biophysics – Softbites

2023-08-29

“Spleen-on-a-chip” gives an inside view of sickle cell disease

Original paper: Microfluidic study of retention and elimination of abnormal red blood cells by human spleen with implications for sickle cell disease

Content review: Arthur Michaut
Style review: Arthur Michaut

Though they may not realise it, anyone who’s taken the subway at rush hour knows how a red blood cell feels passing through the human spleen. Almost home now, just need to get through the gates; but wait, someone’s ticket isn’t working, the crowd is starting to push, the gates are getting jammed… Maybe you should have called a cab.

**Figure 1.** Left: in vivo filtration of red blood cells through the slits of the spleen. Right: in vitro filtration of red blood cells through silicone slits.

Much like turnstiles validating your ticket, the human spleen contains narrow slits that red blood cells must squeeze through to prove they are fit to navigate tight blood vessels while carrying oxygen around the body. The spleen is tasked with ensuring our blood contains the right amount of red blood cells and removing any cells that aren’t in tip-top shape. Shape, however, can be a problem the spleen can’t handle.

People with sickle cell disease produce “sickle” shaped red blood cells due to an inherited genetic mutation. Sickle cell disease patients can experience episodes of acute splenic sequestration, or “spleen crisis” where these misshapen cells clog the slits of the spleen, depriving it of oxygen and leading to swelling that can become life-threatening. Because this process is difficult to observe and monitor in the body, there is little understanding of how and why a spleen crisis might occur. When a spleen crisis occurs, an urgent blood transfusion is needed to treat the problem, however, in some cases, it becomes necessary to surgically remove the spleen.

A group of scientists spanning the USA, France, and Singapore have teamed up to understand how sickle cell disease can become life-threatening. Their device, a silicone model spleen, could be used to predict complications of the disease as well as develop new treatments.

Using a soft material classically used in microfabrication, named PDMS, to cast a mold with slits similar to those in the human spleen (Figures 1 & 2i), researchers were able to directly observe the processes that lead to spleen crises. The group analysed flows of red blood cells from both healthy and sickle cell disease patients through the silicone spleen, simulating splenic blood flow rate and oxygen levels, and measured retention of cells in the slits of the device.

The flow of red blood cells from healthy and sickle cell disease patients through the silicone spleen. — **Figure 2.** (i) The biomimetic “spleen-on-a-chip”, scale bar 10 µm (with higher magnifications outlined in red, right). The majority of red blood cells from healthy patients (ii) pass through the device, however, cells from sickle cell disease patients (iii) are more frequently retained at the slits of the device, and when deprived of oxygen (iv) these cells block the device entirely.

After one minute of blood flow, red blood cells from sickle cell disease patients blocked more than double the number of slits as healthy red blood cells (Figures 3i & 3ii), demonstrating how the spleen can become blocked and swollen in sickle cell disease patients. When the silicone spleen was deprived of oxygen, as occurs during a spleen crisis, red blood cells from sickle cell disease patients became stiffer, more viscous, and more frequently sickled (Figure 3iii). Under this condition, sickled red blood cells completely blocked all of the slits. Upon reintroducing oxygen into the system, many cells return to their normal shape and blockages begin to open up again within seconds (Figures 3iv & 4).

The effects of de- and re-oxygenation on red blood cells from healthy and sickle cell disease patients and the unblocking of the device following reoxygenation. — **Figure 4.** Left: red blood cells from healthy (AA) and sickle cell disease (SS) patients under oxygenation and deoxygenation conditions (scale bar 10 µm). Right: the percentage of open slits in the device quickly increases when oxygen is reintroduced into the blocked system.

The results uncover a viscous cycle leading to spleen crises in sickle cell disease patients. Sickled cells cause blockages in the spleen, which deprives the spleen of oxygen, which in turn causes more cells to become sickled. Additionally, it was shown that the addition of oxygen caused cells to “unsickle” and rapidly cleared blockages in the slits, revealing why immediate blood transfusion can alleviate spleen crises. The researchers speculate that a sudden burst of oxygen-rich red blood cells via transfusion has the same effect as when they reintroduced oxygen to their blocked system.

Researchers believe the spleen-on-a-chip could become a new tool to allow sickle cell disease patients to monitor their condition and allow for early diagnosis of spleen crises, as well as providing a testing ground for new treatments against the disease. Safe travels red blood cells!

Disclosure: The author declares no competing interest.

2022-06-29

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.

