arXiv subjects

Antti J. Niemi

Publications and source records attributed to Antti J. Niemi.

At least 37 records · Page 2Linked to original sources

arXiv2015

Bloch spin waves and emergent structure in protein folding with HIV envelope glycoprotein as an example

We inquire how structure emerges during the process of protein folding. For this we scrutinise col- lective many-atom motions during all-atom molecular dynamics simulations. We introduce, develop and employ various topological techniques, in combination with analytic tools that we deduce from the concept of integrable models and structure of discrete nonlinear Schroedinger equation. The example we consider is an alpha-helical subunit of the HIV envelope glycoprotein gp41. The helical structure is stable when the subunit is part of the biological oligomer. But in isolation the helix becomes unstable, and the monomer starts deforming. We follow the process computationally. We interpret the evolving structure both in terms of a backbone based Heisenberg spin chain and in terms of a side chain based XY spin chain. We find that in both cases the formation of protein super-secondary structure is akin the formation of a topological Bloch domain wall along a spin chain. During the process we identify three individual Bloch walls and we show that each of them can be modelled with a very high precision in terms of a soliton solution to a discrete nonlinear Schroedinger equation.

q-bio.BM↗

arXiv2014

WHAT IS LIFE - Sub-cellular Physics of Live Matter

This is a set of lectures that I presented at the Les Houches 2014 Summer School "Topological Aspects in Condensed Matter Physics". The lectures are an introduction to physics of proteins. To physicists, and by a physicist. My lectures at les Houches were also celebration of the anniversary of Schroedinger's 1944 lectures, and for that reason I decided to share my title with his book.

cond-mat.soft↗

arXiv2014

Virtual reality based approach to protein heavy-atom structure reconstruction

A commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central alpha-carbon coordinates. We employ advances in virtual reality to address the problem. The outcome is a 3D visualisation based technique where all the heavy backbone and side chain atoms are treated on equal footing, in terms of the C-alpha coordinates. Each heavy atom can be visualised on the surfaces of the different two-spheres, that are centered at the other heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters which display strong dependence on the underlying backbone secondary structure. Our method easily detects those atoms in a crystallographic protein structure which have been been likely misplaced. Our approach forms a basis for the development of a new generation, visualisation based side chain construction, validation and refinement tools. The heavy atom positions are identified in a manner which accounts for the secondary structure environment, leading to improved accuracy over existing methods.

q-bio.BM↗

arXiv2014

Aspects of structural landscape of human islet amyloid polypeptide

The human islet amyloid polypeptide (hIAPP) co-operates with insulin to maintain glycemic balance. It also constitutes the amyloid plaques that aggregate in the pancreas of type-II diabetic patients. We have performed extensive in silico investigations to analyse the structural landscape of monomeric hIAPP, which is presumed to be intrinsically disordered. For this we construct from first principles a highly predictive energy function that describes a monomeric hIAPP observed in a NMR experiment, as a local energy minimum. We subject our theoretical model of hIAPP to repeated heating and cooling simulations, back and forth between a high temperature regime where the conformation resembles a random walker and a low temperature limit where no thermal motions prevail. We find that the final low temperature conformations display a high level of degeneracy, in a manner which is fully in line with the presumed intrinsically disordered character of hIAPP. In particular, we identify an isolated family of alpha-helical conformations that might cause the transition to amyloidosis, by nucleation.

q-bio.BM↗

arXiv2014

Gauge field, strings, solitons, anomalies and the speed of life

It's been said that "mathematics is biology's next microscope, only better; biology is mathematics' next physics, only better". Here we aim for something even better. We try to combine mathematical physics and biology into a picoscope of life. For this we merge techniques which have been introduced and developed in modern mathematical physics, largely by Ludvig Faddeev to describe objects such as solitons and Higgs and to explain phenomena such as anomalies in gauge fields. We propose a synthesis that can help to resolve the protein folding problem, one of the most important conundrums in all of science. We apply the concept of gauge invariance to scrutinize the extrinsic geometry of strings in three dimensional space. We evoke general principles of symmetry in combination with Wilsonian universality and derive an essentially unique Landau-Ginzburg energy that describes the dynamics of a generic string-like configuration in the far infrared. We observe that the energy supports topological solitons, that pertain to an anomaly in the manner how a string is framed around its inflection points. We explain how the solitons operate as modular building blocks from which folded proteins are composed. We describe crystallographic protein structures by multi-solitons with experimental precision, and investigate the non-equilibrium dynamics of proteins under varying temperature. We simulate the folding process of a protein at in vivo speed and with close to pico-scale accuracy using a standard laptop computer: With pico-biology as mathematical physics' next pursuit, things can only get better.

