Termite Climate Control

Original Article: Termite mounds harness diurnal temperature oscillations for ventilation (Non-paywall version here.)

Disclosure: The first author of this paper, Hunter King, is a friend of the present writer (CPK).

Termites are among nature’s most spectacular builders, constructing mounds that can reach heights of several meters. Relative to the size of their bodies, these structures are considerably larger than the tallest skyscrapers constructed by humans [1]. Surprisingly, in many termite species, individual termites don’t spend much time in these mounds. Instead, they live in an underground network of tunnels and chambers that can be home to millions of individual insects. But, if not to live in them, why do termites build such intricate and gigantic above-ground structures [2]?

Scientists have suggested several possibilities: mounds might provide protection from predators, or guard against rain or dramatic changes in temperature. Recent research, however, has focused on the idea that a mound’s main purpose could be to provide ventilation. The problem of ventilation is particularly important for species such as Odontotermes obesus, native to the Indian subcontinent, that “farm” a species of fungus [3]. As human cultivators will no doubt be aware, indoor farming requires careful control of atmospheric conditions. According to this picture, the mound functions like a giant lung, enabling the colony to expel carbon dioxide and exchange it for atmospheric oxygen. But how exactly might this lung work?

Human lungs use a muscle, the diaphragm, to mechanically push out old (carbon-dioxide-rich) air, and suck in fresh (oxygen-rich) air. Obviously, termite mounds don’t have moving parts that would allow them to do this. So what is the physical mechanism that drives gas to flow around the ventilation shafts inside the mound? Over the years, researchers have proposed several ideas, including driving by thermal buoyancy (the tendency of hot air to rise upwards) or external wind. The details of these models are controversial: for instance, thermal-buoyancy-driven flows require temperature differences between different parts of the mound. Are these temperature gradients caused by external heating (that is, from the sun), or by heat generated by the bodies of the termites themselves [4]?

In today’s paper, Hunter King, Samuel Ocko and Lakshminarayanan Mahadevan describe a series of experiments that might help to answer some of these questions. To test the “mound-as-lung” model described above, King and co-workers designed and built directional airflow sensors tailored to the cramped environment and low airspeeds found in the ventilation shafts of mounds built by O. obesus. The mounds, shown in Fig 1A, look a bit like a half-folded umbrella, with ripple-like “flutes” decorating a roughly cone-shaped structure.

Untitled.001.jpeg — Figure 1 (A) An O. Obesus termite mound, with a bike shown in the background for scale. (B) Thermal images of the same mound, taken with an IR camera. The left half-image was taken at night, and shows that the interior of the mound is hotter (more yellow) than the flutes. In the half-image on the right, taken during the day, the hot regions are on the outside. Images courtesy of H. King, S. Ocko and N. Ocko.

King and co-workers measure, as a function of time of day, the air flow velocity in the ventilation conduits near the base of the flutes. These measurements, as the authors put it, are “difficult for several reasons,” in particular the “hostile and dynamic” environment inside the mound — the tendency of termites to aggressively attack anything placed inside their nest, and cover it with “sticky construction material.” As well as measuring the air velocity, King and co-workers use temperature sensors to measure the temperature profile of the surface of the mound, and the carbon dioxide concentration in the nest, underneath the mound, and at the “chimney,” near the top of it. To test the role of heat generated by the bodies of the termites, the researchers also study a “dead” — that is, abandoned — mound.

Figure 2: The top two panels show the air velocity and temperature differential for living mounds (top panel) and one dead mound (middle panel). The bottom panel shows the carbon dioxide concentration in the underground nest, and in the chimney, near the top of the mound. Carbon dioxide in the nest builds up when the temperature differential is small and the air flows slowly. It starts to decrease with increasing temperature differential and increasing flow speed (i.e. more negative flow velocity).

The results of some of these experiments are shown above. In particular, King and co-workers observe similar flow and temperature patterns in the “living” and “dead” mounds and conclude that metabolic heating is not the central mechanism driving ventilation. Noting that the direction of the flow reverses during the night, King concludes that “diurnally driven temperature gradients” — that is, temperature differences caused by the day/night cycle — ventilate the nest. This process is facilitated by the most distinctive architectural feature of the mound, the flutes.

Like fins on a radiator, the flutes efficiently exchange heat with their environment. In the heat of the sun, the flutes heat up faster than the interior, as shown in the IR camera image above. This causes the air in the flutes to rise, thus creating circulation inside the mound. The resulting flow carries oxygen-rich air from the chimney down to the nest. During the night, the flutes cool down faster than the interior, causing the flow pattern to reverse. According to the model that King and his colleagues propose, the termite mound performs the unusual feat of extracting useful work from oscillations in an intensive (in the sense of thermodynamics) environmental parameter.

King and his co-workers speculate that this energy-efficient ventilation strategy, which has evolved over millions of years, might provide inspiration for human designers of environmentally friendly architecture.

Note: After this post was written (but before it was published), the same team published a second paper where they try to find out if the same model applies to mound built by another species of termite that lives on a different continent (spoiler: it does, but some of the details differ).

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Notes:

[1]

$latex-image-1.jpg$

$latex-image-2.jpg$

[2] http://www.bbc.com/earth/story/20151210-why-termites-build-such-enormous-skyscrapers

[3] The termites bring partially digested wood back to their nest, where the fungus extracts nutrients and energy from it. In return, the fungus produces fruiting bodies that the termites can eat. The relationship between termite and fungus can be referred to as “farming” or “symbiosis,” depending on your point of view.

[4] The latter mechanism is how honey-bees maintain a constant hive temperature. This ability to preserve “hive homeostasis” is one of the reasons that honeybees can survive in wildly varying climates.

