Author: Andrew Ton

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Trichoplax adhaerens: tropical sea-dweller, microscopic contortionist, and biomechanical marvel

Original paper: Motility-induced fracture reveals a ductile-to-brittle crossover in a simple animal’s epithelia

Content review: Heather Hamilton
Style review: Pierre Lehéricey

Figure 1: The dynamic range of T. adhaerens with size ranging from 100 microns to 10 millimeters. Snapshots taken from live imaging. Images courtesy of the original article.

Meet Trichoplax adhaerens, a microscopic marine animal from one of the oldest known branches of the evolutionary tree. It looks like a microscopic cell sandwich: two layers of epithelial cells (which make up the surfaces of our organs), with a layer of fibre cells in between. As depicted in Figure 1, T. adhaerens takes a wide variety of shapes from disks to loops to noodles and more. Oddly,  T. adhaerens ruptures when it moves around, a self-induced fracture behavior that has recently captured the attention of physicists and engineers. Fracture is the technical term describing the process by which an object breaks into distinct pieces due to stress. These animals push their epithelial tissue to the breaking point, forming incredible and extreme shapes before separating altogether. This is a surprising behavior for epithelia, which usually prefer to maintain their integrity.  By modeling how T. adhaerens rips itself apart when moving, we can improve our understanding of how soft materials and especially biological tissues behave on the verge of breaking.

Prakash, Bull, and Prakash conducted a two-pronged analysis of fracture in T. adhaerens:  live imaging to record the fracturing in real time and computational modeling to simulate the response of the tissue when stretched too far. The drastic mechanical behavior in question also motivated the researchers to perform a more general inquiry into the competition between flow and fracture in materials that are dramatically deformed relatively quickly. Flow is like stretching out a piece of chewing gum, whereas fracture is like snapping the gum in two. The computational model proposed by the authors helped paint a clearer picture of what happens when T. adhaerens rips apart.

Figure 2: Model tissue is described as a collection of balls and springs. Balls represent cells, and springs represent the sticky adhesion between cells. Springs apply restorative forces to the cells, but can break if stretched too far. This model was used to study the ventral (bottom) epithelial layer, which consists of epithelial cells (green) and larger lipophil cells (red). Figure courtesy of the original article (Extended Data).

The computational model that the researchers used is based on a sticky ball and spring model, as shown in Figure 2, where each ball represents a cell and each spring represents the sticky junctions that cells use to adhere to one another.  The springs break if the balls move too far away from each other, which represents cells being unstuck from their neighbors.  Two cell types are represented in the model epithelial layer in Figure 2: epithelial cells, which are small and comprise the bulk of the tissue, and lipophil cells, which are larger and less common.  Using this model for living tissue, the authors conducted computational simulations where the tissue was stretched to a breaking point. They found that there are three possible tissue behaviors that depend on the strength of the driving force applied to the simulated tissue. For weak forcing (low stress), the tissue behaved elastically and so responded in such a way that it could recover its original shape. For intermediate forcing (medium stress), the tissue underwent a “yielding transition” where the material transitioned from elastic response to plastic response. During plastic response, permanent distortions occurred in the material, and the material could not recover its original shape. In this case, the tissue is ductile and undergoes local changes, like cells interchanging with neighboring cells, to relax some of the pent-up stress. For stronger forcing (high stress), the tissue undergoes brittle fracture where the bonds between cells break with little opportunity for relaxation. The three behaviors in the model represent a transition from elastic to ductile to brittle responses. Using this model of tissue response to applied force, the authors mapped the conditions that lead to different tissue behaviors, as sketched in Figure 3.

Figure 3: Tissue phase diagram (elastic-ductile-brittle) generated by the tissue simulations. The elastic regime (i) implies that bonds do not break, and neighbors are not exchanged. Above the yield transition (blue line), cells undergo local relaxations and flow in the ductile yielding regime. To the left of the red line, cell bonds tend to break and form gaps between cells, demarcating the brittle fracture regime.  Figure courtesy of the original article.

Guided by a better understanding of tissue mechanics thanks to the computer model, the authors experimentally measured the brittle and ductile responses in T. adhaerens. They found that both material responses can occur in our microscopic friend. The ability to access both regimes is important because the ductile response yields by flowing (helping form the longer shapes in T. adhaerens) whereas the fracture response accounts for asexual reproduction by splitting into two separate new individuals. The authors’ combined approach of experimental data that motivated the development of a computer model, which in turn guided further experimental inquiry, is an important modern scientific paradigm. Both approaches are incredibly important tools in the biological and soft matter sciences’ toolkit. Joint application of these tools lets us draw general conclusions from specific experiments as well as apply those general conclusions back to answer specific questions – like explaining how T. adhaerens achieves the diversity of shapes in Figure 1 and how this relates to its hardiness and evolutionary goal of reproduction.  Further, the epithelial layer computational modeling technique generalizes this tissue mechanics study to help us describe fracture versus flow in any living tissue, including our own.

