arXiv subjects

Jayanth R. Banavar

Publications and source records attributed to Jayanth R. Banavar.

At least 19 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

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↗

arXiv2020

True scale-free networks hidden by finite size effects

We analyze about two hundred naturally occurring networks with distinct dynamical origins to formally test whether the commonly assumed hypothesis of an underlying scale-free structure is generally viable. This has recently been questioned on the basis of statistical testing of the validity of power law distributions of network degrees by contrasting real data. Specifically, we analyze by finite-size scaling analysis the datasets of real networks to check whether purported departures from the power law behavior are due to the finiteness of the sample size. In this case, power laws would be recovered in the case of progressively larger cutoffs induced by the size of the sample. We find that a large number of the networks studied follow a finite size scaling hypothesis without any self-tuning. This is the case of biological protein interaction networks, technological computer and hyperlink networks, and informational networks in general. Marked deviations appear in other cases, especially infrastructure and transportation but also social networks. We conclude that underlying scale invariance properties of many naturally occurring networks are extant features often clouded by finite-size effects due to the nature of the sample data.

physics.soc-ph↗

arXiv2019

Chain stiffness bridges conventional polymer and bio-molecular phases}

Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnesses -- one yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations including a coil, a globule, a toroid, rods, helices, zig-zag strands resembling $β$-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffness play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.

cond-mat.soft↗

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↗

arXiv2017

Phase diagram of thick ribbons in a bad solvent

Ribbons are topological objects of biological and technological importance. Here, we study the folding of thick ribbons with hydrophobic surfaces in a bad solvent in regimes in which either the ribbon's thickness or the solvent molecule size is not vanishingly small compared to the ribbon's width. Extensive Monte Carlo simulations show that ribbons of various lengths and with a small stiffness adopt several distinct configurations as the ground state that include rolled (Archimedean spiral), curled, twisted and globule conformations. Analytic and numerical calculations based on the consideration of putative ground states lead to phase diagrams that qualitatively agree with the simulation results. A symmetry breaking of the planar rolled configuration in favor of the elongated twisted and the globular ribbons is observed on increasing the solvent size. Interestingly, the twisted ribbon is found as the ground state in the absence of any energetic preference for twisting. We show that the twist of the DNA double helix structure can be stabilized when modeled as a hydrophobic thick ribbon even in the limit of vanishing solvent size.

cond-mat.soft↗

arXiv2016

The geometry of coexistence in large ecosystems

The role of species interactions in controlling the interplay between the stability of an ecosystem and its biodiversity is still not well understood. The ability of ecological communities to recover after a small perturbation of the species abundances (local asymptotic stability) has been well studied, whereas the likelihood of a community to persist when the interactions are altered (structural stability) has received much less attention. Our goal is to understand the effects of diversity, interaction strenghts and ecological network structure on the volume of parameter space leading to feasible equilibria, i.e., ones in which all populations have positive abundances. We develop a geometrical framework to study the range of conditions necessary for feasible coexistence in both mutualistic and consumer-resource systems. Using analytical and numerical methods, we show that feasibility is determined by just a handful of quantities describing the interactions, yielding a nontrivial complexity-feasibility relationship. Analyzing more than 100 empirical networks, we show that the range of coexistence conditions in mutualistic systems can be analytically predicted by means of a null model of random interactions, whereas food webs are characterized by smaller coexistence domains than those expected by chance. Finally, we characterize the geometric shape of the feasibility domain, thereby identifying the direction of perturbations that are more likely to cause extinctions. Interestingly, the structure of mutualistic interactions leads to very heterogeneous responses to perturbations, making those systems more fragile than expected by chance.

q-bio.PE↗

arXiv2015

Phase diagram of the ground states of DNA condensates

Phase diagram of the ground states of DNA in a bad solvent is studied for a semi-flexible polymer model with a generalized local elastic bending potential characterized by a nonlinearity parameter $x$ and effective self-attraction promoting compaction. $x=1$ corresponds to the worm-like chain model. Surprisingly, the phase diagram as well as the transition lines between the ground states are found to be a function of $x$. The model provides a simple explanation for the results of prior experimental and computational studies and makes predictions for the specific geometries of the ground states. The results underscore the impact of the form of the microscopic bending energy at macroscopic observable scales.

q-bio.BM↗

arXiv2015

Uncovering low-dimensional, miR-based signatures of acute myeloid and lymphoblastic leukemias with a machine-learning-driven network approach

Complex phenotypic differences among different acute leukemias cannot be fully captured by analyzing the expression levels of one single molecule, such as a miR, at a time, but requires systematic analysis of large sets of miRs. While a popular approach for analysis of such datasets is principal component analysis (PCA), this method is not designed to optimally discriminate different phenotypes. Moreover, PCA and other low-dimensional representation methods yield linear or non-linear combinations of all measured miRs. Global human miR expression was measured in AML, B-ALL, and T-ALL cell lines and patient RNA samples. By systematically applying support vector machines to all measured miRs taken in dyad and triad groups, we built miR networks using cell line data and validated our findings with primary patient samples. All the coordinately transcribed members of the miR-23a cluster (which includes also miR-24 and miR-27a), known to function as tumor suppressors of acute leukemias, appeared in the AML, B-ALL and T-ALL centric networks. Subsequent qRT-PCR analysis showed that the most connected miR in the B-ALL-centric network, miR-708, is highly and specifically expressed in B-ALLs, suggesting that miR-708 might serve as a biomarker for B-ALL. This approach is systematic, quantitative, scalable, and unbiased. Rather than a single signature, our approach yields a network of signatures reflecting the redundant nature of biological signaling pathways. The network representation allows for visual analysis of all signatures by an expert and for future integration of additional information. Furthermore, each signature involves only small sets of miRs, such as dyads and triads, which are well suited for in depth validation through laboratory experiments such as loss- and gain-of-function assays designed to drive changes in leukemia cell survival, proliferation and differentiation.

q-bio.QM↗