Related papers: A new mathematical model for molecular dynamics 1:…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
In spite of decades of research, much remains to be discovered about folding: the detailed structure of the initial (unfolded) state, vestigial folding instructions remaining only in the unfolded state, the interaction of the molecule with…
When described by a low-dimensional reaction coordinate, the rates of protein folding are determined by a subtle interplay between free-energy barriers and friction. While it is commonplace to extract free-energy profiles from molecular…
Biology stores information and computes at the molecular scale, yet the ways in which it does so are often distinct from human-engineered computers. Mapping biological computation onto architectures familiar to computer science remains an…
Molecular dynamics (MD) simulations allow atomistic insights into chemical and biological processes. Accurate MD simulations require computationally demanding quantum-mechanical calculations, being practically limited to short timescales…
Simulations of biological macromolecules play an important role in understanding the physical basis of a number of complex processes such as protein folding. Even with increasing computational power and evolution of specialized…
The laws of physics have been written in the language of dif-ferential equations for centuries. Neural Ordinary Differen-tial Equations (NODEs) are a new machine learning architecture which allows these differential equations to be learned…
Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as…
Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools.…
Molecular dynamics (MD) simulates the time evolution of atomic systems governed by interatomic forces, and the fidelity of these simulations depends critically on the underlying force model. Classical force fields (CFFs) rely on fixed…
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…
Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
Accurate prediction of energy and forces for 3D molecular systems is one of fundamental challenges at the core of AI for Science applications. Many powerful and data-efficient neural networks predict molecular energies and forces from…
Current all-atom potential based molecular dynamics (MD) allow the identification of a protein's functional motions on a wide-range of time-scales, up to few tens of ns. However, functional large scale motions of proteins may occur on a…
The paradigm that the primary amino acid sequence prescribes structure and thus function has for a long time been central to the understanding of protein science. Though the theory is supported by the behaviour of most structured proteins,…
Understanding the binding dynamics of liquid molecules is of fundamental importance in physical and life sciences. However, nanoscale fast dynamics pose great challenges for experimental characterization. Conventionally, the binding…
It is well known that physical phenomena may be of great help in computing some difficult problems efficiently. A typical example is prime factorization that may be solved in polynomial time by exploiting quantum entanglement on a quantum…
Folding protein dynamics has been an area of high interest for quite some time, especially given the increased focus on the field of Biophysics. Because folding dynamics occur on such short time scales, empirical techniques developed for…
Unraveling the dynamical motions of biomolecules is essential for bridging their structure and function, yet it remains a major computational challenge. Molecular dynamics (MD) simulation provides a detailed depiction of biomolecular…