A ‘Rosetta Stone’ for molecular programs

Penn Engineers have developed a mathematical “Rosetta Stone” that interprets atomic and molecular actions into predictions of larger-scale results, like proteins unfolding, crystals forming and ice melting, with out the necessity for pricey, time-consuming simulations or experiments. That may make it simpler to design smarter medicines, semiconductors and extra.

In a latest paper in Journal of the Mechanics and Physics of Solids, the Penn researchers used their framework, Stochastic Thermodynamics with Internal Variables (STIV), to unravel a 40-year drawback in phase-field modeling, a extensively used device for learning the shifting frontier between two states of matter, just like the boundary between water and ice or the place the folded and unfolded elements of a protein be part of.

“Phase-field modeling is about predicting what happens at the thin frontier between phases of matter, whether it’s proteins folding, crystals forming or ice melting,” says Prashant Purohit, Professor in Mechanical Engineering and Applied Mechanics (MEAM) and one of many paper’s co-authors. “STIV gives us the mathematical machinery to describe how that frontier evolves directly from first principles, without needing to fit data from experiments.”

In a 3rd, associated paper, within the Journal of Non-Equilibrium Thermodynamics, the researchers generalize the framework, giving it broader mathematical energy. “Just as the Rosetta Stone unlocked countless ancient texts, the STIV framework can translate microscopic movements into larger-scale behavior across non-equilibrium systems,” says Celia Reina, Associate Professor in MEAM and the papers’ senior creator. 

“STIV could potentially help us design new materials,” provides Reina. “In the same way the Rosetta Stone allowed scholars to compose in hieroglyphs, this framework could let us start with the property we want and work backward to the molecular movements that create it.”

How STIV Works

In the twentieth century, French physicist Paul Langevin pioneered arithmetic to explain the exercise of atoms and molecules embedded in fluctuating environments. “STIV captures the average evolution of such systems by introducing ‘internal’ variables, extra quantities that capture the non-equilibrium features of a system,” says Travis Leadbetter (Gr’25), the papers’ first creator and a latest Applied Mathematics and Computational Science (AMCS) doctoral graduate. 

Choosing the fitting variables issues: just like the Rosetta Stone, whose alignment of hieroglyphs with Greek and Demotic textual content made translation attainable, STIV is dependent upon choosing the variables that greatest predict the system’s large-scale conduct. “You need to have some sense of the context,” provides Leadbetter. “But once those variables are chosen, STIV gives you their evolution, without having to adjust the mathematics to fit experimental data each time.” 

However, the teams’ first efforts solely confirmed that STIV labored in a slender subset of contexts. “We needed to generalize the mathematics,” says Leadbetter. That resulted within the teams’ most up-to-date paper, which presents three strategies to account for nearly any scenario. “Two are quicker and cover most systems, while the other takes longer to calculate but handles rare cases,” says Leadbetter. “Together they make the framework both practical and universal.”

The Power of STIV 

For centuries, scientists have strived to mathematically describe the world as typically as attainable. The higher math can describe a system, the simpler that system is to investigate and finally management. 

But for complicated programs outdoors equilibrium, attaining that degree of rigor is normally gradual and dear. “If you want a rigorous model, typically it takes a long time to compute, and if you want results fast, you have to simplify and lose accuracy,” says Purohit. STIV guarantees to beat that tradeoff, though the upside is dependent upon the issue to which the framework is utilized. 

In addition to the functions explored by the authors, researchers in the United States and Italy recently used STIV to derive new insights into how organic cells transfer. “STIV gives us a common language for problems that used to be treated in isolation,” says Reina. “That means researchers studying subjects as varied as proteins, crystals and cells can draw on the same framework. That kind of universality points to enormous potential for future discoveries.”

These research had been carried out on the University of Pennsylvania School of Engineering and Applied Science and supported by the National Science Foundation (CAREER award CMMI-2047506, DMR 2212162); the National Defense Science and Engineering Graduate Fellowship Program, sponsored by the Air Force Research Laboratory, the Office of Naval Research and the Army Research Office (FA9550-21-F-0003); the National Institutes of Health (R01 HL-148227); the American Chemical Society (PRF-61793ND10); and the University of Pennsylvania Applied Mathematics and Computational Science graduate group.