et al., 2015; Schotz et al., 2013). Although the story continues to evolve, an extension of similar models that include the effects of agitation attributable to cellular propulsive forces have combined unified many of those factors listed above into one unified jamming phase diagram (Fig. 4) (Bi et al., 2016).

Fig. 4.

Jamming is about more than cellular packing: in non-confluent tissues, as in the systems described by Petridou et al. (2021) or Mongera et al. (2018), jamming is driven in large part by increases in the fraction of space that is packed by cells (Fig. 3). In confluent tissues, by contrast, the packing density of space by cells is complete and the packing fraction is therefore fixed at unity. Nevertheless, in such systems there exist multiple density-independent alternative pathways to jamming and unjamming. For example, the so-called self-propelled Voronoi model of confluent tissues show that unjamming and fluidization increase with increasing magnitude of fluctuating propulsive forces, increasing persistence of those propulsive force, and increasing cell-cell-adhesion. Adapted from Bi et al. (2016).

3. Jamming and unjamming in cell biology

3.1. Jamming and regulation of stem cell fate

The role of jamming or unjamming in stem cell fate selection is unknown, but recent findings are suggestive. For example, the regulation of pluripotent stem cell fate is now known to involve development ERK-mediated changes in membrane tension, adhesion, and cell shape which, taken together, are reminiscent of the very same key controlling factors for jamming/unjamming processes (De Belly et al., 2020). Indeed, as covered below, changes in cell tension associated with jamming can directly influence differentiation in the epidermis and the developing trabecula, which indicates that cell jamming processes can direct cell fate (Miroshnikova et al., 2018; Priya et al., 2020). Changes of cell shapes during the onset of homeostasis in the epithelium of the mouse esophagus are similarly suggestive; these events are guided by the progressive build-up of mechanical strain accompanied emergence of a basal KLF4Bright committed population in a YAP dependent manner (McGinn et al., 2021). Another possibility is the connection between cell jamming and cell volume. Increasing cell density, and hence cell jamming, has been associated with changes in cell volume which has itself been associated with changes in stem cell fate (Guo et al., 2017). Additionally, volumetric compression in intestinal crypts induces intracellular crowding to control intestinal organoid growth via Wnt/b-Catenin signaling (Li et al., 2021). Whether the connection between individual cell compression and collective cell jamming is correlative or circumstantial remains to be definitely addressed.

3.2. Unjamming transition (UJT)? Or Epithelial-to-Mesenchymal Transition (EMT)?

The EMT program is the classical explanation of how the epithelial cell acquires a migratory phenotype (Yang et al., 2020). In the airway epithelium of the lung, the EMT and the UJT programs are now known to be distinct phenomena (Mitchel et al., 2020) although other epithelial systems have yet to be investigated in this regard, in which cases this distinction may not be so clear cut. More generally, the extent to which the EMT and the UJT might work independently, sequentially, or cooperatively to effect morphogenesis, growth, and tissue remodeling remains unclear. It remains unclear as well if unjamming in different contexts is driven by a conserved set of inducing signals, transcriptional regulators and downstream effectors (De Marzio et al., 2020; Kilic et al., 2020; Malinverno et al., 2017; Palamidessi et al., 2019). In the airway epithelium exposed to mechanical compression mimicking bronchospasm, the resulting UJT is mediated by a cascade of processes that promotes actin polymerization through the recruitment of integrin-ECM adhesive complexes and promotes increased cellular motility through activation of AP-1 transcription factors via ERK and JNK pathways (De Marzio et al., 2020; Kilic et al., 2020). These findings, taken together, show that the unjamming program is not the result of any single signaling pathway but rather comprises a coordinated interplay of downstream pathways that are present in development, fate selection, energy metabolism, cytoskeletal reorganization, and adhesive interaction with extracellular matrix.

It is now known that the UJT can exist in the absence of EMT. As such, cells retaining a purely epithelial phenotype can unjam and migrate vigorously on a collective basis and with no compromise of barrier function (Mitchel et al., 2020). The converse proposition —that EMT can exist independent of UJT— remains unclear (Mitchel et al., 2020). If some small subset of cells in an epithelial layer undergoes a partial EMT, each such cell will then be able to generate propulsive forces allowing it to migrate within the layer or even extrude from it.