2017-11-152018-04-14

Brick-by-brick to Build Tiny Capsules

Original paper: Colloidosomes: Selectively Permeable Capsules Composed of Colloidal Particles

Disclosure: The first author of the article discussed in this post, Anthony Dinsmore, is now my Ph.D. advisor. He did his postdoc at Harvard University a while ago, and consequently, I was never involved in this work.

In past two decades, several approaches have been developed and optimized to encapsulate a wide variety of materials, from food to cosmetics and the more demanding realm of therapeutic reagents. Inspired by biological cells, the first attempts were to use either natural or synthetic lipid molecules to form encapsulation vessels, the so-called liposomes. Then, with the increasing awareness of controlled release of cargo, especially for therapeutic purposes, advanced materials such as polymers were developed to form carrying vessels. There has been an enormous progress in encapsulation technologies, however, these methods can be limited in their applicability regarding encapsulation efficacy, permeability, mechanical strength, and for biological applications, compatibility. In this article, Anthony Dinsmore and his colleagues introduce a new platform and structure to encapsulate almost all types of materials with finely controlled and tuned properties.

Colloidosomes

An emulsion is produced typically by application of a shear force to a mixture of two or more immiscible liquids like the classical water-oil mixture. The resulting solution is a dispersion of droplets of one liquid in the other continuous liquid. In such case, an interface between the fluids exists that would impose an energy penalty on the system. Therefore, the system will always attempt to minimize it, in essence by reducing the area of the interface that is to merge the similar liquid droplets. Amphiphilic molecules are known to segregate in such interface to further reduce the energy and to inhibit the merging of droplets. This segregation is not limited solely to molecules though. Solid particles tend to jam in the interface for the same reason to stabilize the emulsions. Inspired by the idea of particle-stabilized emulsions, which are known as Pickering emulsions, Dinsmore, and his colleagues have developed capsules made of solid particles. They adopt the name “Colloidosomes” by analogy to liposomes and demonstrate how the arrangement of these particles can be manipulated and controlled to achieve a versatile encapsulation platform.

Fabricating the Capsules

Colloidosomes are prepared first by making the emulsion in which the continuous phase contains the particles. For instance, in water-in-oil emulsions (“w/o”), water droplets become the core of the colloidosomes and particles are dispersed in the oil phase. Gentle agitation of such system results in particles being trapped in the water-oil interface (see Fig.1). The authors summarize the capsule formation in three main steps:

Screen Shot 2017-10-17 at 01.01.10 — Fig 1. The colloidosome formation process is illustrated schematically in three steps. (A) a water/oil emulsion first is created through gentle agitation of the mixture for several seconds. (B) Particles are adsorbed to the w/o interface to minimize the total surface energy. Through sintering, van der Waals forces, and or addition of polycations ultimately the particles are locked in the interface. (C)In the end, the particle-stabilized droplet is transferred to water via centrifugation.

(a) Trapping and stabilization. When the water-oil interface energy surpasses the difference between particle-oil and particle-water interface energy, particles are absorbed to the water-oil interface and become trapped due to the presence of a strong attractive well. This differs substantially from the case where particles were adsorbed to the interface via electrostatics, which requires the droplets to be oppositely charged to attract the particles. The packing of the particles at the interface is adjusted by controlling their interactions. Typically, the electrostatic interaction between particles, due to their surface chemistry, is utilized to stabilize the packing of the particle. For instance, in this study particles are coated with a stabilizing layer which in contact with water turns into a negatively charged layer.

(b) Locking particles. To form an elastic and mechanically robust shell, the particles must be locked in the interface. This results in an intact capsule that can withstand mechanical forces. One way to obtain such elastic shell is to sinter the particles in place. Sintering is a thermally activated process in which the surface of particles melts and connects them to each other. Upon this local melting, the interstices among particles begin to shrink. With longer sintering times, it is possible to completely block the interstices, which results in very tough capsules with extremely high rupture points. In this study, particles with 5 minutes of sintering yielded a 150 nm interstices size, and with 20 minutes, almost all the holes were blocked. By using particles with different melting temperatures, the sintering temperature can be adjusted over a wide range; this might be advantageous for encapsulants incompatible with elevated temperatures. Other ways of locking particles are electrostatic particle packing and packing via van der Waals forces. In the former case, for instance, a polyelectrolyte of opposite charge can be used to interact with several particles to lock them in place. In the latter case, for the van der Waals force to be effective, the steric repulsions and barrier must be destroyed so the surface molecules can get close enough for the London forces [1] to be strong.

After the Colloidosomes are formed, through gentle centrifuging, the fluid interface can be removed by exchanging the external fluid with one that is miscible with the liquid inside the colloidosome. In this step, having a robust shell to withstand shear forces crossing the water-oil interface is very important. This process ensures that the pores in the elastic shell control the permeability by allowing exchange by diffusion across the colloidosome shell. Now, with these steps and knowing parameters such as surface chemistry and locking condition, a promising system with characteristic permeability or cargo release strategies can be designed.

Tuning Capsule Properties; Permeation and Release

The most important feature of a colloidosome, as a promising encapsulant, is the versatility of permeation of the shell and or the release mechanisms. Sustained release can be obtained via passive diffusion of cargo via interstices that can be tuned via particle size and the locking procedure. With the mechanical properties of capsules optimized, shear forces can be used as an alternative release mechanism. For instance, minimally sintered polystyrene particles of 60 microns in diameter have shown to rupture in stresses that can be tuned by sintering time over a factor of 10. What makes the colloidosomes even more interesting is that one can choose different particles, with different chemistry, to have an auxiliary response, such as swelling, and dissolving of particular particles in response to the medium. It is also conceivable if one coats the colloidosome with the second layer of particles or polymers to improve or sophisticate the colloidosomes response. The latter can also mitigate the effects of any defect in the colloidosome lattice.

