Local sequence‐structure relationships in proteins

We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the putative native state folds from myriad possible conformations? In order to address these questions, we represent the local structure of each C-alpha atom of a protein by just two angles, theta and mu, and we analyze a set of more than 4,000 protein structures from the PDB. We use a hierarchical clustering scheme to divide the 20 amino acids into six distinct groups based on their similarity to each other in fitting local structural space. We present the results of a detailed analysis of patterns of amino acid specificity in adopting local structural conformations and show that the sequence-structure correlation is not very strong compared with a random assignment of sequence to structure. Yet, our analysis may be useful to determine an effective scoring rubric for quantifying the match of an amino acid to its putative local structure

Local sequence-structure relationships in proteins

We seek to understand the interplay between amino acid sequence and local structure in proteins. Are some amino acids unique in their ability to fit harmoniously into certain local structures? What is the role of sequence in sculpting the putative native state folds from myriad possible conformations? In order to address these questions, we represent the local structure of each C-alpha atom of a protein by just two angles, theta and mu, and we analyze a set of more than 4000 protein structures from the PDB. We use a hierarchical clustering scheme to divide the 20 amino acids into six distinct groups based on their similarity to each other in fitting local structural space. We present the results of a detailed analysis of patterns of amino acid specificity in adopting local structural conformations and show that the sequence-structure correlation is not very strong compared to a random assignment of sequence to structure. Yet, our analysis may be useful to determine an effective scoring rubric for quantifying the match of an amino acid to its putative local structure.Comment: 32 pages, 13 figures, 3 tables, 8 supplementary information pages; Accepted for publication in Protein Scienc

Marginally compact phase and ordered ground states in a model polymer with side spheres

We present the results of a quantitative study of the phase behavior of a model polymer chain with side spheres using two independent computer simulation techniques. We find that the mere addition of side spheres results in key modifications of standard polymer behavior. One obtains a novel marginally compact phase at low temperatures, the structures in this phase are reduced in dimensionality and are ordered, they include strands assembled into sheets and a variety of helices, and at least one of the transitions on lowering the temperature to access these ordered states is found to be first order. Our model serves to partially bridge conventional polymer phases with biomolecular phases.Comment: 15 pages; 5 figure

Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

Chain molecules play a key role in the polymer field and in living cells. Our focus is on a new homopolymer model of a linear chain molecule subject to an attractive self-interaction promoting compactness. We analyze the model using simple analytic arguments complemented by extensive computer simulations. We find several striking results: there is a first order transition from a high temperature random coil phase to a highly unusual low temperature phase; the modular ground states exhibit significant degeneracy; the ground state structures exhibit spontaneous dimensional reduction and have a two-layer structure; and the ground states are assembled from secondary motifs of helices and strands connected by tight loops. We discuss the similarities and notable differences between the ground state structures (we call these PoSSuM -- Planar Structures with Secondary Motifs) in the novel phase and protein native state structures.Comment: 14 pages, 5 figure

III. Geometrical framework for thinking about globular proteins: turns in proteins

We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry. $\alpha$-helices and $\beta$-sheets are found to be special geometries that have systematic poking contacts in a repetitive manner with the contacts being local along the $\alpha$-helix and non-local along a pair of adjacent strands within a $\beta$-sheet. Pairwise poking interactions also govern tertiary structure formation, but they are weaker and there are no special geometrical constraints as in secondary structure formation. Here we demonstrate that protein turns, the most prevalent non-repetitive structural element in proteins, are instances of local (as in $\alpha$-helices) and isolated (non-repetitive) poking pairwise contacts for which the geometrical constraints are partially relaxed. This simple and purely geometrical definition of protein turns (also sometimes known as reverse turns, $\beta$-turns, $\beta$-bends, hairpin bends, $3_{10}$ bends, kinks, widgets, ...) provides a simple framework for unifying them. We present the results of a systematic analysis and identify their structural classes as well as their respective amino acid preferences.Comment: 67 pages, 17 figures, 2 table