It was shown in vitro that mixing an increasing fraction of mesenchymal cells with epithelial cells results in increasing collective motility (Gamboa Castro et al., 2016). Yet it is unknown if such cells spontaneously arising in a jammed layer —mesenchymal agitators as it were— can perturb the remaining epithelial cells causing the layer to unjam and the cellular collective to migrate. Interestingly, hallmarks of both cell jamming and unjamming have been reported in mesenchyme of the branching chick airway during development, as described below (Spurlin et al., 2019).

3.3. Is cell unjamming required for branching morphogenesis?

A central architectural process during development of the kidney, mammary gland, or lung, is branching morphogenesis (Goodwin and Nelson, 2020). In lung development, for example, left and right lung buds branch out to form epithelial tubes within the surrounding pulmonary mesenchyme. At later stages, mesenchymal cells differentiate into smooth muscle cells (SMCs) which then wrap helically around the basement membrane of the epithelial tube. A recent study in the developing avian lung reveals well-coordinated molecular and mechanical interactions between epithelial and mesenchymal cells (Spurlin et al., 2019). Dynamics of fluorescent microbeads injected into the mesenchyme, together with projected cell shape quantification, reveal two distinct mesenchymal phenotypes. Adjacent to the non-branching epithelium, microbeads display diffusive uncorrelated random motion together with rounded cell shapes (Fig. 5). These observations suggest a jammed solid-like state of cells within the mesenchyme. In contrast, microbeads adjacent to the tip of the branching epithelium display super-diffusive and persistent correlated motion, together with elongated cell shapes characteristic of an unjammed fluid-like state. The authors suggest that this fluidization is necessary for convection of tenascin C (TNC) through the mesenchyme that surrounds the tip of the epithelial branch; TNC is a high molecular weight protein that facilitates epithelial-mesenchymal interactions during morphogenesis, and is exclusively expressed by epithelial tissue (Midwood and Schwarzbauer, 2002). These data suggest a physical picture in which TNC is convected by the fluid-like mesenchyme and accumulates multiple cell diameters away. In doing so, a distending airway pressure at the branch tip acts to expand and sculpt the unjammed mesenchyme along with the passive epithelium, while a constraining belt of smooth muscle causes the branch tip to bifurcate. Branch extension coincides with deformation of adjacent mesenchymal cells, which elongate and increase local tissue fluidity. Cells with higher aspect ratios, suggesting a greater degree of unjamming, are found in mesenchyme adjacent to the leading edge of the branch (Fig. 5D).

Fig. 5.

Airway branching in the embryonic avian lung. (A) In the lung, buds branch out to form epithelial tubes within the surrounding pulmonary mesenchyme (A, left). Micrographs showing non-branching and branching regions were analyzed (A, right), and the projected shapes of cells at these different regions were quantified by the ratio between the perimeter of a cell and the square root of its area, a parameter also known as the shape index. (B) The distribution of cell shapes demonstrates striking differences that are indicative of jamming in non-branching regions (i.e. low shape index) and unjamming in branching regions (i.e. high shape index) (Atia et al., 2018; Bi et al., 2014, 2015; Park et al., 2015; Schotz et al., 2013). Adapted from Spurlin et al. (2019).

This newly discovered epithelial-mesenchymal interaction during avian airway branching gives rise to three fundamental questions. First, is there an underlying positive feedback in which TNC is secreted by the epithelium to directly unjam and fluidize the adjacent mesenchyme, which further transports TNC so as to unjam a more distant and solid-like mesenchymal region? Second, could it be that branch extension, in which the epithelial basement membrane needs to push against the mesenchyme tissue, is facilitated and made possible because of reduced supracellular stiffness of the mesenchyme caused by unjamming? Third, after the epithelial tube is formed, does the collectively jammed and motionless phase of adjacent mesenchymal cells comprise a mechano-molecular signal that triggers their differentiation into SMCs? The answer to these questions will certainly go beyond avian lung development and may lead to generic biological rules for tissue growth, and perhaps even tumor formation.