With this unique platform, Dinsmore and colleagues stepped into the new realm of encapsulating materials of all kind. From therapeutic cargos to bioreactors, the chemical flexibility and even the ease of post-modification would expand the cargo type beyond molecules. For example, the authors show that living cells can be encapsulated in colloidosomes. Well, you may wonder, WHY? Imagine a protective shell around cells that keep them out of the reach of hostile microorganisms without compromising the cell’s vital activities such as nutrient trafficking and cell-to-cell crosstalk.

[1] London forces arise when the close proximity of two molecules polarizes both molecules. The resultant dipole work as a magnet to glue molecules together. Therefore, London forces are universal forces (and part of van der Waals forces), which takes effect when atoms or molecules are very close to each other.

2017-11-082018-04-14

Water-in-Water Emulsions as Templates for Microcapsules

Cells are complex structures with semipermeable membranes that enclose the cell contents and protect cells from the external environment while at the same time allowing selective transport of molecules into and out of the cell. In an attempt to mimic protocells, researchers have developed synthetic routes to generate microcapsules with membrane properties approximating the cell membrane. A common method to fabricate microcapsules is based on emulsion templates. Traditionally emulsions are formed by mixing of chemically dissimilar fluids such as water and oil in the presence of a stabilizer such as surfactants, particles, lipids, and block copolymers. However, for health foods, solvent-free cosmetics and applications that involve the use of chemically sensitive biomolecules such as proteins the use of an oil phase is undesirable. Replacing the oil phase with an aqueous phase to form emulsions templates can provide an attractive alternative for the above applications.

When mixing two or more aqueous solutions containing hydrophilic incompatible polymers, above a threshold polymer concentration, the solution will phase separate to form two distinct thermodynamic phases. If the phase separation occurs in the presence of a stabilizer, typically particles, stable water-in-water (W/W) emulsion will form. To arrest phase separation and form stable W/W emulsions, it is necessary that the particles adsorb to the W/W interface. Based on thermodynamic derivation, the change of the free energy ($latex \Delta G$) of the system due to adsorption of spherical particles with radius $latex r$ and contact angle $latex \theta$ can be calculated by

$latex \Delta G= \pi r^{2}\gamma_{w/w}(1-|cos \theta|)^{2}$ (1)

where $latex \gamma_{w/w}$ is the interfacial tension between two immiscible aqueous phases. To have particles irreversibly adsorb to the W/W interface (negative ?G), the interfacial tension should be greater than a threshold value set by thermal motion energy of particles; therefore larger particles are preferred (2). However, packing of larger particles at the surface of emulsion droplets typically result in low coverage, making it challenging to fabricate stable emulsions.

Song and coworkers developed a method to generate W/W emulsion templates that combines the advantages of large particles while allowing for effective packing at the W/W interface by starting with a monomers that grow to large mature fibrils. Their method utilized the assembly of pre-seeded protein fibrils at the surface of an emulsion droplet followed by conversion of additional protein monomers into anisotropic fibrils. The rationale behind their approach is that high aspect ratio fibrils will pack more efficiently at the emulsion interface in comparison to spherical particles. W/W dextran-in-poly ethylene oxide emulsions were generated by mixing aqueous solutions of polyethylene oxide and dextran, stabilized in the presence of protein fibrils. Conversion of the proteins monomer into fibrils was achieved by heating the emulsions mixture at 60 °C for three days.

A study of the emulsion stability as a function of the fibril growth stage revealed that only fully mature fibrils resulted in stable W/W emulsions. This confirmed the important role of fibrils in emulsion stabilization. Using microscopy imaging it was determined that majority of the fibrils were located at the emulsion interface thereby allowing high surface coverage of the fibrils at the emulsion interface.

Figure 1 Gilad 1stpost — Figure.1 (a–d) Graphical representation of lysozyme protein assemblies in different stages of their fibrillization process: monomers at pH=7 (a), monomers at pH=2 (b), prefibrillar aggregates (c) and mature fibrils (d). (e–h) The corresponding optical micrographs show the different stabilization properties of lysozyme aggregates in the indicated stages of fibrillization. Only mature fibrils result in robust stabilization of the emulsions. All incubation times corresponding to specific panels. Scale bars, 50 ?m.

For every aqueous two-phase system, there is a minimum interfacial tension ($latex \gamma_{w/w_{min}}$) below which the emulsions are often not stable even after adsorption of chemically-inert particles. Remarkably, the authors demonstrated that growth of bioactive protein fibrils at the emulsion interface is an alternative strategy to stabilize w/w emulsions, with interfacial tension below $latex \gamma_{w/w_{min}}$. Formation of a 2D colloidal network by crosslinking of the fibrils provides the additional energy needed to stabilize the emulsions below $latex \gamma_{w/w_{min}}$. Moreover, the emulsions can be converted into highly robust microcapsules by covalently crosslinking the 2D fibrils network. Lastly, the permeability of the microcapsule membrane was characterized and shown to be selective to molecules based on size.

Figure 2 Gilad 1stpost — Figure 2. (A) Schematics of the formation of protein fibrillosomes by crosslinking fibril-coated droplets. (B) Optical microscope images of monodisperse fibrillosomes obtained after replacing the continuous phase with the same liquid inside the fibrillosomes. Scale bar, 100 ?m. (C) FITC-dextran macromolecules with hydrodynamic diameters of around 30 nm can penetrate through the membrane of fibrillosomes. Scale bar, 200 ?m. (D) Fluorescent nanoparticles with diameters of 50 nm fail to penetrate the fibrillosomes. Scale bar, 200 ?m. (E, F) SEM images of fibrillosomes with their walls consisting of amyloid fibrils. Scale bars; 2 ?m (E); and 200 nm (F).

