Showing papers by "Jean-Pierre Eckmann published in 2016"
TL;DR: In this article, a chain of four interacting rotors (rotators) connected at both ends to stochastic heat baths at different temperatures was studied and it was shown that for non-degenerate interaction potentials the system relaxes, at a stretched exponential rate, to a non-equilibrium steady state (NESS).
Abstract: We study a chain of four interacting rotors (rotators) connected at both ends to stochastic heat baths at different temperatures. We show that for non-degenerate interaction potentials the system relaxes, at a stretched exponential rate, to a non-equilibrium steady state (NESS). Rotors with high energy tend to decouple from their neighbors due to fast oscillation of the forces. Because of this, the energy of the central two rotors, which interact with the heat baths only through the external rotors, can take a very long time to dissipate. By appropriately averaging the oscillatory forces, we estimate the dissipation rate and construct a Lyapunov function. Compared to the chain of length three (considered previously by C. Poquet and the current authors), the new difficulty with four rotors is the appearance of resonances when both central rotors are fast. We deal with these resonances using the rapid thermalization of the two external rotors.
32 citations
TL;DR: A physical model of protein evolution is introduced which suggests a mechanical basis for this map and shows how mutations of the gene and their correlations occur at amino acids whose interactions determine the functional mode.
Abstract: How DNA is mapped to functional proteins is a basic question of living matter. We introduce and study a physical model of protein evolution which suggests a mechanical basis for this map. Many proteins rely on large-scale motion to function. We therefore treat protein as learning amorphous matter that evolves towards such a mechanical function: Genes are binary sequences that encode the connectivity of the amino acid network that makes a protein. The gene is evolved until the network forms a shear band across the protein, which allows for long-range, soft modes required for protein function. The evolution reduces the high-dimensional sequence space to a low-dimensional space of mechanical modes, in accord with the observed dimensional reduction between genotype and phenotype of proteins. Spectral analysis of the space of $10^6$ solutions shows a strong correspondence between localization around the shear band of both mechanical modes and the sequence structure. Specifically, our model shows how mutations of the gene and their correlations occur at amino acids whose interactions determine the functional mode.
11 citations
TL;DR: In this paper, the authors treat proteins as amorphous learning matter: a "gene" encodes bonds in an amino acid network making a "protein" and evolve until the network forms a shear band across the protein, which allows for long-range soft modes required for protein function.
Abstract: We treat proteins as amorphous learning matter: A ‘gene’ encodes bonds in an ‘amino acid’ network making a ‘protein’. The gene is evolved until the network forms a shear band across the protein, which allows for long-range soft modes required for protein function. The evolution projects the high-dimensional sequence space onto a low-dimensional space of mechanical modes, in accord with the observed dimensional reduction between genotype and phenotype of proteins. Spectral analysis shows correspondence between localization around the shear band of both mechanical modes and sequence ripples.
11 citations
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TL;DR: Spectral analysis shows correspondence between localization around the shear band of both mechanical modes and sequence ripples in proteins as amorphous learning matter.
Abstract: We treat proteins as amorphous learning matter: A `gene' encodes bonds in an `amino acid' network making a `protein'. The gene is evolved until the network forms a shear band across the protein, which allows for long-range soft modes required for protein function. The evolution projects the high-dimensional sequence space onto a low-dimensional space of mechanical modes, in accord with the observed dimensional reduction between genotype and phenotype of proteins. Spectral analysis shows correspondence between localization around the shear band of both mechanical modes and sequence ripples.
2 citations