Related papers: Structure Space of Model Proteins --A Principle Co…
The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino…
Voids exist in proteins as packing defects and are often associated with protein functions. We study the statistical geometry of voids in two-dimensional lattice chain polymers. We define voids as topological features and develop a simple…
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based…
Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent to the indispensability of proteins for living cells is the fact that a given protein…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
We fit the Fourier transforms of solvent accessibility and hydrophobicity profiles of a representative set of proteins to a joint multi-variable Gaussian. This allows us to separate the intrinsic tendencies of sequence and structure…
Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these…
A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable.…
Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the…
We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular…
Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the…
The hydrophobic/polar HP model on the square lattice has been widely used to investigate basics of protein folding. In the cases where all designing sequences (sequences with unique ground states) were enumerated without restrictions on the…
In the In recent times, the research community has explored diverse structures and novel fabrication methods for amorphous solids. This work investigates structural trends among different classes of amorphous materials to identify universal…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
We study the statistical properties of hydrophobic/polar model sequences with unique native states on the square lattice. It is shown that this ensemble of sequences differs from random sequences in significant ways in terms of both the…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…
We exemplarily investigate how optical properties of single scatterers in interacting multi-particle systems influence measurable structure factors. Both particles with linear gradients of their scattering length density and core-shell…
We numerically analyse the density field of three-dimensional randomly jammed packings of monodisperse soft frictionles spherical particles, paying special attention to fluctuations occurring at large lengthscales. We study in detail the…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
We examine the reduced density matrix of the centre of mass on position basis considering a one-dimensional system of $N$ non-interacting distinguishable particles in a infinitely deep square potential well. We find a class of pure states…