Overall, the study presented here provides an attractive approach for capsule fabrication based on W/W emulsions templates. The use of self-growing protein fibrils as a stabilizer allow efficient packing at the droplet interface and results in higher emulsion stability compared to protein monomer stabilizers. In addition, the formation of multilayer fibrils network at the emulsion interface allow generation of stable W/W stable emulsion even at ultra-low interfacial tensions. Considering the mild preparation conditions of W/W emulsions stabilized by fibrils, we expect this system to have wide use in biomedical applications which require encapsulation and selective release of bioactive molecules.

(1) $latex \Delta G$ is the change in free energy of the system. $latex \Delta G$ tells us weather a process will be spontaneous or not; meaning will it simply happen on its own. If delta G is negative the process is spontaneous.

(2) At very low interfacial tensions, such as in water/water systems (1 ?N/m to 1000 ?N/m), reduction in interfacial tension contribution to $latex \Delta G$ term diminishes.

2017-11-022018-04-14

When Bending Comes at A Cost: Vesicle Formation and Size Distribution

Original paper: Formation and size distribution of self-assembled vesicles

I’m going to start this post with an experiment. Find a piece of smooth and unwrinkled A4 or paper of a similar size, and hold it by gripping an edge between your thumb and forefinger. Due to the gravitational force, the paper is pulled down and is bent. Now crumple the same paper, then unfold and hold it by the edge again. What happened? The paper can now resist gravity! This wrinkling strategy is a simple trick to improve the mechanical response of a thin 2D sheet. Astonishingly in biology, by such simple ways, cells tune the mechanics of their thin membrane to form tiny capsules called vesicles in order to uptake nutrients, to dump waste, and to communicate. But how such a thin sheet can address all these needs? What are the mechanisms behind these tunings? Are there consequences other than mechanical improvements? In today’s paper, Changjin Huang and colleagues investigate the critical parameters governing the vesicle formation process (or vesiculation) and the size distribution of vesicles.

The Vesiculation Process

A class of molecules called amphiphiles contain two parts: a water-loving (hydrophilic) head and a water-fearing (hydrophobic) tail. When amphiphiles are dispersed in water, the hydrophobic tails are frustrated and get together (self-assemble) to stay away from water. Based on the geometry of these two parts, different structures emerge (see note [1]). One such structure is the bilayer structure (Fig. 1A).

Fig. 1. A through D is the evolution of a vesicle, starting from a membrane patch (A) bending to (B) and closing at (C ) to form vesicles. The spontaneous decrease in systems’ energy by closing the patch is opposed by the energy required to bend the patch. The competition between these two energies is determined by factors such as patch size(l), membrane thickness (d), curvature (1/R), and bending stiffness ($latex k_b$). Combination of any of these factors can result in either or combination of above morphologies.

A bilayer structure composed of two layers of molecules with the hydrophobic tails turned inward (Fig 1A). This bilayer arrangement still is not the favored structure, since the water-fearing tails are exposed to water on the edges of the bilayer. An energy is imposed on the system by such exposure. This energy is called the interface energy and usually is shown by ?. This interfacial energy is the only driving force for the bilayer to bend in order to minimize the system’s energy. Thereby, the bilayer attempts to bend into spherical structures (Fig 1B & C). But bending comes at a cost! The system needs to exert force to bend the bilayer. In other words, energy is required to curve the bilayer. In this work, Huang and colleagues model this process with an energy-minimization approach to realize the critical parameters that determine the fate of this competition.

Parameters Affecting the Vesiculation

The quick paper experiment highlighted the essential role of local curvature in sheet’s rigidity, but that’s not all. The authors of this study theoretically demonstrate that besides local curvature, membrane thickness, membrane bending resistance (bending stiffness) and the membrane patch size (size of the paper sheet) all play a crucial role in the vesiculation process. When the authors considered the role of membrane thickness, they could predict morphologies other than vesicles such as disks and cups which we observe in real-life experiments.

Many models have been developed in recent decades to explain the vesiculation process, and none were able to predict the intermediate morphologies. In all of these models, the membrane is treated as a 2D sheet with no thickness such that when it is bent, only undergoes linear elastic deformation. Before we proceed, let’s briefly elaborate on ” linear elasticity”.

Imagine a spring that is being pulled by a force that you apply. The magnitude of extension is proportional to the force exerted. This example corresponds to a linear response. However, there is a threshold force after which the extension magnitude is not proportional to the force, and to predict the behavior of spring, you may need to consider non-linear terms in the model. The same consideration applies to the vesiculation process. To model the energy required to bend a membrane patch we need to consider non-linear terms since our material is a very, very thin 2D sheet undergoing an enormous deformation when bent. So, for small bendings, the small value of $latex h$ in Fig 1B, the linear term will suffice. But if membrane bends to final stages of closing itself, larger $latex h$, then we need to consider the non-linear term as well.

With this combination of linear and non-linear terms, an energy minimization model is proposed by the authors upon which a critical membrane bending length is obtained. At lengths, smaller than the critical length, the bending energy barrier increases dramatically, making it hard for the membrane to bend. At lengths larger than the critical length, bending energy barrier tends to zero and the membrane can readily bend (see note [2]). Now if we know the parameters to change this critical length, then we would be able to alter the vesicle size or to understand the mechanics of different vesicles produced by both healthy and diseased cells.

