QnAs with Daan Frenkel

The self-assembly of biological molecules and systems is a common phenomenon in nature. Linear chains of protein molecules fold into functional 3D structures in one example of biological self-assembly (1). Computational scientist Daan Frenkel at the University of Cambridge seeks to explore how self-assembly might be applied to fields such as nanoscience, manufacturing, and robotics, among others (2). Elected to the National Academy of Sciences in 2016, Frenkel uses numerical modeling to mimic the behavior of atomistic and molecular systems and unravel the principles of self-assembly. Frenkel spoke to PNAS about some of the challenges involved in studying self-assembly using numerical modeling.

Daan Frenkel. Image courtesy of Daan Frenkel.

PNAS: In your work, you use numerical computer simulations to evaluate properties of self-assembling structures and materials. Can you give our readers an overview of the state of the field?

Frenkel: The field is developing rapidly in volume and scope. Self-assembly has a long prehistory, much of which was based on lithography techniques. In recent years, people realized that it could be possible to design complex structures that would actually assemble themselves, rather than being assembled by using lithography. The availability of materials like DNA and other materials that can make particles bind selectively to other particles has enabled the possibility of designing complex materials that have large numbers of distinct building blocks. This is certainly the direction people want to go, and the dream is to have truly complex materials consisting of as many different building blocks by self-assembly. In the past 5 years, there have been important experimental advances that could enable huge developments. Mainly, my interest is to try to understand why earlier approaches failed, and why the present approaches seem to work.

PNAS: What are the practical applications of artificial self-assembly structures?

Frenkel: Currently, the number of applications of man-made structures is still quite limited. At the moment, people are working hard to show that you can make very diverse objects. Mostly, these objects have been based on “DNA origami,” which involves folding a long DNA strand into a desired shape. For instance, people have designed a box-like DNA origami structure that could trap particles or molecules for drug delivery. At the moment, applications in drug delivery are being explored. But this is just the tip of the iceberg.

Apart from self-assembly, I am also very interested in interfacial and phoretic transport [the transport of particles or fluids due to thermal, electrical, or concentration gradients along interfaces]. This is an area of huge practical importance that could be relevant to nanofluidics, transport in porous media, and possibly even phoretic transport in biological systems. Microscopic modeling of these phenomena remains underdeveloped. But the field is opening up, and I expect that there will be future applications.

PNAS: Can you expand on some of the research methods you use, such as molecular dynamics and Monte Carlo simulations?

Frenkel: The two work-horses of classical molecular simulations are molecular dynamics (MD) simulations, which basically solve Newton’s equations for a large number of interacting particles, and the Markov chain Monte Carlo (MCMC) method, which allows us to compute the structural and thermal properties of classical many-body systems.

The MD method was based on the realization by Berni Alder and Tom Wainwright that direct simulations of observable properties using computers would outcompete analytical theories that required the numerical evaluation of high-dimensional integrals (3). Anees Rahman then showed that with MD, we could model and understand experiments that had been very difficult to interpret beforehand.

In contrast, the MCMC method was a truly brilliant discovery by Nicholas Metropolis, Arianna Rosenbluth, Marshall Rosenbluth, Augusta Teller, and Edward Teller (4). In essence, the method allows us to compute expectation values of observables that depend on many variables. The algorithm was developed in the early 1950s. Although the method has been extended since, it basically has never been improved upon. For the kind of problems that most people study, it is pretty much as good as it gets.

PNAS: What are some of the challenges you encounter in your work?

Frenkel: For quantitative predictions, our description of the interaction between atoms and molecules is often inadequate. People very often use approximate quantum mechanical methods combined with fitting to experimental data to determine approximate potentials of force fields that describe the interactions between atoms and groups of atoms. Nature is quantum mechanical, but true quantum simulations are prohibitively expensive for all but the smallest systems. Hence, there is a great need for reliable hybrid or multiscale approaches.

There is also a problem when extracting information from increasingly high-throughput experiments. Often our experimental knowledge, though data-rich, is still incomplete and noisy. The same holds for simulations. We need to integrate experiment and simulation to extract as much information as possible. Apart from these issues, the simulation of true, many-body quantum dynamics remains incredibly challenging.

PNAS: Your PNAS Inaugural Article focuses on multivalent targeting of diseased cells and tissues (5). Can you describe the methods you used, and the findings from the study?

Frenkel: Strangely, the core of this paper is not simulation, but relatively simple analytical theory. The Monte Carlo simulations were only meant to validate the approximate theoretical approach. I have been working on multivalent interactions for several years now, but I should stress that the design principles in this paper are all due to my PhD student Tine Curk.

In essence, the problem is related to targeting cells that overexpress certain receptors. For instance, let’s take the context of drug delivery. In drug delivery you want to target cells that are diseased, but not healthy cells. Very often the diseased cells overexpress certain receptors. So, a drug delivery vehicle coated with an object, such as an antibody, that binds to these receptors would be useful. But one extremely strong-binding antibody would also bind to healthy cells and cause side effects.

In the paper (5), we found that it is useful to have many ligands that bind individually quite weakly. In particular, two design rules came out for the functionalization of delivery particles to recognize a particular expression profile. First, the number of different ligands on the particles should be exactly equal to the concentration of the different receptors on the surface, which you could have expected. But what surprised us was that these ligands should be bound to their cognate receptors only 71.5% of the time. That’s a very simple design rule to determine how to make your ligands so that they do not bind too strongly. That was a very interesting observation. We hope that experimentalists will try this out.

PNAS: What excites you about the future of this field?

Frenkel: First of all, the increase in the power of computers, some 15 orders-of-magnitude since the early 1950s, should not be seen as a quantitative change. It is a qualitative change. It changes the kind of questions we dare to ask. This is particularly obvious in the field of data-analytics. As we move to more complex systems, we need to use data-analytics, based on physical concepts, to discover if, maybe, we have been asking the wrong questions all along. What I find exciting is that I can see areas, such as climate science, where this approach could yield very novel insights.