Copper(II) Inhibition of the SARS-CoV-2 Main Protease.

In an analysis of the structural stability of the coronavirus main protease (Mpro), we identified regions of the protein that could be disabled by cobalt(III)-cation binding to histidines and cysteines [1]. Here we have extended our work to include copper(II) chelates, which we have docked to HIS 41 and CYS 145 in the Mpro active-site region. We have found stable docked structures where Cu(II) could readily bond to the CYS 145 thiolate, which would be lethal to the enzyme.

Unfolding cytochromes c-b562 and Rd apo b562.

We have analyzed the early stages of unfolding of cytochromes c-b562 (PDB ID: 2BC5) and Rd apo b562 (PDB ID: 1YYJ). Our geometrical approach proceeds from an analysis of the crystal structure reported for each protein. We quantify, residue-by-residue and region-by-region, the spatial and angular changes in the structure as the protein denatures, and quantify differences that result from the seven residues that differ in the two proteins. Using two independent analyses, one based on spatial metrics and the second on angular metrics, we establish the order of unfolding of the five helices in cyt c-b562 and the four helices in the apo protein. For the two helices nearest the N-terminal end of both proteins, the ones in the apo protein unfold first. For the two helices nearest the C-terminal end, the interior helix of the apo protein unfolds first, whereas the terminal helix of the holo protein unfolds first. Excluded-volume effects (repulsive interactions) are minimized in turning regions; the overall range in Δ values is Δ = 36.3 Å3 for cyt c-b562 and Δ = 36.6 Å3 for the apo protein, whereas the span for all 20 amino acids is Δ = 167.7 Å3. As our work indicates that the interior helix of cytochrome c-b562 is the first to fold, we suggest that this helix protects the heme from misligation, consistent with ultrafast folding over a minimally frustrated funneled landscape.

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 Å3. 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.

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.

Structural stabilities of calcium proteins: Human intelectin-1 and frog lectin XEEL.

We extend our study of the structural stability of helical and nonhelical regions in chain A of human intelectin-1 to include a second human intelectin (4WMY) and the frog protein "Xenopus embryonic epidermal lectin" (XEEL). These unique lectins have been shown to recognize carbohydrate residues found exclusively in microbes, thus they could potentially be developed into novel microbe detection and sequestration tools. We believe that by studying the structural stability of these proteins we can provide insights on their biological role and activities. Using a geometrical model introduced previously, we perform computational analyses of protein crystal structures that quantify the resiliency of the native state to steric perturbations. Based on these analyses, we conclude that differences in the resiliency of the human and frog proteins can be attributed primarily to differences in non-helical regions and to residues near Ca ions. Since these differences are particularly pronounced in the vicinity of the ligand binding site, they provide an explanation for the finding that human intelectin-1 has a higher affinity for a ligand than XEEL. We also present data on conserved and position-equivalent pairs of residues in 4WMY and XEEL. We identify residue pairs as well as regions in which the influence of neighboring residues is nearly uniform as the parent protein denatures. Since the structural signatures are conserved, this identification provides a basis for understanding why both proteins exhibit trimeric structures despite poor sequence conservation at the interface.

Relaxation of structural constraints during Amicyanin unfolding.

We study the thermal unfolding of amicyanin by quantifying the resiliency of the native state to structural perturbations. Three signatures characterizing stages of unfolding are identified. The first signature, lateral extension of the polypeptide chain, is calculated directly from the reported crystallographic data. Two other signatures, the radial displacement of each residue from Cu(II) and the angular spread in the chain as the protein unfolds, are calculated using crystallographic data in concert with a geometrical model we introduced previously (J.J. Kozak, H. B. Gray, R. A. Garza-López, J. Inorg. Biochem. 155(2016) 44-55). Particular attention is paid to the resiliency of the two beta sheets in amicyanin. The resiliency of residues in the near neighborhood of the Cu center to destabilization provides information on the persistence of the entatic state. Similarly, examining the resiliency of residues intercalated between structured regions (beta sheets, the alpha helix) provides a basis for identifying a "hydrophobic core." A principal focus of our study is to compare results obtained using our geometrical model with the experimental results (C. La Rosa, D. Milardi, D. M. Grasso, M. P. Verbeet, G. W. Canters, L. Sportelli, R. Guzzi, Eur. Biophy. J.30(8),(2002) 559-570) on the denaturation of amicyanin, and we show that our results support a classical model proposed by these authors.

Structural Stability of Intelectin-1.