3.4. More on tissue fluidization in development

While it is clear by now that there exist several routes to a fluid-like to solid-like transition in multicellular tissues, it is not always clear which factor is dominant. In the formation of the anteroposterior body axis during zebra fish embryo morphogenesis, for example (Fig. 6), direct measurements of local cellular stresses and local yield-stresses reveal that the elongating tip of the posterior tissue (i.e., the mesodermal progenitor zone) is unjammed and fluid-like while the tissue that is left behind the tip (presomitic mesoderm) is jammed and solid-like (Mongera et al., 2018). Mongera et al. do not report a gradient in cadherin expression, but do show an N-cadherin-dependent anteroposterior gradient in yield stress. In the tip region (where the yield stress is low) the inhibition of N-cadherins does not change the rate of cellular rearrangements, while in the presomitic mesoderm the loss of these cell-cell adhesions leads to an increase in extracellular space. They conclude that cell-cell adhesions gives rise to an anteroposterior gradient in extracellular spaces and tissue mechanical integrity. The fluid-like nature of the tip region seems to be enabled by a local decrease in the expression of the cadherin-family proteins at the cell-cell junctions. This lower concentration of cell-cell binding molecules gives rise to lower energy barriers and smaller friction for cellular rearrangements, which result in frequent cellular exchanges driven by the agitation of active cellular forces (Garcia et al., 2015; Kim et al., 2021). These forces can be in the form of traction forces, where cells glide on each other, and by cells exerting contractile pulling forces. The active forces produced by the cells do not seem to vary significantly from the back to the tip along the body axis, and thus the reduced barriers in tip result in increased agitation which fluidizes the tail bud.

Fig. 6.

Sagittal and frontal sketches (a) and A-P cross-sectional images (b) of vertebrate body axis elongation in the zebrafish embryo. Computational model shows cells entering the mesodermal progenitor zone (MPZ) alongside fluid-like unjammed and solid-like unjammed regions (c). Unidirectional body axis elongation arises in the presence of a fluid-to-solid jamming transition (d) but not in its absence (e). Inset shows the cellular velocity field. Adapted from Mongera et al. (2018).

Indeed, a continuum mathematical description of this system was recently developed in terms of a viscosity gradient across the fluid-solid transition (Banavar et al., 2021). Furthermore, low cell-cell binding at the tip lowers the local effective surface tension, and thus facilitates local inflation of the tip into a spherical shape, as well as error tolerant unidirectional growth. By “surface-tension” we refer to the effective tension within the outer layer of cells, at the surface of the tissue. This tension is driven by the contractility of cells, that is related to the strength of the cell-cell junctions that transmit the individual cellular contractility across the whole surface of the tissue. The transition to a solid-like phase behind the fluid tip, as cadherin-based cell-cell junctions grow and mature, provides stabilization of the tissue into its elongated body-axis shape (Fig. 6d).

3.5. Jamming in tissue homeostasis

Even after an inanimate passive system has transitioned from a liquid-like to a solid-like phase, density driven changes still matter (Mattsson et al., 2009). Do similar considerations apply in multicellular tissue? For example, in a jammed tissue where motility is low and cell density is high, how do changes in cell density due to division, apoptosis, or extrusion affect overall system behavior? And do these jamming-related changes play an important role in tissue development?

In homeostatic conditions of an epithelial layer, cell proliferation and cell death are in balance. It is also possible, however, for cell crowding —due to either division or migration— to trigger cell extrusion from the layer (Eisenhoffer et al., 2012). In the mature epithelium at least, this process is mediated by stretch activated ion channels; by interfering with the function of these channels, extrusion can be abrogated, suggesting a central role for changes in cell tension. A similar response is observed in the refinement of the Drosophila fly notum (Marinari et al., 2012), wherein tissue remains relatively constant in size yet cell division and delamination events persist and facilitate topological rearrangements. Under these conditions, delamination is a stochastic process that is not controlled by cell lineage, position, or developmental time. Instead, it appears that forces mediated by cell crowding set the delamination locus. As cells undergo stochastic fluctuations, the competition for area results in some cells losing cell-cell junctions and being extruded from the layer. Interestingly, the delamination process is significantly promoted in regions where cell anisotropy is high; higher cell anisotropy is associated with unjamming and hence we would expect larger and more frequent fluctuations in cell motion (Atia et al., 2018; Ranft et al., 2010; Su and Lan, 2016).

Beyond simply maintaining cell number and facilitating rearrangements, cell extrusion can facilitate tissue development. In the developing embryonic mouse epidermis, the basal layer appears jammed with little to no motion (Miroshnikova et al., 2018). Extrusion from the layer appears to correlate with areas of high cell crowding and differential cellular contractility. To confirm this behavior, in vitro experiments were used to measure local cellular forces in a jammed epidermal progenitor cell monolayer. Under these conditions, cell division changes the local force balance in three ways: cell-cell junctions are weakened during the mitotic process, cell tension drops, and the surrounding tissue is compressed. These combined processes cause the cells to assume an asymmetric shape and appear to locally unjam in a manner consistent with previous findings (Connelly et al., 2010; Kilian et al., 2010; Watt et al., 1988). Asymmetry in contractile stress can promote differentiation in this system. As one cell differentiates, it is extruded from the monolayer, which returns to its jammed state. Interestingly, as the differentiated cell delaminates, it significantly increases its applied tension to the now underlying cells. Given that low tension appears to promote delamination, an interesting question is what regulatory mechanism prevents excessive delamination.

