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

Abstract

It's been said that mathematics is biology's next microscope, only better; biology is mathematics' next physics, only better [1]. 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.This article is dedicated to Ludvig Faddeev on the occasion of his 80 th birthday. * Electronic address: Antti.Niemi@physics.uu.se 1 arXiv:1406.7468v3 [math-ph]

Phase diagram and the pseudogap state in a linear chiral homopolymer model

“…Accordingly, it has been concluded [8][9][10][11][12][13] that -in the unitary gauge -to the leading non-trivial order the free energy has the form…”

Gauge symmetries and structure of proteins

“…The considered properties of the proteins can be formally described by an appropriate geometric description of protein. A such model can be formulated within the approach that use description of the local geometry of proteins based on the formalism of discrete Frenet coordinates [6]. Under this formalism proteins are considered as one-dimensional discrete uniformity, which determined the free energy functional, defined solely by the angles of curvature and torsion.…”

“…One of the solutions of the problem can be obtained with the help of coarse grain modelling within effective field theory, which allows a natural way to introduce the collective degree of freedom and nonlinear topological structures based on fundamental principles of gauge symmetry. The corresponding field theory model is based on local symmetry of proteins that will dynamically define tertiary structure of proteins [6].…”

Solution x-ray scattering and structure formation in protein dynamics

“…Thus the free energy E(κ, τ ) can be expanded in the powers of the differences ∆κ i . A detailed analysis which builds on extensive symmetry considerations, in particular on the requirement that the functional form of the energy should remain invariant under local frame rotations, shows [7,8,[25][26][27][28][29][30][31] that in the limit of small variations in ∆κ i the following expansion of the free energy can be used in the case of proteins…”

“…Finally, the last term (V ) includes various long distance two-body interactions such as Coulomb and Lennard-Jones interaction between the residues. In the leading order this contribution can be approximated by a hard ball Pauli repulsion [7,8,[25][26][27][28][29][30][31]; see [32] for more general long range interactions.…”