2021-03-10

“I don’t think there will be a return journey, Mr. Frodo”: how thermodynamic irreversibility makes life flourish

Original paper: Statistical Physics of Self-Replication

Content review: Adam Fortais
Style review: Andrew Ton

Understanding the origin of life is one of the most enduring and fundamental scientific challenges there is. Of all branches of science, physics is probably not the first place one would think to go to for enlightenment. Life seems too complicated and multi-layered to be captured by the simplistic frameworks of physics. Today’s paper tackles a small part of understanding the origin of life – the physics of self-replication.

This paper begins by considering two macroscopic states, shown in Figure 1A, which are “one bacterium in a petri dish” and “two bacteria in a petri dish”, and considers transitions between these states. The biggest challenge here is relating a macroscopic change — the replication of a cell or collection of complex molecules — to a set of microscopic operations, also known as chemical reactions. But these reactions are tremendously complicated. How can we know what to expect from them? The answer lies within the art of thermodynamics.

**Figure 1.** Some of the pathways considered in the process of cell division. The probability of cell division (A) occurring is much higher than that of the disintegration of a single cell (B), highlighting the irreversibility of this event. Image courtesy of the original article.

According to thermodynamics, the governing quantities in a typical chemical reaction are energy, heat, and entropy. During a reaction, they can gain or lose any of these three as long as the total energy is kept balanced. Entropy, however, is a bit more special than the other two. Roughly speaking, entropy is a way of counting the number of possible ways a system can be in a certain state. So if a reaction involves several small molecules binding together to form a larger molecule, that involves a big loss in entropy. This is because there are many more ways to organize a large number of molecules than ways to organize one. Thermodynamics tells us that heat must be released to “pay for” this change in entropy. This heat flow increases the entropy of the environment, leading to an overall increase. All other things being equal, systems tend towards states of high entropy, simply because there are more ways of being in those states. This is usually referred to as the Second Law of Thermodynamics.

These are abstract descriptions of thermodynamic processes — how does the author use these to construct more concrete, quantitative models? First, they derive a version of the Second Law which relates the heat released by the transition to the irreversibility of the transition: the harder it is to undo a process, i.e. the more irreversible it is, the more heat must be released. Combining this observation with a simple model of replication, England reaches an important result: for a self-replicating system, the more efficiently it uses the available energy, the more rapidly it will replicate.

England uses thermodynamics as a set of rules to calculate whether cell division for a bacterium is physically possible. While we already know the answer, the author is seeking to understand if this simple theory contains enough details to make accurate estimates about bacterial replication. The hard part of this problem isn’t to calculate the heat or entropy released, but rather to put a physical constraint on the likelihood of the reverse process. After all, we don’t ever see bacteria spontaneously dissolve back into their constituents. But with some clever thinking, this problem can be circumvented. Instead of considering the probability of a bacterium dissolving, the author simply considers the probability of every single chemical bond inside it spontaneously breaking. This is an extremely unlikely event, and yet it’s not as unlikely as the cell spontaneously being unmade, as shown in Figure 1B, and so it can give us a lower bound for the irreversibility of cell division. Combined with careful estimates of heat and entropy transfers, this gives a full (and very approximate) thermodynamic accounting of the process of cell division.

What can we do with this? We can perform some comparisons: first of all, the irreversibility of a process turns out to be a much larger thermodynamic barrier than the entropic difficulty of organizing all the constituents of a daughter bacterial cell, which is a highly structured object! This is surprising at first, but hindsight is 20/20: living systems are doing a lot of work to make things that don’t dissolve back into water. Another surprising conclusion of this argument is that real bacteria are tremendously efficient! With the coarse estimates used here, the author gets a replication rate close to that of a real E. Coli bacterium. This is an astonishing result, since the process considered here is not nearly as irreversible as that of a real cell division.

The takeaway here isn’t simply learning something about bacteria or replication. The real lesson is about the power of the methods of statistical physics. The division of a bacterium is frighteningly complicated, and no physicist could write down the chain of reactions necessary for the proper replication and division of this complex system. Despite this intricacy, biological processes must still follow the unambiguous laws of physics. And that implies one thing: more life, more complexity, and more entropy. While this is by no means an answer to the question “where does life come from?”, it gives us hope that physics will continue to play an important role in the story of answering this question.

2021-03-032021-02-28

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

2021-01-202021-01-20

Squid reveal the secret to a “perfect” lens

Original paper: Eye patches: Protein assembly of index-gradient squid lenses

Evolution usually solves challenges differently than human engineers—something easy for biology is often difficult for us, and vice versa. Learning from biology can help us solve difficult challenges more easily. One example of this is making complex optical lenses.

