Category: research

We are writing summaries of research papers.

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Using sound to build a wall: how physicists measure pressure in active systems

Original paper: Acoustic trapping of active matter

You know how sometimes you tell to yourself things like “life is complicated”? Theoretical physicists are constantly reminded of this fact when studying living organisms. Recently, a new field of physics has emerged, inspired by the observation of living systems. What forces do cells exert during metastasis in cancer? What are the growth dynamics of biofilms of bacteria? How can a school of fish organize itself and move simultaneously? These are questions raised in the physics of active matter. Active matter is an assembly of objects able to move freely and capable of organizing into complex structures by consuming energy from their environment. Active matter can be composed of living or artificial self-propelled particles.

However, active systems differ from a simple gas or liquid because they are out-of-equilibrium. A system is in equilibrium if there is an energy balance between the system and the environment. When the energy isn’t balanced, the system will evolve toward an equilibrium state. Imagine a ball on a hilltop: it is in an out-of-equilibrium state until it has rolled down and stopped at bottom of the hillside. Now imagine that the ball is an active particle. This means it can consume energy from its environment to propel itself back up the hill, which drives the system out of equilibrium.
But physical notions such as pressure or temperature, are defined in thermodynamics only at equilibrium. This is why bridging the gap between physics and active matter has been a new challenge for theoretical physicists. Today’s paper focuses on the definition of a new quantity called swim pressure and highlights how researchers achieved its experimental measurements using an acoustic trap.

Rather than dealing with living organisms in this study, Sho and his collaborators used a system of artificial self-propelled particles, called Janus particles. They are made of two half faces; one in polystyrene and one in platinum [1]. Once immersed in a liquid, the platinum coating reacts with hydrogen peroxide contained in the liquid. The available energy resulting from this chemical reaction is then converted into motion. Particles move individually and randomly (analogous to an atom’s motion in a gas).

Due to self-propelled motion, active particles exert a mechanical force on their surrounding boundaries. In other words, a particle would naturally swim away in space unless confined by walls. The pressure exerted by active particles on the walls that confine them is the swim pressure. This is analogous to the definition of pressure from a microscopic point of view, which is the result of atoms colliding on a surface. Now that the theory is set, researchers try to measure swim pressure experimentally. But to control, confine and observe micro-particles between walls that you can remove at will is quite a challenge.

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Figure 1. The curves represent two profile of an acoustic wave throughout time. Particles migrate to nodes due to the difference in acoustic pressure between nodes and antinodes.

Sho and his collaborators at California Institute of Technology did not actually use physical walls in their experiment but instead used sound. When an acoustic wave propagates through a material, the deformation of the material causes a local pressure. Using this acoustic pressure, researchers can move objects between specific locations called nodes, which are special locations where the pressure wave is stable in time. The local pressure is minimal at nodes, while pressure is maximal at antinodes (see Figure 1). Since objects move from high to low pressure, the particles become trapped at nodes (see Figure 1). This technique is called an acoustic tweezer, or acoustic trap. Here, researchers built an acoustic trap such that many particles are confined over a large trap area.

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Figure 2: a-c. Snapshot of Janus particles in an acoustic trap (watch movie here). The red spot is the center of the trap and the white dashed line represents the contour of the acoustic trap. d. The figure shows trajectories of Janus particles moving randomly inside the trap (images adapted from Sho and coworkers’ original paper).

The researchers also adjust the size and force of the trap as a function of the velocity of active particles. Over time, more particles get trapped, and a densely packed cluster forms (see Figure 2). Particles can move within the trap area, but cannot exit (see Figure 2d). Then, when the acoustic tweezers are turned off, the cluster explodes! Meaning that free from confinement, active particles spontaneously disperse (see Figure 3). Thus, knowing the acoustic pressure and measuring the dispersion of particles over time allows researchers to measure the swim pressure.

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Figure 3. Snapshots of Janus particles at different times after the acoustic trap has been released (watch movie here). The active cluster explodes, resulting in Janus particle dispersion (Images adapted from Sho and coworkers’ original paper).

When you inflate a soccer ball with a pump, the walls will experience more collisions with the air molecules, meaning pressure increases. Similarly, squeezing the ball reduces space between the molecules and also results in an increase in pressure. These types of pressure changes are analogous to those observed in Sho and collaborators’ experiments. As shown in Figure 4, swim pressure increases over time as more particles get trapped (like pumping air into the soccer ball). Swim pressure also gets stronger for smaller trap area (like squeezing the soccer ball). But despite the analogy, we must not overlook the complexity behind the physics. Swim pressure is different from the pressure we experience every day, which comes from atoms and molecules. Here the classical model of pressure is an inspiration to build a new model. And as Figure 4 illustrates, the theory is consistent with experimental observations and validates this concept of swim pressure.

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Figure 4. Evolution of the swim pressure as a function of time for two different size area. The swim pressure is higher for smaller trap areas. Researchers compare here experimental data with numerical simulations and theory (adapted from Sho and coworkers’ paper).

To conclude, today’s paper shows how classical physics quantities can be redefined to describe a new phenomenon in active matter. Sho and his collaborators used an ingenious device to measure the swim pressure exerted by active particles for different degrees of confinement and different crystal size. Their results confirm experimentally the theory of swim pressure established in a new approach of active matter, and open ways to a better description of the living world (from molecular to cells dynamics, bio-films formation, collective motion…). So indeed, life might be complicated, but from the point of view of scientists, this is what keeps them excited.

[1] these particles were named Janus particles in reference to the Hall-faced Roman God Janus.

