arXiv subjects

Tatjana Škrbić

Publications and source records attributed to Tatjana Škrbić.

15 recordsLinked to original sources

arXiv2025

Space-filling discrete helices

Proteins are linear chain molecules that play a central role in life and health. Protein native state folds are modular assemblies of space-filling building blocks of α-helices, \{beta}-sheets and tight turns. Here we deduce the structures of a countable set of space-filling helical forms of a uniform discrete thick string from first principles with no additional input or adjustable parameters. These forms occur in correspondence with the natural numbers, loosely analogous to the energy levels in a Bohr atom. We find the remarkable result that one of these helical forms is an excellent candidate for an α-helix through seemingly improbable quantum chemistry coincidences that fit the geometrical requirements. Our work suggests that geometry and chemistry are complementary ways of looking at proteins and suggests a route for developing a unified framework for understanding proteins.

physics.bio-ph↗

arXiv2024

Phase behaviour and self-assembly of semiflexible polymers in poor-solvent solutions

Using Langevin dynamics complemented by Wang-Landau Monte Carlo simulations, we study the phase behavior of single and multiple semiflexible polymer chains in solution under poor-solvent conditions. In the case of a single chain, we obtain the full phase diagram in the temperature-bending rigidity (stiffness) plane and we provide connections with a classical mean field result on a lattice as well as with past results on the same model. At low bending rigidity and upon cooling, we find a second order coil-globule transition, followed by a subsequent first order globule-crystal transition at lower temperatures. The obtained crystals have the shape of a twisted rod whose length increases with the increase of the stiffness of the chain. Above a critical value of the stiffness, we also find a direct first order globule-crystal transition, with the crystal having the form of a twisted toroid. Close to the triple point, we find a region with isoenergetic structures with frequent switching from rods to toroids, with the toroid eventually becoming the only observed stable phase at higher stiffness. The model is then extended to many thermally equilibrated chains in a box and the analogous phase diagram is deduced where the chains are observed to first fold into a globule bundle at low stiffness upon cooling, and then rearrange into a nematic bundle via a nucleation process involving an isotropic-nematic transition. As in the single chain counterpart, above a critical stiffness the chains are observed to undergo a direct transition from a gas of isotropically distributed chains to a nematic bundle as the temperature decreases in agreement with recent suggestions from mean field theory. The consequences of these findings for self-assembly of biopolymers in solutions are discussed.

cond-mat.soft↗

arXiv2024

Solvent Quality and Nonbiological Oligomer Folding: Revisiting Conventional Paradigms

We report on extensive molecular dynamics atomistic simulations of a \textit{meta}-substituted \textit{poly}-phenylacetylene (pPA) foldamer dispersed in three solvents, water \ce{H2O}, cyclohexane \ce{cC6H12}, and \textit{n}-hexane \ce{nC6H14}, and for three oligomer lengths \textit{12mer}, \textit{16mer} and \textit{20mer}. At room temperature, we find a tendency of the pPA foldamer to collapse into a helical structure in all three solvents but with rather different stability character, stable in water, marginally stable in n-hexane, unstable in cyclohexane. In the case of water, the initial and final number of hydrogen bonds of the foldamer with water molecules is found to be unchanged, with no formation of intrachain hydrogen bonding, thus indicating that hydrogen bonding plays no role in the folding process. In all three solvents, the folding is found to be mainly driven by electrostatics, nearly identical in the three cases, and largely dominant compared to van der Waals interactions that are different in the three cases. This scenario is also supported by the analysis of distribution of the bond and dihedral angles and by a direct calculation of the solvation and transfer free energies via thermodynamic integration. The different stability in the case of cyclohexane and n-hexane notwithstanding their rather similar chemical composition can be traced back to the different entropy-enthalpy compensation that is found similar for water and n-hexane, and very different for cyclohexane. A comparison with the same properties for \textit{poly}-phenylalanine oligomers underscores the crucial differences between pPA and peptides. To highlight how these findings can hardly be interpreted in terms of a simple "good" and "poor" solvent picture, a molecular dynamics study of a bead-spring polymer chain in a Lennard-Jones fluid is also included.

cond-mat.soft↗

arXiv2024

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 Cα 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.

cond-mat.soft↗

arXiv2023

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. $α$-helices and $β$-sheets are found to be special geometries that have systematic poking contacts in a repetitive manner with the contacts being local along the $α$-helix and non-local along a pair of adjacent strands within a $β$-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 $α$-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, $β$-turns, $β$-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.

cond-mat.soft↗

arXiv2023

A geometrical framework for thinking about proteins

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity.