math-ph↗

arXiv2014

On spinors, strings, integrable models and decomposed Yang-Mills theory

This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three dimensional string-like structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented; while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is show how the Lax pair of the integrable nonlinear Schroedinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation and it is described how a spinor based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schroedinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauss-Godazzi equation that describes surfaces in three dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two dimensional and four dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two dimensional integrable models as embedded structures in the four dimensional decomposed SU(2) Yang-Mills theory are presented.

hep-th↗

arXiv2014

Leapfrogging vortex rings in the Landau-Lifshitz equation

Vortex rings are ubiquitous in fluids, with smoke rings being a familiar example. The interaction of multiple vortex rings produces complex dynamical behaviour, such as the leapfrogging motion first analysed by Helmholtz more than a century and a half ago. Here we report on numerical investigations of vortex ring dynamics in a different setting from fluids, namely, as solutions of the Landau-Lifshitz equation that models the evolution of the local magnetization in a ferromagnetic medium. We present the results of the first study on the dynamics of interacting magnetic vortex rings and provide a novel link between fluids and magnetism, by showing that a range of phenomena familiar in fluids are reproduced in ferromagnets. This includes the leapfrogging motion of a pair of vortex rings and evidence for the chaotic dynamics of a trio of rings.

cond-mat.mes-hall↗

arXiv2013

Long range correlations and folding angle in polymers with applications to α-helical proteins

The conformational complexity of linear polymers far exceeds that of point-like atoms and molecules. Polymers can bend, twist, even become knotted. Thus they may also display a much richer phase structure than point particles. But it is not very easy to characterize the phase of a polymer. Essentially, the only attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, discloses the phase of the polymer. Moreover, in any finite length chain there are corrections to scaling, that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle, a novel tool to identify and scrutinize the phases of polymers. We argue for a mean-field relationship between its values and those of the scaling exponent in the radius of gyration. But unlike in the case of the radius of gyration, the value of the folding angle can be evaluated from a single structure. As an example we estimate the value of the folding angle in the case of crystallographic α-helical protein structures in the Protein Data Bank (PDB). We also show how the value can be numerically computed using a theoretical model of α-helical chiral homopolymers.

physics.bio-ph↗

arXiv2012

On Energy Functions for String-Like Continuous Curves, Discrete Chains, and Space-Filling One Dimensional Structures

The theory of string-like continuous curves and discrete chains have numerous important physical applications. Here we develop a general geometrical approach, to systematically derive Hamiltonian energy functions for these objects. In the case of continuous curves, we demand that the energy function must be invariant under local frame rotations, and it should also transform covariantly under reparametrizations of the curve. This leads us to consider energy functions that are constructed from the conserved quantities in the hierarchy of the integrable nonlinear Schrödinger equation (NLSE). We point out the existence of a Weyl transformation that we utilize to introduce a dual hierarchy to the standard NLSE hierarchy. We propose that the dual hierarchy is also integrable, and we confirm this to the first non-trivial order. In the discrete case the requirement of reparametrization invariance is void. But the demand of invariance under local frame rotations prevails, and we utilize it to introduce a discrete variant of the Zakharov-Shabat recursion relation. We use this relation to derive frame independent quantities that we propose are the essentially unique and as such natural candidates for constructing energy functions for piecewise linear polygonal chains. We also investigate the discrete version of the Weyl duality transformation. We confirm that in the continuum limit the discrete energy functions go over to their continuum counterparts, including the perfect derivative contributions.

