Using dice, fuzzy or not, to move molecules

This post has been a long tine coming... I wrote it back in May 2015, and somehow in the middle of things, I forgot to hit "publish." While we have done quite a bit of work with this model since then, maybe you'll still enjoy our crazy analogy to playing dice with particles at the mesoscale...

Some time ago, I published what might seem as yet another paper describing the properties of our model for (coarse-grained) large-scale macromolecules. A critical part of the model is that we roll dice every time these particles collide so as to decide whether they bounce or go through each other. They can overlap, because at intermediate length scales, they don't behave like rocks even if they occupy space. Despite our simple (and dicey) model, in our earlier papers, we showed that our particles give rise to the same structure as the corresponding particles that would interact through typical (so-called soft) interactions. But Einstein's famous quote about God not playing dice with the universe (albeit in a different context) serves as a warning that our particles might not move in analogous ways to those driven by Newton's deterministic laws. In our most recent paper, we confirmed that our particles (if they live in one dimension) do recover deterministic dynamics at sufficiently long (that is, coarse-grained) length scales. That's a baby step towards using our model in human-scale (three) dimensions. So there are more papers to come!

The work was performed (and the paper was written) with my recent Ph.D. graduate, Dr. Galen Craven, and a Research Scientist, Dr. Alex Popov. It's basic research and I'm happy to say that It was supported by the National Science Foundation. The title of the article is "Stochastic dynamics of penetrable rods in one dimension: Entangled dynamics and transport properties," and it was recently published at J. Chem. Phys. 142, 154906 (2015).

Balls of ice cream

When you go to your local ice cream shop, you likely ponder the question of how many scoops you wish to order. I, on the other hand, prefer to order balls of ice cream. The scoop corresponds to the void that is to be filled, but a ball corresponds to the filling. It seems to me that I'd rather order balls of ice cream rather than empty space. My wife suggests that this is just a matter of my literal mistranslation of "bolas de helado" rather than any deeper significance over the ontology of balls verses scoops. As an optimist, I certainly prefer for them to be more than half-filled, and hence naturally prefer balls of ice cream to voids, that is scoops.

This argument extends to the nanoscale. Are the properties of a particle driven by itself or by the space which it occupies? If the latter, then its properties are independent of the nanoparticle aside from its shape. As a chemist, this is a disappointing possibility because I would like to tailor the properties of the particles, such as how they assemble, by changing the atoms or molecules at the surface (and the interior). The good news is that such control can be exercised. That is why we have been studying so-called Janus particles and other patchy particles. In our rendering, they look like ice cream balls made of blueberry and strawberry ice cream halves or layers.  The blueberry faces like to face the strawberry faces (because they correspond to charges and opposites attract), and this gives rise to their interesting patterns and response to changes from the outside.

Check out our some of our recent papers on Janus and striped particles and stay tuned for the next ones!

M. C. Hagy and R. Hernandez, "Dynamical simulation of electrostatic striped colloidal particles," J. Chem. Phys. 140, 034701 (2014). (doi:10.1063/1.4859855)
M. C. Hagy and R. Hernandez, "Dynamical simulation of dipolar Janus colloids: Dynamical properties," J. Chem. Phys. 138, 184903 (2013). (doi:10.1063/1.4803864)
M. C. Hagy and R. Hernandez, "Dynamical Simulation of Dipolar Janus Colloids: Equilibrium Structure and Thermodynamics," J. Chem. Phys. 137, 044505 (2012). (doi:10.1063/1.4737432)

Controlling chemical reactions by kicking their environs

Chemists dream of controlling molecular reactions with ever finer precision. At the shortest chemical length scales, the stumbling block is that atoms don’t follow directions. Instead, we “control” chemical reactions by way of putting the right molecules together in a sequence of steps that ultimately produce the desired product. As this ultimate time scale must be sufficiently short that we will live to see the product, the rate of a chemical reaction is also important. If the atoms don’t quite move in the right directions quickly enough, then we are tempted to direct them in the right way through some external force, such as from a laser or electric field. But even this extra control might not be enough to overcome the fact that the atoms forget the external control because they are distracted by the many molecules around them.