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Plants detect gravity by going with the (granular) flow

Original paper: Gravisensors in plant cells behave like an active granular liquid

Content review: Adam Fortais
Style review: Heather S.C. Hamilton

Plants need to know the direction of gravitational pull in order to grow their roots downward and their stems upward. This information is crucial whether the plant grows in your garden, on a cliffside, or even on the International Space Station [1]. While it’s been said that it took a falling apple for Newton to figure out how gravity works, our photosynthetic friends use a more intricate microscale sensor to detect gravity. This sensor consists of starchy granules called statoliths which can be found on the bottom of specialized cells called statocytes. An accumulated pile of around 20 statoliths at the bottom of a statocyte cell is shown in Figure 1. If the cells are tilted like in Figure 2, the pull of gravity initiates a statolith avalanche that indicates the direction of gravity. The position of statoliths is part of a complicated signaling network that tells the plants how to correct its growth towards or against the direction of gravitational pull. 

Figure 1. Microscope images of statolith piles in gravity-sensing statocyte cells of wheat coleoptiles, which are the sheaths covering an emerging shoot of wheat. Arrows indicate the direction of gravity. (Left) Statolith piles are visible as dark areas on the bottom of the cells. The scale bar represents 100 µm. (Right) Close-up view of the statolith piles. The scale bar represents 20 µm. Images courtesy of the original article. Inset: Standard granular pile just below the avalanche angle. Schematic courtesy of Andreotti et. al., Granular Media Between Fluid and Solid.
Figure 2. Movie made from microscopic images of statolith avalanches in wheat coleoptiles after the cells are tilted 70 degrees. Statolith piles are dark spots. Movie runs at 40x speed for a total duration of 10 real minutes. Courtesy of the original article.

However, Bérut et. al. realized that this description of statolith piles didn’t totally agree with our knowledge of granular materials. There are two major issues. First, granular piles are known to initiate avalanches only when the slope of the pile reaches a critical angle, usually between 5° and 30° depending on the characteristics of the grains. In the case of the statoliths, the critical angle was found to be around 10°. When the slope is lower than the critical angle, the pile should be completely immobile due to frictional forces between the grains. However, plants are able to detect even the slightest changes in gravity — involving angles much smaller than 10° — indicating that avalanches are not the whole story. Secondly, upon tilting as in Figure 2, the grains seem to avalanche until they establish a flat surface layer. This is in direct contrast to classical granular materials. If statoliths behaved classically, we would expect them to avalanche until the critical angle of 10° is reached, rather than their actual final angle of around 0°. How can we explain the shocking sensitivity of these granular piles?

Figure 3. (A) Two observed dynamical regimes in the averaged angular decay of statolith pile slopes over time. Each curve corresponds to different initial inclination angles. (Inset) Initial and final configurations of a statolith pile after being tilted by 70°.  (B) Close-up video of a statolith avalanche (when tilted 15°)  highlighting the random motion of individual statoliths. Movie is played at 80x speed, for a real duration of 14 minutes. Images and video courtesy of the original article.

By studying the flow response of the statoliths to gentle inclinations, Bérut et. al. found that the statoliths in fact flow, liquid-like, from a pile into a puddle with or without prior avalanches!  Figure 3A shows a statolith pile angle slowly creeping from 10° (or less) to 0° in 10-20 minutes. This creeping response occurs at any slope. Under the microscope, the statoliths are seen to vibrate, with each individual statolith undergoing random motion shown in Figure 3B. The statoliths are agitated, the origin of which is likely biological processes within the cell rather than random thermal motion, as thermal energy is too small to drive the observed grain activity. While we know that classical granular piles do not flow below the critical avalanche angle, this is not the case for active granular materials. Agitation allows the grains to free themselves from the pile, turning an otherwise static mountain into a fluid-like substance. Long before we had an understanding of the physical world, nature was already building and refining amazing biological machines. We have only recently begun to understand the properties of agitated granular materials, meanwhile plants have been using active grains to detect gravity all this time. Given plants’ long-time expertise with gravity, perhaps the apple that fell on Newton’s head was nature’s way of telling humans to hurry up and figure it out. 

