Gauge field, 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". 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.

arXiv commentA section on thermostatting has been reformulated

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Cited by in corpus (8)

• Thermal unfolding of myoglobin in the Landau-Ginzburg-Wilson approach
• Gauge symmetries and structure of proteins
• Towards multistage modelling of protein dynamics with monomeric Myc oncoprotein as an example
• Aspects of structural landscape of human islet amyloid polypeptide
• On phase diagram and the pseudogap state in a linear chiral homopolymer model
• Generalized Maxwell-Higgs vortices in models with enhanced symmetry
• Poisson Hierarchy of Discrete Strings
• Chern-Simons-Higgs Model as a Theory of Protein Molecules