In order to control chemical reactions at the atom scale, we are therefore working to determine the extent to which chemical reaction rates can be affected by driven periodic force. Building on our recent work using non-recrossing dividing surfaces within transition state theory, we succeeded in obtaining the rates of an albeit relative simple model reaction driven by a force that is periodic (but not single frequency!) in the presence of thermal noise. It is critical that the external force is changing the entire environment of the molecule through a classical (long-wavelength) mode and not a specific vibration of the molecule through a quantum mechanical interaction. The latter had earlier been seen to provide only subtle effects at best, but the former can be enough to dramatically affect the rate and pathway of the reaction as we saw in our recent work. Thus while our most recent work is limited by the simplicity of the chosen model, it holds promise for determining the degree of control of the rates in more complicated chemical reactions.

This work was performed by my recently graduated student, Dr. Galen Craven, in collaboration with Thomas Bartsch from Loughborough University. The tile of the article is "Chemical reactions induced by oscillating external fields in weak thermal environments."The work was funded by the NSF, and the international partnership (Trans-MI) was funded by the EU People Programme (Marie Curie Actions). It was just released at J. Chem. Phys. 142, 074108 (2015).

LiCN taking a dip in an Ar bath

We all know that it’s easier to move through air than water. Changing the environment to molasses means that you’ll move even slower. Thus it’s natural to think that the thicker (denser) the solvent (bath), the slower a particle will swim through it. More precisely, what matters is not the density but the degree to which the moving particle interacts with the solvent, and this can be described through the friction between the particle and the fluid. Chemical reactions have long known to be increasingly slower with increasing friction. The problem with this seemingly simple concept is that Kramers showed long ago that there exists a regime (when the surrounding fluid is very weakly interacting with the particle) in which the reactions actually speed up with increasing friction. This crazy regime arises because reactants need energy to surmount the barriers leading to products, and they are unable to get this energy from the solvent if their interaction is very weak. A small increase of this weak interaction facilitates the energy transfer, and voila the reaction rate increases. What Kramers didn’t find is a chemical reaction which actually exhibits this behavior, and the hunt for such a reaction has long been on…

A few years ago, my collaborators in Madrid and I found a reaction that seems to exhibit a rise and fall in chemical rates with increasing friction. (I wrote about one of my visits to my collaborators in Madrid in a previous post.) It involves the isomerization reaction from LiCN to CNLi where the lithium is initially bonded to the carbon, crosses a barrier and finally bonds to the nitrogen on the other side. We placed it inside an argon bath and used molecular dynamics to observe the rate. Our initial work fixed the CN bond length because that made the simulation much faster and we figured that the CN vibrational motion wouldn’t matter much. But the nagging concern that the CN motion might affect the results remained. So we went ahead and redid the calculations releasing the constraint on the CN motion. I’m happy to report that the rise and fall persisted. As such the LiCN isomerization reaction rate is fastest when the density of the Argon bath is neither too small nor too large, but rather when it is just right.

The article with my collaborators, Pablo Garcia Muller, Rosa Benito and Florentino Borondo was just published in the Journal of Chemical Physics 141, 074312 (2014), and may be found at this doi hyperlink. This work was funded by the NSF on the American side of the collaboration, by Ministry of Economy and Competiveness-Spain and ICMAT Severo Ochoa on the Spanish side, and by the EU’s Seventh Framework People Exchange programme.

