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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.

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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.

 

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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. ^

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“Precise” Polymers Promote Fast Proton Transport

Original paper: Self-Assemble Highly Ordered Acid Layers in Precisely Sulfonated Polyethylene Produce Efficient Proton Transport

Global climate change has necessitated the development of ways to harvest electricity from renewable sources, such as the wind and the sun. However, because the wind isn’t always blowing and the sun isn’t always shining, we need to store some of the harvested energy for later use. We can store this energy by converting it into fuels such as methanol and hydrogen, but we need a way to convert it back into electricity when it’s needed. One device that allows us to do this is the fuel cell.

508px-Solid_oxide_fuel_cell_protonic
Figure 1: Example proton exchange membrane fuel cell. Hydrogen gas mixed with water vapor enters on the left-hand side of the device and reacts to produce protons and electrons. The protons drift rightward through the center of the device to react with oxygen to produce water. [1]
Fuel cells are electrochemical devices that can convert a stored simple fuel, like hydrogen or methanol, directly into electricity. Because these fuels can be stored and easily converted near homes, vehicles, and businesses, fuel cells can be used to produce energy on demand. One type of fuel cell is the proton exchange membrane (PEM) fuel cell, which uses hydrogen and oxygen gases to make electricity and water. Hydrogen gas reacts at the anode (the negatively charged electrode) to lose its electrons, forming protons (denoted H+ in Figure 1). The electrons flow first through the fuel cell’s load (e.g. a home or business), powering it, and subsequently to the fuel cell’s cathode. The protons must drift across the proton exchange membrane to meet the electrons and oxygen to form water.

One of the greatest challenges of making PEM fuel cells is designing the membrane after which they are named. Engineers would love to have a membrane that transports protons quickly and efficiently. Although there are polymeric materials (e.g. Nafion) that can do this fairly well, there is still a need for faster transport. This week’s paper investigates the role of a polymer’s “precise” structure in facilitating fast proton transport.

Designing polymers, which are large molecules consisting of repeating units called monomers, with a given role relies on interspersing functional groups along the polymer chain. These functional groups are atoms that may contain some important features, such as electrical charge, necessary for the role of polymer. Under most synthetic schemes, the spacing between these functional groups is random. In the case of a typical proton exchange membrane, such as Nafion, negatively charged groups known as sulfonic acids love to interact with each other and with water present in the fuel cell, forming channels that facilitate proton transport, as shown in Figure 2.

fig2.png
Figure 2: Structure of (left panel) disordered and (right panel) ordered polymer materials. Black lines are the polymer backbone, yellow spheres are sulfonic acid groups, blue spheres are water molecules, and green spheres are water molecules with protons attached. Adapted from current work.

However, because the locations of these groups along the polymer chain are random, each chain cannot organize uniformly, forming disordered channels (Figure 2 left panel). In contrast, Edward Trigg and coauthors were able to attach these sulfonic acids at controlled, repeating locations along the polymer chain. Because the sulfonic acid groups are uniformly dispersed along the polymer (every twenty one carbon atoms to be exact), the chains can fold precisely in the same way, forming a uniformly layered structure and ordered channels filled with protons and water and lined with sulfonic acid (Figure 2 right panel).

The authors of this work first compared this material with Nafion, a widely used PEM polymer that is currently one of the best performing materials available. Like Nafion, this material readily absorbs water into the channels formed by the sulfonic acid groups from the air. The water widens the channels and transports protons more quickly as a result. At high levels of humidity, the new polymer performs as well as Nafion. However, as mentioned earlier, Nafion’s structure is amorphous and disordered because of the random placement of its functional groups (see Figure 2 left panel). Why then is a membrane structure so different from Nafion able to transport protons just as well?

The authors used simulation to answer this question. Specifically, they examined the dynamics of water contained in channels. Faster proton transport is facilitated by faster water dynamics. They compared the ordered and disordered versions of their polymer. The water dynamics in the ordered structure were faster than those in the disordered structure, suggesting slower proton transport in the disordered material. They attributed the slower water dynamics to the nonuniform size and the poor connectivity of the water channels in the disordered structure. These findings suggest that PEM membrane materials like Nafion can be further improved by creating ordered, rather than disordered, channels.