Effect of Curvature

The proposed model in the original study reveals that by introducing wrinkles, we can modify the critical length, however, the model also shows that decrease or increase of the critical length by wrinkles (or membrane spontaneous curvature-see note [3]) depends on curvature direction. Under negative spontaneous curvature, the membrane is curved in the opposite direction of bending (Fig 2A). Under this condition, the model shows that the critical length is larger than when the spontaneous curvature is positive. Note how in Fig 2B, for a negative curvature the bending energy barrier diminishes only at larger critical length. So, if a given membrane bilayer has specific molecules mostly inducing negative curvature, the critical length for that membrane will be larger, meaning that the patch needs to grow more to reach the critical length after which there would be no barrier for bending. Under such condition, larger vesicles will form in contrast to the membrane with positive spontaneous curvature, which can bend itself at lower critical length, thus, forming small vesicles.

Fig2 — Fig 2. Effect of spontaneous curvature on membrane critical length. (A) schematics showing two types of curvatures; positive (left) and negative (right) both under same bending direction. (B) Total bending energy is calculated with respect to the spontaneous curvature, $latex c_0$ and the critical length, $latex a$. The heat map shows the barrier energy for bending. Amphiphilic molecules shown with darker tails were aimed to induce curvature based on their geometries.

Effect of Membrane Bending Stiffness

Bending stiffness, shown by $latex k_b$ is the bending resistance of the membrane and thus it is a membrane property. Sometimes cells recruit molecules such as cholesterol to their membrane to increase the membrane bending stiffness. On the other hand, viruses are known to decrease the membrane stiffness so that they can readily bend the host’s cell membrane. In regard to vesicle size distribution analysis, the proposed model showed that the critical length is proportional to bending stiffness. In other words, for the stiffer membrane, the critical length is larger and these membranes tend to form larger vesicles.

Effect of Membrane Thickness

So far, for our analysis of the membrane (or sheet for our analogy) thickness was fixed. To consider the membrane thickness, the authors adopt a simple approximation. They first argue that membrane stiffness varies as a function of membrane thickness squared ($latex k_b \propto d^2$). Then, assuming that membrane is free to bend (its size is larger than the critical length), they obtain the minimum diameter of the vesicle formed from this membrane size as $latex D_{min}=(critical\ length) + (membrane\ thickness)$. But $latex critical\ length \propto k_b$. Therefore, from their argument we can write:

$latex D_{min}=d^{2} + d$

With this approach, membrane thickness is considered as a non-linear concept. The proposed model reveals that for thicker membrane the critical length is larger, and thus these membranes will more likely form larger vesicles. In contrast, for the thinner membranes, the critical length is shorter and these membranes are prone to form small-sized vesicles.

Conclusion

The vesiculation model developed by Huang and his colleagues has contributed to our understanding of how vesicles form. Understanding the parameters that govern vesicle formation is critical for the design of vesicles for applications such as drug delivery, where nanoscale vesicles are needed to move drugs into a cell. In addition, the identified vesiculation parameters could be used as diagnostic measures, as it has been shown that the vesicles produced by cancer cells or by cells infected with viruses have mechanical properties different from healthy cells.

[1] Known as Israelachvili’s packing parameter, the volume of the hydrophobic part divided by the product of effective hydrophilic area and the length of the hydrophobic part,$latex p=\dfrac{v}{l*a}$, defines the favored morphology. when p < $latex \frac{1}{3}$ spherical micelles, $latex \frac{1}{3}$ < p < $latex \frac{1}{2}$ cylindrical micelles, p > $latex \frac{1}{2}$ bilayer structures are expected to form.

[2] Cut an unwrinkled A4 paper in half and see the bending response. If you continue cutting you will notice that after a certain length the paper doesn’t bend. That length is the critical length.

[3] Spontaneous curvature is the natural curvature of the membrane because of asymmetries between two monolayers of the bilayer. These asymmetries can be due to the presence of proteins or geometrical difference of different amphiphilic molecules making the membrane.

2017-10-312018-04-14

Color made from structures inspired by bird feathers

Original paper: Biomimetic Isotropic Nanostructures for Structural Coloration

There’s a reason why the word “peacock” has become a verb synonymous with commanding attention. Of course, the size of the peacock tail is enough to turn heads, but it wouldn’t be nearly as beautiful without its signature iridescent, or angle-dependent, color. The brilliant colors of the peacock come from the interaction of light with the nanoscale structure of the feathers, which is much different from the origin of color in regular dyes and pigments. In today’s paper, Jason Forster and his colleagues in the Dufresne group developed a simple way to make colors that is inspired by the structures in certain bird feathers.

Figure 1. An iridescent peacock feather. Source: http://www.publicdomainpictures.net/pictures/100000/velka/peacock-feather.jpg

Colors come from the way our brain interprets different wavelengths of light. Most colors we encounter in dyes and paints are a result of absorption. Certain chemicals absorb specific wavelengths of light, and the other wavelengths are reflected; the colors we see are due to those reflected wavelengths. However, not all colors come from absorption. The color of the sky is perhaps the most widely seen example of this. The molecules that make up air scatter much more light at small wavelengths, which corresponds to blue light.

The iridescence of the colors in the peacock feather is caused by constructive interference due to the nanoscale structure of the feather. To explain this, let’s look at a simplified picture. If you have a layered stack of materials, some light will be reflected from each layer in the stack (Figure 2). Since the light reflected from the layers at the bottom stack will have traveled farther, the different sets of reflected waves will be shifted out of phase. When the waves are shifted by exactly one wavelength, they add constructively and give a stronger reflection. This constructive interference happens at a wavelength which depends on the thickness of the layers, their index of refraction, and the angle at which the light is sent and detected. Structural color is a result of the stronger reflectance at a particular wavelength due to this constructive interference of light.

bragg stack — Figure 2. Diagram depicting path length difference from reflection from different layers that gives rise to constructive interference.

