1,721,019 research outputs found
Seeing the forest for the trees through metabolic scaling
Full text link8 pagesWe demonstrate that when power scaling occurs for an individual tree and in a forest, there is great resulting simplicity notwithstanding the underlying complexity characterizing the system over many size scales. Our scaling framework unifies seemingly distinct trends in a forest and provides a simple yet promising approach to quantitatively understand a bewilderingly complex many-body system with imperfectly known interactions. We show that the effective dimension, Dtree, of a tree is close to 3, whereas a mature forest has Dforest approaching 1. We discuss the energy equivalence rule and show that the metabolic rate–mass relationship is a power law with an exponent D/(D + 1) in both cases leading to a Kleiber’s exponent of 3/4 for a tree and 1/2 for a forest. Our work has implications for understanding carbon sequestration and for climate science
Maximum entropy approach for deducing amino Acid interactions in proteins
Full text linkWe present a maximum entropy approach for inferring amino acid interactions in proteins subject to constraints pertaining to the mean numbers of various types of equilibrium contacts for a given sequence or a set of sequences. We have carried out several kinds of tests for a two-dimensional lattice model with just two types of amino acids with very promising results. We also show that the method works very well even when the mean numbers of contacts are not known and therefore can be applied to real proteins
Chain stiffness bridges conventional polymer and bio-molecular phases
No full textChain 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, and 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 stiffnesses 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
Local sequence‐structure relationships in proteins
Full text linkWe 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
Spontaneous dimensional reduction and ground state degeneracy in a simple chain model
No full textChain 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 phase and protein native state structures
Space-filling discrete helices
Full text linkProteins 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, β-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
III. Geometrical framework for thinking about globular proteins: Turns in proteins
Full text linkWe 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, etc.) 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
Marginally compact phase and ordered ground states in a model polymer with side spheres
No full textWe 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 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
Inverse problem for multivariate time series using dynamical latent variables
No full textFactor analysis is a well known statistical method to describe the variability among observed variables in terms of a smaller number of unobserved latent variables called factors. While dealing with multivariate time series, the temporal correlation structure of data may be modeled by including correlations in latent factors, but a crucial choice is the covariance function to be implemented. We show that analyzing multivariate time series in terms of latent Gaussian processes, which are mutually independent but with each of them being characterized by exponentially decaying temporal correlations, leads to an efficient implementation of the expectation-maximization algorithm for the maximum likelihood estimation of parameters, due to the properties of block-tridiagonal matrices. The proposed approach solves an ambiguity known as the identifiability problem, which renders the solution of factor analysis determined only up to an orthogonal transformation. Samples with just two temporal points are sufficient for the parameter estimation: hence the proposed approach may be applied even in the absence of prior information about the correlation structure of latent variables by fitting the model to pairs of points with varying time delay. Our modeling allows one to make predictions of the future values of time series and we illustrate our method by applying it to an analysis of published gene expression data from cell culture HeLa
Proteins -- a celebration of consilience
Full text linkProteins 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.Comment: 18 pages; 1 table; 6 figure
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