Taming the multiplicity of pathways in the restructuring of proteins

The average work to move molecular scale objects closer together or further apart is difficult to predict because the calculation depends on the many other objects in the surroundings. For example, you might find if easy to cross a four-lane street of grid-locked cars (requiring a small amount of work) but nearly impossible to cross a highway with cars speeding by at 65mph (requiring a lot of work.) When the system is a protein whose overall structure is expanded or contracted, there exist a myriad possible configurations which must be included to obtain the average required work. Such a calculation is computationally expensive and likely inefficient. Instead, we have been using a method (steered molecule dynamics) developed by Schulten and coworkers based on Jarzynski's equality. It helps us compute the equilibrium work using (driven) paths far outside of equilibrium. The trouble is that the surroundings get in the way and drive the system along paths that get out of bounds quickly.

In previous work, we tamed these naughty paths by reigning them all in to a tighter region of structures. Unfortunately, this may be too aggressive.  The key is to realize that not all paths are naughty. That is, that there may be more than one region of structures that contribute significantly to the calculation of the work. We found that we could include such not-quite-naughty paths and still maintain the efficiency of our adaptive steered molecular dynamics. I described the early work on ASMD in my recent ACS Webinar.

This research project was truly performed in collaboration. My recent graduate student, Gungor Ozer, did the work while he was a postdoc at Boston University. Tom Keyes hosted him there and gave great insight on the sampling approach. Stephen Quirk, as always, grounded us in the biochemistry.

The title of the article is "Multiple branched adaptive steered molecular dynamics.” The work was funded by the NSF. It was just released at J. Chem. Phys. 141, 064101 (2014). Click on the JCP link to access the article.

Getting to the shore when riding a wave from reactant to product

Suppose that you were trying to get across a floor that goes side to side like a wave goes up and down. If you started on the start line (call it the reactants), how long would it take you to cross to the finish line (call it the products) on the other side? In earlier work, we found “fixed” structures that could somehow tell you exactly when you were on the reactant and product sides even while the barrier was waving side to side. Just like you and I would avoid getting seasick while riding such a wave, the “fixed” structure has to move, but just not as much as the wave. So the structure of our dividing surface is “fixed” in the sense that our planet is always on the same orbit flying around the sun. This latter analogy can’t be taken too far because we know that our planet is thankfully stable. In the molecular case, the orbit is not stable. We just discovered that the rates at which molecular reactants move away from the dividing surface can be related to the reaction rate between reactant and products in a chemical reaction. (Note that the former rates are called Floquet exponents.) This is a particularly cool advance because we are now able to relate the properties of the moving dividing surface directly to chemical reactions, at least for this one simplified class of reactions.

The work involved a collaboration with Galen Craven from my research group and Thomas Bartsch from Loughborough University. The title of the article is "Communication: Transition state trajectory stability determines barrier crossing rates in chemical reactions induced by time-dependent oscillating fields.” The work was funded by the NSF, and the international partnership (Trans-MI) was funded by the EU People Programme (Marie Curie Actions). It was just released as a Communication at J. Chem. Phys. 141, 041106 (2014). Click on the JCP link to access the article.

The relaxation of striped spheres… ( #AIP_JCP #justpublished )

When was the last time that you took a bunch of pool balls, suspended them in a thick oil, and watched how they assembled? Pool balls being what they are, they will simply stack on themselves, though there is some question as to how efficiently they do so. If you start to shake the container, thereby maintaining some average kinetic energy (that is, temperature), they probably started to jiggle. They probably won't rotate much. Even if they do, it won't matter much because they collide with each other in the same way no matter what. So now take the balls and paint them with some pattern of red and blue paint, and suppose that there is a difference in the forces between the spheres depending on which colored surfaces are near each other. Now when they collide with each other, they have preferred relative orientation. The emergence of structure (or patterns in the positions and orientation) of the pool balls should presumably be very sensitive to how you painted them.