We study the structural stability of helical and nonhelical regions in chain A of human intelectin-1. Using a geometrical model introduced previously, we carried out a computational analysis based on the recently reported crystal structure of this protein by Kiessling et al. to quantify the resiliency of the native state to steric perturbations. Response to these perturbations is characterized by calculating, relative to the native state, the lateral, radial, and angular displacements of n-residue segments of the polypeptide chain centered on each residue. By quantifying the stability of the protein through six stages of unfolding, we are able to identify regions in chain A of intelectin-1 that are markedly affected by structural perturbations versus those that are relatively unaffected, the latter suggesting that the native-state geometry of these regions is essentially conserved. Importantly, residues in the vicinity of calcium ions comprise a conserved region, suggesting that Ca ions play a role not only in the coordination of carbohydrate hydroxyl groups but also in preserving the integrity of the structure.

Cytochrome unfolding pathways from computational analysis of crystal structures.

We have developed a model to study the role of geometrical factors in influencing the early stages of unfolding in three cytochromes: cyt c', cyt c-b562 and cyt c. Each stage in unfolding is quantified by the spatial extension λ̂i of n-residue segments, and by their angular extension 〈ßn〉. Similarities and differences between and among the three cytochromes in the unfolding of helical and non-helical regions can be determined by analyzing the data for each signature separately. Definite conclusions can be drawn when spatial and angular changes are considered in tandem. To facilitate comparisons, we present graphical portraits of the three cytochromes at the same stage of unfolding, and in relation to their native state structures. We also display specific segments at different stages of unfolding to illustrate differences in stability of defined domains thereby allowing us to make specific predictions on the unfolding of corresponding internal and terminal helices in cyt c' and cyt c-b562. Our work accords with an earlier experimental report on the presence and persistence of a hydrophobic core in cyt c.

Lattice statistical theory of random walks on a fractal-like geometry.

We have designed a two-dimensional, fractal-like lattice and explored, both numerically and analytically, the differences between random walks on this lattice and a regular, square-planar Euclidean lattice. We study the efficiency of diffusion-controlled processes for flows from external sites to a centrosymmetric reaction center and, conversely, for flows from a centrosymmetric source to boundary sites. In both cases, we find that analytic expressions derived for the mean walk length on the fractal-like lattice have an algebraic dependence on system size, whereas for regular Euclidean lattices the dependence can be transcendental. These expressions are compared with those derived in the continuum limit using classical diffusion theory. Our analysis and the numerical results quantify the extent to which one paradigmatic class of spatial inhomogeneities can compromise the efficiency of adatom diffusion on solid supports and of surface-assisted self-assembly in metal-organic materials.

Reaction efficiency of diffusion-controlled processes on finite, planar arrays. II. Crystal surfaces.

We consider 36 planar nets identified by O'Keeffe and Hyde and calculate for each, using the theory of finite Markovian processes, the overall mean walk length n (first passage time) of a reactant diffusing randomly on a finite platelet before being trapped at a reaction center; the results are analyzed in terms of the total number N of lattice sites, the number N(b) of boundary sites, the average valence nu, and the bond orientation function Psi. We establish that crystalline platelets that are members of the same compatible class are characterized by very comparable catalytic efficiencies. The results obtained are also linked to an analysis of the kinetics of docking in postnucleation stages of protein self-assembly and to a recent conjecture on the symmetries of planar nets and the hard disk freezing transition.

Kinetics of docking in postnucleation stages of self-assembly.

In a previous study, the early stages of self-assembly in nanophase materials were explored by coupling a kinetic mean-field analysis with a lattice-based stochastic theory [J. J. Kozak et al., J. Chem. Phys. 126, 154701 (2007)]. Recent experimental results on the postnucleation stages of zeolite assembly and protein crystallite formation have suggested a new study, presented here, in which the docking of a platelet on the existing surface of a structured crystallite is similarly investigated. A model is designed which allows the quantification of factors affecting docking efficiency; principal among these is the structure of the template itself, which here is assumed to be either unstructured or bifurcated into terraces and edges/ledges. Going beyond our earlier study (in which diffusion was restricted to d=2 dimensions), the diffusion space here is enlarged to consider both d=2 and d=3 dimensional flows. By expanding the external diffusion space systematically, we are able to document the consequences (as regards docking efficiency) of diffusive flows in the near neighborhood of a developing crystallite versus surface-only processes. Particularly in regimes where the barriers to surface diffusion are high, and/or the probability of desorption significant, we find that d=3 dimensional processes (leading to a "direct hit") can compete kinetically with surface-only mediated processes. Although the crystallite model studied here is simple, it can be diffeomorphically distorted into a manifold of possible geometries; in analogy with the classical theory of corresponding states, we argue that the familial relationship among these structures suggests that the generic results obtained provide a qualitatively correct description of the kinetics of docking on structured surfaces.