arXiv subjects

Antti J. Niemi

Publications and source records attributed to Antti J. Niemi.

At least 55 records · Page 3Linked to original sources

arXiv2011

Solitons and Physics of the Lysogenic to Lytic Transition in Enterobacteria Lambda Phage

The lambda phage is a paradigm temperate bacteriophage. Its lysogenic and lytic life cycles echo competition between the DNA binding CI and CRO proteins. Here we address the Physics of this transition in terms of an energy function that portrays the backbone as a multi-soliton configuration. The precision of the individual solitons far exceeds the B-factor accuracy of the experimentally determined protein conformations giving us confidence to conclude that three of the four loops are each composites of two closely located solitons. The only exception is the repressive DNA binding turn, it is the sole single soliton configuration of the backbone. When we compare the solitons with the Protein Data Bank we find that the one preceding the DNA recognition helix is unique to the CI protein, prompting us to conclude that the lysogenic to lytic transition is due to a saddle-node bifurcation involving a soliton-antisoliton annihilation that removes the first loop.

q-bio.BM↗

arXiv2011

On universal aspects of the left-handed helix region

We inspect the geometry of proteins by identifying their backbones as framed polygons. We find that the left-handed helix region of the Ramachandran map for non-glycyl residues corresponds to an isolated and highly localized sector in the orientation of the $C_β$ carbons, when viewed in a Frenet frame that is centered at the corresponding $C_α$ carbons. We show that this localization in the orientation persists to $C_γ$ and $C_δ$ carbons. Furthermore, when we extend our analysis to the neighboring residues we conclude that the left-handed helix region reflects a very regular and apparently residue independent collective interplay of at least seven consecutive amino acids.

q-bio.BM↗

arXiv2011

The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation does reproduce the generalized Frenet equation. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of $C_β$ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this $C_β$ framing relates intimately to the discrete Frenet framing. We also explain how inflection points can be located in the loops, and clarify their distinctive rôle in determining the loop structure of foldel proteins.

q-bio.BM↗

arXiv2010

Towards Quantitative Classification of Folded Proteins in Terms of Elementary Functions

A comparative classification scheme provides a good basis for several approaches to understand proteins, including prediction of relations between their structure and biological function. But it remains a challenge to combine a classification scheme that describes a protein starting from its well organized secondary structures and often involves direct human involvement, with an atomary level Physics based approach where a protein is fundamentally nothing more than an ensemble of mutually interacting carbon, hydrogen, oxygen and nitrogen atoms. In order to bridge these two complementary approaches to proteins, conceptually novel tools need to be introduced. Here we explain how the geometrical shape of entire folded proteins can be described analytically in terms of a single explicit elementary function that is familiar from nonlinear physical systems where it is known as the kink-soliton. Our approach enables the conversion of hierarchical structural information into a quantitative form that allows for a folded protein to be characterized in terms of a small number of global parameters that are in principle computable from atomary level considerations. As an example we describe in detail how the native fold of the myoglobin 1M6C emerges from a combination of kink-solitons with a very high atomary level accuracy. We also verify that our approach describes longer loops and loops connecting $α$-helices with $β$-strands, with same overall accuracy.

q-bio.BM↗

arXiv2010

On Relations Between Electroweak Hierarchy Problem, Fluctuating Three Branes And General Covariance

We inquire whether a resolution to the electroweak hierarchy problem could reside in symmetries that relate the bosonic Weinberg-Salam Lagrangian with a higher dimensional generally covariant theory. For this we consider a three-brane that moves under the influence of a seven dimensional pure Hilbert Einstein-like generally covariant theory. We introduce a change of variables that combines the conformal scale of the metric tensor with the brane fluctuations, so that the conformal scale becomes the modulus and the fluctuations become the angular field degrees of freedom of a polarly decomposed Higgs. When we assume that the four dimensional space-time background of the generally covariant theory is locally conformally flat and that the internal space is a squashed three-sphere, we arrive at one massless and three massive vector fields akin those in the Weinberg-Salam model and recover all the familiar ingredients of the symmetry broken bosonic Weinberg-Salam model, except that there is no bare Higgs mass. The Higgs mass is subject to dimensional censorship, its presence is forbidden by general covariance. This proposes that a resolution to the electroweak hierarchy problem might well reside in higher dimensions, in a Ward-Takahashi like identities for general covariance that relate a non-vanishing Higgs mass to dynamical breaking of general covariance. Moreover, the two electroweak gauge couplings are both determined by the squashing parameter of the internal three sphere and when we impose the condition that the vector boson masses must be in line with custodial symmetry we arrive at the classical level to the Weinberg angle sin^2 θ_W = 0.296.

hep-th↗

arXiv2010

On Solutions to the "Faddeev-Niemi" Equations

Recently it has been pointed out that the "Faddeev-Niemi" equations that correspond to the Yang-Mills equations of motion for a decomposed gauge field, can have solutions that obey the standard Yang-Mills equations with a source term. Here we present a general class of such gauge field configurations.

hep-th↗

arXiv2010

Discrete Nonlinear Schrodinger Equation, Solitons and Organizing Principles for Protein Folding

We introduce a novel generalization of the discrete nonlinear Schrödinger equation. It supports solitons that describe how proteins fold. As an example we scrutinize the villin headpiece HP35, an archetypal protein for testing both experimental and theoretical approaches to protein folding. Using explicit soliton profiles we construct its carbon backbone with an unprecedented accuracy.

physics.bio-ph↗

arXiv2010

A Gauge Field Theory of Chirally Folded Homopolymers with Applications to Folded Proteins