hep-th↗

arXiv2012

On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics

We construct an energy function that describes the crystallographic structure of spermwhale myoglobin backbone. As a model in our construction, we use the Protein Data Bank entry 1ABS that has been measured at liquid helium temperature. Consequently the thermal B-factor fluctuations are very small, which is an advantage in our construction. The energy function that we utilize resembles that of the discrete non-linear Schrodinger equation. Likewise, ours supports solitons as local minimum energy configurations. We describe the 1ABS backbone in terms of solitons with a precision that deviates from 1ABS by an average root-mean-square distance, which is less than the experimentally observed Debye-Waller B-factor fluctuation distance. We then subject the multisoliton solution to extensive numerical heating and cooling experiments, over a very wide range of temperatures. We concentrate in particular to temperatures above 300K and below the theta-point unfolding temperature, which is around 348K. We confirm that the behavior of the multisoliton is fully consistent with Anfinsen's principle, up to very high temperatures. We observe that the structure responds to an increase of temperature consistently in a very similar manner. This enables us to characterize the onset of thermally induced conformational changes in terms of three distinct backbone ligand gates. One of the gates is made of the helix F and the helix E. This is a pathway that is presumed to have a major role in ligand migration between the heme and the exterior. The two other gates are chosen similarly, when open they provide a direct access route for a ligand to reach the heme. We find that out of the three gates we investigate, the one which is formed by helices B and G is the most sensitive one to thermally induced conformational changes. Our approach provides a novel perspective to the important problem of ligand migration.

physics.bio-ph↗

arXiv2012

Protein loops, solitons and side-chain visualization with applications to the left-handed helix region

Folded proteins have a modular assembly. They are constructed from regular secondary structures like alpha-helices and beta-strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe this modular structure. In complement to the widely employed Ramachandran plot that is based on toroidal geometry, our approach utilizes the geometry of a two-sphere. Unlike the more conventional approaches that only describea given peptide unit, ours is capable of describing the entire backbone environment including the neighboring peptide units. It maps the positions of each atom to the surface of the two-sphere exactly how these atoms are seen by an observer who is located at the position of the central C-alpha atom. At each level of side-chain atoms we observe a strong correlation between the positioning of the atom and the underlying local secondary structure with very little if any variation between the different amino acids. As a concrete example we analyze the left-handed helix region of non-glycyl amino acids. This region corresponds to an isolated and highly localized residue independent sector in the direction of the C-beta carbons on the two-sphere. We show that the residue independent localization extends to C-gamma and C-delta carbons, and to side-chain oxygen and nitrogen atoms in the case of asparagine and aspartic acid. When we extend the analysis to the side-chain atoms of the neighboring residues, we observe that left-handed beta-turns display a regular and largely amino acid independent structure that can extend to seven consecutive residues. This collective pattern is duu to the presence of a backbone soliton. We show how one can use our visualization techniques to analyze and classify the different solitons in terms of selection rules that we describe in detail.

physics.bio-ph↗

arXiv2012

On correlation between protein secondary structure, backbone bond angles, and side-chain orientations

We investigate the fine structure of the sp3 hybridized covalent bond geometry that governs the tetrahedral architecture around the central C$_α$ carbon of a protein backbone, and for this we develop new visualization techniques to analyze high resolution X-ray structures in Protein Data Bank. We observe that there is a correlation between the deformations of the ideal tetrahedral symmetry and the local secondary structure of the protein. We propose a universal coarse grained energy function to describe the ensuing side-chain geometry in terms of the C$_β$ carbon orientations. The energy function can model the side-chain geometry with a sub-atomic precision. As an example we construct the C$_α$-C$_β$ structure of HP35 chicken villin headpiece. We obtain a configuration that deviates less than 0.4 Ȧ in root-mean-square distance from the experimental X-ray structure.

physics.bio-ph↗

arXiv2012

Solitons and Collapse in the lambda-repressor protein

The enterobacteria lambda phage is a paradigm temperate bacteriophage. Its lysogenic and lytic life cycles echo competition between the DNA binding $λ$-repressor (CI) and CRO proteins. Here we scrutinize the structure, stability and folding pathways of the $λ$-repressor protein, that controls the transition from the lysogenic to the lytic state. We first investigate the super-secondary helix-loop-helix composition of its backbone. We use a discrete Frenet framing to resolve the backbone spectrum in terms of bond and torsion angles. Instead of four, there appears to be seven individual loops. We model the putative loops using an explicit soliton Ansatz. It is based on the standard soliton profile of the continuum nonlinear Schrödinger equation. The accuracy of the Ansatz far exceeds the B-factor fluctuation distance accuracy of the experimentally determined protein configuration. We then investigate the folding pathways and dynamics of the $λ$-repressor protein. We introduce a coarse-grained energy function to model the backbone in terms of the C$_α$ atoms and the side-chains in terms of the relative orientation of the C$_β$ atoms. We describe the folding dynamics in terms of relaxation dynamics, and find that the folded configuration can be reached from a very generic initial configuration. We conclude that folding is dominated by the temporal ordering of soliton formation. In particular, the third soliton should appear before the first and second. Otherwise, the DNA binding turn does not acquire its correct structure. We confirm the stability of the folded configuration by repeated heating and cooling simulations.