Crowding-induced differentiation and delamination also control trabeculation of the developing heart in zebrafish (Priya et al., 2020). Using imaging of markers for actomyosin activity and laser ablation experiments to measure local heterogeneity of cellular tensions, it was found that at the onset of trabeculation cells at higher tension delaminate and seed the trabecular layer. Interestingly, differential tension rather than net tension appeared to drive delamination. Surprisingly, contractility induced delamination was sufficient to induce differential Notch signaling and hence trigger Notch-mediated fate specification even when Nrg2a-Erbb2 signaling was blocked, contrary to previous findings (Han et al., 2016; Jiménez-Amilburu et al., 2016). As cells delaminate and differentiate, they activate Notch signaling in adjacent cells which reduces actomyosin activity and hence tension, preventing further delamination.

It is interesting to contrast the differentiation and delamination process in an epithelial layer with the process of trabeculation. In both cases, changes in contractility are critical to initiate differentiation and delamination. Furthermore, after delamination, the newly extruded cell engages in processes which should inhibit further cell loss, but the mechanical trigger is different. In the epithelial layer, it is cells at low contractility which are more likely to delaminate whereas during trabeculation it is higher tension cells that delaminate. In epithelial layer formation, division drives changes in contractility but during trabeculation it is not immediately apparent what is the driver of tension heterogeneity. While proliferation-induced changes in cell forces are possible, an alternative explanation exists. Increasing tension heterogeneity was found to correlate with cell crowding; increasing tension heterogeneity is also a hallmark of the jamming transition in cells. Previous work has demonstrated that as cells jam the fields of velocity and intercellular stress within the monolayer become much more heterogeneous (Park et al., 2015). These dynamic heterogeneities vary in time and space across the monolayer as it ages. Could these dynamic heterogeneities play a role in directing cell fate during trabeculation or in other developmental tissues? Methods for directly visualizing cell stress are becoming available and will be able to directly answer such questions.

4. Jamming and unjamming: epiphenomena? Or essential?

In biological systems, it is critical to control system behavior over wide scales of length and time. Numerous processes exist which can participate in this regulation, be they genetic networks, biochemical networks, or mechanical networks. While potentially robust, such active interventions require energy expenditures and ongoing feedback. By contrast, jamming is a self-organized process which occurs even in simple inert systems. In inert and living materials alike, a small change in a relevant control parameter, such as volume fraction, can lead to dramatic tuning of material properties without concomitant large-scale structural reorganizations (Fig. 3). Cells comprising a multicellular tissue are subject to similar physical constraints but are also active and responsive. As such, determining the appropriate control parameter for jamming of the multicellular collective can be challenging. Nonetheless, it is clear that jamming plays a role in setting cell behavior and tissue micro-mechanics. In a range of developmental systems, we have seen that crowding and associated changes in cell jamming can induce delamination and in some cases differentiation. Since the governing processes are the same across the tissue, cells respond to local cues while remaining coordinated with distant partners. Interestingly, a similar innate coordination exists when cells are removed from the layer; the balance of forces reorients dividing cells to reduce the tension created by cell loss and maintain layer integrity (Campinho et al., 2013; Miroshnikova et al., 2018). Thus, it might be that the jammed cell layer in a developing tissue coordinates its response globally, at least in part, simply by relying on local environmental cues and working to reduce layer tension, either by extruding cells due to overcrowding or orienting dividing cells to best fill gaps in the layer.

Cell jamming also enables coordination of cells on the tissue length scale. During doming in the zebrafish blastoderm, differential adhesion allows the tissue to transiently become mechanically heterogeneous and allow for the necessary large-scale motions (Petridou et al., 2021). A final example of where jamming and disordered motion offers significant advantages is in the development of the presomitic mesoderm (Mongera et al., 2018). Cells entering from the dorsal medial zone are relatively ordered; however, cell motions become disordered in the progenitor zone (Das et al., 2017). If the ordered state is maintained, elongation is more rapid but is prone to amplifying small errors which would lead to asymmetry in body development. Instead, by operating near the jamming threshold but in a disordered fluid-like state, migration speed can be maximized at the trailing edge while maintaining a high degree of error tolerance at the leading edge.