**Figure 1.** Lenses use refraction and geometry to direct light. (Figure by the author)

When light enters a new material it refracts, changing velocity and direction. A lens uses geometry and material properties to direct light on a specific path. You can see in Figure 1 how the shape and refractive index of a biconvex lens combine to direct light at a single spot. In biology, complex eyes like those found in most vertebrates and in squid have a lens that directs light onto the retina at the back of the eye, forming an image to be processed by the brain. Squid use spherical lenses to do this, but spherical lenses have a problem. As you can see in Figure 2, if you make a spherical lens out of one material (like glass), the light rays overlap after exiting the lens and the resulting image is blurry. This is called “spherical aberration.” Human engineers use spherical lenses a lot, and we correct for spherical aberration by combining multiple lenses. Squid, on the other hand, have evolved a lens that self-corrects for this distortion.

**Figure 2.** Spherical lenses usually produce blurry images, but not in squid. (Figure by the author)

We know, in theory, how a squid might do this. In 1854, the famous physicist James Clerk Maxwell mathematically designed a spherical lens with “perfect” focus. He showed that if the density of the lens changes along the radius, forming a density gradient that he called a “perfect medium,” then the lens will produce a clear image. Today engineers can make gradient index lenses like this, but the process is difficult and energy intensive. Squid evolved to grow them easily. Could understanding how squid make these lenses help human engineers learn to do the same thing? This question inspired Dr. Jing Cai and Prof. Alison Sweeney to study the structure of the squid lens.

**Figure 3.** A squid lens has rings, which could combine to create a “perfect medium.” (Figure by the author, photograph from the *Museum of Museum of New Zealand Te Papa Tongarewa, as reported by* *Nerdist*)

You can see in Figure 3 that when you crack open the lens in a squid eye you find rings like the inside of a tree trunk. If each of these rings has a slightly different density, they could combine to create a perfect medium. The lens of an eye is made out of proteins called crystallins, which fold into individual particles before linking together into a single material. Cai and her collaborators discovered that the lenses of the Longfin inshore squid (Doryteuthis pealeii) use 53 different crystallin proteins of different sizes. They also found that the different proteins are used in different parts of the lens, and each layer of the lens has a slightly different structure. As you can see in Figure 4, small proteins at the center of the lens are densely packed together so that each protein is connected to six other proteins. However, the larger proteins at the edge of the lens have more space between them, and each protein only touches two others.

**Figure 4.** Protein particles assemble differently in different parts of the lens, creating a “perfect medium.” (Figure by the author)

This makes sense when you think about the cells that make these proteins. Cells rely on diffusion to bring building blocks to the right place for protein assembly and to send each assembled protein out to where it’s needed. When finished proteins link together to grow the lens, they disrupt this diffusion and stop protein production. By growing from dense to less dense and using so many different proteins (53 in the Longfin inshore squid), the cells are able to start and stop the growth of different layers while maintaining a single particle network. No part of the lens separates out or turns opaque, but there are still large enough regions with different densities to diffract light into alignment.

Cai and her collaborators showed that squid lenses definitely use a density gradient similar to Maxwell’s perfect medium to correct for spherical aberration. It’s likely that this density gradient not only creates a perfect medium, but also helps control lens assembly. Now that we know how squid build a perfect spherical lens, it is easier to envision how human engineers could grow our own complex optical materials.

2020-12-072021-01-20

Who needs polymer physics when you can get worms drunk instead?

Original paper: Rheology of Entangled Active Polymer-Like T. Tubifex Worms (arXiv here)

If you speak to a soft matter physicist these days, within a few minutes the term “active matter” is bound to come up. A material is considered “active” when it burns energy to produce work, just like all sorts of molecular motors, proteins, and enzymes do inside your body. In this study, the scientists are focusing specifically on active polymers. These are long molecules which can burn energy to do physical work. Much of biological active matter is in the form of polymers (DNA or actin-myosin systems for example), and understanding them better would give direct insight into biophysics of all kinds. But polymers are microscopic objects with complex interactions, making them difficult to manipulate directly. To make matters worse, physicists have yet to fundamentally understand the behaviors of active materials, since they do not fit into our existing theories of so-called “passive” systems. In this study, Deblais and colleagues decided to entirely circumvent this problem by working with a much larger and easier-to-study system that behaves similarly to a polymer solution: a mixture of squirming worms in water.

