Molecular Self-Assembly Can "Think" Like a Neural Network

Sometimes hearing just a few notes of a song is enough to take us back through time to a moment long forgotten. Our brains can reconstruct entire memories through small pieces: Perhaps the scent of a perfume reminds you of your grandmother, or the taste of a casserole reminds you of home. How does this work?

The human brain is composed of billions of neurons working collectively. Neurons are like the building blocks of thought, and each one can serve multiple purposes. For example, different memories are encoded by different patterns of activity within the same neurons. The process is similar to how your smartphone screen can display different pictures using the same pixels, or how the same LEGO blocks can be used to construct different objects.

How neurons do this has been a rapidly developing area of research in recent decades, and sophisticated models of neural networks are now commonplace in digital computers. Perhaps surprisingly, this type of computation is not unique to neurons: The same computational principles can arise in other biological and even purely physical processes.   

A new study by researchers at Caltech, the University of Chicago, and Maynooth University in Ireland has now demonstrated how neural-network-like abilities are intrinsic to the natural dynamics of molecules as they self-assemble into structures. The phenomenon is analogous to how neurons work together to recall and reassemble memories, and thus may be considered a form of "associative recall." The research was conducted in the laboratory of Erik Winfree (PhD '98), professor of computer science, computation and neural systems, and bioengineering; and is described in a paper appearing in the journal Nature on January 18.

"The phenomenon of neural-network-like computing arises whenever a set of molecules have the capacity to come together in multiple distinct ways," says Arvind Murugan (BS, MS '04), associate professor of physics at the University of Chicago and co-author of the paper. "In our case, we used short DNA strands in a test tube, but it could have been other kinds of self-assembling molecules. Our study shows that, if certain molecules are more common in a given solution, they can trigger the formation of a 'seed' that subsequently grows into just one of the distinct possible structures—analogous to how a full memory can be formed out of just a 'seed' of recollection."

To understand what is happening in this test tube full of molecules, imagine a giant swimming pool containing hundreds of LEGO pieces. LEGO pieces can be assembled in many different ways, enabling you to create a car, or a castle, or a caterpillar, all out of the same building blocks. The idea of how self-assembly performs associative recall is: if you give the swimming-pool mixture a 'seed' of a design—say, some pieces already snapped together to create a wheel and windshield—could the rest of the components assemble themselves into the desired final product (in this case, a car)? This is an example of a successful process of associative recall. Or would the pool of blocks assemble into a Frankenstein-like hybrid of partial structures—a car windshield snapped on to half a caterpillar? This scenario would be a failure to recall.

In this study, the team designed 917 different molecules, or "molecular tiles," that can be combined to form three different two-dimensional shapes: the letters H, A, or M. (These letters were chosen as a nod to a particular kind of neural network architecture called a Hopfield Associative Memory). As an analogy, imagine a 917-piece jigsaw puzzle that can be put together in three different ways to yield three distinct images.

The team put three trillion of these molecules, with relatively equal amounts of each of the 917 variations, into a test tube and observed that the pieces would indeed self-assemble to form many tiny H's, A's, and M's. Though some of the letters only formed partially, there were no accidental hybrids of two or three letters. This was an important first discovery of the study.

"This was an example of a molecular system behaving like a neural network: assembling distinct shapes out of the same components, like how the same neurons can encode multiple distinct memories," says Constantine Evans (MS '11, PhD '14), the study's first author.

Then, inspired by how the human brain processes different scents, the team examined what would happen if the test tube contained different concentrations of the molecules. Olfaction, the sense of smell, distinguishes different scents based on the concentration of odor molecules present. The brain can distinguish scents, even if the molecules are the same, because of the differing concentrations.

"Classifying concentration patterns is a familiar task to all of us: an "odor" is characterized by a pattern of which molecules are present in high, intermediate, or low concentrations. So, distinguishing grandma's lasagna from a floral bouquet or an oily mechanic's garage is a matter of classifying concentration patterns," Winfree says.

The team wanted to find out the extent to which the self-assembly process acts like a neural network as it classifies the concentration patterns.

Of the 917 distinct kinds of molecular tiles, some appeared in all three shapes—the team called these "purple" tiles. Those that were unique to H were called "pink"; to A, "green"; and to M, "blue." Any given purple tile would appear in all three letters, but in different regions of the shape with different neighbors. For example, a cluster of purple tiles may be located together—or "co-localized"—in H, but those same tiles would be scattered throughout A and M. 

What happens in a tube with an increased concentration of certain purple tiles that are co-localized in one shape—for example, H? Though these tiles are found in A and M, could their co-localization in H create a seed that generates more H tiles than A or M? The team was excited to find that this was indeed true: A high concentration of certain molecules found throughout all shapes but only co-localized in one led to the nucleation of that one shape.

"Throughout biology, you find carefully self-assembled structures. But some components are found in multiple structures—for example, the yeast cyclin-dependent kinase Cdc28," Murugan says. "These structures are not always present; they need to come into being at the right times and in the right places, and the kinetics of nucleation is what governs this. So, if biology also exploits the neural-network-like collective modes of nucleation that we demonstrated in this work, then ubiquitous biological self-assembly might be hiding, in plain sight, powerful information processing and decision-making capabilities."

"It's exciting when concepts from one scientific field can, when you look at it right, be seen to appear in a seemingly unrelated field," Murugan adds. "Before our use of co-localization in molecular self-assembly as the principle underlying pattern recognition, a very similar computational architecture was discovered in the brain for how an animal can recognize where it is—the so-called 'place cells' of the hippocampus. Now we are looking for this principle of how nucleation can perform decision-making in other kinds of biomolecular processes, such as multicomponent condensates and genetic regulatory networks." 

The project builds on several decades of work in the Winfree lab.

Evans says: "What's exciting about DNA nanotechnology is that it's really the only molecular design technology today that allows one to investigate sophisticated theories of molecular computation in the large N limit—here almost a thousand different kinds of molecules all working together. Thankfully, at Caltech, we had access to technology that could automate the experimental preparation of samples with that many components mixed in arbitrary ratios, as well as access to a high-speed atomic force microscope capable of imaging individual molecular assemblies in great detail."

"Coming back to Caltech, my alma mater, to participate in the experiments with my own two hands was a really special experience for me," Murugan says. "Not only because of the personal connection and opportunities to reminisce about the good old days, but more deeply because it is an inspiring thing to see a beautiful theoretical idea come to life before one's eyes."

The paper is titled "Pattern recognition in the nucleation kinetics of non-equilibrium self-assembly." In addition to Evans, Murugan, and Winfree, Jackson O'Brien of the University of Chicago is a co-author. Funding was provided by the National Science Foundation, the Evans Foundation for Molecular Medicine, the European Research Council, Science Foundation Ireland, and the Carver Mead New Adventures Fund.