Amino acid characteristics in protein native state structures

We present a geometrical analysis of the protrusion statistics of side chains in more than 4,000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of C{\alpha} atoms and consider just the heavy atoms of the side chains. We study the large variety of behaviors of the amino acids based on both rudimentary structural chemistry as well as geometry. Our geometrical analysis uses a backbone Frenet coordinate system for the common study of all amino acids. Our analysis underscores the richness of the repertoire of amino acids that is available to nature to design protein sequences that fit within the putative native state folds.Comment: 46 pages, 6 figures, 4 table

Building blocks of protein structures -- Physics meets Biology

The native state structures of globular proteins are stable and well-packed indicating that self-interactions are favored over protein-solvent interactions under folding conditions. We use this as a guiding principle to derive the geometry of the building blocks of protein structures, alpha-helices and strands assembled into beta-sheets, with no adjustable parameters, no amino acid sequence information, and no chemistry. There is an almost perfect fit between the dictates of mathematics and physics and the rules of quantum chemistry. Our theory establishes an energy landscape that channels protein evolution by providing sequence-independent platforms for elaborating sequence-dependent functional diversity. Our work highlights the vital role of discreteness in life and has implications for the creation of artificial life and on the nature of life elsewhere in the cosmos.Comment: 32 pages, 6 figures, 2 tables; Added key sentence about the important role of amino acid side chains in providing steric constraint

Local symmetry determines the phases of linear chains: a simple model for the self-assembly of peptides

We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric constraint that non-consecutive beads cannot overlap, and with a pairwise attractive square well potential accounting for the hydrophobic effect and promoting compaction. We then discuss the consequences of the successive breaking of spurious symmetries. First, we allow the partial interpenetration of consecutive beads. In addition to the standard high temperature coil phase and the low temperature collapsed phase, this results in a new class of marginally compact ground states comprising conformations reminiscent of α-helices and β-sheets, the building blocks of the native states of globular proteins. We then discuss the effect of a further symmetry breaking of the cylindrical symmetry on attaching a side-sphere to the backbone beads along the negative normal of the chain, to mimic the presence of side chains in real proteins. This leads to the emergence of a novel phase within the previously obtained marginally compact phase, with the appearance of more complex secondary structure assemblies. The potential importance of this new phase in the de novo design of self-assembled peptides is highlighted

In Silico and In Vitro Studies of Alchemilla viridiflora Rothm-Polyphenols' Potential for Inhibition of SARS-CoV-2 Internalization

Since the outbreak of the COVID-19 pandemic, it has been obvious that virus infection poses a serious threat to human health on a global scale. Certain plants, particularly those rich in polyphe- nols, have been found to be effective antiviral agents. The effectiveness of Alchemilla viridiflora Rothm. (Rosaceae) methanol extract to prevent contact between virus spike (S)-glycoprotein and angiotensin- converting enzyme 2 (ACE2) and neuropilin-1 (NRP1) receptors was investigated. In vitro results revealed that the tested samples inhibited 50% of virus-receptor binding interactions in doses of 0.18 and 0.22 mg/mL for NRP1 and ACE2, respectively. Molecular docking studies revealed that the compounds from A. viridiflora ellagitannins class had a higher affinity for binding with S-glycoprotein whilst flavonoid compounds more significantly interacted with the NRP1 receptor. Quercetin 3-(6”-ferulylglucoside) and pentagalloylglucose were two compounds with the highest exhibited interfering potential for selected target receptors, with binding energies of −8.035 (S-glycoprotein) and −7.685 kcal/mol (NRP1), respectively. Furthermore, computational studies on other SARS-CoV-2 strains resulting from mutations in the original wild strain (V483A, N501Y-K417N-E484K, N501Y, N439K, L452R-T478K, K417N, G476S, F456L, E484K) revealed that virus internalization activity was maintained, but with different single compound contributions