The researchers focused on the viscous properties of this living material, which behaves somewhat like a fluid. Viscosity is a measure of a fluid’s resistance to gradients in the flow. Polymer fluids are highly viscous because the long molecules in a polymeric liquid get tangled up in one another. Physical descriptions of most fluids assume that viscosity is a constant (so called Newtonian fluids), but many materials exhibit what is called shear thinning. This is when a fluid flows more easily as one applies an increasing shear force, that is, a force pulling the system apart. We encounter shear thinning at the dinner table all the time when struggling to pour ketchup, another polymeric fluid, out of a bottle. If the bottle is shaken fast enough, increasing the shear force applied, the ketchup flows smoothly like a liquid. In polymer systems (like xanthan gum in the ketchup) shear thinning happens when polymers are pulled apart fast enough that they tend to align together, which loosens the entanglements that held the system together before.

In this study, the researchers asked: how does shear thinning behavior change if the polymers in question were alive? To answer this question, they set out to measure the shear thinning properties of a mixture of worms at various levels of worm activity. Here, “worm activity” refers to how fast the worm is wriggling, which is calculated by measuring how quickly the distance between the two ends of a given worm changes. This leads to two logistical questions: how is the level of worm activity being modified, and how is the viscosity being measured?

Figure 1. This movie shows two worms, one in water (left) and one in a water + alcohol mixture (right). The worm on the right shows a decrease in activity when they are exposed to alcohol, which is one of the two ways the researchers modified worm activity in this study. Video taken from the original article.

The answer to the first question should be familiar to many humans. To make the worms less active, they were put into a solution containing water and a small amount of ethanol, the same type of alcohol found in beer, wine, and spirits. Once the worms were nice and drunk, the researchers noticed that they squirmed about more slowly, as shown in Figure 1. Thankfully, when the ethanol was removed, the worms returned to their previous level of activity! To make sure the alcohol wasn’t doing anything funny to the worms, they found a second way to reduce the activity — by reducing the temperature of the worm solution. Colder temperatures made for more chilled out worms, no pun intended.

Figure 2. This movie shows the functioning of the rheometer. The worms are placed inside a chamber between two plates. The top plate rotates with respect to the bottom plate, and the response of the material is measured. Video taken from the original article.

The researchers used a device called a parallel-plate rheometer to understand the shear thinning behavior of this living polymer system. As seen in Figure 2, a parallel-plate rheometer sandwiches a sample in between two flat plates and viscosity is measured by determining how much force is necessary to rotate the top plate, effectively pushing the material by twisting its surface. The viscosity of the worm mixtures was first determined at three different temperatures, and for worms drunk on ethanol. The results were surprising! The rheological behaviour of the low-activity worm mixtures matched with theories of polymer shear thinning quite well. It seems the worms have the same alignment properties as passive polymer solutions under shear!

So what happens when the worms are sober, more active, and wriggling around? They saw that the required twisting rate needed to thin the mixture decreased. In this case, the worm activity allowed for easier and quicker rearrangement while the mixture was pulled apart by the rheometer’s twisting motion. One can imagine that instead of needing to pull all the worms to the point of alignment, it may have been enough to nudge them in that direction and their wriggling did the rest. We can now imagine that the same thing might be true for non-living polymers: if a polymer material with shear thinning behavior is given an extra source of activity, then its thinning behavior may become more significant.

The lesson to be learned here is partly about worms, polymers, and the adverse effects of ethanol, but really this experiment is a testament to the power and generality of physical descriptions. This study teaches us about the possible behavior of an active polymer system with processes that are relevant on the scale of a few micrometers, by studying real life worms that you can see with the naked eye! In general, it is usually possible to find analog systems that have the desired properties for your study, but which are easier to manipulate. Physics then gives you the bridge between the system of interest and your simpler analog, allowing you to harness the power of interdisciplinary science to ask questions previously unanswerable.

Featured image for the article is taken from the original article.

2020-08-26

Lifehack: How to pack two meters of chromatin into your cell’s nucleus, knot-free!

Original paper: The fractal globule as a model of chromatin architecture in the cell

The entirety of our genetic information is encoded in our DNA. In our cells, it wraps together with proteins to form a flexible fiber about 2 metres long known as chromatin. Despite its length, each cell in our body keeps a copy of our chromatin in its nucleus, which is only about 10 microns across. For scale, if the nucleus was the size of a basketball, its chromatin would be about 90 miles long. How can it all fit in there? To make matters worse, the cell needs chromatin to be easily accessible for reading and copying, so it can’t be all tangled up. It’s not surprising then that scientists have been puzzled as to how this packing problem can be reliably solved in every cell. The solution is to pack the chromatin in a specific way, and research suggests that this may be in the form of a “fractal globule”.

