Energy Bilocalization Effect and the Emergence of Molecular Functions in Proteins

Abstract

Proteins are among the most complex molecular structures, which have evolved to develop broad functions, such as energy conversion and transport, information storage and processing, communication, and regulation of chemical reactions. However, the mechanisms by which these dynamical entities coordinate themselves to perform biological tasks remain hotly debated. Here, a physical theory is presented to explain how functional dynamical behavior possibly emerge in complex/macro molecules, thanks to the effect that we term bilocalization of thermal vibrations. More specifically, our approach allows us to understand how structural irregularities lead to a partitioning of the energy of the vibrations into two distinct sets of molecular domains, corresponding to slow and fast motions. This shape-encoded spectral allocation, associated to the genetic sequence, provides a close access to a wide reservoir of dynamical patterns, and eventually allows the emergence of biological functions by natural selection. To illustrate our approach, the SPIKE protein structure of SARS-COV2 is considered.

Keywords: dynamics; localization; protein; rate promoting vibrations; vibrations.

FIGURE 1

The Spike (S) protein as an example of a disordered system (A) consists of three monomers (B), white, blue and red. Each monomer is a periodic chain of amino acids with a period of 0.38 nm (C). A protein is a folded chain where order and disorder intermingle.

FIGURE 2

The effective confining potential of high frequencies. The high frequency confinement predicted by W _h is in agreement with the structure of the density of vibrational states (here $X_i^2$ ) on a band corresponding to the highest frequencies (A). 3D representation of W _h for the complete protein (S) (B) with a zoom on the first monomer (C).

FIGURE 3

Effective confinement potentials.

FIGURE 4

Bilocalization effect The modulus of the normal modes are plotted and shifted according to their eigenvalues by C − ω ² (dark points). The confinement potentials corresponding to high (red) and low frequency modes (blue) are spatially complementary. The modal amplitude decays exponentially inside the potential.

FIGURE 5

Localization and reciprocal space Top: Localized wave and the reciprocal spaces (A) Dispersion relation of (S) compared to a perfect chain of the same size (red) (A). The range of the power spectral density of a localized mode is enlarged (C) compared (B) to a delocalized mode (standing wave). Bottom: The eigenvalues counting function predicted by the effective potential (dark) as well as that obtaiFed from the eigenvalues of Λ. Their derivative correspond to the DOS (Inset).

FIGURE 6

The fold encoded functional dynamics of SARS-Cov2 Spike protein The translation of the RNA into a protein structure gives rise to two hidden landscapes of localized modes corresponding to fast and short timescales. The localization landscapes allow to predict functional domains such as the fusion machinery (FM) as well as the bond cleavage (BC) (Walls et al., 2020), the scanning (Turoňová et al., 2020) as well as the binding (AC) with the host cell surface (Huang et al., 2020), the binding with potential neutralizing antibodies (BA). Other soft domains, allow to facilitate motions interfering with antibody (MA) (Turoňová et al., 2020) and subjected to several mutations. This illustrates the quantitative relationship between the expression of the DNA code and the physical origin of functional domains.

FIGURE 7

Network centrality, rigidity and localization landscape The inherent ability of a protein structure to generate confining potentials (top plot)–which in turn will define energy transport properties–is intrinsically linked to its rigidity (grey), which in turn can be seen as a modulation of connectivity or centrality (red and blue).

FIGURE 8

Selective parametric excitation and anisotropic heat transport. A parametric excitation at the highest frequency (A) and (C) produces a non-equilibrium transport phenomenon. Tracking the progression (B,D) of heat fields by molecular dynamics depending on whether the system is excited in a region of high (A) or low (B) potential (or connectivity) localization illustrates the anisotropic nature of the thermal relaxation.