Phase Transitions in Biological Systems: Understanding the Analogies with Physical States of Matter

nature COMMUNICATIONS

PERSPECTIVE

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.

Phase transitions in tissue morphogenesis

Biological tissues require the appropriate organization of their constituent components-the cells-needed for maintaining proper structure and function. Similar to any multi-component system, interactions between the constituent components largely dictate the overall behavior or the macroscopic state. For instance, the three states of matter-solid, liquid, and gas-are characterized by distinct interactions between its component particles at the microscopic level that manifests in macroscopic properties such as fluidity, rigidity, resistance to changes in shape and volume.

Biological systems also display a rich phenomenology of such states of matter that result from the interaction of cells with their neighbors and the extracellular media, which is also often created by the cells themselves. For example, bones, cartilage, or tree barks are examples of solid-like materials seen in biology. Fluid-like behavior is generally more commonly observed in biological tissues, especially within the animal kingdom. Particularly during the development of embryos whose shape changes are due to an interplay between individual cell shape changes and cell topological rearrangements- for example in gastrulation-embryonic tissues behave like liquids that cannot strongly resist changes in shape. Some epithelial tissues exhibit the characteristics of fluid phases with a high degree of long-range orientational order, like liquid crystals. In some cases, it is justified to consider the state of tissues as gas-like where interactions between individual cells are minimal and their movements are analogous to those for gas molecules. Plant cells, on the other hand, owing to their saturating turgor pressure from vacuoles within a cellulose-based cell wall display more "permanent" solid-like behavior in collectives (e.g., plant roots, plant vasculature). However, a true solid-like behavior, distinguished by resistance to shape and volume changes, is often displayed in scenarios when the cells are completely replaced by their own extracellular matrix or mineral secretions over time (such as in crustacean or insect shells, bone or tree barks, or cartilage).

The specific molecular makeup and neighbor arrangements result in different supracellular properties in cohorts of cells for both epithelial and mesenchymal types and as a result either can behave like solid or fluid. Generally, strong adhesiveness and tight packing of cells are achieved in the epithelial state and large-scale cellular rearrangements characterize loosely packed mesenchymal cells. Yet a collection of mesenchymal cells can still be confined within a small region despite large movements at the individual level and therefore result in the overall structural stability of the region. Evidence of such a fluid-to-solid transition in mesenchyme was recently elucidated in the context of the gradual "solidification" of tissue in the zebrafish mesodermal progenitor zone as cells move into presomitic mesoderm, where they are more packed. In this case, the cell density affects the local tissue stiffness, and thus controls the solidification process. In confluent tissues where cell density is constant, solidification results from changes in cell-cell adhesion and cortical tension or in cell-cell and cell-substrate adhesion. Similarly, a tightly packed epithelium can be "fluid-like" with its cells rearranging and/or moving collectively. Different phases can coexist in a tissue; for example, cells can form fluid-like clusters that are exchanging cells with a gas-like phase. Such coexistence of cellular phases is observed in vitro and for tumors where individual (gas-like) cells emanate ("evaporate") from a fluid or even solid-like tumor. Cell clusters behaving like fluid droplets are able to migrate from a primary tumor and disseminate while maintaining their epithelial character.

Unlike most inert physical systems, biological systems are characterized by growth and changes in material properties of its constituent cells at different timescales. For example, a population of cells can change its macroscopic (supracellular) behavior by changes in its microscopic (intracellular) properties such as specific cell surface or membrane proteins, rearrangement of intracellular cytoskeleton, changes in the number, size, and distribution of internal organelles such as vacuoles in plant cells. As a result, the state of a tissue is often transitory and the tissue can change its state in a rapid or slow manner depending upon the molecular processes involved. Epithelial to mesenchymal transition in animal cells is one such example and the timescale of this can range from a few minutes (zebrafish gastrulation) to several hours (mouse gastrulation) to several days (cancer). Zebrafish blastoderm has been shown to change its state from a more solid-like to fluid-like on a one-hour timescale by modulating the timescale of its cell-cell contacts.

It seems that such transitions from a rigid to a flowing state, which can be conceptualized as the tissue's solid-like and liquidlike phases, and vice versa define much of what happens in many biological processes especially during tumorigenesis and morphogenesis. It is important to note that while a biological tissue can change its hitherto mentioned transitory state by changes at the molecular level, mixed solid and fluid-like behavior is also an inevitable consequence of the fact that most cellular systems are viscoelastic. Similar to inert viscoelastic materials, biological tissues also display a solid-like behavior at a shorter timescale and viscous fluid-like behavior at longer timescales. It is possible that this viscoelastic timescale itself can change dramatically over time depending upon the molecular composition of the tissue and such changes can amount to a phase transition over the relevant timescale. However, as we will describe next, changes between solid to fluid behavior over a given viscoelastic timescale are not true phase transitions. It is therefore crucial to consider the timescale of the process when analyzing changes in a biological system from a particular state (rigid or fluid-like) to another.

The hallmark of a phase transition is a change in the order of the system. Such changes in properties can be abrupt (i.e., discontinuous, first-order phase transitions) or gradual (i.e., continuous, second-order phase transitions). For example, liquid to solid transition in water results in an abrupt change in the organization of water molecules as a periodic lattice whereas ferromagnetic materials are known to display gradual changes in the internal order. Such changes-abrupt or gradual-typically result from gradual changes in external conditions (control parameters) such as temperature, pressure, or density. In biological systems, though, changes in conditions are often internal such as growth rate, cell division, migration, adhesion, arrangement, etc. Unlike in a true fluid-to-solid transition where a spontaneous emergence of long-range crystalline order occurs, the rigid phase transitions in biological systems are characterized by the persistence of a disordered state of matter both in the solid and liquid states. Such phase transitions, known as jamming, have been discussed extensively for inert materials such as foams, emulsions, granular materials, and glasses. Motivated by the work done in physics and engineering, jamming has turned out to be an effective paradigm for conceptualizing the emergence of rigidity in biological tissues in both two-dimensional and three-dimensional contexts, whereby crowding, tension-driven rigidity, and reduction of fluctuations-all three mechanisms individually or simultaneously-can arrest cell motion resulting in a "jammed tissue." Analogous to multi-particle systems where the particles can interact with each other and show sub-populations characterized by specific velocities, biological systems can also display kinetic phase transitions and jamming in collectively moving confluent cells.

In this Perspective, we will discuss the above-mentioned phase transitions, both from theoretical perspective as well as experimental evidence in biological systems. In particular, we will discuss what the concepts of ordered and disordered systems mean in the biological context, what are the main physical determinants for fluid-to-solid transitions in biological tissues which would play a role analogous to stress, density, and especially temperature in the conventional matter and which criteria determine such phase transitions in tissues. We will then present approaches to detect such phase transitions in situ. Toward the end, we will also speculate about molecular realizations of fluid/solid transitions and critically discuss the opportunities and limitations of the analogy between collective effects in living systems and conventional phase transitions.