In short, Edward Trigg and his colleagues opened a new potential path to better performing fuel cells through the design of a well-ordered polymeric proton exchange membrane. They demonstrated that the ordered polymeric structure within their PEM leads to faster proton transport than in a disordered version of the structure. With further refinement of the synthesis techniques, membranes like these may yield faster proton transport than is currently achievable, leading to exceptional performance in PEM fuel cells. With better performance, PEM fuel cells may be more readily available to quickly convert stored energy for use in domestic and industrial applications when renewable sources are not immediately available.

[1] https://en.wikipedia.org/wiki/Fuel_cell

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Not Just Spinning Their Gears: Extracting Useful Work from Bacterial Swarms

Original papers: Bacterial Ratchet Motors, Swimming bacteria power microscopic gears

Imagine you and your friends are trapped by a super-villain in a cage. There is a giant gear with a diameter half the length of a football field in the center. The only way to open the cage door, get out, and stop the villain’s evil plans will be to rotate this gear by one full revolution. This is a daunting task for one person — but if you have enough friends, you can grab the gear’s teeth and push it together to escape. An analogous task is faced by flocks of tiny bacteria in today’s two featured papers. In “Bacterial ratchet motors”, Di Leonardo and colleagues discuss the mechanics of bacteria pushing a single gear, and in “Swimming bacteria power microscopic gears”, Sokolov and colleagues discuss how bacteria can interact to power more than one gear.

Two types of bacteria were used in these studies — B. Subtilis and a harmless strain of E. Coli. A single bacterium is tiny, with a pill-shaped cell body only a couple of microns in length. One bacterium has no hope of pushing a gear one hundred times its size.  It swims around in a random, “run-and-tumble” motion. During a “run” the bacterium swims straight. It then stops and “tumbles”, changing its direction randomly, and then swims straight, or “runs” for a while longer. While bacteria swimming together in large aggregations can align and make interesting flow patterns, up to now their motion has been hard to harness to provide useful work. If this technique were perfected, bacteria-powered gears could be used to power micro-devices, such as very small robots, without using an external power source.

The bacteria used in both studies swam in a liquid medium, which contained the nutrients and oxygen that they need to survive, together with one or two gears. In both of today’s articles, the gears were resting on the bottom of the liquid medium suspended above air. In Di Leonardo’s study, the drop of medium hung from a concave part of a glass slide with 48-80 micron diameter gears; in Sokolov’s study, the medium was stretched in a film between two wires with 380-micron diameter gears. The two setups are shown in Figure 1.

gear setups
Figure 1: A gear within a bacterial suspension. Di Leonardo’s setup is shown in (a), with the gear suspended above a coverslip. Sokolov’s setup is shown in (b), with the gear suspended in a film. Figures adapted from original articles.

A swarm of bacteria can’t push just any kind of gear. Di Leonardo and colleagues show that if the gear is symmetric, the bacteria can’t rotate it. In this case, there will be an equal chance of bacteria pushing on the left and the right of the gear tooth, not generating an overall rotation. To generate continuous spinning, more bacteria need to push on one side of the tooth than the other. To achieve this, the gears had asymmetric teeth, as in Figure 2a. When bacteria swim towards the corner (like the left bacterium in Figure 2a), they get stuck in the corner. The bacteria can’t escape by swimming straight, so they rotate the gear until “tumbling” and breaking free. When bacteria encounter a tooth while swimming away from the corner (like the right bacterium in Figure 2a), they swim straight off of it. This way, the gear only rotates in one direction. When several bacteria are trapped in the same corner, they spontaneously align and push the gear together, as shown in Figure 2b. This results in a larger force on the gear. The rotation of a single gear is shown in Figure 2c.

Di Leonardo results
Figure 2: Results from Di Leonardo’s paper. (a) A bacterium (represented by red rods with white heads) rotates a gear by getting stuck in a corner. Arrows represent reaction forces experienced by the gear as the bacteria hit it. The green areas and the red areas show the angle of approach when a bacterium is guided towards the corner or not. (b) Four bacteria pushing against a single tooth at the same time. (c) Bacteria spinning a gear at 1 rpm.    

