Exact geometric theory of dendronized polymer dynamics

The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the agents interaction range and (b) a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.

Favourable native-like helical local interactions can accelerate protein folding

weak interaction is one of the least understood topics in particle physics. is one of the four kinds of force that physicists recognize in nature, and, as its name indicates, it is much weaker than two of the others, the strong (nuclear) interaction and electromagnetism. has therefore been difficult to study because its effects are usually masked by the two stronger forces. In a few years the world will have at least two particle accelerators with capacities of hundreds of billions of electron-volts energy, and physicists hope that these machines may allow the beginning of a new era of systematic and vigorous investigation of the weak force. There is a finite chance that in our lifetime we'll see something interesting in the weak David B. Cline of the University of Wisconsin told the recent Coral Gables Conference on Fundamental Interactions at High Energy at the University of Miami. first manifestation of the weak interaction that physicists noticed was nuclear beta decay. In beta decay a neutron inside an atomic nucleus turns into a proton, emitting by the way an electron (called in the old days a beta ray) and an antineutrino. In recent years many other particles have been found that decay radioactively under the influence of the weak interaction. From these decay activities alone it is hard to arrive at a good mathematical description of the weak force or to test rival theories. That can be better done by investigating how the force acts in particle collisions in accelerator experiments. But the two stronger forces blot out the effect of the weak force unless one party to the collision is a neutrino. (Neutrinos are the only known kind of particle that responds to the weak force but to neither of the two stronger ones.) To do experiments with neutrinos requires a copious and energetic beam of them. world's two new accelerators (the National Accelerator Laboratory now in operation at Batavia, Ill., and CERN II beginning construction near Geneva) will provide such beams. They may be used to study the weak force itself and to use it as a means of probing the structure of other particles. The new accelerators may very well provide a new era in neutrino spectroscopy, A. K. Mann of NAL told the Coral Gables Conference. It may be the new optics of the remainder of this century. One of the most important questions to be decided by forthcoming experiments is whether the weak force is a local interaction or a nonlocal one. A local interaction is one in which the two interacting particles affect each other directly, rather like two billiard balls colliding. In a nonlocal interaction, the interacting particles exchange an intermediarly particle, and this particle mediates the effect of one to the other. In the strong interaction, the intermediary particle is a virtual meson; in electromagnetism it is a virtual photon. Formulations of both kinds have been suggested for the weak interaction. In the traditional nonlocal formulation, the intermediary is called the intermediate vector boson. Lately some theorists, most prominently T. D. Lee of Columbia University (SN: 10/9/71, p. 252) and Steven Weinberg of Massachusetts Institute of Technology, have been trying to work out a combined theory of the weak interaction plus electromagnetism. In this case there is a family of intermediaries among which both the vector boson and the photon find a place. local formulations arouse dismay because in them the particles most concerned with the weak interaction, the class called leptons (the electron, the muon, the two kinds of neutrino and their respective antiparticles), are point particles; like a formal geometric point, they have zero dimensions. is difficult to visualize a body with mass that does not occupy space, and, when one tries, all sorts of disturbing paradoxes come forth: particles have infinite mass densities, infinite self-energies, infinite electric charge densities and other infinities, some of which appear to be at variance with known properties of the particles. A nonlocal weak interaction allows the particles to occupy space. also does away with the troublesome infinities. Besides its esthetic qualities, what evidence is now in hand tends to incline some people toward the nonlocal theory. The point theory of the weak interaction cannot be exact, says Mann. He and others expect that the inexactness will become clear in the new range of energies about to be opened up. At energies near 300 billion electron-volts (GeV) something new may happen, he suggests. Some structure may appear in the interaction: maybe a vector boson propagator, maybe new kinds of leptons, maybe new neutrinos, maybe higher~~~~~~~~~~~~~~~~~~~~~~~~~~~~~lr i,.,...,...,.~~~~~~~~~~~~~~~~-,-----------------'>.' s

Energetics of protein thermodynamic cooperativity: contributions of local and nonlocal interactions

Engrailed homeodomain (EngHD), a highly charged transcription factor regulating over 200 genes, is a fast-folding protein. Recent studies have shown that the abundant charged residues in EngHD not only facilitate protein-DNA interactions but also influence the conformational disorder of its native structure. However, the mechanisms by which electrostatic interactions modulate the folding of EngHD remain unclear. Here, we employ a coarse-grained structure-based model that incorporates the salt-dependent Debye-Hückel model to investigate the (un)folding behavior of EngHD under various salt concentrations. Our findings demonstrate that increasing salt concentrations enhance both folding stability and cooperativity, while the folding barrier height remains relatively constant due to the distinct electrostatic effects on individual residues. By modulating the energetic balance between local and nonlocal interactions, we shift the folding of EngHD from a downhill process to a two-state process. Notably, we observe a nonmonotonic relationship between the strength of local interactions and residue-level coupling degree during (un)folding, likely attributed to the repulsive electrostatic interactions present in the native structure of EngHD. Additionally, we identify a critical turning point in the dependence of folding cooperativity on salt concentration, classified by the energetic balance of local and nonlocal interactions. Our results provide valuable insights into how electrostatic interactions influence the folding of EngHD, contributing to the theoretical framework for engineering highly charged proteins.

