RESUMEN

Reciprocal regulation of genome topology and function is a fundamental and enduring puzzle in biology. The wealth of data provided by Hi-C libraries offers the opportunity to unravel this relationship. However, there is a need for a comprehensive theoretical framework in order to extract topological information for genome characterization and comparison. Here, we develop a toolbox for topological analysis based on Circuit Topology, allowing for the quantification of inter- and intracellular genomic heterogeneity, at various levels of fold complexity: pairwise contact arrangement, higher-order contact arrangement, and topological fractal dimension. Single-cell Hi-C data were analyzed and characterized based on topological content, revealing not only a strong multiscale heterogeneity but also highly conserved features such as a characteristic topological length scale and topological signature motifs in the genome. We propose that these motifs inform on the topological state of the nucleus and indicate the presence of active loop extrusion.

RESUMEN

A wide range of physical systems can be formally mapped to a linear chain of sorted objects. Upon introduction of intrachain interactions, such a chain can "fold" to elaborate topological structures, analogous to folded linear polymer systems. Two distinct chain-topology theories, knot theory and circuit topology, have separately provided insight into the structure, dynamics, and evolution of folded linear polymers such as proteins and genomic DNA. Knot theory, however, ignores intrachain interactions (contacts), whereas chain crossings are ignored in circuit topology. Thus, there is a need for a universal approach that can provide topological description of any folded linear chain. Here, we generalize circuit topology in order to grasp particularities typically addressed by knot theory. We develop a generic approach that is simple, mathematically rigorous, and practically useful for structural classification, analysis of structural dynamics, and engineering applications.

RESUMEN

A broad variety of materials, ranging from composites and heat transfer nano-fluids to electrochemical energy storage electrodes, widely employ cylindrical particles of various aspect ratios, such as carbon nanotubes. These particles are generally excellent conductors of heat and electricity and when dispersed in a continuous medium influence dramatically the transport properties of the heterogeneous material by forming a percolating network. Numerous theories exist to predict key parameters such as particle concentration at the percolation threshold and transport properties at concentrations beyond the threshold. The microstructure formed by connecting particles in the material is an important determinant toward such parameters but often requires complex numerical models to resolve. In this paper, we present an analytical, probabilistic model capturing the microstructure of a system of randomly positioned, soft-core, cylindrical particles with a finite aspect ratio, valid at arbitrary particle concentration. Our analytical framework allows for the calculation of the particle contact number distribution and percolation probability of the particle system. We show that our analytical model is more accurate than excluded volume theory for predicting the percolation threshold for spherocylinders of finite aspect ratios, and agrees well with the corresponding numerical results. Our theory describes the percolating network topology above the percolation threshold and can serve as the foundation for analytical composition-structure-property relationships for heterogeneous materials with conducting cylindrical particles.

RESUMEN

This article presents an ab initio metadynamics study of elementary hydronium ion transitions at dense arrays of surface groups with sulfonic acid head groups. Calculations simulate minimally hydrated conditions of the interfacial ionic system. The specific focus is on the influence of the surface group density on hydronium ion transport. Results reveal a high sensitivity of the activation free energy of hydronium translocations to the surface group density. A spontaneous concerted transition with low activation barrier is found at a surface group separation of 6.8 Å. When hydroniums translocate concertedly, the activation barrier of the transition drops by more than a factor of two to the value of 0.25 eV. An approach is presented to determine interaction constants of hydronium ions and anionic surface groups as well as the surface group flexibility from the analysis of frequency spectra. These properties are discussed in the context of a recently developed soliton theory of interfacial proton transport.

Asunto(s)

Simulación de Dinámica Molecular , Compuestos Onio/química , Enlace de Hidrógeno , Protones , Termodinámica

RESUMEN

We present a theoretical study of surface proton mobility at a minimally hydrated array of protogenic surface groups. At dense packing, the array assembles into a 2D bicomponent lattice that is formed by sulfonate anions, which are only allowed to fluctuate about fixed equilibrium positions, and mobile hydronium ions. Proton transport on the lattice proceeds by collective translocations of hydronium ions. This type of motion is described within the framework of soliton theory. Our main objective in this article is to establish the relation between microscopic surface structure and effective proton mobility. To this end, we present an approach to calculate microscopic interaction parameters that determine hydronium ion motion. The developed formalism enables us to theoretically derive an expression for soliton mobility at a given surface structure and compare it with experimentally measured mobilities.

RESUMEN

Surface proton conduction is of utmost importance in biology, materials science, and electrochemistry; yet experimental findings of ultrafast proton transport at densely packed arrays of anionic surface groups have remained controversial and unexplained. We present an ab initio molecular dynamics study of proton dynamics at sulfonic-acid terminated surface groups. Results furnish a highly efficient collective mechanism of hydronium ion translocations at a critical surface group separation of ~6.5 Å. Orientational fluctuations of SG trigger hydrogen bond breaking that sets off the hydronium ion motion. The activation free energy of this process is 0.3 eV (±0.1 eV). The soliton-like nature of this mechanism is owed to the trigonal symmetry of sulfonate anions and exceptionally strong interfacial hydrogen bonding. These insights should stimulate surface conductance studies at SG monolayers with sulfonic acid groups, and they bolster efforts in designing proton conducting polymers conducive to fuel cell operation above ~100 °C.

Asunto(s)

Simulación de Dinámica Molecular , Enlace de Hidrógeno , Compuestos Onio/química , Protones , Sulfitos/química

RESUMEN

We present a theoretical study of collective proton transport at a 2D array of end-grafted protogenic surface groups with sulfonic acid head groups. The graft positions of the surface groups form a regular hexagonal lattice. We consider the interfacial array at a high packing density of the surface groups and under minimal hydration with one water molecule added per head group. For these conditions, the stable interfacial conformation consists of a bicomponent lattice of hexagonally ordered sulfonate anions and interstitial hydronium cations. Hydronium ion motion occurs as a travelling solitary wave. We analyse the microscopic parameters of the solitons and study the influence of different potential profiles on the proton motion created by rotation and tilting of sidechains and sulfonate anions. Using soliton solutions of the equation of motion, we establish relations between the energy and mobility of the solitons and the microscopic structural and interaction parameters of the array.

Asunto(s)

Simulación de Dinámica Molecular , Protones , Transporte Biológico , Biofisica/métodos , Electrólitos , Iones , Cinética , Modelos Estadísticos , Modelos Teóricos , Movimiento (Física) , Compuestos Onio/química , Soluciones/química , Propiedades de Superficie , Agua/química

RESUMEN

The analytical solution of the Poisson-Nernst-Planck equations is found in the linear regime as response to a dc-voltage. In deriving the results a new approach is suggested, which allows to fulfill all initial and boundary conditions and guarantees the absence of Faradaic processes explicitly. We obtain the spatiotemporal distribution of the electric field and the concentration of the charge carriers valid in the whole time interval and for an arbitrary initial concentration of ions. A different behavior in the short- and the long-time regime is observed. The crossover between these regimes is estimated.