 [1] NASA Plant Gravity Perception Project

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Supersoft matter bounces back: Softer, Better, Stronger

Original paper: Solvent-free, supersoft and superelastic bottlebrush melts and networks

Polymers are made of long molecules (polymer chains) consisting of shorter, repeating units called monomers. Like cooked spaghetti noodles, many polymer chains coexist in the same shared space and when too many of them overlap entanglement may occur (Figure 1). Such entangled messes of polymer chains are stiff and hard to deform, limiting the elasticity of polymer-based synthetic materials. One way of softening materials is by disentangling the polymer chains via soaking the polymer chains in a solvent, such as water. The solvent molecules in hydrogels occupy space between polymer chains driving the chains away from each other, similar to how pouring water overcooked spaghetti drives the noodles apart. This led to the discovery of hydrogels, the primary component of soft contact lenses and tissue implants [1]. But if you’ve ever worn soft contact lenses, you may know that they dry out and harden if they are not stored in a solution. This pervasive issue of hydrogel materials occurs when the solvent leaks or evaporates, affecting their mechanical properties. In this week’s post, polymer scientists develop super-soft dry elastomers (very elastic or rubbery polymers) that surpass the softness and elasticity of hydrogels, all without getting their hands wet.

Figure 1. Spaghetti pomodoro e basilico. The noodles demonstrate how long, flexible objects intertwine with each other to form an entangled complex, resembling polymer networks in hydrogels. Image courtesy of Wikipedia.

What does it take to design a polymer material that intrinsically avoids entanglement without using a large amount of solvent? William Daniel and his colleagues tackle this issue by designing a polymer chain geometry resembling a bottlebrush (shown in Figure 2). The bottlebrush geometry consists of a linear polymer backbone onto which short side chains, called bristles, are grafted. These bottlebrush-shaped chains are soft even in the absence of solvent. Instead of relying on small solvent molecules, bottlebrush networks use their bristles to keep polymer chains away from each other because bristles are too short to participate in the entanglement. As a result, the bottlebrush chains have an overall repulsion effect that resembles the repulsion effect of solvent molecules in hydrogels. Bristle repulsion allows bottlebrush polymers to surpass the elasticity of hydrogels! As an example, Figure 3 shows a compression test where a bottlebrush elastomer (on the right) retains its structure whereas a hydrogel material (on the left) fractures when compressed. Despite their similar elastic moduli, the bottlebrush elastomer displayed much greater compressibility than the hydrogel.

Figure 2. Schematic of three bottlebrush polymer chains. Each bottlebrush chain consists of a polymer backbone (linear chain) onto which short side chains (bristles) are attached. Figure adapted from the original article.

But what is an elastic modulus and why does it matter? The elastic modulus is a measure of the stiffness of a material and is given by the ratio of stress, the force causing deformation per area, to strain, the relative length by which the material is deformed by the stress. In these terms, a small modulus corresponds to low force per area resulting in significant deformation during compression – exactly what we expect of soft materials! As the entanglement density increases, a polymer chain network becomes more crowded resulting in a stiffer material [2]. Since bottlebrush bristles are too short to entangle, increasing the bristle density further reduces the entanglement density. Thus the elastic modulus of bottlebrush elastomers can be tuned by controlling the number of bristles grafted onto the polymer backbone. These bristles comprise the majority of the mass of the elastomer, e.g. 87% of the mass of the elastomer described in Figure 3. 

Figure 3. Compression test of a hydrogel versus a bottlebrush elastomer. Left: PAM or poly(acrylamide) hydrogel made of 10% by weight polymer chains and 90% solvent. Right: bottlebrush elastomer made of 8% by weight backbone chains, 87% bristles and 5% solvent. Both materials have similar moduli (~2000 Pa). During compression, the bottlebrush elastomer kept its form while the hydrogel fractured. Figure adapted from the original article.

In addition to super-softness, bottlebrush networks are also highly compressible. The stress measurement in Figure 4 shows that bottlebrush elastomers (red curve) tolerated five times more stress before fracture compared to hydrogels (blue curve). Furthermore, the compression ratio (equilibrium length to compression length) of bottlebrushes was three times higher before fracturing. This means that bottlebrush elastomers are capable of sustaining much more deformation, and hence strain, than hydrogels. 

Figure 4. Stress measured during compression of a bottlebrush elastomer (red curve) and a hydrogel (blue curve). The bottlebrush elastomer achieved a compression ratio (equilibrium length to compressed length) of about 10 while the hydrogel fractured at a compression ratio equal to 3. Image adapted from the original paper.

The idea of attaching bristles onto a polymer backbone in high density gave William Daniel and his colleagues control over the stiffness due to entanglement. This work expands scientists’ understanding of material properties consisting of branched polymer chains and points to a new frontier of dry supersoft materials. These new materials could play an important role in the development of soft robotics and synthetic biological tissues.

[1] Swell gels (2002). 

[2] In polymers, the entanglement contribution to the elastic modulus is given by the modulus equation:

Ge = neRT, 

where ne is the number of chains involved in entanglement per unit volume, R is the universal gas constant, and T is the temperature. The modulus equation suggests that polymer materials become stiffer when heated. As temperature increases, the polymer network gains kinetic energy to attain structures with more “randomness”, or entropy. This increased randomness in polymer networks leads to more entangled states (higher entropy) that makes the material less prone to lengthening, hence more resistant to deformation.