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The Ketchup Conundrum and Molecular Dynamics: Unraveling the Mystery of Shear Thinning

Original paper: Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids

We’ve all been there. We try pouring ketchup onto our fries from the bottle, but it doesn’t come out. So we tap the back of the bottle a few times, and suddenly, the ketchup rushes out and your entire meal is covered with it. Why does the ketchup exhibit such behavior?

This behavior is called shear thinning, and only some special fluids exhibit it. For fluids, such as water and alcohol (these are called “classical” or “Newtonian” fluids) viscosity only depends on temperature. Therefore, if the temperature doesn’t change, the viscosity remains constant (see the red curve in Figure 1). However, in non-Newtonian fluids, viscosity depends on another variable called the shear stress. Shear stress is the stress felt by materials when they undergo deformation caused by slip or slide. In shear-thinning fluids, which are a type of non-Newtonian fluids, the viscosity decreases when the shear stress increases (see the blue curve in Figure 1). Ketchup, with other suspension fluids such as blood and nail polish, falls into this category of shear-thinning fluids. So, by tapping the ketchup bottle, we apply shear stress to the ketchup inside, causing the viscosity to drop and making the ketchup flow out of the bottle. But, even though this phenomenon has been on scientists’ radar for a long time, the microscopic mechanism for shear thinning is still unknown for certain fluids.

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Figure 1. Shear stress vs. viscosity of Newtonian and shear-thinning fluids.

Another type of fluid that exhibits shear-thinning behavior is the  “supercooled” liquids. As shown in Figure 2, when a liquid – any liquid – is rapidly cooled below its freezing point, instead of crystallizing and solidifying (like what we typically see when water freezes in an ice-cube tray), it forms a supercooled liquid. When the temperature of this highly viscous liquids drops even further below its glass-forming temperature, it turns into a disordered glass-like phase [1]. That is why supercooled liquids are also called glass-forming liquids.

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Figure 2. The relationship between the volume of liquid and supercooled liquid. Tf and Tg indicate freezing point and glass-forming temperature, respectively.

To understand the flow behavior of supercooled liquids, Trond Ingebrigtsen and Hajime Tanaka of the Institute of Industrial Science at the University of Tokyo ran molecular dynamics simulations. Molecular dynamics simulation is a computational method for studying the interactions of atoms or molecules. From the simulations, Ingebrigtsen and Tanaka were able to confirm what other scientists had previously suspected: shear thinning is linked to the increase in structural disorder of the liquid molecules (as illustrated in Figure 3(a) and 3(b)). To be more specific, it is linked to the structural disorder of molecules in the flow direction.

As a model for supercooled liquids, the authors chose to simulate a colloidal system, where molecules interact in a similar way to realistic fluids. After verifying that the simulates system acts like a supercooled liquid (for example, its viscosity decreases with increasing shear rate), they investigated the origin of shear thinning using this model. The molecular simulation revealed that as the shear rate increases, the molecular structure becomes more disordered. This is illustrated in Figure 3(a) and 3(b). More notably, the structural disorder was more prominent in the direction of the fluid flow compared to the structural disorder measured in any other directions relative to the flow. This can be seen from the black line of Figure 4(a), where the steep decrease of structural order could be observed with increasing shear rate.

Indeed, the structural disorder turned out to be the culprit behind the shear-thinning behavior in supercooled liquids. As shown in Figure 4(b), when the molecular structure becomes more disordered, the viscosity of the liquid decreases, a behavior expected in shear-thinning fluids. To understand this result, let’s picture molecules in the fluid. The shear applied in the direction of the flow would open up more space for molecules to rearrange themselves as the fluid expands, like it is shown in Figure 3(c). This leads to the decreased viscosity and the easier fluid flow.

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Figure 3. (a) Structurally ordered molecular system. (b) A molecular system with increased disorder. (c) System after shear deformation in the flow direction.

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Figure 4. (a) Shear rate versus structural order of the supercooled liquid model used in the molecular simulation. The black line represents the flow direction (blue and red each represents other two directions relative to the flow.) (b) Structural order versus viscosity. (Note the log scale on the y-axis.) All figures are adapted from the original paper.

This study sheds light on the previously unknown mechanism of shear thinning in supercooled liquids. Ingebrigtsen and Tanaka, however, insert that the microscopic mechanism for their observation should be further studied to fully understand the shear-thinning behavior. So, next time a disaster happens on your fries, chill out and think that you are just carrying out a super cool non-newtonian experiment!

 

(This post was updated on March 4th, 2020 to answer a comment that was made on the French translation of this post.)

 

[1] Technically, glass isn’t a phase, though I used that word for simplicity. Glass is an amorphous solid that has a disordered molecular structure (unlike ice, which has a well-defined crystalline structure). See Figure 3(b) for a visualization of a disordered molecular structure.

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Tiny Tubes Racing in a Donut-Shaped Track

Original paper: Transition from turbulent to coherent flows in confined three-dimensional active fluids

The shape of a container can affect the flow of the fluid inside it. Water in a narrow stream flows smoothly, but once the water molecules make their way into a pond, they spread out and no longer flow coherently. If you blow into a long, narrow straw, the air will go straight through. Once the air flows into the large room you are standing in, it slows down as it mixes with the air around it, so someone standing five feet away from you won’t feel a breeze at all.

The above examples show how the shape of a container affects the flow of passive fluids. In today’s study, Kun-Ta Wu and colleagues investigated how the motion of active fluids, fluids that flow using an internal source of energy, is also affected by the shape of their container. They used a system of microtubules, chains of proteins assembled into long, stiff rods. Clusters of a protein called kinesin exert a force on microtubules by “walking” along them. Microtubules interact with each other to form swarms or turbulent-like flows.

Wu and colleagues created 3D toroidal racetracks with rectangular cross-sections to confine the microtubule bundles. They saw coherent flows in racetracks with square cross-sections, but if the channels got either too thin and wide or too tall and narrow, the flow became turbulent (Figure 1). This result is described in this Softbites post from last year.

