Related papers: Synchronization as a unifying mechanism for protei…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the…
Proteins created by combinatorial methods in vitro are an important source of information for understanding sequence-structure-function relationships. Alignments of folded proteins from combinatorial libraries can be analyzed using methods…
Suspensions of swimming micro-organisms provide examples of coordinated active dynamics. That has stimulated the study of a phenomenological theory combining synchronization and polar order in active matter. Here, we consider another…
We carry out a theoretical study of the vibrational and relaxation properties of naturally-occurring proteins with the purpose of characterizing both the folding and equilibrium thermodynamics. By means of a suitable model we provide a full…
In the cell, protein complexes form relying on specific interactions between their monomers. Excluded volume effects due to molecular crowding would lead to correlations between molecules even without specific interactions. What is the…
Using the Helmholtz decomposition of the vector field of folding fluxes in a two-dimensional space of collective variables, a potential of the driving force for protein folding is introduced. The potential has two components. One component…
Protein sequences serve as a natural record of the evolutionary constraints that shape their functional structures. We show that it is possible to use only sequence information to go beyond predicting native structures and global stability…
The effects of cooperativity are studied within Go-Lennard-Jones models of proteins by making the contact interactions dependent on the proximity to the native conformation. The kinetic universality classes are found to remain the same as…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
Fractionation is necessary for self-assembly in multicomponent mixtures. Here, reversible fractionation and crystallization are realized and studied in a two-dimensional binary colloids which is supersaturated by enhancing the attraction…
We study two mechanisms for the formation of protein patterns near membranes of living cells by mathematical modelling. Self-assembly of protein domains by electrostatic lipid-protein interactions is contrasted with self-organization due to…
The processes by which protein sidechains reach equilibrium during a folding reaction are investigated using both lattice and all-atom simulations. We find that rates of sidechain relaxation exhibit a distribution over the protein…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…
With the help of lattice Monte Carlo modelling of heteropolymers, we show that the necessary condition for a protein to fold on short call is to proceed through partially folded intermediates. These elementary structures are formed at an…
We perform extensive Monte Carlo simulations of a lattice model and the Go potential to investigate the existence of folding pathways at the level of contact cluster formation for two native structures with markedly different geometries.…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
We consider here a model previously introduced to describe the collective behavior of an ensemble of cold atoms interacting with a coherent electromagnetic field. The atomic motion along the self-generated spatially-periodic force field can…