This is precisely the problem that Matthew Hagy and I have been studying over the past couple of years. Our pool balls are actually colloidal particles of a couple hundred nanometers in diameter. The paint corresponds to the charges encoded on the surface of the colloids. Opposite charges attract. Initially we studied Janus particles that literally have two faces, one hemisphere is positively charged and the other negative. (If interested, you can also check out my earlier blog post on the dynamics of Janus particles.) In the work that was just published in the Journal of Chemical Physics, we now consider the case in which the spheres are coated in stripes of alternating charge. This generalizes the surface pattern of the Janus particles to three, four, five, six, and more stripes. The funny thing is that very little happens to the packing of the particles because that property is so strongly dominated by the shape of the particles. But their motion, and the timescales in which they relax from a given deformation is highly sensitive to the number of stripes and perhaps also to how they are striped. In a sense, this says that if you want to maintain their behavior, you can fatten them up a little but you can't change their stripes.

The title of the article is "Dynamical simulation of electrostatic striped colloidal particles," and the work was funded by the NSF. It was released recently at J. Chem. Phys. 140, 034701 (2014), and featured on the cover!  Click on http://dx.doi.org/10.1063/1.4859855 to access the article.

Tricking hard collisions into soft interactions(#AIP_JCP #justpublished)

One of the simplest ways to describe atoms or molecules is to pretend that they are balls with some effective diameter (roughly on the order of nanometers.) If you ignore the fact that they can collide, you recover the ideal gas law you might remember from college chemistry classes. On the other hand, because they occupy space, they must collide. These collisions can be "hard" if the balls are treated like billiard balls that hit each other without changing their shape. But actual molecules are more like tennis balls in that they deform during the collision and the nearest approach depends on their velocities. That is, molecular-scale particles undergo soft interactions. Unfortunately, it takes a lot more computational effort to simulate soft particles and we'd like to avoid the extra expense. The question my coworkers and I asked is whether we could mimic soft particles using a model in which the particles moved like hard particles some of the time and like ideal particles the rest of the time. It's a little tricky because the ideal gas particles don't occupy space so we had to calculate the effective density of a given system as a function of the degree to which the particles collided with each other as hard or soft. Meanwhile, the comparison between our model and corresponding soft particle systems with the same density gave us similar structure! We intend to use this model to understand more complicated reactions, and the degree to which we can understand the behavior of complex solvents that interact with the reacting system at comparable time scales.

The title of the article is "Stochastic dynamics of penetrable rods in one dimension: Occupied volume and spatial order" and the work was funded by the National Science Foundation. It was released just this week at J. Chem. Phys. 138, 244901 (2013). (doi:10.1063/1.4810807).

On the dynamics of Janus colloids (#JChemPhys)

Janus colloids are particles that like the Roman god, Janus, have two faces. Chemically, the two faces in a Janus colloid correspond to different interactions based on what is coating the surface of each of the two halves. (In principle, they don't have to be spherical. There's some recent work on cylinders emerging as well.) We, and others, have been curious about whether a container of Janus particles would have different structure than spherically attractive particles. We showed in earlier work that, at equilibrium, such containers can indeed be quite similar. This was disappointing, in part, because it meant that you couldn't make new equilibrium structures by carefully making Janus particles. It may not be surprising to you, though, because it simply means that if you are in a room filled with people, then most of the time, you can turn your head so that you are facing someone you like. As such, you can ignore the direction you don't like. Similarly we can, for the most part, ignore the unhappy contacts in a container of Janus colloids (in the fluid regime.)

But what about the motion of this system? It turns out that this is indeed highly dependent on the Janus particle interaction strengths. Equally interesting is the fact that if you try to remove degrees of freedom from this system, you get some crazy results. First of all, if you get rid of them without doing anything else, then the particles move too quickly. (This is a known problem in coarse-graining.) If you trick the system to get the rates of particle diffusion right (as is often done), then other stuff breaks down. We found in the Janus colloids, that the association of the particles (that is which are neighbors are next to which) is highly dependent on the Janus particle interactions strengths. This means that performing coarse-grained molecular dynamics simulations to model the motion of large assemblies of molecules is more difficult to do correctly(!) than we had anticipated...

These latter findings are available, in far too much detail, in our second article on Janus Colloids which just appeared on line in J. Chem. Phys. (doi:10.1063/1.4803864).