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Figure 1: Comparison of coherent and turbulent flows around a track. The left side of each track shows the motion in an instant, while the right side shows the average motion over a long time. The color represents the local direction of spinning and the black arrows indicate the direction of motion. Microtubules in a red spot are spinning clockwise, those in a yellow spot are not spinning, and those in a blue spot are spinning counterclockwise. Image adapted from original article.

After Wu and colleagues got microtubules to flow by themselves, they placed them in increasingly complicated tracks. Active flows happened in any closed loop with an approximately square cross-section. Microtubule flows solved a maze, as in Figure 2, by flowing through the connected straight and curved sections, but not sections leading to dead ends. The dead ends slowed down the flow in the connected sections to about half the speed of a toroidal racetrack with an equivalent length.

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Figure 2: Microtubules flow in straight and curved sections of the maze in closed loop, and no net flow loop in sections leading to dead ends. Black arrows show the direction of the flow and colorful arrows point to sections at which mean flows are measured. Figure adapted from original article.

Wu and colleagues then created tracks made out of overlapping tori, or donuts. In the tori, microtubules spontaneously flowed in the same or in different directions, as in Figure 3. When the active flow was clockwise in one torus and counterclockwise in the other, the direction of flow in the overlap was the same, and the flow kept going (A). When they were both counterclockwise, two flows came into the overlap in opposite directions, and there was no flow in between the tori (B). Watch a video of this here.

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Figure 3: Microtubules can flow in connected tori in (A) the same direction and (B) opposite directions. Figure adapted from original article.

Microtubules created an active flow when a third torus was added (Figure 4A). They also navigated a square racetrack, although the corners created small vortices and slowed them down (Figure 4B). Finally, microtubules still flowed in a very long torus made out of a 1.1 meter-long tube joined at the ends by a needle (Figure 3C).

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Figure 4: (A) Flows in 3 overlapping tori. (B) Microtubules flow around a square racetrack in the direction of the blue arrow. (C) Microtubules even flowed around a very long (1.1 meter) track. The closeup shows a time-averaged flow inside a small section of the tube. Figure adapted from original article.

 

Thus, these flows of microtubules aren’t just a one-time phenomenon that’s hard to replicate—no matter how much the researchers changed the system, as long as there was a closed loop with an appropriate cross-sectional aspect ratio, there was a flow.

These flows inside channels are interesting—but are they useful? The researchers suggest that a system like this could act as an internal power source for very small devices, but this application is still far in the future. It is also possible that a similar motion is used inside living cells to transport materials in a process called cytoplasmic streaming. More importantly, these flows are a beautiful example of collective motion induced by physical forces, helping scientists elucidate how swarms can form at all length scales.

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Spell Checking Boiolgy

Original paper: Kinetic Proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high specificity

Cells are sacks of chemicals that, through the trials and tribulations of evolution, have gained the ability to read information from their environment and then produce an output that assists in the larger organism’s survival. Mis-handling this information can lead to cell malfunction, mutation, or death, so it is important to understand how this works and how often it doesn’t. Using simple thermodynamic calculations, error rates are estimated to be thousands of times higher than they actually are (lucky for us!). Fundamentally, cells must obey the laws of thermodynamics, so some unknown intermediate process(es) must be dramatically reducing the number of errors in information processing. The question then becomes, what is that process? In a classic paper from 1974, J.J. Hopfield gives us an answer in a process he called kinetic proofreading. In doing so, Hopfield introduced the field of biophysics to the fundamental trade-offs that cells must make between using energy, accurately making a decision and the speed with which decisions can be made.

Before getting into kinetic proofreading, let’s get a better feel for our process of interest: protein synthesis. The central dogma of molecular biology can be summarized as DNA ? RNA ? Proteins. For the sake of simplicity, we will focus a bit more on the RNA ? Proteins part. Like DNA, RNA molecules are long polymers that can be written down (or coded) as a simple sequence of letters. What’s really important is each three letter group called a codon. As the name suggests, each codon is a three-letter code associated with a specific amino acid [1]. When chained together in the order dictated by RNA, amino acids form a protein. Proteins then go on to perform almost every biological function you can imagine.

The RNA and the proteins are the input and output for our simplistic thermodynamic error estimate above (the one which predicts too many mistakes). Well, it turns out that this picture isn’t quite complete — there is also an emissary between the RNA and amino acids called “transfer” RNA, or tRNA. The tip of the tRNA directly binds onto the right amino acid, holding it in place as the growing protein gets formed.

It is extremely important that tRNA can (1) bind the right amino acid and (2) hold on to it for long enough to build the protein. Let’s call the tRNA binding site c and the amino acid X. When c and X meet, they create a combined unit cX, which is then produced into a protein. This can be written as the following reaction equation:

$latex c + X \underset{k_{on}}{\overset{k_{off}}{\leftrightharpoons}} cX \overset{W}{\rightarrow} protein$.

Let’s step through it. It says that X and c combine at an on-rate kon to form combined product cX, which we can think of as the amino acid attached to the tRNA molecule. cX can then either break apart at an off-rate koff, or it can go on to create the protein at a rate W. It turns out that kon doesn’t vary much for different amino acids, but the off-rates do. Experiments have measured that tRNA bound to the correct amino acid has a lower off-rate, giving more time for it to be produced into the correct protein. While tRNA unbinds a wrong amino acid faster, it still might go on to make a protein by accident. You can think of the wrong amino acid as being more “slippery” than the right one — tRNA can grab either one, but it is harder to hang on to the wrong amino acid. Using these differences in off-rates, one can estimate what the expected error fraction would be for proteins. The problem is that this estimate is way bigger than measured error fractions! Hopfield hypothesized that there must be something actively happening to close the gap. He named the exact mechanism he came up with kinetic proofreading.