physics.bio-ph↗

arXiv2011

Soliton driven relaxation dynamics and universality in protein collapse

Protein collapse can be viewed as a dynamical phase transition, during which new scales and collective variables become excited while the old ones recede and fade away. This causes formidable computational bottle-necks in approaches that are based on atomic scale scrutiny. Here we consider an effective dynamical Landau theory to model the folding process at biologically relevant time and distance scales. We reach both a substantial decrease in the execution time and improvement in the accuracy of the final configuration, in comparison to more conventional approaches. As an example we inspect the collapse of HP35 chicken villin headpiece subdomain, where there are detailed molecular dynamics simulations to compare with. We start from a structureless, unbend and untwisted initial configuration. In less than one second of wall-clock time on a single processor personal computer we consistently reach the native state with 0.5 Angstrom root mean square distance (RMSD) precision. We confirm that our folding pathways are indeed akin those obtained in recent atomic level molecular dynamics simulations. We conclude that our approach appears to have the potential for a computationally economical method to accurately understand theoretical aspects of protein collapse.

physics.bio-ph↗

arXiv2011

The protein dynamical transition is a pseudogap changeover

The emergence of biochemical activities in a protein seem to commence with the onset of atomic mean-square displacements along the protein lattice. The ensuing protein dynamical transition has been discussed extensively in the literature, and often with conflicting conclusions. Here we clarify the phenomenon by establishing a deep connection between the dynamical transition and the pseudogap state where high-temperature superconductivity comes to its end. For this we first show how to endow proteins with an order parameter akin the quasiparticle wave function in superconductors. We then present universality arguments to claim that the protein dynamical transition takes place in tandem with a pseudogap transmutation. We confirm that available experimental data fully supports our proposal.

physics.bio-ph↗

arXiv2011

Soliton concepts and the protein structure

Structural classification shows that the number of different protein folds is surprisingly small. It also appears that proteins are built in a modular fashion, from a relatively small number of components. Here we propose to identify the modular building blocks of proteins with the dark soliton solution of a generalized discrete nonlinear Schrodinger equation. For this we show that practically all protein loops can be obtained simply by scaling the size and by joining together a number of copies of the soliton, one after another. The soliton has only two loop specific parameters and we identify their possible values in Protein Data Bank. We show that with a collection of 200 sets of parameters, each determining a soliton profile that describes a different short loop, we cover over 90% of all proteins with experimental accuracy. We also present two examples that describe how the loop library can be employed both to model and to analyze the structure of folded proteins.

physics.bio-ph↗

arXiv2011

Protein Regge Trajectories, Phase Coexistence and Physics of Alzheimer's Disease

Alzheimer's disease causes severe neurodegeneration in the brain that leads to a certain death. The defining factor is the formation of extracellular senile amyloid plaques in the brain. However, therapeutic approaches to remove them have not been effective in humans, and so our understanding of the cause of Alzheimer's disease remains incomplete. Here we investigate physical processes that might relate to its onset. Instead of the extracellular amyloid, we scrutinize the intracellular domain of its precursor protein. We argue for a phenomenon that has never before been discussed in the context of polymer physics: Like ice and water together, the intracellular domain of the amyloid precursor protein forms a state of phase coexistence with another protein. This leads to an inherent instability that could well be among the missing pieces in the puzzle of Alzheimer's disease.

q-bio.BM↗

arXiv2011

Covalent bond symmetry breaking and protein secondary structure

Both symmetry and organized breaking of symmetry have a pivotal rôle in our understanding of structure and pattern formation in physical systems, including the origin of mass in the Universe and the chiral structure of biological macromolecules. Here we report on a new symmetry breaking phenomenon that takes place in all biologically active proteins, thus this symmetry breaking relates to the inception of life. The unbroken symmetry determines the covalent bond geometry of a sp3 hybridized carbon atom. It dictates the tetrahedral architecture of atoms around the central carbon of an amino acid. Here we show that in a biologically active protein this symmetry becomes broken. Moreover, we show that the pattern of symmetry breaking is in a direct correspondence with the local secondary structure of the folded protein.

q-bio.BM↗