We combine the principle of gauge invariance with extrinsic string geometry to develop a lattice model that can be employed to theoretically describe properties of chiral, unbranched homopolymers. We find that in its low temperature phase the model is in the same universality class with proteins that are deposited in the Protein Data Bank, in the sense of the compactness index. We apply the model to analyze various statistical aspects of folded proteins. Curiously we find that it can produce results that are a very good good match to the data in the Protein Data Bank.

cond-mat.stat-mech↗

arXiv2010

Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem

We present a numerical Monte Carlo analysis of a continuos spin Ising chain that can describe the statistical proterties of folded proteins. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a cross-over transition. We also compare the predictions of the model to a phenomenological elastic energy formula, proposed by Huang and Lei to describe folded proteins.

cond-mat.stat-mech↗

arXiv2010

Re-dressing Emperor: Four Dimensional Yang-Mills Theory, Gauge Invariant Mass And Fluctuating Three Branes

We consider the coupling between four dimensional Yang-Mills field and a three brane that fluctuates into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional space-time under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original space-time $\mathbb R^4$: The presence of the brane becomes entirely invisible, except for the mass.

hep-th↗

arXiv2010

Topological Solitons and Folded Proteins

We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by assembling the solitons together, one after another. We present a simple theoretical model that realizes our proposal and apply it to a number of biologically active proteins including 1VII, 2RB8, 3EBX (Protein Data Bank codes). In all the examples that we have considered we are able to construct solitons that reproduce secondary structural motifs such as alpha-helix-loop-alpha-helix and beta-sheet-loop-beta-sheet with an overall root-mean-square-distance accuracy of around 0.7 Angstrom or less for the central alpha-carbons, i.e. within the limits of current experimental accuracy.

physics.bio-ph↗

arXiv2009

Knots and Swelling in Protein Folding

Proteins can sometimes be knotted, and for many reasons the study of knotted proteins is rapidly becoming very important. For example, it has been proposed that a knot increases the stability of a protein. Knots may also alter enzymatic activities and enhance binding. Moreover, knotted proteins may even have some substantial biomedical significance in relation to illnesses such as Parkinson's disease. But to a large extent the biological role of knots remains a conundrum. In particular, there is no explanation why knotted proteins are so scarce. Here we argue that knots are relatively rare because they tend to cause swelling in proteins that are too short, and presently short proteins are over-represented in the Protein Data Bank (PDB). Using Monte Carlo simulations we predict that the figure-8 knot leads to the most compact protein configuration when the number of amino acids is in the range of 200-600. For the existence of the simplest knot, the trefoil, we estimate a theoretical upper bound of 300-400 amino acids, in line with the available PDB data.

cond-mat.soft↗

arXiv2009

Baryon number violation and a new electroweak interaction

We introduce a new supercurrent in the electroweak sector of the standard model. Its interaction with the hypergauge field influences the mass of the Z boson but has no effect on the W^\pm-boson masses. In the leptonic sector it affects the numerical value of the vector and axial coupling constants between neutral currents and the Z boson, and a comparison with experimental values yields an upper bound to the strength of the coupling between the supercurrent and the hypergauge field. In the baryonic sector the supercurrent gives a new contribution to the anomaly equation for baryon number current. As a consequence it may have an effect on baryogenesis.

hep-ph↗

arXiv2009

On Lorentz Invariance, Spin-Charge Separation And SU(2) Yang-Mills Theory

Previously it has been shown that in spin-charge separated SU(2) Yang-Mills theory Lorentz invariance can become broken by a one-cocycle that appears in the Lorentz boosts. Here we study in detail the structure of this one-cocycle. In particular we show that its non-triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also explicitely present the finite version of the cocycle.

hep-th↗

arXiv2008

Non-Abelian Supercurrents and de Sitter Ground State in Electroweak Theory

We show that gauge symmetry breaking in the Weinberg-Salam model can be implemented by a mere change of variables and without any explicit gauge fixing. The change of variables entails the concept of supercurrent which has been widely employed in the study of superconductivity. It also introduces a separation between the isospin and the hypercharge, suggesting that our new variables describe a strongly coupled regime of the electroweak theory. We discuss the description of various embedded topological defects in terms of these variables. We also propose that in terms of our variables the Weinberg-Salam model can be interpreted in terms of a gravity theory with the modulus of Higgs field as dilaton and the de Sitter space as the ground state.

hep-th↗

arXiv2008

Embedding Brans-Dicke gravity into electroweak theory

We argue that a version of the four dimensional Brans-Dicke theory can be embedded in the standard flat spacetime electroweak theory. The embedding involves a change of variables that separates the isospin from the hypercharge in the electroweak theory.

hep-ph↗

arXiv2006

Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory

In the low energy domain of four-dimensional SU(2) Yang-Mills theory the spin and the charge of the gauge field can become separated from each other. The ensuing field variables describe the interacting dynamics between a version of the O(3) nonlinear $σ$-model and a nonlinear Grassmannian $σ$-model, both of which may support closed knotted strings as stable solitons. Lorentz transformations act projectively in the O(3) model which breaks global internal rotation symmetry and removes massless Goldstone bosons from the particle spectrum. The entire Yang-Mills Lagrangian can be recast into a generally covariant form with a conformally flat metric tensor. The result contains the Einstein-Hilbert Lagrangian together with a nonvanishing cosmological constant, and insinuates the presence of a novel dimensionfull parameter in the Yang-Mills theory.

hep-th↗

arXiv2006

Spin-Charge Separation and the Pauli Electron

The separation between the spin and the charge converts the quantum mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian Georgi-Glashow model, notorious for its magnetic monopoles and confinement. The independent spin and charge fluctuations both lead to the Faddeev model, suggesting the existence of a deep duality structure and indicating that the fundamental carriers of spin and charge are knotted solitons.

quant-ph↗