The paper in Nature Chemistry is here: https://go.nature.com/2re3aEK

We tend to think of crystals like we do most other solids: stiff, brittle perhaps, but not flexible. The concept of liquid crystals is a little closer to a flexible solid, but these do not remain crystalline in the absence of external stimuli. One can imagine my surprise then, when shortly after arriving in graduate school, I found myself listening to Prof. Akif Tezcan present a 2D protein crystal, which undergoes large-scale conformational changes while retaining its crystallinity. What I now know is that in reality, flexible (or rather, dynamic) protein crystals can be found in many types of biological contexts. A favorite example is microtubules, which are essential components of the cytoskeleton, crystalline along their length, and can rapidly grow/disassemble in response to chemical stimuli. While these natural systems are fairly well understood, at the time there was effectively no mechanistic understanding of what was happening with the synthetic protein crystals developed in the Tezcan Lab.

When I joined the Tezcan Lab, neither of us was sure how my interest in solving this problem would turn out. Fresh out of my previous lab, where my crash-course in x-ray crystallography opened the door for my first taste of computational chemistry, I had joined a purely experimental group as a first year theoretical chemist. Fortunately for me, Akif assured me I could do some theory in his lab as long as I did experiments too. This turned out to be key.

In the beginning what we knew was that ^C98RhuA, a square-shaped protein with a cysteine at its four corners, could self-assemble into 2D crystals upon oxidation, creating a checkerboard-like pattern of proteins and square-shaped pores. Due to the flexibility of the disulfide bonds and large porosity of the crystals, the proteins could rotate about their axes of symmetry and form a close-packed conformation, which appeared to be the thermodynamically preferred state. This opening-closing motion was reversible upon mixing of the suspension, providing the mechanical force necessary to reopen the lattices. There were two hypotheses: 1) there was some protein-protein interactions at the interfaces which favored their association, or 2) this was a purely mechanical transition, and perhaps the close-packing of proteins simply “locked” them into place until additional force was applied. After a long and convoluted journey, we learned that neither of these were correct.

(Animation of ^C98RhuA conformational changes. The proteins are in white and connected at their four corners by disulfide bonds. This animation is created by interpolating between experimentally obtained TEM images.)

Initially, we figured that we should simulate as many proteins as we could, so we turned to coarse-grained simulations that would capture only the mechanical motion of the lattices. However, after optimizing the simulation protocols and accumulating several microseconds of sampling, none of our crystals were closing more than ~50%. Furthermore, if the crystals were initialized in the closed conformation, they popped right open! I also simulated (and experimentally characterized) a mutant of ^C98RhuA, which we would have expected to have a reduced capacity for mechanical motion. There were indeed differences in the two constructs, but nothing definite enough to assign blame. With these results in hand, now the better part of a year later, we ruled out the second hypothesis.

It was clear that if the proteins were not simply getting “stuck” then there must be something holding them in place. All-atom simulations offered the chance for an up-close-and-personal look at the process, but we had to be much more conservative with our simulation size. Ultimately, we opted for a 2x2 array of proteins, creating a single pore. I carried out umbrella sampling simulations to map the free energy of the crystal as it closed, and was surprised to find that we got a smooth landscape with a deep minimum near the closed state. The computation matched the experiment! Despite my elation, it rapidly became apparent from the trajectories that there was very little interaction going on between neighboring proteins, and later calculations of related parameters (for example, buried surface area) all agreed with that assessment, so the first hypothesis was also ruled out. Now our computation had recapitulated the experiment, but in doing so raised a new questions.

Around this time I gave a progress presentation on campus, and one of the faculty members raised a question regarding the entropy of the solvating waters. I confessed that I had not really thought of it at all, but that I would keep it in mind. Several months later, while taking a break from working up a crystal structure, I stumbled into some papers on proteins with positive enthalpies of crystallization, but negative free energies of crystallization. What this was attributed to was a reduction in the number of waters bound to the protein surface upon complexation, which freed the water molecules and increased their entropy. I emailed Akif as fast as I could and immediately started looking for ways I could try to compute this quantity. Fortunately for me, a technique called GIST had recently been developed, and one of the primary authors is a professor at UCSD, Mike Gilson. I arranged a meeting.

Mike was very generous with his limited time, and we met on several occasions, with the other GIST authors sometimes included in Skype meetings. When preliminary analysis of the umbrella sampling simulations proved promising (but too noisy to use), I set up new ones specifically for GIST, and repeated the calculations. Lo and behold, we got a near mirror image of the free energy landscape! The closed state was thermodynamically preferred, but not for the reason we expected. At this point I was lucky that one of our neighbors was Prof. Francesco Paesani, whose expertise is in water. Entropy is difficult to understand, and even harder to rationally engineer. It’s mysterious for a reason, so Francesco encouraged restraint from being too bold in our claims, but pointed me to a number of structural characterizations we could try out. It’s well known that solvation of biomolecules creates non-bulk-like water up to a nanometer away from their surfaces, so in an effort to contextualize our findings, we investigated changes to the water structure in the vicinity of our crystal. What we found was that a large number of waters, particularly those residing outside of the immediate hydration shell, were essentially “squeezed out” into the bulk solvent by the close approach of neighboring proteins. By releasing these molecules from the influence of the protein, the molecules are expected to gain freedom of movement, creating an increase in entropy. While this is itself an interesting observation, most exciting was the recognition that this should be a fairly general biomolecular phenomenon, since it arises from a general solvation effect. Furthermore, Francesco noted that understanding the behavior of water under nanoscale confinement remains an open problem, particularly since most studies utilize only model systems. In our case, we have a real system with a single degree of freedom that leads to confined water, making it ideal for adding to and commenting on the existing literature. We are currently engaged in a follow up study doing just this.

To test our ability to rationally reshape the energy landscape, we decided to go with what we know as protein engineers: enthalpy-driven design. After deciding on installing negatively charged mutations within the crystal pores, my first construct nearly ended in disaster – as my new simulations were running, my attempts to purify the protein showed that it was misfolded and aggregating in solution! After backtracking and swapping out one of the mutations for a different location, all was well, and it was satisfying to see the anticipated effect captured not only in the computation, but also in the experiment. Now, computational predictions had both directed our experiments and set us up for the finale. With the idea that we should be able to “turn off” our engineered perturbation with the addition of salt or metal counterions, TEM experiments revealed Ca²⁺ to be capable of binding to the carboxylate sidechains and allowing the crystals to relax into the closed conformation. This effectively creates three different conformational switching modes, two more than the fully open-fully closed switch of the original construct.

What we hope to do now is continue to take advantage of our newfound molecular-level understanding of these conformational changes to design new types of filters or nanoscale displays with tunable porosity/spacing. ^C98RhuA is an amazing protein with a lot of room to be creative, and this is hopefully just the first step of many towards understanding not just how it ticks, but how we can apply some of these lessons to create other novel dynamic materials. Importantly, what allowed us to get this far was the marriage of experimental and computational techniques. Without the computation to look for potential interactions and estimate thermodynamic quantities associated with the conformational changes, it’s very unlikely we would have arrived at the answer we found. Without experiment to verify these predictions (particularly the metal binding, which is poorly captured in classical MD simulations) and to pose the question in the first place, it would be harder to say with confidence that what we found is reasonable. As we move forward as protein designers (with a chemical twist), we expect that the synergy between theory and experiment will continue to grow. We’ll need all the tricks we can muster if we truly seek to match the elegance and complexity of the molecular materials and machines found in nature. 

The paper in Nature Chemistry is here: https://go.nature.com/2re3aEK