An overriding fact is that the systems examined here all exist in close proximity to the jamming transition. Because the jamming transition allows for large mechanical changes with relatively small changes in state variables, as illustrated in Fig. 3, it gives cells remarkable mechanical control of responsiveness to the micro-environment (Fredberg, 2014). But operating near a jamming transition may also entail risks. For example, continued differentiation and delamination in a mature tissue due to fluctuations in cellular tension are undesirable and could compromise tissue function. There is evidence, however, that this risk too can be mitigated. In the developing mouse esophagus, the esophagus initially grows at the same rate as the surrounding tissue (McGinn et al., 2021). As esophageal growth slows, however, the surrounding tissue continues to grow more rapidly. Because the esophagus is anchored to those surrounding issues, this induces a permanent strain on esophageal tissues which helps to maintain progenitor cells in their committed state.

Of course energy metabolism is central, but data relating energy metabolism to jamming and unjamming remain sparse. Wound healing studies in the confluent monolayer of MDCKII cells show that as the leading edge becomes more migratory, fluid-like, and unjammed, the cytoplasmic redox ratio becomes progressively smaller, the NADH life-time becomes progressively shorter, and the mitochondrial membrane potential and glucose uptake become progressively larger (DeCamp et al., 2020). In that system, unjamming entails a shift of energy metabolism toward glycolysis, which is faster than oxidative phosphorylation but less efficient in terms of numbers of ATPs per glucose molecule. The switch toward glycolysis in unjamming is reminiscent of the Warburg effect in cancer cells.

4.1. Concluding speculations

Are cell jamming and unjamming essential for multicellular development, or perhaps even multicellular life? The answer to this question remains unclear. Nevertheless, selected examples addressed above suggest that the jammed phase of the multicellular tissue is consistent with a selective evolutionary pressure favoring an energetically economical and mechanically metastable basal rest state. The unjammed phase, by contrast, is consistent with an essential but energetically costly adaptation of the multicellular tissue to perturbations requiring responses that include collective cellular migration, fluidization, or remodeling. Given that jamming and unjamming are primitive physical processes of which even inert particulate systems are capable, it is plausible to wonder, further, whether evolutionary pressures attributable to jamming and unjamming might have been at work even in the most primitive early multicellular organisms. Taken together, this line of reasoning leads to the novel suggestion that jamming and unjamming transitions may be requisite events for economical tissue maintenance punctuated by energetically costly but error-tolerant episodes of embryonic development, organ growth, or tissue remodeling.

Glossary

Adhesion protein

Each cell produces specialized proteins, such as cadherins, syndecans, and integrins, that reside in the cell membrane and allow the cell to bind and thereby adhere to external substrates or neighboring cells, and thus form multi-cellular clusters and tissues. When this binding is transient and cells are moving relative to matrix or to each other, adhesion gives rise to an effective friction (Garcia et al., 2015)

Agitation

Agitation refers to any force fluctuation that acts upon constituent particles of a system. For example, agitation arises from thermal fluctuations —which are random and proportional to thermal energy k_BT, where k_B is Boltzmann’s constant— or additionally from external forces, such as shaking or shearing of granular materials. For cytoskeleton and living cells, spontaneous metabolic agitation far exceeds thermal fluctuations (Guo et al., 2014), and arises from hydrolysis of ATP during the procession of molecular motors such as acto-myosin; such events typically releases 20–25 k_BT per ATP molecule hydrolyzed. Agitation can also arise from the action of many molecular motors acting in concert, such as during pulsed actomyosin contractions that occur during gastrulation (Martin et al., 2009), or when a cell pulls on its neighbors, or when cells are stretched (Trepat et al., 2007). In disordered system with metastable configurations, agitation, if large enough, often results in system fluidization

Amorphous solid

The configuration of particles comprising solid matter is often ordered, as in a crystal. The configuration of particles comprising fluid matter, by contrast, is disordered. When cooled or compressed, some fluids fail to freeze into an ordered minimum energy configuration and instead become trapped away from thermodynamic equilibrium, undergoing a glass transition to form an amorphous solid-like material

Fluid-like versus solid-like behavior

In amorphous materials the distinction between solids versus fluids is often not clear because the material can retain features of both. In general, fluid-like multicellular systems are associated with higher velocities, higher neighbor exchange rates, higher cell-shape aspect ratios and less coherent motion of neighbors