An equilibrium globule is the state that a polymer (a long repetitive molecular sequence, like chromatin) takes when it is left for a long time in a liquid that doesn’t dissolve it well. In such a liquid, the polymer is more attracted to itself than the molecules around it, so it collapses into a globule to minimize the amount of contact between itself and its surroundings. The resulting object is much denser than typical polymers in good solvents and is dense enough to fit inside a nucleus. However, like stuffing headphone cables into your pocket, it develops many knots and its different regions mix with one another.

On the other hand, if you change the polymer’s environment fast enough that it doesn’t have the time to fully equilibrate, then every piece of the polymer will locally collapse into its own globule. In other words, the polymer forms a globule made of smaller globules and is called a fractal globule. Fractals are objects which look the same at all scales, like the edge of a cloud or the coastline of England. If you zoom in or out on either of these objects, they look more or less the same. This isn’t an “equilibrium” state, meaning it will slowly fall out of this configuration. However, until the whole polymer equilibrates (which takes a long time), the chain has many desirable properties.

Figure 1. Simulated examples of fractal (A,C) and equilibrium globules (B,D), showing compartmentalization of different portions of the polymer. The chain color goes from red to blue as shown above. Compartmentalization means that parts of the chromatin stay near other parts with the same color (adapted from paper [1]).

We are interested in these globule states because they are dense enough that a globule of chromatin can fit inside of a cell nucleus. But it’s not enough to simply fit inside; the cell needs chromatin to avoid forming knots, since getting tangled would prevent the cell from properly reading its own DNA. Live cells also keep their chromatin nicely compartmentalized, that is, different regions along the genome stay spatially separated from one another. Unlike equilibrium globules, fractal globules have few knots and are also compartmentalized! To get a better picture for what this means, Leonid Mirny performed simulations of the different types of globules. Figure 1 shows the results of these simulations, highlighting how different the two states look in terms of knotting and separation of regions of the polymer.

So it seems that the fractal globule state has all the properties we need for a good model of chromatin! But, as scientists, we know that no matter how well a theory fits the characteristics we want it to have, we need experimental evidence before believing anything. In the case of this fractal globule model for genome organization, evidence has come in the form of “contact probability maps”. These are collected from large populations of cells whose DNA is cut, spliced, and read in such a way that allows for a measurement of the probability that any two sites on the chromatin are touching at any given time. Among other things, these maps give us information about how chromatin is packed. So the question becomes, “what does the fractal globule model predict a contact probability map to look like?”

The fractal globule model doesn’t make exact predictions about where one will find specific segments of chromatin, but it does predict a contact probability as a function of distance between two sites, s. Specifically, the model predicts that the contact probability between two sites scales like 1/s. Meaning, if I look at sites that are twice as far apart along the polymer, then they are half as likely to be touching. This 1/s scaling is what was observed on intermediate scales (about 100,000 to 6 million base pairs) by looking at contact probability maps averaged over a whole population of cells.

We still don’t know how the cell maintains and tunes this fractal globule state, and we still have not developed a dynamic version of this picture, which is necessary since it is well-established that the chromatin in our cells is far from static. But this study gives us a new picture of how chromatin is organized inside cells. It isn’t randomly configured like headphone cables in your pocket or a ball of yarn. Rather it is folded onto itself in a self-similar way. This model is attractively simple, requires little fine-tuning, all while producing a long-lived state with segregated territories and easily accessible genes.

[1] Mirny, Leonid (2011), The fractal globule as a model of chromatin architecture in the cell. Chromosome Res.

Featured image for the article is taken from Wikimedia Commons.

2020-02-202020-02-20

Researchers play with elastic bands to understand DNA and protein structures.

Topology, Geometry, and Mechanics of Strongly Stretched and Twisted Filaments: Solenoids, Plectonemes, and Artificial Muscle Fibers

Much of how DNA and proteins function depends on their conformations. Diseases like Alzheimers’ and Parkinsons’ have been linked to misfolding of proteins, and unwinding DNA’s double-helix structure is crucial to the DNA self-copying process. Yet, it’s difficult to study an individual molecule’s mechanical properties. Manipulating objects at such a small scale requires tools like optical and magnetic tweezers that produce forces and torques on the order of pico-Newtons, which are hard to measure accurately. One way around these difficulties is by modeling a complicated molecule as an elastic fiber that deforms in predictable ways due to extension and rotation. However, there are still many things we don’t know about how even a simple elastic fiber behaves when it is stretched and twisted at the same time. Recently, Nicholas Charles and researchers from Harvard published a study that used simulations of elastic fibers to probe their response to stretching and rotation applied simultaneously. The results shed light on how DNA, proteins, and other fibrous materials respond to forces and get their intricate shapes.