Sokolov and colleagues investigated different shapes and arrangements of gears. They showed that gears with teeth either on the inside or on the outside will rotate, as in Figure 3, A-H. They then added a second gear for bacteria to spin. If two gears are close enough to each other, then their teeth ‘catch’ as in Figure 3, I and J.

Sokolov results
Figure 3: Time lapses of bacteria pushing gears with teeth on the outside (A – D), teeth on the inside (E – H), and two gears at once (I and J). Red arrows correspond to the spinning direction of the gear and black arrows point to the tracked spot on the gear. Image from original article.

Bacteria turning a gear are an example of a non-equilibrium system.  A system at equilibrium doesn’t consume any energy and doesn’t produce useful work. This might be surprising, but if a gear was placed in an equilibrium system, such as atoms in a gas, it would never rotate. An atom encountering a wall or a corner of a gear will simply bounce off, and the net torque produced by all the atoms bouncing off the gear is zero, no matter what shape it is. The difference between atoms in a gas and bacteria in a fluid is that bacteria have their own internal source of energy, and hence are not at thermodynamic equilibrium. A “running” bacterium will not just bounce off of the wall of a gear corner. Instead, its swimming will rotate the gear by the corner until the next time the bacterium “tumbles” and reorients.

 

Are gears rotated by bacteria actually a useful system? Sokolov and colleagues estimate that the power generated by the bacteria is $latex 10^{-15}$ watts. Most electronic components, such as the ones in a cell phone, require power on the order of $latex 10^{-6}$ watts. These bacteria are not — as yet — generating nearly enough power for real-world machines. Although the rotation of the gear is not powerful enough to be useful, it is amazing that such small creatures are able to do so at all.  

 

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The Lutetium Project: combining research, arts and outreach on YouTube

What does a physicist study? If you ask this question to the general public, you’re likely to hear back either about the extremely small—quantum physics, particle physics—or the extremely large—general relativity or cosmology. Indeed, those are probably the most visible fields of physics, having been depicted in Hollywood movies and TV series, and being prominently featured on the cover of popular science books and magazines.

Picture1
Desperately looking for soft matter in the Map of Physics, from youtu.be/ZihywtixUYo

At the Lutetium Project, we want to show that this is not all there is to physics. We believe that one field, in particular, is more relatable to our everyday experiences, as long as we pay attention to its beauty and its complexity. Soft matter physics is the study of systems that can easily be deformed at our time- and length-scales, of objects that cannot easily be classified as solids or liquids. Research in soft matter physics is often pursued at the intersection with other fields, such as fluid dynamics, biology, chemistry or statistical physics. For example, soft matter physicists try to answer questions like: Why do foams change over time, and how can we make them more stable? Why does toothpaste behave like a liquid when squeezed out from a tube and like a solid when left alone? Why do biological tissues grow differently on rough versus smooth surfaces? Can we learn the general principles that guide the collective behaviour of flocks of birds or of schools of fish? And many more keep popping up every day!

 

Picture2
Physics Confession, by xkcd.

 

Soft matter physics is well-suited to video: one needs only an optical microscope to see the movement of defects in liquid crystals, or a high-speed camera to record the bounce of water droplets on a hydrophobic surface. As a group of Ph.D. students, we have this kind of equipment in our labs, and we know how to use it. This is why we decided to launch a YouTube channel primarily showcasing high-quality footage of our experiments.

 

Picture3
Defects in liquid crystals under the polarized microscope, Guillaume Durey for the Lutetium Project.

 

We teamed up with talented art students, who developed a visual identity for the project, composed original soundtracks for the videos, and coordinated all the cinema-related aspects of the channel, in order to produce three categories of videos. In the first category, we explain scientific concepts from our studio, such as microfluidics and granular matter, using motion design and footage from the labs. In the second one, we interview our colleagues, whether young scientists or project leaders, about their current experiments. In the third one, we immerse the viewer in one single research experiment, which we explain using short pieces of text. We set these videos to an original soundtrack whose melody reflects the physics of the experiment. This last series is our most successful to date: we were thrilled to be awarded a prize from the American Physical Society for one of these videos, featuring bursting droplets!

