Favourable native-like helical local interactions can accelerate protein folding

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

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

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.

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.

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.

The denatured state ensemble (DSE) represents the starting state for protein folding and the reference state for protein stability studies. Residual structure in the DSE influences the kinetics of protein folding, the propensity to aggregate, and protein stability. The DSE that is most relevant for folding is the ensemble populated under native conditions, but the stability of proteins and the cooperativity of their folding normally prevent direct characterization of this ensemble. Indirect experiments have been used to infer residual structure in the DSE under nondenaturing conditions, but direct characterization is rare. The N-terminal domain of ribosomal protein L9 (NTL9) is a small mixed α-β domain that folds cooperatively on the millisecond time scale. A destabilized double mutant of NTL9, V3A/I4A-NTL9, populates the DSE in the absence of denaturant and is in slow exchange with the native state on the nuclear magnetic resonance time scale. The DSE populated in buffer was compared to the urea-induced DSE. Analysis of (1)H and (13)C chemical shifts reveals residual secondary structure in the DSE in buffer, which is stabilized by both local and long-range interactions. (15)N R2 relaxation rates deviate from random coil models, suggesting hydrophobic clustering in the DSE. Paramagnetic relaxation enhancement experiments show that there are transient long-range contacts in the DSE in buffer. In contrast, the urea-induced DSE has significantly less residual secondary structure and markedly fewer long-range contacts; however, the urea-induced DSE deviates from a random coil.

Contact order, transition state placement and the refolding rates of single domain proteins

Proteins fold and function in the crowded environment of the cell's interior. In the recent years it has been well established that the so-called "macromolecular crowding" effect enhances the folding stability of proteins by destabilizing their unfolded states for selected proteins. On the other hand, chemical and thermal denaturation is often used in experiments as a tool to destabilize a protein by populating the unfolded states when probing its folding landscape and thermodynamic properties. However, little is known about the complicated effects of these synergistic perturbations acting on the kinetic properties of proteins, particularly when large structural fluctuations, such as protein folding, have been involved. In this study, we have first investigated the folding mechanism of Trp-cage dependent on urea concentration by coarse-grained molecular simulations where the impact of urea is implemented into an energy function of the side chain and/or backbone interactions derived from the all-atomistic molecular dynamics simulations with urea through a Boltzmann inversion method. In urea solution, the folding rates of a model miniprotein Trp-cage decrease and the folded state slightly swells due to a lack of contact formation between side chains at the terminal regions. In addition, the equilibrium m-values of Trp-cage from the computer simulations are in agreement with experimental measurements. We have further investigated the combined effects of urea denaturation and macromolecular crowding on Trp-cage's folding mechanism where crowding agents are modeled as hard-spheres. The enhancement of folding rates of Trp-cage is most pronounced by macromolecular crowding effect when the extended conformations of Trp-cast dominate at high urea concentration. Our study makes quantitatively testable predictions on protein folding dynamics in a complex environment involving both chemical denaturation and macromolecular crowding effects.

Impact of Local and Non-local Interactions on Thermodynamics and Kinetics of Protein Folding

Exact geometric theory of dendronized polymer dynamics

Energy properties of discrete breathers

There is currently much interest in predator–prey models across a variety of bioscientific disciplines. The focus is on quantifying predator–prey interactions, and this quantification is being formulated especially as regards climate change. In this article, a stability analysis is used to analyse the behaviour of a general two-species model with respect to the Allee effect (on the growth rate and nutrient limitation level of the prey population). We present a description of the local and non-local interaction stability of the model and detail the types of bifurcation which arise, proving that there is a Hopf bifurcation in the Allee effect module. A stable periodic oscillation was encountered which was due to the Allee effect on the prey species. As a result of this, the positive equilibrium of the model could change from stable to unstable and then back to stable, as the strength of the Allee effect (or the ‘handling’ time taken by predators when predating) increased continuously from zero. Hopf bifurcation has arose yield some complex patterns that have not been observed previously in predator-prey models, and these, at the same time, reflect long term behaviours. These findings have significant implications for ecological studies, not least with respect to examining the mobility of the two species involved in the non-local domain using Turing instability. A spiral generated by local interaction (reflecting the instability that forms even when an infinitely large carrying capacity is assumed) is used in the model.

The transcriptional antiterminator protein LicT regulates the expression of Bacillus subtilis operons involved in beta-glucoside metabolism. It consists of an N-terminal RNA-binding domain (co-antiterminator (CAT)) and two phosphorylatable phosphotransferase system regulation domains (PRD1 and PRD2). In the activated state, each PRD forms a dimeric unit with the phosphorylation sites totally buried at the dimer interface. Here we present the 1.95 A resolution structure of the inactive LicT PRDs as well as the molecular solution structure of the full-length protein deduced from small angle x-ray scattering. Comparison of native (inactive) and mutant (constitutively active) PRD crystal structures shows massive tertiary and quaternary rearrangements of the entire regulatory domain. In the inactive state, a wide swing movement of PRD2 results in dimer opening and brings the phosphorylation sites to the protein surface. This movement is accompanied by additional structural rearrangements of both the PRD1-PRD1 ' interface and the CAT-PRD1 linker. Small angle x-ray scattering experiments indicate that the amplitude of the PRD2 swing might even be wider in solution than in the crystals. Our results suggest that PRD2 is highly mobile in the native protein, whereas it is locked upon activation by phosphorylation.

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.

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.