The key to kinetic proofreading is to extend the time that the amino acid and the tRNA stay bound. This way, the tRNA is more likely to let go of the wrong, “slippery” amino acid, but hang on to the right one. Hopfield proposes putting an intermediate step between cX and the product. However, to be actually useful, going into the intermediate step has to be irreversible. To make something irreversible means to break time-reversal symmetry, which requires the consumption of free energy, usually in the form of “burning” ATP, the fuel used by cells. By burning this fuel, a slightly different form of cX is created, let’s just call it cX*. This new combined product is the one that then goes on to make the final product.  By adding this new intermediate step — the act of using up ATP to create cX* — it is possible for the amino acid to stay bound to the tRNA for twice as long as without the intermediate step. You get to run the process of discriminating between right and wrong amino acids twice, decreasing the error fraction significantly.

This argument that spending free energy can increase the accuracy of synthesizing proteins, has become a staple in understanding biophysics. Cells operate out-of-equilibrium by consuming energy and therefore are able to accomplish tasks much more accurately. Another trade-off is that the decision to be made, i.e. making the right protein, is done more slowly. These energy-speed-accuracy trade-offs are essential not only for protein synthesis but also DNA replication and triggering immune responses by T-cells recognizing foreign invaders. Equilibrium is death. By consuming energy from our surroundings, we are able to fend off the onslaughts of entropy and remain alive.

[1] There are approximately 20 amino acids, and there are different codon sequences that code for the same amino acid. ^

 

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Spider silk: Sticky when wet

Original paper: Hygroscopic Compounds in Spider Aggregate Glue Remove Interfacial Water to Maintain Adhesion in Humid Conditions 

If you were Spider-Man, how would you catch your criminals? You could tangle them up in different types of threads, but to really keep them from escaping you would probably want your web to be sticky (not to mention the utility of sticky silk for swinging between buildings). Like Spider-Man, the furrow spider spins a web with sticky capture silk to trap its prey. This silk gets its stickiness from a layer of glue that coats the thread. What makes this capture silk really interesting is that, unlike commercial glues, these spider glues don’t fail when wet.

The tendency for water to interfere with glues should come as no surprise. For example, sticky bandages become unstuck when they’re wet, whether it’s because of swimming, taking a shower, or going for a run on a humid day. This interference occurs on the microscopic scale, where water prevents the components of a glue from forming adhesive chemical bonds. Even just high humidity provides enough water vapor in the air for it to condense on nearby surfaces and interfere with adhesion. One would naturally expect this very general and simple mechanism to cause problems for spiders that lay traps near water, as our furrow spider does. As you may have guessed, our furrow spider is a bit more clever than that: their glues are highly effective regardless of the water content of the air, and this humidity-resilience has caught the attention of Saranshu Singla and colleagues at the University of Akron, Ohio.

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Figure 1. A spider unperturbed by the water droplets formed on its sticky web.

The furrow spider glue being studied by Singla and co-workers is essentially a cocktail of 3 main components: specialized “glycoproteins” that act as the primary adhesive molecule, a group of smaller low molecular mass compounds (LMMCs), and water. The LMMCs group covers a wide range of chemicals (both organic and inorganic), but the main distinguishing feature of this group is that they are hygroscopic, which means they are water absorbing. The exact recipe of this glue is specific to each spider species, and previous research has shown that individual species’ glues stick best in the climate that spiders evolved in—rather than humidity causing them problems, tropical spider webs are in fact most effective in humid conditions.

To understand how spiders achieve this, the researchers used a combination of spectroscopy [1] techniques to observe the arrangement of molecules during adhesion. They took a densely packed layer of web threads collected from the furrow spider and stuck them to one side of a sapphire prism, an ideal surface for its smoothness and transparency to the light rays used for spectroscopy (See Figure 1 for experimental schematic). They then measured the chemical bonds at the point of contact between the glue droplets and the sticking surface over a range of humidity conditions. These measurements allowed them to figure out what happens when these sticky glues get coated in water.

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Figure 2. Experimental setup schematic from the manuscript. The white scale bar in c is 0.1 mm. Here “flagelliform” refers to the silk material prior to the glue layer being added, and “BOAS” refers to the classic beads-on-a-string structure that droplets form on threads. SFG stands for “sum frequency generation” spectroscopy, the noninvasive technique used in this research for analyzing the molecular arrangement at the sticking interface between the glue droplets and the sapphire surface.

Singla and her colleagues find that there is very little liquid water at the sticking interface, despite water being one of the three main glue elements. They concluded that the hygroscopic LMMCs are drawing water away from the droplet surface and storing it near the center. The LMMCs make it possible for the sticky glycoproteins to fulfill their role: in high humidity the glue droplet first absorbs nearby water, and then draws that water away from the droplet surface, preventing it from interfering with the sticky molecules’ adhesive chemical bonds. The researchers also conclude that the glue’s efficiency at drawing water to the center of the droplet is controlled by the local humidity and the ratio of the three components. Tweaking this ratio would then make the glue better adapted to different humidities. This suggests that the addition of hygroscopic compounds provides a simple method to tune adhesives to suit specific environments.

This continues to be an exciting time for materials science as scientists unlock the secrets of nature, but perhaps more importantly, Peter Parker can now rest easy with the knowledge that Humidity-Man will be a highly ineffective foe.