Non-local reaction-diffusion equation is an important area to study the dynamics of the individuals which compete for resources. In this paper, we describe a prey-dependent predator-prey model with Holling type II functional response with a generalist predator. In particular, we want to see the behavior of the system in the presence of non-local interaction. Introduction of non-local intraspecific competition in prey population leads to some new characteristics in comparison with the local model. Comparisons have been made between the local and non-local interactions of the system. The range of non-local interaction enlarges the parametric domain on which stationary patterns exist. The periodic oscillation for the local model in the Hopf domain can be stabilized by suitable limit of strong non-local interaction. An increase in the range of non-local interaction increases the Turing domain up to a certain level, and then, it decreases. Also, increasing the range of non-local interaction results in the overlap of nearby foraging areas and hence alters the size of the localized patches and formation of multiple stationary patches. Numerical simulations have been carried out to validate the analytical findings and to establish the existence of multiple stationary patterns, oscillatory solution, two-periodic solution and other spatiotemporal dynamics.

Energy properties of discrete breathers

We study existence of patterns for a reaction-diffusion system of population dynamics with nonlocal interaction. We address the system as a bifurcation problem (the bifurcation parameter being the diffusivity of one species), and investigate the possibility of patterns bifurcating out of a constant steady state solution via Turing destabilization. It is shown that the nonlocal character of the interaction enhances the possibility that patterns exist with respect to the case of the companion problem with local interaction.

We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

Chameleon sequences (ChSeqs) refer to sequence strings of identical amino acids that can adopt different conformations in protein structures. Researchers have detected and studied ChSeqs to understand the interplay between local and global interactions in protein structure formation. The different secondary structures adopted by one ChSeq challenge sequence-based secondary structure predictors. With increasing numbers of available Protein Data Bank structures, we here identify a large set of ChSeqs ranging from 6 to 10 residues in length. The homologous ChSeqs discovered highlight the structural plasticity involved in biological function. When compared with previous studies, the set of unrelated ChSeqs found represents an about 20-fold increase in the number of detected sequences, as well as an increase in the longest ChSeq length from 8 to 10 residues. We applied secondary structure predictors on our ChSeqs and found that methods based on a sequence profile outperformed methods based on a single sequence. For the unrelated ChSeqs, the evolutionary information provided by the sequence profile typically allows successful prediction of the prevailing secondary structure adopted in each protein family. Our dataset will facilitate future studies of ChSeqs, as well as interpretations of the interplay between local and nonlocal interactions. A user-friendly web interface for this ChSeq database is available at prodata.swmed.edu/chseq.

We previously elucidated principles for designing ideal proteins with completely consistent local and non-local interactions which have enabled the design of a wide range of new αβ-proteins with four or fewer β-strands. The principles relate local backbone structures to supersecondary-structure packing arrangements of α-helices and β-strands. Here, we test the generality of the principles by employing them to design larger proteins with five- and six- stranded β-sheets flanked by α-helices. The initial designs were monomeric in solution with high thermal stability, and the nuclear magnetic resonance (NMR) structure of one was close to the design model, but for two others the order of strands in the β-sheet was swapped. Investigation into the origins of this strand swapping suggested that the global structures of the design models were more strained than the NMR structures. We incorporated explicit consideration of global backbone strain into the design methodology, and succeeded in designing proteins with the intended unswapped strand arrangements. These results illustrate the value of experimental structure determination in guiding improvement of de novo design, and the importance of consistency between local, supersecondary, and global tertiary interactions in determining protein topology. The augmented set of principles should inform the design of larger functional proteins.

A genetic algorithm that seeks native states of peptides and proteins

We introduce new lattice-gas and lattice-Boltzmann models for simulating miscible fluids in two dimensions. The inclusion of a nonlocal interaction produces a lattice gas with lower diffusivity than achieved before. To overcome some observed unphysical properties of this lattice gas, we introduce a lattice-Boltzmann analogue of the model. We first formulate a miscible two-component lattice-Boltzmann model with local interactions only, and show that its diffusivity is determined by an eigenvalue of the linearized collision operator. Diffusivity is then reduced by including nonlocal interactions. The utility of the model is demonstrated by a simulation of two-dimensional viscous fingering.

We generalize and study, within the framework of quantum mechanics and working with 1-dimensional, manifestly non-Hermitian Hamiltonians H=−d2/dx2+V, the traditional class of exactly solvable models with local point interactions V=V(x). We discuss the consequences of the use of nonlocal point interactions such that (Vf)(x)=∫K(x,s)f(s)ds by means of the suitably adapted formalism of boundary triplets.

The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a black box” on which boundary the spectral energy flux is given. It is assumed that the spectrum is formatted due to intermodal interactions being local in the wave-number space that leads to a cascade mechanism of energy transfer along the wave-number spectrum and the possibility of using the renormalization-group method related to the Markovian features of the process under consideration. The obtained formula for energy spectrum is valid in a wide wave-number range and at arbitrary values of fluid viscosity. It is shown that in functional formulation of the statistical theory of turbulence, the procedure of separating local intermodal interactions, which govern energy transfer (straining effect), and filtering out nonlocal interactions, which have no influence on energy transfer (sweeping effect), is directly described without providing additional arguments or conjectures commonly used in the renormalization-group analysis of turbulent spectra.