Before continuing, I would recommend finding a rubber band. A deep understanding of this work can be gained by playing along with this article.

Long and thin elastic materials, (like DNA, protein, and rubber bands), are a lot like springs. You can stretch or compress them, storing energy in the material proportional to how much you change its length. However, compressing them too much may make the material bend sideways, or “buckle”. It might be more natural to think of this process with a stiff beam like in Figure 1, where a large compressive load can be applied before the beam buckles. But since your rubber band is soft and slender, it buckles almost immediately.

A stick is compressed and at a certain pressure, buckles. — **Figure 1.** A straight, untwisted stick is compressed and buckles. It’s stiffer and thicker than your rubber band, so it sustains a higher load before buckling. (https://enterfea.com/what-is-buckling-analysis/)

Likewise, twisting your rubber band in either direction will store energy in the band proportional to how much it’s twisted. And, like compression, twisting can also cause it to deform suddenly. Instead of buckling, the result is a double-helix-like braid that grows perpendicular to the fiber’s length, as shown in Figure 2. An important caveat is that the ends of the rubber band are allowed to come together. But what happens when the ends of the band are fixed?

An elastic fiber is twisted into a plectoneme. It looks like a double-helix. — **Figure 2.** An elastic fiber is held with little to no tension and twisted. A double-helix, braid-like structure is formed. (Mattia Gazzola, https://www.youtube.com/watch?v=5WRkBWXUCNs)

Fixing the ends of a rubber band forces it to stretch as it twists. When this happens, a different kind of deformation can occur that combines extending, twisting, and bending the fiber. By stretching and bending simultaneously, the band forms a solenoid that is oriented along the long-axis of the band, reminiscent of the coil of a spring. An example of the solenoid shape appears in Figure 3.

An elastic fiber is held under tension and twisted. A solenoid structure is produced. — **Figure 3.** An elastic fiber is held at high tension and twisted. A solenoid structure is formed. (Mattia Gazzola, https://www.youtube.com/watch?v=0LoIwE37aNo)

All of the phenomena described above can be seen by playing with rubber bands, yet a quantitative understanding of how these states form and how to transition between them has remained elusive. To tackle this problem, Charles and coworkers used a computer simulation to calculate the energy stored at each point along an elastic fiber when it is stretched and twisted. The simulated fiber was allowed to deform and search for its lowest energy configuration, a process critical to navigating the system’s instabilities and finding the state you would expect to find in nature.

Figure 4 summarizes some of the different conformations attained by a fiber that is first stretched, then twisted to different degrees. We can see how a fiber with the same tension and different degrees of twist can lead to any one of a wide range of conformations. For instance, a fiber remains straight (yellow dots) when it’s stretched to a length $latex L$ that is 10% longer than its original length $latex L_{0}$ $latex (L/L_{0} = 1.1)$ until it is twisted by $latex \Phi a \approx 1$, where $latex \Phi a$ is the degree of twist multiplied by the fiber’s width divided by its length. Above this value of $latex \Phi a$, the simulated fiber twists into the braided helix structure seen in Figure 2 (blue dots). Likewise, when $latex L/L_{0} = 1.2$, the fiber remains straight until it has a much higher twist, $latex \Phi a \approx 1.5$, where it forms a solenoid (red dots).

Phase diagram of fiber conformations as a function of twist and stretch. — **Figure 4.** Conformation of a simulated fiber under constant extension $latex L/L_{0}$, twisted by $latex \Phi$ normalized by the fiber dimensions $latex a$. Orange dots are straight, blue dots are double-helix braids, red dots are solenoids, and green dots are mixed states. Black and grey symbols are experimental results from a previous study.

Considering the vast understanding of the universe that physics has given us, it may be surprising that there is so much left to learn from the lowly rubber band. While it’s fun to play with, understanding the way fibers deform could help researchers understand all sorts of biological mysteries. For instance, your DNA is a unique code that contains all of the information needed to create any type of cell you have, but depending on where the cell is in your body, that same DNA only makes some specific cell types. The cell can do this by selectively replicating sections of its DNA while ignoring others. One way it does this is by hiding away certain regions of DNA through folding. Exploring the way simple elastic fibers deform could help explain the way DNA knows how to make the right cells, in the right places.

2019-01-172019-01-17

Fold and Unfold

Original Paper: Mechanically switching single-molecule fluorescence of GFP by unfolding and refolding

For the most part of biology, it is form that follows function. Proteins are a perfect example of this — they are made of a sequence of amino acids (the protein building units), which are synthesized by the ribosome. Once synthesized, the long strings of amino acids fold up into a particular 3D shape or conformational state. Proteins take less than a thousandth of a second to attain their preferred conformational state (called “native state”) that — if nothing goes wrong — ends up being the same for a given sequence. This process is called protein folding. Explaining how a protein finds its folding preference out of all possible ways in such a short time is a longstanding problem in biology.