1. Broadly, spectroscopy is a study of the interaction between matter and light. There are many different types of spectroscopy, as there are many different ways that light and matter interact, but typically, a beam of light covering a range of the electromagnetic spectrum (hence the “spectro” prefix) is shone onto a substance, and then regathered by a light detector. The brightness of the detected light at each wavelength can then be used to carefully analyze the properties of the substance. Here, the researchers combined infrared spectroscopy and SFG, a non-invasive technique that is specifically tailored to probe molecular arrangements at interfaces, and so is perfectly suited for probing interfacial adhesion.

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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.

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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.

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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.

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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.

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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.

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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

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Flocking rods in a sea of beads: swarms through physical interactions

Original papers: Flocking at a distance in active granular matter

Many living creatures, such as birds, sheep, and fish, make coherent flocks or swarms. Flocking animals travel together, coordinating their speed and turns in an often visually striking manner. This can have benefits for the animals – flocking birds can use aerodynamics to fly more efficiently, sheep can move together as a group to evade predators, and fish can use collective sensing to find preferred locations in their environment. Flocks emerge in biological systems because animals try to follow their neighbors.

But how about non-living things? Can they spontaneously form swarms without any biological motive?

In “Flocking at a distance in active granular matter”, Nitin Kumar and colleagues investigate how non-living rods can form flocks just like animals do. They create a flock of self-propelled rods in a sea of spheres and show how a small concentration of these rods can transport a large load of passive spheres.

In this study, the active agents are cone-shaped brass rods, as in Figure 1a, that move through a layer of aluminum beads. The rods and beads are placed in a flower-shaped dish, as shown in Figure 1b, and covered by a glass lid. The surface vibrates, making the rods bounce up and down. Friction between the floor and ceiling propels a rod in the direction of its tip. Thus, each otherwise immobile rod moves by itself. Because the rod shape isn’t perfect, it turns a little with each movement, and randomly wanders around the surface.

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Figure 1: (a) Schematic of a cone-shaped rod. (b) Experimental setup of brass rods moving through aluminum beads. The flower shape is used to prevent rod clumping at the walls. Figure adapted from the original article.

 

At low concentrations of both rods and beads, the rods wander around randomly and independently of one another. Past some critical concentration of either, however, the rods suddenly align and swarm around the surface in a random direction. Once the rods begin swarming clockwise or counterclockwise, they do not change which way they swarm.

A comparison of randomly moving and aligned rods is shown in Figures 2a and 2b. The motile rods drag the inactive beads alongside them. The flow of the beads then reorients rods throughout the surface, until the rods are aligned. This is similar to what happens in biological flocks, where each animal tries to follow their nearest neighbors. Small turns of individuals turn the entire flock, forming beautiful patterns.

The researchers created a “phase diagram” of rod and bead concentrations in the experiment (Figure 2c). At rod and bead concentrations below the black line, the rods move randomly. When either rod or bead concentration is increased, swirling begins. Increasing the number of rods increases the number of agents that can interact with each other. Increasing the number of beads increases the density of material through which the rod forces propagate. Finally, if the concentrations are too high, the system becomes jammed, and the rods can’t move enough to align in the first place.

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Figure 2: (a) Randomly moving rods. (b) Aligned rods swirling in the same direction. (c) Phase diagram showing transitions between the different behaviors of the rods and beads depending on how concentrated they are. Image adapted from the original article.

So far we’ve just discussed the motion of the rods. But what about the beads themselves? The flocking rods push them in a coherent pattern, the velocity field of which is shown in Figure 3. The rods don’t just align – they also affect their surroundings, and transport the beads as cargo.

4-3
Figure 3: Velocity field of beads that are pushed around by swirling rods.

To figure out how rods align and swarm, Kumar and colleagues developed a mathematical model for the sea of beads and rods as a “fluid” of moving beads (since there are many more beads than rods) and simulated the motion of all the rods and beads. They identified two key parameters in their equations that corresponded to:

  • Adding more rods or stronger rods results in more beads being dragged, increasing the force on each rod.
  • The “weathercock effect” affects how easily rods turn to follow the flow of the beads surrounding them. A rod with an off-center pivot (as in Figure 4) that experiences a force from the surrounding beads will turn in the direction of the forcing.

The interplay of rods pushing beads, and beads reorienting rods, form a swarm.

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Figure 4: “Weathercock effect” reorients rods with an off-center pivot in the direction of the flow of the surrounding beads.

This study shows that simple mechanical interactions can cause swarms. Living creatures, such as fish and bacteria, may have taken advantage of the swarms caused by their interactions with each other to survive as they evolved.

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The Origin of Random Forces Inside Cells

Original paper: Probing the Stochastic, Motor-Driven Properties of the Cytoplasm Using Force Spectrum Microscopy 

Place yourself in a bumper car at a carnival waiting to bump into your friends. Soon enough you hear the small engine of your bumper car start and you begin to move around, bumping into anyone in your way. While the motion of your car is mostly controlled by the steering wheel, random events—like fluctuations in the motor power, your car hitting small bumps on the floor, and other cars hitting you—can affect the motion as well. What if I told you that a cell and its parts function in a similar way? Just as your car is powered by electricity, molecular motors—bio-molecules that can convert chemical energy into mechanical work—power the movement of living organisms by generating forces. In order to produce these forces, molecular motors depend on an organic molecule called ATP [Footnote: Adenosine TriPhosphate]. And just like the fluctuations in the motor power of the bumper car, random fluctuations can also be produced by the molecular motors.

The motion caused by molecular motors is necessary for the functionality of the cell—for example, division and contraction. However, it’s not this directed motion that’s studied in today’s paper, but rather the random fluctuations that accompany it.  But how can we extract useful data from random movements like those in the cytoplasm? One way is to measure the mean squared displacement (MSD) of a particle in the fluid. The MSD is a measure of how far a particle moves from its starting point over time. Going back to the example of the bumper car, you could find your MSD by tracing your path and seeing how far you have moved from your starting point over time1.