Structural color can arise in many different types of structures, from bird feathers and butterfly wings to soap bubbles and opals, but today’s paper is about a type of structural color made from plastic spherical particles. These spheres are only a few hundred nanometers in diameter, on the order of the wavelength of visible light, and they are so small that they can remain suspended in water for long periods of time, forming a colloidal suspension. Jason Forster and his colleagues in the Dufresne group made structurally colored films by starting with a small volume of a colloidal suspension of these particles and allowing it to dry, causing the particles to pack together and self-assemble into structures with color.

The way the particles packed greatly impacted the color of the film. When the researchers used spheres that were all the same size, the particles formed a crystal (an ordered arrangement made of a repeating unit cell) as the suspension dried. In a crystalline structure such as the peacock feather, the structural color is iridescent, or angle-dependent. This angle-dependence of color arises because the angle that light is sent into the sample will affect the distance it travels through the material, therefore changing the wavelength at which the light will constructively interfere. However, the researchers found that when they mixed spheres of two different sizes, the spheres could no longer form a crystal, and instead formed a disordered structure (Figure 3, top). This structure was isotropic, meaning that it looked the same from any angle. The structural color of a crystalline sample is iridescent because light travels different path lengths through it at different angles. Because the isotropic structure is essentially the same at all angles, the color is the same at all angles.

colloid and bird feather — Figure 3. *Top left:* Photo of a structurally colored film. *Top right*: Scanning electron micrograph of particles in a film comparable to the one on the left. *Bottom left*: Photo of bird feathers of *Lipodothrix Coronata*. *Bottom right*: Tunneling electron micrograph of bird feathers on the left.
Adapted from Forster *et al.*

By making a more disordered structure, Forster and his colleagues were able to make a more uniform color! These disordered assemblies of spheres bear a striking resemblance to the nanoscale structures found in bird feathers such as Lipodothrix Coronata (Figure 3, bottom), which are made up air spheres embedded in a disordered array inside a matrix of beta-keratin. These bird feathers have a color similar to the particle films made by the researchers: a blue color that doesn’t change with angle.

Our eyes are a useful tool for observing colors, but they are not the most precise way to measure light. If we want to compare colors precisely and quantitatively, the best way to do that is by looking at a reflectance spectrum. A reflectance spectrum tells you the amount of light reflected from an object at a range of wavelengths. You can measure a reflectance spectrum by shining light at a colored sample and using a spectrometer to detect the reflected light. Combined with a computer, a spectrometer allows you to record an intensity value for a range of wavelengths, giving you a full intensity spectrum. The reflectance spectrum is found by normalizing this data against a perfect reflector such as a mirror or a white material, giving you the percent of light reflected at each wavelength. So if you were to measure the reflectance of a blue material, you would have a spectrum with a peak in the wavelengths that correspond to blue light (~450-495 nm).

One way to infer the reflectance spectrum of a material that has no absorption is to measure transmittance. To measure the transmittance spectrum, you can move the detector to the side opposite to the incident light, so it detects the light that goes through the sample. If you were to measure the transmittance spectrum of this same blue material, you would expect to see a dip corresponding to the blue wavelengths. The blue light would not make it through to the other side because it was reflected.

The researchers measured the transmittance spectra for their structurally colored samples and found that the blue isotropic structural color and the blue crystalline structures both showed a dip in the blue wavelengths (Figure 4). However, the dip in the isotropic structure data was much broader and more shallow, meaning that less light was reflected at that wavelength, making the color less bright and saturated.

But the quality of the color wasn’t the only thing that changed in the spectra of the isotropic structures. In these samples, the transmittance dip stayed at the same range of wavelengths even when the measurement angle changed, while the dip in the spectrum of the crystalline structure shifted as the measurement angle was changed. By eye, the researchers also saw that the disordered structures made angle-independent color, and the ordered structures made iridescent color. The measurements of the crystalline and isotropic structures show that there is a tradeoff between saturation and angle-independence in structural color.

The thickness of these isotropic structurally colored films also greatly affected the saturation of their color. Films that were just a few micrometers thick had a bright blue color, while much thicker films looked nearly white. The researchers found that adding some carbon black– black nanoparticles that absorb light at all visible wavelengths– made the colors of the thick films more vibrant (Figure 5). The carbon black works by reducing the effective thickness of the samples, absorbing light before it can travel through the entire layer of the sample and causing it to look like a thinner sample.

carbon black colloid films — Figure 5: Isotropic structurally colored films with different amounts of carbon black. The concentrations of carbon black as weight percent are listed beneath the samples.
Adapted from Forster *et al.*

This work showed that structural color, both iridescent and angle-independent, can be made using simple methods that could potentially make the colors in large volumes for real-world applications. Because these colors come from structure and not absorption, they will not fade over time as current dyes do. In addition, one material can be used to make a range of different colors by tuning the structure, so these assemblies could be used as colorimetric sensors that change color in response to environmental changes such as strain or temperature.

2017-10-272018-04-14

Fluids That Flow Themselves

Original paper: Transition from turbulent to coherent flows in confined three-dimensional active fluids (Non-paywall version here.)

Disclosure: The first author of the paper discussed in this post, Kun-Ta Wu, did his Ph.D. at New York University, in the same research group as the present writer (CPK). At NYU, both Wu and CPK worked on topics unrelated to the research discussed here.

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When we think about fluid flow, we generally think of motion in response to some external force: rivers run downhill because of gravity, while soda moves through a straw because of the pressure difference created by sucking on one end. Recently, however, scientists have become interested in a class of fluids that have the capacity to move all by themselves — the so-called “active fluids.” Active materials — of which active fluids are a subset — are distinct from regular materials because energy is injected into the system at the level of individual molecules. In today’s paper, Kun-Ta Wu and his co-workers explore how such a material can turn its stored chemical energy into useful work: cargo transport.