After four years of hard work, we have set up a YouTube channel that relies equally on current experimental research, artistic creation, and scientific outreach. Its name is a callback to lutetium, a chemical element named after Paris, a city that pioneered the study of soft matter physics. We hope that our videos will stir your imagination; if that sounds appealing to you, you can follow us at youtube.com/thelutetiumproject, or @TheLuProject on Twitter: we’d be delighted to have you!

Thanks to our friends at Softbites for giving us this opportunity to present our project, and thanks to our funders (ESPGG, Université PSL, ESPCI Paris, ESPCI Alumni, Fonds ESPCI Paris) for making it possible.

The Lutetium Project team

 

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EuroScience Open Forum 2018

“ESOF (EuroScience Open Forum) is the largest interdisciplinary science meeting in Europe. It is dedicated to scientific research and innovation and offers a unique framework for interaction and debate for scientists, innovators, policy makers, business people and the general public.” [1]

This year ESOF was in Toulouse, and I was fortunate enough to be able to attend, so I want to share a few snippets of my time there, and my main takeaways.

There was a huge range of different topics on their programme from science communication and careers, to atomic clocks and plastic pollution. I found choosing between parallel sessions was often difficult. But even though I went to a variety of different sessions, I am going to focus on one major theme kept cropping up. Namely, trust.

How can we, as scientists, build trust in science? How can we trust one another?

For this science and scientists need to be seen as credible. There are no quick fixes, but openness was touted by many at ESOF as a huge step towards building more trust. After all if ‘science is not finished until it’s communicated’ [2] then the public are a huge part of science! Not to mention that for most of us, we are in fact paid by taxpayers.  

Here are some of the different types of openness that people discussed at ESOF2018:

  1. Open Access

Currently, many scientific journal articles are behind paywalls – this means institutions without access to a particular journal are locked out. Even when a journal allows institutes to post papers open access from the institute, this is often after long embargo periods restricting access to the latest science.

  1. Open Data

Even if a paper is open access. The methods and the data shown are often too little for experiments or analysis to be easily reproduced. For private and sensitive data – this is not possible but we can strive for the data to be as open as possible and only unavailable when necessary. If the data is accessible and readable, then anyone can reproduce their analysis, particularly if codes are also made accessible and usable.

  1. Open Communication

To share our research with the public, making something understandable to people outside your field is not enough. We need to open a dialogue between scientists and the public so that the outreach activities are catered to their interests. In particular for influencing policy, the people who our science affects need to be heard.

  1. Open Science

Science is a part of our culture, our history and our future. It would be difficult to find anyone who isn’t affected by science. Allowing people to take part is great for building trust. New initiatives and new technologies are opening the ‘ivory tower’ of academia. Citizen science or crowd-sourced science can bring together the public and scientists, for mass collection of data. And new make-spaces, fab-labs and open source software are making it easier for people to conduct their own experiments, build their own devices and explore science in their free time.

A bit of a culture shift needs to occur within science to highlight these aspects of science. I think, most scientists agree openness is important but often these ‘extra’ activities get put on the back burner as publications, teaching responsibilities and funding applications dominate our time. So, more time needs to be invested in openness, but not at the expense of an individual scientist’s career (or home life). Hiring practices, funders and fellow scientists need to reward and encourage openness within science. So I think it is great that so many people from a range of different places were talking about how to increase openness. 

Overall I thought ESOF2018 was a very friendly conference, with so many passionate people working towards a better scientific process. To hear them talk so passionately, either in how science is funded, publishing, science policy, collaborations with industry, scientific careers, science communication and even the science of science communication was a fantastic experience. 

Let us know if you have any experiences, thoughts, or difficulties on accessing science or how to open up science over twitter (@softbites17 or @emilyeriley) or in the comments down below.

[1] https://www.esof.eu/en/

[2] Quote from Sir Mark Walport, who was Chief Scientific Adviser to the UK government.