Aggregation of dipolar colloidal particles: Geometric effects

To understand the importance of confinement and the influence of translational degrees of freedom on aggregation of dipolar colloidal particles, we calculate numerically-exact values for the mean encounter time for two nonspherically symmetric molecules to form a two-molecule cluster, regarded here as a precursor to aggregation. A lattice model is formulated in which the asymmetry of the molecules is accounted for by representing each as a "dimer" in the sense that each molecule is specified to occupy two adjacent lattice sites. The two dimers undergo simultaneous translation, and the mean times for their encounter are determined. Exact numerical results are obtained via application of the theory of finite Markov processes. The results allow one to examine in a detailed way the interplay among such factors as geometrical confinement, system size, translational motion, and specific orientational effects in influencing the aggregation event. The results are compared with previously reported theoretical predictions and experiments on the behavior of dipolar colloidal particles in the presence of an applied magnetic field

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice: topology and boundary effects

The role of dimensionality (Euclidean versus fractal), spatial extent, boundary effects and system topology on the efficiency of diffusion-reaction processes involving two simultaneously-diffusing reactants is analyzed. We present numerically-exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via application of the theory of finite Markov processes, and via Monte Carlo simulation. As a general rule, we conclude that for sufficiently large systems, the efficiency of diffusion-reaction processes involving two synchronously diffusing reactants (two-walker case) relative to processes in which one reactant of a pair is anchored at some point in the reaction space (one walker plus trap case) is higher, and is enhanced the lower the dimensionality of the system. This differential efficiency becomes larger with increasing system size and, for periodic systems, its asymptotic value may depend on the parity of the lattice. Imposing confining boundaries on the system enhances the differential efficiency relative to the periodic case, while decreasing the absolute efficiencies of both two-walker and one walker plus trap processes. Analytic arguments are presented to provide a rationale for the results obtained. The insights afforded by the analysis to the design of heterogeneous catalyst systems are also discussed.Comment: 15 pages, 8 figures, uses revtex4, accepted for publication in Physica

Funneled angle landscapes for helical proteins

We use crystallographic data for four helical iron proteins (cytochrome c-b₅₆₂, cytochrome c′, sperm whale myoglobin, human cytoglobin) to calculate radial and angular signatures as each unfolds from the native state stepwise though four unfolded states. From these data we construct an angle phase diagram to display the evolution of each protein from its native state; and, in turn, the phase diagram is used to construct a funneled angle landscape for comparison with the topography of its folding energy landscape. We quantify the departure of individual helical and turning regions from the areal, angular profile of corresponding regions of the native state. This procedure allows us to identify the similarities and differences among individual helical and turning regions in the early stages of unfolding of the four helical heme proteins

Geometrical Description of Protein Structural Motifs

We present a geometrical method that can identify secondary structural motifs in proteins via angular correlations. The method uses crystal structure coordinates to calculate angular and radial signatures of each residue relative to an external reference point as the number of nearest-neighbor residues increases. We apply our approach to the blue copper protein amicyanin using the copper cofactor as the external reference point. We define a signature termed Δβ which describes the change in angular correlation as the span of nearest neighbor residues increases. We find that three turn regions of amicyanin harbor residues with Δβ near zero, while residues in other secondary structures have Δβ greater than zero: for β-strands, Δβ changes gradually residue by residue along the strand. Extension of our analysis to other blue copper proteins demonstrated that the noted structural trends are general. Importantly, our geometrical description of the folded protein accounts for all forces holding the structure together. Through this analysis, we identified some of the turns in amicyanin as symmetrical anchor points

Synchronous vs Asynchronous Chain Motion in α-Synuclein Contact Dynamics

α-Synuclein (α-syn) is an intrinsically unstructured 140-residue neuronal protein of uncertain function that is implicated in the etiology of Parkinson’s disease. Tertiary contact formation rate constants in α-syn, determined from diffusion-limited electron-transfer kinetics measurements, are poorly approximated by simple random polymer theory. One source of the discrepancy between theory and experiment may be that interior-loop formation rates are not well approximated by end-to-end contact dynamics models. We have addressed this issue with Monte Carlo simulations to model asynchronous and synchronous motion of contacting sites in a random polymer. These simulations suggest that a dynamical drag effect may slow interior-loop formation rates by about a factor of 2 in comparison to end-to-end loops of comparable size. The additional deviations from random coil behavior in α-syn likely arise from clustering of hydrophobic residues in the disordered polypeptide

A Euclidean perspective on the unfolding of azurin: spatial correlations

We investigate the stability to structural perturbation of Pseudomonas aeruginosa azurin using a previously developed geometric model. Our analysis considers Ru(2,2′,6′,2″-terpyridine)(1,10-phenanthroline)(His83)-labelled wild-type azurin and five variants with mutations to Cu-ligating residues. We find that in the early stages of unfolding, the β-strands exhibit the most structural stability. The conserved residues comprising the hydrophobic core are dislocated only after nearly complete unfolding of the β-barrel. Attachment of the Ru-complex at His83 does not destabilize the protein fold, despite causing some degree of structural rearrangement. Replacing the Cys112 and/or Met121 Cu ligands does not affect the conformational integrity of the protein. Notably, these results are in accord with experimental evidence, as well as molecular dynamics simulations of the denaturation of azurin

A Euclidean perspective on the unfolding of azurin: chain motion

We present a new approach to visualizing and quantifying the displacement of segments of Pseudomonas aeruginosa azurin in the early stages of denaturation. Our method is based on a geometrical method developed previously by the authors, and elaborated extensively for azurin. In this study, we quantify directional changes in three α-helical regions, two regions having β-strand residues, and three unstructured regions of azurin. Snapshots of these changes as the protein unfolds are displayed and described quantitatively by introducing a scaling diagnostic. In accord with molecular dynamics simulations, we show that the long α-helix in azurin (residues 54–67) is displaced from the polypeptide scaffolding and then pivots first in one direction, and then in the opposite direction as the protein continues to unfold. The two β-strand chains remain essentially intact and, except in the earliest stages, move in tandem. We show that unstructured regions 72–81 and 84–91, hinged by β-strand residues 82–83, pivot oppositely. The region comprising residues 72–91 (40 % hydrophobic and 16 % of the 128 total residues) forms an effectively stationary region that persists as the protein unfolds. This static behavior is a consequence of a dynamic balance between the competing motion of two segments, residues 72–81 and 84–91

Structural stability of the SARS-CoV-2 main protease: Can metal ions affect function?

We have investigated the structural stability of the SARS (Severe acute respiratory syndrome)-CoV-2 main protease monomer (Mpro). We quantified the spatial and angular changes in the structure using two independent analyses, one based on a spatial metrics (δ, ratio), the second on angular metrics. The order of unfolding of the 10 helices in Mpro is characterized by beta vs alpha plots similar to those of cytochromes and globins. The longest turning region is anomalous in the earliest stage of unfolding. In an investigation of excluded-volume effects, we found that the maximum spread in average molecular-volume values for Mpro, cytochrome c-b₅₆₂, cytochrome c’, myoglobin, and cytoglobin is ~10 ų. This apparent universality is a consequence of the dominant contributions from six residues: ALA, ASP, GLU, LEU, LYS and VAL. Of the seven Mpro histidines, residues 41, 163, 164, and 246 are in stable H-bonded regions; metal ion binding to one or more of these residues could break up the H-bond network, thereby affecting protease function. Our analysis also indicated that metal binding to cysteine residues 44 and 145 could disable the enzyme