Related papers: Synchronization as a unifying mechanism for protei…
Synchronization is crucial for the correct functionality of many natural and man-made complex systems. In this work we characterize the formation of synchronization patterns in networks of Kuramoto oscillators. Specifically, we reveal…
One of the most puzzling and unsolved challenges in molecular biology is understanding how proteins fold. Despite having advanced predictive tools that can accurately estimate the native structures of proteins, we still lack a comprehensive…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…
Protein folding is a phenomenon that has been studied for about 50 years and still remains as an unsolved problem. The main feature of this process is that it occurs as an all or none process, so a protein, can jump directly between folded…
Increasing evidence suggests that chromosome folding and genetic expression are intimately connected. For example, the co-expression of a large number of genes can benefit from their spatial co-localization in the cellular space.…
The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a…
Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in…
Synchronization is an important phenomenon in a wide variety of systems comprising interacting oscillatory units, whether natural (like neurons, biochemical reactions, cardiac cells) or artificial (like metronomes, power grids, Josephson…
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it…
Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing…
Understanding the mechanism of protein secondary structure formation is an essential part of protein-folding puzzle. Here we describe a simple model for the formation of the $\beta$-hairpin, motivated by the fact that folding of a…
We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
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…
These lectures will address two questions. Is there a simple variational principle underlying the existence of secondary motifs in the native state of proteins? Is there a general approach which can qualitatively capture the salient…
Protein folding cooperativity is defined by the nature of the finite-size thermodynamic transition exhibited upon folding: two-state transitions show a free energy barrier between the folded and unfolded ensembles, while downhill folding is…
Protein structure prediction and folding are fundamental to understanding biology, with recent deep learning advances reshaping the field. Diffusion-based generative models have revolutionized protein design, enabling the creation of novel…
Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…