 

Screen Shot 2018-09-11 at 9.24.32 PM.png
Figure 1: Trajectories of particles inside a cell show Brownian-like motion.

To investigate the motion of particles in the cytoplasm, Guo and colleagues injected tiny particles into the cells and tracked their motion using confocal microscopy—a technique that allows for the precise tracking of the 3D position of micro-particles. After tracking the particles over time, Guo calculated the MSDs of the particles2.

Guo and colleagues observed that at short timescales, t ? 0.1s, the MSDs were nearly time independent, meaning that they did not change over time (see Figure 2A). This type of motion is typically observed in elastic solids, where particles can never move very far from their starting points. At longer timescales measured, 10s ?t ? 0.1s, the MSDs grew linearly with time. This type of motion is called Brownian motion and is usually observed in particles moving in viscous fluids under the influence of thermal forces. This association between linear MSDs and Brownian motion is strong enough that researchers have sometimes assumed that that particles inside cells move primarily due to thermal forces.  However, as discussed earlier, molecular motors generate forces inside the cytoplasm. Is it possible that random forces from molecular motors affect the motion of the particles?

In order to answer this question, Guo and his colleagues reduced the amount of ATP in cultured cells, thus reducing the activity of the molecular motors. They observed that the MSDs of particles inside ATP-depleted cell didn’t exhibit the linear MSDs seen in the untreated cells (see Figure 2B). This observation means that forces causing Brownian motion in the cytoplasm were ATP-dependent and therefore not generated by random thermal motion alone.

 

Screen Shot 2018-09-11 at 9.26.01 PM.png
Figure 2: MSDs of Microinjected Particles
(A) The average MSDs of different sized particles were plotted against time. On the plot, the dashed line corresponds to Brownian motion. (B) The MSDs normalized by particle diameter 3 in untreated (normal, ATP-containing) and ATP-depleted cells. The particles in ATP depleted cells move much less, and do not exhibit Brownian motion.

 

In short, Guo and colleagues showed that molecular motors impact the random motion inside the cytoplasm of a cell. The team proved this by measuring the MSD of particles inside cultured cells. They then depleted ATP in the cells to observe any changes in the MSDs of the particles inside. They found that movement inside the cytoplasm was largely affected by random molecular forces produced by molecular motors and not solely due to thermal forces.  However, this discovery raised more questions. For example: why do these molecular motors, which exert directed forces, exhibit random movements? We’ll answer this question in a follow-up post by considering the elastic network that couples molecular motors.

1. Note that a post by Christine Middleton has gone over a slightly different application of the MSD here: https://softbites.org/2018/04/25/the-matter-of-maternal-mucus-permeability-and-preterm-birth.?

2. Mean Squared Displacement: <?r2(?)> ; < ?r(?) > = r(t+?)-r(t) ?

3. The purpose of normalizing the data is to more easily compare the data between different particle sizes. ?

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From errant to coherent motion

Original paper

Emergence of macroscopic directed motion in populations of motile colloids. By Bricard A., Caussin J-B, Desreumaux N., Dauchot O. & Bartolo D.

Have you ever seen those wide shapes moving in the sky at dawn, made of thousands of starlings, or the swarms of fish swimming in the ocean (see Figure 1)? The ability to organize and move in groups without a leader is called collective motion and has been observed at various spatial scales in the living world, from birds to locusts, cells, and bacteria. Even humans can perform collective motion in some situations, as it has been modeled in crowd movements (for example Mosh pits). Physicists have gazed at this phenomenon over the last couple of decades trying to answer questions such as: How can different organisms exhibit the same behavior? What common features do all these organisms have that allow them to move in such a synchronized way?

The key to the emergence of collective motion is interactions, the ability of individuals to modify their behavior to coordinate their movements with those of their neighbors. The details of these interactions are difficult to model and control in many living or man-made systems, or may even still be unknown. Yet, in today’s paper, Antoine Bricard and colleagues showed how collective motion can arise solely from known physical interactions.

birds_fishes
Figure 1. Examples of collective motion in nature. (a) a flock of starlings (image adapted from howitworksdaily.com), (b) a swarm of fish (image adapted from scielo.br).

One of the first scientists who tackled these questions was Tamas Vicsek in the 90’s. He showed how collective motion can emerge from simple rules using a computer simulation. Although numerous theoretical and numerical studies followed, only few experiments were done. The biggest difficulty in studying collective motion experimentally is gaining control and reproducibility over a living system. Raising thousands of birds in a lab might not be the most convenient way of study, and even simpler biological systems, like bacteria, have problems of their own. Luckily, if you don’t want to deal with a biological system, you can build an artificial one. This is what Antoine Bricard and collaborators did, at Ecole Normale Supérieure de Lyon. To study collective motion, they built an artificial system made of millions of tiny, plastic beads (5 µm diameter) that were able to move freely, interact with their neighbors, and even self-organize as a group.

To put these inert beads in motion, researchers used a phenomenon called Quincke electro-rotation. The idea is to convert electrostatic energy into mechanical rotation. Here, the rotation is triggered by an electric field, $latex E_0$, applied to insulating beads, which are immersed in a conductive liquid. Under this field, small fluctuations in the charge distribution tilt the orientation of the bead. Then, the small rotational perturbation is amplified, resulting in a constant rotation and the bead rolling on the bottom of a pool. The researchers refer to these activated beads as “rollers”. All rollers move at the same speed, directly controlled by $latex E_0$, yet they don’t move in the same direction but rather randomly. As you can see in Figure 2, the beads move individually in different directions and there is no general directed motion. So how can this disordered system switch to an ordered motion?