But, how do scientists know if – and when – a protein is in its folded state? The most straightforward way to do this is by observing its function — the way that a protein performs some biochemical task within the cell. If the protein is functionally active, then it has achieved its proper structure. However, most proteins are too small to observe directly without damaging the cell. To solve this problem researchers frequently use Green Fluorescent Protein (GFP), a protein that glows when it is hit by light of a specific wavelength. By attaching GFP to other proteins, researchers can see exactly where those proteins are at different timepoints. GFP’s stability, lack of interaction with other proteins, and non-toxicity make it an extremely popular candidate for visualizing protein localization. In other words, one “function” of GFP is to fluoresce. Today’s paper seeks to understand how structure correlates with function in GFP, one of biology’s most important tools.

To control the folding process, the authors used dual optical tweezers to mechanically stretch and relax the protein. Optical tweezers — as the name suggests — manipulate the position of particles (beads) using laser light. These beads are typically in the size range of micrometers. To apply forces on the GFP, the beads are attached to the protein via DNA “handles,” so that a DNA strand attached to the protein will stick to the DNA strand attached to the bead. These strands are then bound together ensuring that the force on the beads is transferred to the GFP. The construct looks as follows:

Bead – DNA – Protein – DNA – Bead

When the beads move apart, the protein is stretched to its maximal possible length (also called its contour length) and is unfolded, but when the beads get closer together, the protein folds back to its preferred structure. This process is illustrated in Figure 1.

The authors observed that during unfolding, the GFP protein has undergone two intermediate states before unfolding completely. After unfolding, the beads were brought closer together and the protein folded itself back through the intermediate stages. The GFP molecule stopped emitting light when it was unfolded, which was expected. However, it started fluorescing only when it was completely in its folded state. This important finding showed that this protein is functionally inactive in any of the intermediate folding stages. The authors also observed that this process is reversible; they could unfold and refold the GFP molecule multiple times (see Figure 2).

Correlation between Fluorescence and Contour Length of the protein — Figure 2: Fluorescence signals of the GFP protein as it cycles through the unfolding and folding states. (A) The unfolded protein (light gray line) emits very little light (green signal) and its length fluctuates (purple line). Once the protein refolds (*) it emits more light and its length becomes shorter and consistent (dark gray line). † is the point where the force and state conformation are correlated(B) Cycled transition from dark (unfolded) to bright (folded). The purple circles represent the average contour length of each time. (Image adapted from Ganim’s and Rief’s paper).

These findings contribute towards understanding the functionality of proteins that could be used as in vivo optical sensors in force transduction. This work also opens up new avenues in studying biomolecules at the single-molecule level, such as DNA-protein complexes that can induce changes in conformation. Although the experiment only pulled the protein along one axis, this technique could be extended to pulling in several directions at once. If one could control the applied force in 3D, then it could be possible to gain more information on how exactly the protein folds and/or what happens during that process.

2018-10-052018-10-05

Sticky light switches: Should I stay or should I go?

Original paper: Adhesion of Chlamydomonas microalgae to surfaces is switchable by light

“One day it’s fine and next it’s…” red? Microscopic algae depend on photosynthesis, so they follow the light. Previous research has shown that their swimming is directed towards white light but not to red light. New work shows that light-activated stickiness allows microscopic algae to switch between different movement methods.

“This indecision’s buggin’ me” – should I stick or should I swim? Different types of motility are needed to move through different environments. Microscopic algae live in a variety of different conditions, including soils, rocks, and sands, all surrounded by water. In general, we can split these conditions into two groups: those where the algae move within the water, or those where the algae move across a surface. Today’s paper studies how a unicellular algae changes from its free swimming state to a surface attached gliding state.

Figure 1: Left: Chlamy’s normal swimming beat pattern, with different colors showing different time points. The cell body is shown in blue and the eyespot in red. Image adapted from [1]. Right: Gliding Chlamy moves due to proteins moving within the flagella. Image adapted from [2].