Fluidization and solidification

Fluidization and its inverse, solidification, are the process by which a solid-like material is transformed to a fluid-like material, or conversely. Conventional phase transitions (as when water freezes or melts), glass transitions, and jamming transitions can cause fluidization and solidification. But not all fluidization or solidification processes can be attributed to such transitions, however. For example, the actin-severing protein cofilin facilitates fluidization whereas the actin binding protein zyxin facilitates solidification (Lan et al., 2018; Smith et al., 2010)

Glass transition

During familiar phase transitions, such as water freezing or melting, the system at all times remains at thermodynamic equilibrium. During the glass transition, by contrast, constituent particles become trapped away from thermodynamic equilibrium. This trapping occurs when constituent particles become caged by their neighbors but agitation energy is insufficient to overcome associated energy barriers. Approaching the transition to a glassy phase, system viscosity becomes so large, and internal dynamics become so slow, that particles become stuck in an amorphous non-equilibrium configuration. As distinct from a phase transition in equilibrium systems, in which system properties can change in a discontinuous fashion, in a glass transition system properties change in a continuous fashion. On the experimental time scale, for all practical purposes glassy systems approximate a solid-like amorphous phase

Jamming transition

By contrast with the glass transition, the jamming transition in the strict sense of the term does not depend upon agitation, whether thermal or otherwise. Rather, the jamming transition depends solely upon geometrical factors and spatial constraints imposed between neighboring particles, and thus formally represents a zero-activity limit and kinetic arrest (Atkinson et al., 2014; Berthier et al., 2019; Parisi and Zamponi, 2010). But because the word ‘jamming’ is more easily grasped than is ‘glassy’, the word jamming has come into common usage in cell biology to describe both phenomena notwithstanding that agitation of one form or another, and at one level or another, is virtually ever-present in the cell (Berthier et al., 2019; Guo et al., 2014; Tjhung and Berthier, 2020)

Kinetic arrest

When particles of a system become so tightly caged that they are quite unable to move, even at finite temperature, they are said to have undergone kinetic arrest. The jammed phase is typified by kinetic arrest

Percolation

Within a system composed of many particles, percolation occurs when there is a connected path that that spans the system. In relation to the jamming transition, for example, percolation is said to represent a connected path for force transmission and is associated with a transition of the system from fluid-like to a solid-like behavior

Phase transition

By contrast with a glass transition, which by definition is a process in which the system becomes trapped away from thermodynamic equilibrium, a phase transition is a process that occurs while the system remains at all times at thermodynamic equilibrium. When subjected to slow deceases of temperature, increases of density, or other environmental changes, the configuration of constituent particles transitions from disorder (amorphous), as typifies a fluid, to order (crystalline), as typifies a solid, while maintaining minimum free energy. These changes often occur in a discontinuous fashion, as in freezing of water

Soft glassy materials (SGMs)

This is the class of glassy materials that includes foams, pastes, clays, slurries and, importantly, the eukaryotic cytoskeleton (Fabry et al., 2001; Sollich et al., 1997). In addition to being glassy, these system are typified, most notably as by being soft —with shear moduli typically in the range of 10–1000 Pa. By contrast, soft rubbers often times are stiffer by few orders of magnitude. SGMs are also typified by weak power-law rheology and by a frictional modulus (or loss) that is on the order of 10% of the shear modulus. Certain materials, such as cytoskeleton, also falls into the class of active glassy matter (Janssen, 2019)

Thermodynamic equilibrium

At a given temperature, a system at thermodynamic equilibrium must exhibit: 1) maximum entropy; 2) minimum free energy; 3) no flows of matter or energy. Systems that dissipate energy, as do those that hydrolyze ATP, are typically far from thermodynamic equilibrium

Yield stress

Within a solid, each particle is confined by local energy barriers due to the interactions with its neighbors. When forces are applied on the particles, they effectively reduce these energy barriers in the direction of the force. When the applied force reaches the “yield stress” the barrier is overcome to the extent that the particle can flow and exchange places with its neighbors, and it is said that the solid has “yielded”

Zero-activity limit

In jammed systems, thermal energy fluctuations are far smaller than the energy barriers that prevent rearrangements among particles. When thermal motion is so small as to be irrelevant, this is sometimes referred to as the athermal limit, the zero-activity limit, or the zero temperature limit