Computer simulations help materials scientists and biochemists study the motion of macromolecules, advancing the development of new drugs and sustainable materials. However, these simulations pose a challenge for even the most powerful supercomputers.
A University of Oregon graduate student has developed a new mathematical equation that significantly improves the accuracy of the simplified computer models used to study the motion and behavior of large molecules such as proteins, nucleic acids and synthetic materials such as plastics.
The breakthrough, published last month in Physical Review Letters , enhances researchers' ability to investigate the motion of large molecules in complex biological processes, such as DNA replication. It could aid in understanding diseases linked to errors in such replication, potentially leading to new diagnostic and therapeutic strategies.
"We want to understand how molecules move, twist and function," said Jesse Hall, a physics doctoral candidate who worked with theoretical physical chemistry professor Marina Guenza to develop the new model. "With this new equation, we can simulate larger protein complexes and gain deeper insight into how these molecular machines work in the body."
Hall's research has made progress on a problem computational scientists have been working on for more than 50 years: how to accurately calculate the friction biomolecules experience within their chaotic, viscous environment.
Biomolecules — molecules produced by a living organism, such as proteins — are surrounded by thousands of water molecules, along with other proteins, nucleic acids and other types of molecules. Within this environment, they're in constant motion; they fold, unfold and bind to nucleic acids and other proteins.
"They're wriggling around in there, and the mechanics of what they do is very important for understanding how DNA replication works or developing drugs to target a certain mechanism," Hall said.
Rather than synthesizing physical samples to study, scientists use computer models as a virtual lab. That allows them to alter the molecules they're analyzing by modifying their code so they can then study the effects of the change.
"When you have a good, coarse-grained model, you can simulate large systems," said Guenza, who is co-author of the study. "For example, one can see how molecules move together, rearrange, combine and function as a machine. You can change one amino acid and see how the mutation affects the way the molecules perform their biological function."
Because biomolecular systems are so large and complex, researchers rely on coarse-grained mathematical models, which simulate molecular movements without having to depict each individual atom. That helps keep computing costs down while speeding up computation.
But scientists have struggled for decades to accurately calculate the value of friction, which is part of the data used when running coarse-grained simulations, Guenza said.
As molecules move through fluid, the resulting friction creates a drag effect, affecting both their internal fluctuations and their external movements.
"To describe how a protein moves, you have to balance the different forces: the viscous forces, the random forces from collision with surrounding molecules, and the internal forces that keep the molecule together," Guenza said.
Other researchers have devised mathematical solutions starting from a formula known as the "Einstein relation," which establishes the relationship between a particle's diffusion, or how quickly it spreads out, and its mobility, or how easily it can be moved. But those solutions have their limits.
"There's a lot of good work out there for describing one aspect of a protein's motion, but we need more complete models that can describe several aspects of a protein's motion at once," Hall said. "We've basically come up with a much more general form of the Einstein relation, which offers a lot more choice and freedom. It allows us to flexibly tune our calculations to a specific system and get more reliable results."
Hall's equation is the first to simultaneously describe friction for both a molecule's internal fluctuations and its external diffusion through the fluid, Guenza said.
"This is a brilliant solution," she said. "Jesse's work provides a highly accurate tool that can be applied to both simple and complex molecular systems, making simulations of these large systems both faster and more accurate."
For many years, the Guenza group has focused on developing accurate theoretical tools that accelerate molecular simulations, tools that are essential for designing new polymer-based materials and for studying how proteins interact with DNA during replication. Errors in DNA replication play a role in the development of cancer and can lead to a broad range of genetic disorders.
"We realized we needed to build some more tools to get really accurate, precise mathematical models," Hall said.
Although his research is primarily theoretical, "we're building toward some more practical tools we can use later," Hall said. "Hopefully this is a tool that other people can use to work on projects that never even would have occurred to me."