Figure quincke
Figure 2. (a) The propulsion mechanism of a bead under an electric field, $latex E_0$, inducing an electric polarization, P. When P is tilted, the bead starts to rotate and moves forward at a constant speed, v. (b) A superposition of 10 images taken at successive timesteps showing the trajectories of 4 rollers activated by the Quincke electro-rotation. (Image adapted from the Antoine Bricard and coworkers’ paper.)

Using Quincke electro-rotation, the exact interactions between the rollers were described by the research team mathematically. Firstly, the beads interact through electrostatics, like two magnets, via an interaction that depends on how far they are from each other. Secondly, the beads interact through hydrodynamics, because when a bead moves in a liquid a flow is generated around it. This generates a pull similar to a swimmer who is feeling the flow produced by another swimmer nearby. What’s more, the theory shows that the combination of these two physical interactions tends to align a group of rollers. When two beads are close enough to each other, they slightly change their course to roll in the same orientation and they all eventually move in the same direction.

To study rollers for millions of particle lengths, the researchers chose to put them in a racetrack-shaped area (Figure 3 a). The rollers spontaneously organized, and a large band made of millions of rollers moved around the track. Of course, rollers had to be close enough in order for interactions to be effective. Figures 3 b-d show how the rollers changed behavior as they get more densely packed. In Figure 3 b, the rollers look like they are wandering in random directions because they are too far from each other to interact, while in Figure 3 d high-density rollers move in the same direction. And as more rollers are added in the same area, the interactions between rollers become more effective. This transition from a disordered state to an ordered state is called a phase transition. In most familiar cases, for example, water-to-ice, phase transitions are driven by temperature. Here density is the control parameter, meaning the research team measured what is the minimum density required for a collective motion to emerge. And being able to couple this observation with a theoretical description of the interactions, the key ingredient underpinning of the system, is what got them further than anyone else at the time.

Figure 3
Figure 3. (a) The racetrack band (watch the movie here) made of millions of self-organized rollers circulating around the area. (b-d) Screenshots of rollers at different densities; (b) at low density, (c) at the front of the band, and (d) at high density of rollers (watch the close view here). (Image adapted from the Antoine Bricard and coworkers’ paper.)

Collective motion seems natural in many living organisms but is still poorly understood by scientists. This paper highlights the importance of interactions between individuals in a group during the process of collective motion. Even though this study is specific and does not account for the mechanisms at work in most biological systems, it was a great achievement toward understanding this phenomenon. Comparing these results with the studies of biologists, ethologists, and mathematicians make me wonder: if a scientist working in his/her lab is like a random walker, then, what beautiful picture will emerge from the work of thousands of scientists interacting with each other to understand collective motion?

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Scaling up biology

Original paper

A General Model for the Origin of Allometric Scaling Laws in Biology. By Geoffrey B. West, James H. Brown, and Brian J. Enquist. Science 1997

Physics is a discipline that attempts to develop a unifying, mathematical framework for understanding diverse phenomena. It connects things as different as planets orbiting the sun and a ball thrown through the air by showing that both these motions come from a single equation [1]. Living things do not seem to obey such simplicity, but hidden beneath all the diversity and complexity of life are remarkably universal patterns called scaling laws. In a landmark 1997 paper by Geoffrey West, James Brown, and Brian Enquist, a simple explanation is given for how all organisms, from fleas to whales to trees, can be thought of as non-linearly scaled versions of each other.

A scaling law tells you how a property of an object, say the rate at which energy is consumed by an organism (its metabolic rate), changes with the object’s size. Just by looking at the data, many quantities scale as a power law of the mass, 

$latex A \propto M^{\alpha}$    (Eq. 1)

where ? is some number that, from the data, always seems to be a multiple of 1/4 [2]. West, Brown, and Enquist build a theory showing how biology could have come up with this 1/4 power law, but in this article, I’m just going to focus on one specific example. I’m going to walk through the author’s arguments for how the metabolic rate, the rate at which an organism consumes energy, scales with an exponent of 3/4. They show that it all comes up from some basic assumptions about the networks that distribute nutrients to your body — your circulatory system [3].

These networks are assumed to have two characteristics [4]. First, they are space-filling fractals. Fractals are shapes made of smaller, repeating versions of themselves no matter how far you zoom into it. However, our fractal blood vessels can’t get arbitrarily small, they have a “terminal unit”— the capillary. The second assumption about these networks is that all terminal units are the same size, regardless of organism size. With these two assumptions, the authors are able to derive the 3/4 power law for metabolic rate.

Branching veins representing as a regular, branching network
Figure 1: Cartoon of a mammalian circulatory system on the left, which can be represented as a branching network model on the right. Adapted from Figure 1 of the original paper.

First, let’s build up a picture of what these networks look like. Figure 1 shows how the circulatory system can be thought of as a network structured into N levels, where each level k has $latex N_k$ tubes. At each level, a tube breaks into a number ($latex m_k$) of smaller tubes. Each one of these tubes is idealized as a perfect cylinder with length $latex l_k$ and radius $latex r_k$, as shown in Figure 2.

Tube parameters
Figure 2: Illustration of the different parameters that each tube on the kth level of the network has. Adapted from Figure 1 of the original paper

How does blood move through this network? Well, the blood flow rate at each level of the network must be equal to the blood flow rate at every other level. Otherwise, you would have the equivalent of traffic jams in your arteries. You don’t want those. If the blood flow speed through one tube in the kth level is $latex u_k$, the blood flow rate through the entire kth level is

$latex \dot{Q}_k = N_k \pi r_k^2  u_k = N_{cap} \pi r_{cap}^2 u_{cap} = \dot{Q}_{cap}$    (Eq. 2)

Your metabolic rate, B, depends on the flow rate through your capillaries, $latex \dot{Q}_{cap}$, so the authors assume that the two are proportional to each other: $latex B \propto \dot{Q}_{cap}$. Because all terminal units are the same size, the only variable left in Eq. 2 to relate to an animal’s mass is $latex N_{cap}$. Assuming that B scales like $latex B \propto M^{\alpha}$, and the authors predict

$latex N_{cap} \propto M^{\alpha}$    (Eq. 3)

branchingRatios-01
Figure 3: Schematic of a branching point along the network, illustrating the definitions of the ratios $latex \beta_k$ and $latex \gamma_k$. In this case, $latex m_k = 2$.