cond-mat.soft↗

arXiv2023

II. Geometrical framework for thinking about globular proteins: the power of poking

Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed a consistent approach for understanding the formation of the two key common building blocks of helices and sheets as well as the compatible assembly of secondary structures into the tertiary structure through the notion of poking pairwise interactions. Here we benchmark our predictions with a detailed analysis of structural data of over 4000 proteins from the Protein Data Bank. We also present the results of detailed computer simulations of a simplified model demonstrating a pre-sculpted free energy landscape, determined by geometry and symmetry, comprising numerous minima corresponding to putative native state structures. We explore the consequences of our model. Our results suggest that symmetry and geometry are a powerful guide to capture the simplicity underlying protein complexity.

cond-mat.soft↗

arXiv2021

Proteins -- a celebration of consilience

Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discuss the consequences of this framework on protein behavior.

q-bio.BM↗

arXiv2021

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.

cond-mat.soft↗

arXiv2021

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.

cond-mat.stat-mech↗

arXiv2021

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.

q-bio.BM↗

arXiv2021

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.

q-bio.BM↗

arXiv2018

The elixir phase of chain molecule

A phase of matter is a familiar notion for inanimate physical matter. The nature of a phase of matter transcends the microscopic material properties. For example, materials in the liquid phase have certain common properties independent of the chemistry of the constituents: liquids take the shape of the container; they flow; and they can be poured -- alcohol, oil and water as well as a Lennard-Jones computer model exhibit similar behavior when poised in the liquid phase. Here we identify a hitherto unstudied `phase' of matter, the elixir phase, in a simple model of a polymeric chain whose backbone has the correct local cylindrical symmetry induced by the tangent to the chain. The elixir phase appears on breaking the cylindrical symmetry by adding side spheres along the negative normal direction, as in proteins. This phase, nestled between other phases, has multiple ground states made up of building blocks of helices and almost planar sheets akin to protein native folds. We discuss the similarities of this `phase' of a finite size system to the liquid crystal and spin glass phases. Our findings are relevant for understanding proteins; the creation of novel bio-inspired nano-machines; and also may have implications for life elsewhere in the cosmos.

cond-mat.soft↗

arXiv2018

Universal effects of solvent species on the stabilized structure of a protein

We investigate the effects of solvent specificities on the stability of the native structure (NS) of a protein on the basis of our free-energy function (FEF). We use CPB-bromodomain (CBP-BD) and apoplastocyanin (apoPC) as representatives of the protein universe and water, methanol, ethanol, and cyclohexane as solvents. The NSs of CBP-BD and apoPC consist of 66$\%$ $α$-helices and of 35$\%$ $β$-sheets and 4$\%$ $α$-helices, respectively. In order to assess the structural stability of a given protein immersed in each solvent, we contrast the FEF of its NS against that of a number of artificially created, misfolded decoys possessing the same amino-acid sequence but significantly different topology and $α$-helix and $β$-sheet contents. We find that for both CBP-BD and apoPC, the energetic component dominates in methanol, ethanol, and cyclohexane, with the most stable structures in these solvents sharing the same characteristics described as an association of a-helices. In water, the entropic component is as strong as or even stronger than the energetic one, with a large gain of translational, configurational entropy of water becoming crucially important, so that the relative contents of $α$-helix and $β$-sheet and the content of total secondary structures are carefully selected to achieve sufficiently close packing of side chains. Our analysis, which requires minimal computational effort, can be applied to any protein immersed in any solvent and provides robust predictions that are quite consistent with the experimental observations for proteins in different solvent environments, thus paving the way toward a more detailed understanding of the folding process.

cond-mat.soft↗

arXiv2016

From polymers to proteins: effect of side chains and broken symmetry in the formation of secondary structures within a Wang-Landau approach

We study the equilibrium properties of a single flexible homopolymers where consecutive monomers are represented by impenetrable hard spherical beads tangential to each other, and non-consecutive monomers interact via a square-well potential. To this aim, we use both replica exchange canonical simulations and micro-canonical Wang-Landau techniques. We perform a close comparative analysis of the corresponding results, and find perfect agreement between the two methods as well as the past results. The model is then refined in two different directions. By allowing partial overlapping between consecutive beads, we break the spherical symmetry and thus provide a severe constraint on the possible conformations of the chain. This leads to a single helix or a double helix ground state, depending on the range of the interactions. Alternatively, we introduce additional spherical beads at specific positions to represent the steric hindrance of the side chains in real proteins. The ground state in this case is found to be again a globule, thus showing that contrary to some recent suggestions, side chains alone are not sufficient to insure a protein-like structure. Finally, we show that a combination of the above two effects increases the stability of the obtaining secondary structures, in agreement with previous results. The fundamental role played by the range of the square-well attraction is highlighted, and it is shown that they play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.

cond-mat.soft↗