Universality of vibrational spectra of globular proteins

Abstract

Abstract. It is shown that the density of modes of the vibrational spectrum of globular proteins is universal, i.e., regardless of the protein in question, it closely follows one universal curve. The present study, including 135 proteins analyzed with a full atomic empirical potential (CHARMM22) and using the full complement of all atoms Cartesian degrees of freedom, goes far beyond previous claims of universality, confirming that universality holds even in the frequency range that is well above 100 cm −1 (300 -4000 cm −1 ), where peaks and turns in the density of states are faithfully reproduced from one protein to the next. We also characterize fluctuations of the spectral density from the average, paving the way to a meaningful discussion of rare, unusual spectra and the structural reasons for the deviations in such "outlier" proteins. Since the method used for the derivation of the vibrational modes (potential energy formulation, set of degrees of freedom employed, etc.) has a dramatic effect on the spectral density, another significant implication of our findings is that the universality can provide an exquisite tool for assessing and improving the quality of potential functions and the quality of various models used for NMA computations. Finally, we show that the arXiv:1507.07491v2 [physics.bio-ph] 28 Jan 2016 input configuration too affects the density of modes, thus emphasizing the importance of simplified potential energy formulations that are minimized at the outset. In summary, our findings call for a serious two-way dialogue between theory and experiment: Experimental spectra of proteins could now guide the fine tuning of theoretical empirical potentials, and the various features and peaks observed in theoretical studies -being universal, and hence now rising in importance -would hopefully spur experimental confirmation.

Kinematic Flexibility Analysis: Hydrogen Bonding Patterns Impart a Spatial Hierarchy of Protein Motion

“…Comparison of reduced ENM models to full NMA previously revealed that agreement of low-frequency modes is conserved but that higher-frequency modes can differ significantly. 57 Figure 8 shows the iMOD spectrum of eigenfrequencies (A) and collectivity of eigenmodes (B) for our 183 single-chain protein data set. Although the spectral variables in ENM and our approach are different, this comparison sheds light on general characteristics of normal modes, rigidity-theory based and kinematic flexibility modes.…”

“…Similarly to our spectrum, eigenfrequency distributions are broadly conserved across structures, confirming results from previous NMA and ENM analysis. 11,57 Modes with low to medium eigenfrequency are most abundant. Similar to kinematic flexibility, the most abundant modes are also most collective.…”

“…This is consistent with experimental data from low-frequency Raman spectroscopy 80 and eigenfrequencies from detailed NMA. 10,57 Detailed NMA captures additional differences between folds in high-frequency regimes such as the amide I, II, or III bands. 57 These higher-frequency differences can also be detected experimentally with infrared spectroscopy and have been used to determine secondary structure content.…”

“…10,57 Detailed NMA captures additional differences between folds in high-frequency regimes such as the amide I, II, or III bands. 57 These higher-frequency differences can also be detected experimentally with infrared spectroscopy and have been used to determine secondary structure content. 81,82 Simplified elastic network analysis using iMOD failed to identify this shift toward stiffer modes, highlighting a limitation in the simplified force-fields of most ENM.…”

A comparison of the innate flexibilities of six chains in F1-ATPase with identical secondary and tertiary folds; 3 active enzymes and 3 structural proteins

“…The set of frequencies obtained by diagonalization of the object's Hessian, called the eigenspectrum, has a characteristic distribution for proteins, different from other solids 15–17 . The highest frequencies arise from rapid vibrations of the stiffest elements while the slowest frequency is a function of the mass and shape of the molecule and is roughly 0.1 THz for a 50 kDa protein (spectroscopists attempt to probe such motions by delivering photons with identical frequencies and often report this in terms of the corresponding photon wavenumber of 3 cm −1 ).…”