To figure out the value of the exponent $latex \alpha$, the key is to get $latex N_{cap}$, which depends on the size of the organism, in terms of the capillary dimensions $latex r_c$ and $latex l_c$, which do not. To do this, the authors use relations derived using the self-similar geometry of the fractal network. When a tube breaks into smaller tubes, it does so with a ratio between the successive radii, $latex \beta_k = r_{k+1} / r_k$, and another ratio between the successive lengths, $latex \gamma_k = l_{k+1}/l_k$. This is illustrated in Figure 3. Because the network is fractal, the number of tubes each branch breaks into,  $latex m_k$, the ratio of radii, $latex \beta_k$, and the ratio of lengths, $latex \gamma_k$, are all assumed to be constant for every k,

$latex \beta_k = \beta, \; \gamma_k = \gamma, \; m_k = m \;\; \forall k$

Since, at every level, each branch breaks into m smaller branches, the total number of capillaries (i.e. the number of branches at level N) is $latex m^N$. Plugging this into Eq. 3,

$latex \alpha = \frac{N \ln(m)}{\ln(M/M_0)}$    (Eq. 4)

Where  $latex M_0^{\alpha}$ is the proportionality constant between $latex N_{cap}$ and $latex M^{\alpha}$. Remember, we’re trying to show that $latex \alpha = 3/4$.

Now that $latex N_{cap}$ has been rewritten in terms of network properties, the authors next turn their attention to  another quantity that scales with the organism size — its mass, M. To do this, the authors use the empirical fact that the total volume of blood, $latex V_b$, is proportional to the total mass of the organism, $latex V_b \propto M$. The total volume of blood is given by:

$latex V_b = \sum_{k=0}^N V_k N_k = \sum_{k=0}^N \pi r_k^2 l_k m^k \propto \left( \gamma \beta^2 \right)^{-N} \propto M$    (Eq. 5)

In the above equation, the first proportionality sign (summing the series) requires a calculation that’s given here. The main idea of this calculation is that, because the ratios $latex r_{k+1} / r_k$ and $latex l_{k+1}/l_k$ are each constant, the sum in Eq. 5 can be turned into a geometric series which can be summed analytically. Plugging the final proportionality from Eq. 5 into Eq. 4,

$latex \alpha = – \frac{\ln(m)}{\ln(\gamma \beta^2)}$    (Eq. 6)

To make further progress, we have to know something about $latex \gamma$ and $latex \beta$. Every tube of the network gives nutrients to a group of cells. As every good physicist does, the authors will assume that this group of cells has the volume of a sphere with a diameter equal to the length of the tube. The volumes serviced by each successive level are approximately equal to each other,  $latex 4/3 \pi (l_{k+1} / 2)^3 N_{k+1} \approx 4/3 \pi (l_k / 2)^3 N_k$. From this, they get an expression for $latex \gamma$:

$latex \gamma_k^3 \equiv \left(\frac{l_{k+1}}{l_k}\right)^3 \approx \frac{N_k}{N_{k+1}} = \frac{1}{m}$    (Eq. 7)

which means

$latex \gamma \approx m^{-1/3}$

Now the authors move on to $latex \beta$. Earlier, I argued that the flow rate has to be the same from one level of the network to the next to avoid “traffic jams” of blood. Since the tubes are assumed to be perfect cylinders, this boils down to the idea that the cross-sectional area of a parent tube being equal to the total cross-sectional area of its daughter tubes, $latex \pi r_k^2 = \pi r_{k+1}^2 m$. From this, the authors find an expression for $latex \beta$:

$latex \beta_k^2 \equiv \left( \frac{r_{k+1}}{r_k} \right)^2 = \frac{1}{m}$     (Eq. 8)

Similar to the expression for $latex \gamma$, this means

$latex \beta \approx m^{-1/2}$

Plugging in the expressions for $latex \gamma$ and $latex \beta$ in terms of m, we finally arrive at our desired result:

$latex \alpha =  – \frac{\ln(m)}{\ln(\gamma \beta^2)} = – \frac{\ln(m)}{\ln(m^{-1/3}(m^{-1/2})^2)} = 3/4$    (Eq. 9)

What West and his colleagues have done is use the fact that all organisms have to deliver nutrients to their individual parts to derive a general, universal scaling law. The authors go on to show that when you add a pump to the system, such as our heart, the analysis may get more complicated, but the ultimate result remains unchanged. All living things, regardless of size, seem to have arrived at the same solution for nutrient supply, building systems that are space-filling, fractal, and have the same size “terminal units”. Turns out we’re not so different after all.

[1] $latex F = Gm_1 m_2 / r^2$. ^

[2] For example:

  • $latex \alpha = 3/4$ for cross section area of aortas of mammals, tree trunk sizes
  • $latex \alpha = -1/4$ for cellular metabolic rate, heartbeat rate, population growth
  • $latex \alpha = 1/4$ for time of blood circulation, life span, embryonic growth rate ^

[3] All the arguments hold for other distribution systems, such as our pulmonary system, plant vascular systems, and insect respiratory systems. ^

[4] There’s an additional assumption that the network is designed to minimize energy, but that won’t come into play in the part of the author’s arguments that I will be presenting here. ^