Related papers: Relationship Between Structural Fractal and Possib…
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…
The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of…
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…
The ability to absorb mutations while retaining structure and function, or mutational robustness, is a remarkable property of natural proteins. In this Letter, we use a computational model of organismic evolution [Zeldovich et al, PLOS Comp…
Proteins are biomolecules of life. They fold into a great variety of three-dimensional (3D) shapes. Underlying these folding patterns are many recurrent structural fragments or building blocks (analogous to `LEGO bricks'). This paper…
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the space dimension. We also address how the response function…
In polymers melts and supercooled liquids, the glassy dynamics is characterized by the rattling of monomers or particles in the cage formed by their neighbors. Recently, a direct correlation in such systems, described by a universal scaling…
The fractal properties of four-dimensional Euclidean simplicial manifold generated by the dynamical triangulation are analyzed on the geodesic distance D between two vertices instead of the usual scale between two simplices. In order to…
Folded protein hydrogels are prime candidates as tuneable biomaterials but it is unclear to what extent their mechanical properties have mesoscopic, as opposed to molecular origins. To address this, we probe hydrogels of the muscle-derived…
The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary…
The quantitative description of model protein folding kinetics using a diffusive collective reaction coordinate is examined. Direct folding kinetics, diffusional coefficients and free energy profiles are determined from Monte Carlo…
New definitions of the structural susceptibilities based on the fluctuations of distances to the native state of toy protein models are proposed. The calculation of such susceptibilities does not require the basin of native state and the…
Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and…
Cellular phenotype is characterized by different components such as cell size, protein content and cell cycle time. These are global variables that are the outcome of multiple internal microscopic processes. Accordingly, they display some…
In a recent Letter, Gutin, Abkevich, and Shakhnovich (GAS) reported on a series of dynamical Monte Carlo simulations on lattice models of proteins. Based on these highly simplified models, they found that four different potential energies…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
The biological activity and functional specificity of proteins depend on their native three-dimensional structures determined by inter- and intra-molecular interactions. In this paper, we investigate the geometrical factor of protein…
Fractal scaling--a power-law behavior of the number of boxes needed to tile a given network with respect to the lateral size of the box--is studied. We introduce a new box-covering algorithm that is a modified version of the original…
The authors address the problem of downhill protein folding in the framework of a simple statistical mechanical model, which allows an exact solution for the equilibrium and a semianalytical treatment of the kinetics. Focusing on protein…
Predicting the three-dimensional (3D) functional structures of proteins remains an important computational milestone in molecular biology to be achieved. This feat is hinged on a clear understanding of the mechanism which proteins use to…