Why are active materials so interesting? For one thing, many biological systems are active — for example the actin filaments that drive muscle contraction or bacterial swarms. Although active systems are both common and important in our everyday lives, the physical laws that govern their behavior are not well understood [1]. Studying artificial active systems, which are much simpler than living ones, might give us insight into this difficult problem.

As well as helping us to understand basic physics and biology, Wu and his co-workers hope that their research will move us closer to producing artificial materials that transport cargo without adding energy from an external source — a self–powered fluidic conveyer belt [2]. Such a material would be totally different from those that we currently use, and would greatly expand the possibilities available to engineers in fields such as microfluidics and soft robotics.

Wu’s research focuses on a system made up of protein molecules that assemble into cylindrical rods called microtubules. While microtubules are very important in biology [3], Wu uses these tiny rods, suspended in water, to make an artificial active fluid. As well as microtubules, Wu adds two other critical ingredients: kinesin molecular motors, and ATP (adenosine triphosphate), a chemical that many biological systems use as an energy source [4].

fig1 — A sliding force is generated between microtubules by the action of molecular motors. (Adapted from Figure 1 of the original paper.)

A single kinesin molecule attaches to two parallel microtubules and creates a lateral force that slides or “walks” them along each other. A single “step” of this walk involves a chemical reaction that converts one ATP molecule into ADP (adenosine diphosphate), a lower-energy state, thereby converting chemical potential energy into motion. A collection of millions or billions of microtubules (and a similar number of kinesin and ATP molecules) forms a material that writhes and squirms without any forces acting upon it. In the following video, Wu records the motion of both the microtubules themselves (they’re tagged with a fluorescent red dye), and micrometer-sized green particles, which he uses to trace the flow.

Video 1 Using fluorescence microscopy, Wu and colleagues can observe the motion of microtubules (red), as well as test cargo — colloidal particles (green) that are carried along in the flow generated by the motion of microtubules. (Movie 1 of the original paper.)

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But converting energy into useful work doesn’t just require motion; it requires motion that is controlled, directed, and uniform over time — coherent motion. This brings us to the main finding of Wu and coworkers: in the microtubules-motors-ATP system, coherent motion can be produced by controlling the shape of the container. Placed in a large rectangular box, the flow in the middle of the box (“in the bulk”) is turbulent but directionless (see panel A of the below figure). However, when placed in a ring with appropriate dimensions, the flow spontaneously organizes into large-scale circular patterns that are capable of transporting cargo — like fluorescent colloidal particles — over lengths of centimeters or even longer (panel B below).

Interestingly, whether or not this happens is controlled only by the aspect ratio of the container: the channel width divided by its height [5]. Coherent flow is observed when the aspect ratio is between ? and 3; in other words, it disappears if the ring is too flat or too tall. Additionally, Wu shows that the direction of the flow– whether it goes clockwise or counterclockwise — can be controlled by decorating the outside of the container with appropriately shaped notches, which Wu calls ratchets.

Finally, the researchers show that the appearance of directed flow coincides with the onset of nematic order: in circulating samples, the rod-like microtubules tend to align with their neighbors, while in the turbulent samples, they are oriented randomly. According to Wu, this alignment allows the fluid to collectively push itself off the walls of the container, thus generating global circulation.

fig3 — Wu and co-workers use ratchets — small asymmetrical notches on the outside of the ring — to control whether the flow is clockwise (CW) or counterclockwise (CCW). The scale bar shows that flow is coherent over lengths of centimeters. (Adapted from Figure 3 of the original paper.)

Of course, this paper only scratches the surface of the technological potential of active materials. Research on this, and similar ideas, continues both at Brandeis University, where this research was done, and in Worcester Polytechnical Institute, where Wu has recently been appointed professor. Here, according to his website, Wu aims to “advance our understanding of self-organization of active matter as well as to create unprecedented bio-inspired materials.”

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[1] Physical systems at thermodynamic equilibrium obey the Boltzmann distribution — a formula that (in principle) allows us to calculate macroscopic properties of many-body systems, if we know the interactions between the constituent particles. We don’t know of a similar theory that describes the behavior of out-of-equilibrium systems, and active systems are by definition out of equilibrium.

[2] Of course, the energy ultimately has to come from somewhere. In the case of the material studied by Wu et al, the conveyer belt would have to be “charged” with fresh ATP before use.

[3] In particular, microtubules are the most important structural component of the mitotic spindle – the sub-cellular structure that pulls chromosomes copies apart during cell division.

[4] Wu also adds a chemical known as a depletant, which makes the microtubules bundle together, allowing the kinesin to slide them along each other.

[5] Wu also studies cylinders and shows that a similar geometrical parameter controls the appearance of coherent flow.

2017-10-272018-04-14

Embryonic cell sorting: the living Rubik’s cube

Original paper: Simulation of biological cell sorting using a two-dimensional extended Potts model

We all started as one single cell. This cell contains all the information to make a complex adult body. Developmental biologists try to understand how this cell will first divide to make a dull ball of cells which will then start making dramatic changes in shape to pattern the future organs of the body. One of the difficult questions is how cells that will form the same structure are able to find one another and sort from the mix of other cell types. In a famous experiment in 1955, Philip Townes and Johannes Holtfreter showed that different cell types had an intrinsic ability of sorting, even when they were completely mixed. They took two different cell types from a frog embryo and mixed them to make a heterogeneous aggregate of cells like you would shuffle a Rubik’s cube. After some time, the heterogeneous aggregate spontaneously evolved to a two-layer structure with each layer containing only one cell type. If only a Rubik’s cube could spontaneously solve itself!

holtfreter — Figure 1. Cell sorting of two cell types (adapted from Townes and Holtfreter 1955)

A popular explanation for this phenomenon has been brought by Malcolm Steinberg in 1970 who presented his ‘Differential Adhesion Hypothesis’: each cell type has a certain pattern of adhesion molecules at its surface. As a result, adhesion between cells of the same type is different from adhesion between cells of different types. This system seems really analogous to emulsions in which the interfacial energy drives droplets of the same phase together. When you whip oil and vinegar together, you separate the two phases into droplets that quickly coalesce to reduce the total surface of the interface. This ‘Differential Adhesion Hypothesis’ raises the question: is it an analogous process to oil-vinegar emulsions that drives cell sorting? Is there an interfacial energy which sorts the cells?

