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Register a new userUniversality of Vibrational Spectra of Globular Proteins
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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 high-frequency range (300- 4000 1/cm), 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 various models used for NMA computations. Finally, we show that the input configuration too affects the density of modes, thus emphasizing the importance of simplified potential energy formulations that are minimized at the outset.
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Using a coarse-grained model, self-organized assembly of proteins (e.g. CorA and its inner segment iCorA) is studied by examining quantities such as contact profile, radius of gyration, and structure factor as a function of protein concentration at a range of low (native phase) to high (denature phase) temperatures. Visual inspections show distinct structures, i.e. isolated globular bundles to entangled network on multiple length scales in dilute to crowded protein concentrations. In native phase, the radius of gyration of the protein does not vary much with the protein concentration while that of its inner segment increases systematically. In contrast, the radius of gyration of the protein shows enormous growth with the concentration due to entanglement while that of the inner segment remains almost constant in denatured phase. The multi-scale morphology of the collective assembly is quantified by estimating the effective dimension D of protein from scaling of the structure factor: collective assembly from inner segments remains globular (D aroud 3) at almost all length scales in its native phase while that from protein chains shows sparsely distributed morphology with D around 2 in entire temperature range due to entanglement except in crowded environment at low temperature where D around 2.6. Higher morphological response of chains with only the inner-segments due to selective interactions in its native phase may be more conducive to self-organizing mechanism than that of the remaining segments of the protein chains.
We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier, 1-parameter formulation (M. Tirion, PRL 77, 1905 (1996)) that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function which is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states over all frequencies, not merely the slow ones. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface sidechains. Second, we take into account the atomic identities and the distance of separation of all pairwise interactions. With these modifications we obtain stable, reliable eigenmodes over a wide range of frequencies.
Previous studies of the flexibilities of ancestral proteins suggests that proteins evolve their function by altering their native state ensemble. Here we propose a more direct method of visualizing this by measuring the changes in the vibrational density of states (VDOS) of proteins as they evolve. Through analysis of VDOS profiles of ancestral and extant proteins we observe that $beta$-lactamase and thioredoxins evolve by altering their density of states in the terahertz region. Particularly, the shift in VDOS profiles between ancestral and extant proteins suggests that nature utilize dynamic allostery for functional evolution. Moreover, we also show that VDOS profile of individual position can be used to describe the flexibility changes, particularly those without any amino acid substitution.
Localization properties of residue fluctuations in globular proteins are studied theoretically by using the Gaussian network model. Participation ratio for each residue fluctuation mode is calculated. It is found that the relationship between participation ratio and frequency is similar for all globular proteins, indicating a universal behavior in spite of their different size, shape, and architecture.
The free energy of globular protein chain is considered to be a functional defined on smooth curves in three dimensional Euclidean space. From the requirement of geometrical invariance, together with basic facts on conformation of helical proteins and dynamical characteristics of the protein chains, we are able to determine, in a unique way, the exact form of the free energy functional. Namely, the free energy density should be a linear function of the curvature of curves on which the free energy functional is defined. This model can be used, for example, in Monte Carlo simulations of exhaustive searching the native stable state of the protein chain.
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