To achieve these goals, we developed a suite of numerical techniques capable of extracting key information from diverse data sets, independent of their source. These methods build on our earlier work in “memory extraction” techniques within a common framework provided by the generalized Langevin equation (GLE). The GLE is a standard theoretical model for systems with memory effects. It consists of differential equations that incorporate environmental noise, an energy landscape from force interactions, and a memory-dependent friction term that couples to the system’s full history, introducing a dynamic environment into the model. Memory extraction refers to determining the functional form of this friction term directly from time-series data, providing a complete system characterization within our general NoMaMemo framework.
Overall, we made significant advances in the projection methodology, the primary theoretical framework for constructing GLEs and defining the role of friction. Our techniques for handling complex dependencies beyond simple linear friction are now widely adopted, and our group is at the forefront of developing non-equilibrium projection methods. These are essential for understanding the stochastic nature of living systems and for analyzing other complex phenomena, including meteorological patterns and economic dynamics.
We have achieved a broad range of applications. In the area of protein folding, we demonstrated that accurately predicting long-timescale folding kinetics requires the full multi-timescale friction profile. More fundamentally, we showed that basic units of molecular conformation, such as rotating dihedral bonds, deviate strongly from expected diffusion laws because of the complex nature of solvent coupling at the molecular level. In ultrafast molecular vibrational spectroscopy, we extracted time-dependent friction acting on chemical bonds, allowing us to predict infrared spectra in excellent agreement with experiment. Our models also reproduce the dynamics of complex biological systems, such as active cytoskeletal networks and red blood cell flickering. Finally, we showed that the swimming behavior of single-cell organisms can be classified by features of non-Markovian dynamics. By analyzing the stochastic search strategies seen in many foraging animals, we found that memory in the search path improves efficiency when target locations are correlated.
As part of dissemination, we organized the international conference “Memory of Rare and Non-Equilibrium Events” in Tashkent, Uzbekistan, and published an invited review, Memory and Friction: From the Nanoscale to the Macroscale, in Annual Review of Physical Chemistry.