To answer this question, in 1992, François Graner and James Glazier decided to run a computer simulation of cell sorting with the interfacial energy as the driver of the sorting. Previous simulations had been run before, but the geometries of the cells were not realistic. The authors derived their model from the Potts model which was inspired by the classical Ising model used to study the behavior of magnetic materials. The Ising model relies on a discrete representation of space by a lattice with sites occupied by one of two possible numbers, usually 1 or -1, which in the case of magnetization represent atomic spin. In the Pott’s model, the sites can be occupied instead by numbers 1,2,…N, and in the application of the model in this work, the numbers are used to identify individual cells in a two-dimensional system. A region where all the sites share the same number is a single cell; the i-th cell is made of all the sites with the index i. This region needs to be simply-connected, i.e. there is no hole in the region. This idea which was introduced by Renfrey Potts in 1952 has been generalized to describe grain growth and froth systems. In other words, this model shows a pixelated image of a cellular material.

potts.001 — Figure 2. Schematics of the Ising and Potts models

Such a system has an energy which is minimized when it has reached the equilibrium. The Potts energy is just the total length of interfaces between cells. So, it has a simple expression:

$latex H_{Potts} = \sum\limits_{(i,j),(i’,j’)\ neighbors} 1- \delta_{\sigma(i,j),\sigma(i’,j’)} $ (1)

with $latex \sigma(i,j)$ the value of the cell index on the lattice site of coordinates $latex (i,j)$.

Graner and Glazier modified the Potts model by taking into account that cells, unlike bubbles in a froth, have a characteristic size from which they cannot deviate too much. They added a second term to the energy of the system:

$latex H_{extended\ Potts} = $ interface term + area constraint (2)

The area constraint assumes a linear elasticity of the cells: they can be compressed or dilated but the difference between their area and the target area increases the energy with the square of this difference. In addition, they modified the first term so that the interface term is not constant for all the interfaces.

In order to study the cell sorting, they introduce different cell types. The interface energy between two cells of different cells type is greater than the one between two cells of the same cell type. In this paper, the authors mimic Townes’ and Holtfreter’s experiment by considering two cell types (they actually consider a third cell type which represents the surrounding media, for which they remove the area constraint). To simulate the dynamics of sorting, they use a Monte Carlo algorithm, which is a common simulation method that uses random sampling to obtain numerical results for complex problems. In short, a site of the lattice is randomly selected and its cell index value is changed to one of the neighboring cells. If this change decreases the energy, it is accepted, if it increases it is accepted with a probability depending on the energy increase. Transiently accepting unfavorable configuration allows to explore a larger region of the energy landscape and avoid being trapped in local minima. In this way, the cell interfaces move along the simulation.

They start their simulation from a cellular aggregate of cells with two cell types (grey and black). The geometry of this aggregate has been produced by running the simulation on a square aggregate with only one cell type and by randomly assigning the cell types afterward. This aggregate exhibits an overall round shape found commonly in biology, and it is made up of cells with classical cell shapes. However, the interfaces are biased towards the 45° direction due to the discretization anisotropy (because of the pixels, the length between neighbors is not equal in all directions). After running the simulation over 10000 Monte Carlo time steps, the cells are able to sort into two distinct layers, in a very similar fashion to Townes’ and Holtfreter’s experiment.

potts.002 — Figure 3. Monte Carlo simulation of aggregate cell sorting (adapted from Graner and Glazier 1992)

Graner’s and Glazier’s model has therefore been able to recapitulate the general evolution of a mixed cellular aggregate by just using the interface properties and the cell deformability. Although this model cannot handle a realistic time and its discretization leads to anisotropic artifacts, it is still widely used to model biological tissues. This paper has been an important step to show that a surface tension exists in biological tissues and can drive morphogenetic processes. Surface tension in biology is still a hot topic today since other ingredients, like the cell contractility (see especially this paper from Carl-Philipp Heisenberg’s lab), have been shown to be involved in the surface tension.

(1) The energy is the sum over all the faces between sites. If the two neighboring sites are from different cells, they have different indices $latex \sigma,\ \sigma’$, and the Kronecker delta $latex \delta_{\sigma \sigma’} = 0$. Therefore $latex 1 – \delta_{\sigma \sigma’}$ adds one to the sum.

(2) Here is the detailed expression of the extended Potts energy:

$latex H_{extended\ Potts} =\sum\limits_{(i,j),(i’,j’)\ neighbors} J\big(\tau (\sigma(i,j),\tau(\sigma(i’,j’))) \big)\big( 1- \delta_{\sigma(i,j),\sigma(i’,j’)}\big) + \lambda \sum\limits_{cell\ index\ \sigma} \big( a(\sigma)-A_{\tau(\sigma)}\big)^2 $

$latex J(\tau,\tau ‘)$ is the energy of an interface between cells of types $latex \tau$ and $latex \tau’,\ \lambda$ is the strength of the area constraint and $latex A_{\tau}$ is the area target of a cell of type $latex \tau$.