Kreis and co-workers investigate the unicellular green algae called Chlamydamonas reinhardtii, or Chlamy for short. It has two whip-like arms, called flagella, that it uses to move. In the swimming state, the flagella beat in a breaststroke to pull the cell forward, as shown in Figure 1A. In the gliding state, the flagella are stuck to a surface and the transport of proteins inside each flagellum pulls on the surface so the Chlammy moves across the surface, as shown in Figure 1B.

micropipetteFM2008 — Figure 2: In micropipette force microscopy a small glass tube holds the cell. A surface (the substrate) can then be moved towards or away from the cell. The deflection of the micropipette as this occurs determines how sticky the cell is. All of this is done in water, where Chlamy lives normally. Image adapted from Kreis and coworkers’ paper.

To transition between these two movement methods, the Chlamy must attach and detach from the surface. The researchers measure the force Chlamy exerts on a surface when it attaches using micropipette force microscopy, shown in Figure 2. This method uses a micropipette, which is a small glass tube, to hold a single Chlamy cell in place with suction. The surface is moved towards or away from the cell, deflecting the micropipette from its original position based on the force the cells exert on the surface. The relationship between deflection distance and force is measured beforehand with calibration experiments. So, during the experiment, micropipette deflection yields how strongly cells are stuck. To understand how this force relates to the two movements methods, let’s look at the results.

frontandback2008 — Figure 3: Adhesion force as a function of distance from the surface to the cell. The surface is initially 20 micrometers away from the cell and is moved closer, so the cell and surface touch. As the surface is moved away again we can see if the flagella-facing cell (a) or the back-facing cell (b) attach to the surface from the adhesion force that is built up. Figure adapted from Kreis and coworkers’ paper.

Figure 3 shows two force measurements, one where the flagella are facing the surface and another where the back of the cell is facing the surface. When the surface touches the flagella or back of the cell body, the micropipette is first deflected upwards, giving a positive force. As the surface is moved away, the micropipette moves back to its original zero-force position.

As the surface is moved further away, the flagella-facing cell and back-facing cell behave differently. The flagella-facing cell deflects the micropipette downwards, shown by the build-up of a largely negative force, whereas the back-facing cell does not deflect the micropipette and no force is exerted. This means that the flagella-facing cell sticks to the surface, whereas the back facing cell does not stick.

pullandgraph1009 — Figure 4: Top row – left to right shows successive images of Chlamy pulling itself towards a surface – dashed red line shows the movement of the micropipette. The flagella are marked by solid red lines. Bottom row – micropipette deflection over time as the light is turned on and off as indicated by the arrows. Figure adapted from Kreis and coworkers’ paper.

The flagella not only stick but actively pull themselves towards the surface. At the top of Figure 4, we see the flagella touch the surface during their swimming beat cycle. First, just a small part of one flagellum is stuck to the surface. Then, the flagella actively pull themselves towards the surface until both are completely stretched out and ready for gliding. This process is reversible: as the light is turned on and off, so is the adhesion force. The Chlamy can pull themselves up again and again – transitioning between their stuck and free state.

difflight2008 — Figure 5: Force-distance curves for the retraction of a surface under different wavelengths of light. The flagella only stick when shorter wavelengths of light are present. Figure adapted from Kreis and coworkers’ paper.

But what controls the transition? To answer this, the researchers repeated the experiment under different wavelengths of light. In Figure 5, we see that the stickiness peak is absent for red and green light but present for blue and purple light. Two potential light sensors could be responsible. One is on the cell’s eyespot and controls cell swimming to guide the cell towards the light. The other is on the flagella and controls the cell life cycle and several aspects of the cell’s mating process. But we don’t yet know which light sensor controls the stickiness, or which specific proteins make the flagella sticky.

So for the Chlamy, the decision to stay or go is made by checking if the lights are on! If they ‘go’ they can seek lighter environments, and if they ‘stay’ they can bask in the sunny spot. Watching Chlamy cells stick and un-stick as we flick a light switch is very cool, but why should we care about Chlamy? Chlamy is used in bioreactors to create biofuels and other bioproducts. Stuck Chlamy prevents light and nutrients from getting to all the cells in the reactor, so we need to understand how to control the sticking process. Plus – if we understand how a simple unicellular organism solves the problems of life, we can use this bio-inspiration for new technologies – in this case possibly new light-switchable adhesives.

[0] Should I Stay or Should I go?

[1] Antiphase Synchronization in a Flagellar-Dominance Mutant of Chlamydomonas

[2] Intraflagellar transport drives flagellar surface motility

Featured image for the article is taken from the original article.

[1] Mirny, Leonid (2011), The fractal globule as a model of chromatin architecture in the cell. Chromosome Res.Featured image for the article is taken from Wikimedia Commons.

[1] Mirny, Leonid (2011), The fractal globule as a model of chromatin architecture in the cell. Chromosome Res.

Featured image for the article is taken from Wikimedia Commons.