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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.
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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.
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.
In multi-resolution simulations, different system components are simultaneously modelled at different levels of resolution, these being smoothly coupled together. In the case of enzyme systems, computationally expensive atomistic detail is needed in the active site to capture the chemistry of substrate binding. Global properties of the rest of the protein also play an essential role, determining the structure and fluctuations of the binding site; however, these can be modelled on a coarser level. Similarly, in the most computationally efficient scheme only the solvent hydrating the active site requires atomistic detail. We present a methodology to couple atomistic and coarse-grained protein models, while solvating the atomistic part of the protein in atomistic water. This allows a free choice of which protein and solvent degrees of freedom to include atomistically, without loss of accuracy in the atomistic description. This multi-resolution methodology can successfully model stable ligand binding, and we further confirm its validity via an exploration of system properties relevant to enzymatic function. In addition to a computational speedup, such an approach can allow the identification of the essential degrees of freedom playing a role in a given process, potentially yielding new insights into biomolecular function.
Protein-fragment seqlets typically feature about 10 amino acid residue positions that are fixed to within conservative substitutions but usually separated by a number of prescribed gaps with arbitrary residue content. By quantifying a general amino acid residue sequence in terms of the associated codon number sequence, we have found a precise modular Fibonacci sequence in a continuous gap-free 10-residue seqlet with either 3 or 4 conservative amino acid substitutions. This modular Fibonacci sequence is genuinely biophysical, for it occurs nine times in the SWISS-Prot/TrEMBL database of natural proteins.
Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, much of physical behavior of transcription remains largely unknown. Understanding torsional mechanics of DNA and RNAP together with its nascent RNA and RNA-bound proteins in transcription maybe the first step towards deciphering the mechanism of gene expression. In this study, based on the balance between viscous drag on RNA synthesis and torque resulted from untranscribed supercoiled DNA template, a simple model is presented to describe mechanical properties of transcription. With this model, the rotation and supercoiling density of the untranscribed DNA template are discussed in detail. Two particular cases of transcription are considered, transcription with constant velocity and transcription with torque dependent velocity. Our results show that, during the initial stage of transcription, rotation originated from the transcribed part of DNA template is mainly released by the rotation of RNAP synthesis. During the intermediate stage, the rotation is usually released by both the supercoiling of the untranscribed part of DNA template and the rotation of RNAP synthesis, with proportion depending on the friction coefficient in environment and the length of nascent RNA. However, with the approaching to the upper limit of twisting of the untranscribed DNA template, the rotation resulted from transcription will then be mainly released by the rotation of RNAP synthesis.
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