Related papers: Universal behavior of localization of residue fluc…
It is not merely the position of residues that are of utmost importance in protein function and stability, but the interactions between them. We illustrate, by using a network construction on a set of 595 non-homologous proteins, that…
We used statistical thermodynamics of conformational fluctuations and the elements of algebraic graph theory together with data from 2000 protein crystal structures, and showed that folded native proteins with harmonic interactions exhibit…
Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal…
Stochastic kinetic models of genetic expression are able to describe protein fluctuations. A comparative study of the canonical and a feedback model is given here by using stochastic simulation methods. The feedback model is skeleton model…
It is shown how the universal correlation function of Brezin and Zee, and Beenakker, for random matrix ensembles of Wigner-Dyson type with density support on a finite interval can be derived using a linear response argument and macroscopic…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
In this work, the dynamics of fluctuations in gene expression time series is investigated. By using collected data of gene expression from yeast and human organisms, we found that the fluctuations of gene expression level and its average…
We investigate universal features of the off-equilibrium sequential and conservative fragmentation processes with the dissipative effects which are simulated by the Gaussian random inactivation process. The relation between the fragment…
We discuss the phenomenon of universal fluctuations in mesoscopic systems and nuclei. For this purpose we use Random Matrix Theory (RMT). The statistical $S$-matrix is used to obtain the physical observables in the case of Quantum Dots,…
Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under…
Protein structures can be studied as complex networks of interacting amino acids. We study proteins of different structural classes from the network perspective. Our results indicate that proteins, regardless of their structural class, show…
We present an analysis of different sets of gravitational N-body simulations, all describing the dynamics of discrete particles with a small initial velocity dispersion. They encompass very different initial particle configurations,…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
Selfsimilar space-time fractal fluctuations are generic to dynamical systems in nature such as atmospheric flows, heartbeat patterns, population dynamics, etc. The physics of the long-range correlations intrinsic to fractal fluctuations is…
Shape had been intuitively recognized to play a dominant role in determining the global motion patterns of bio-molecular assemblies. However, it is not clear exactly how shape determines the motion patterns. What about the local…
Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of…
The dynamical characterization of proteins is crucial to understand protein function. From a microscopic point of view, protein dynamics is governed by the local atomic interactions that, in turn, trigger the functional conformational…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…