Conventional Normal Mode Analysis Research Articles

Efficient perturbation-tracking method for directly probing the spectral phonon properties from molecular dynamics simulations.

Existing methods for directly extracting the spectral phonon properties from molecular dynamics (MD) simulations, like the normal mode analysis (NMA) and spectral energy density analysis, all require a very long simulation time to produce reliable results with good convergence. So far, these methods are mainly applied in studies using small systems and with empirical potentials, as the heavy computational load has greatly hindered their further applications. Here we propose a perturbation-tracking (PT) method for directly probing the mode-wise phonon anharmonic frequencies and lifetimes. We show that results obtained from our method are in excellent agreement with those from the conventional NMA approach, using Si as the model material system. Comparing with the NMA approach, the PT method offers a greater accuracy and significant improvement of efficiency. It takes an average of two orders of magnitude and up to three orders of magnitude less simulation time to obtain the same lifetime result of a phonon mode with intermediate to high accuracy. Meanwhile, our method preserves all the dynamics of probed phonon mode from a particular state, which means it is capable of studying the transient thermal transport processes in a nonequilibrium system. Besides the exceptional efficiency, our method also comes with freedom to choose to probe only those modes of interest. This makes it ideal for use with large systems and in computationally demanding applications, such as ab initio MD simulations. Moreover, the PT method we propose here is very straightforward and easy to implement.

Excitation of vibrational soft modes in disordered systems using active oscillation

We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional athermal jammed system by giving a small amplitude of active oscillation to each particle's size with an identical driving frequency. The response is then obtained as the real time displacements of the particles. We show remarkable correlations between the real time displacements and the eigen vectors obtained from conventional normal mode analysis. More importantly, from these real time displacements, we can measure the participation ratio and spatial polarization of particles' vibrations. From these measurements, we find three distinct frequency regimes which characterize the spatial distribution and correlation of particles' vibrations in jammed amorphous solids. Furthermore, we can possibly apply this method to a much larger system to examine the low frequency behaviour of amorphous solids with a much higher resolution of the frequency space.

CNMA: a framework of encounter complex-based normal mode analysis to model conformational changes in protein interactions.

Motivation: It remains both a fundamental and practical challenge to understand and anticipate motions and conformational changes of proteins during their associations. Conventional normal mode analysis (NMA) based on anisotropic network model (ANM) addresses the challenge by generating normal modes reflecting intrinsic flexibility of proteins, which follows a conformational selection model for protein–protein interactions. But earlier studies have also found cases where conformational selection alone could not adequately explain conformational changes and other models have been proposed. Moreover, there is a pressing demand of constructing a much reduced but still relevant subset of protein conformational space to improve computational efficiency and accuracy in protein docking, especially for the difficult cases with significant conformational changes.Method and results: With both conformational selection and induced fit models considered, we extend ANM to include concurrent but differentiated intra- and inter-molecular interactions and develop an encounter complex-based NMA (cNMA) framework. Theoretical analysis and empirical results over a large data set of significant conformational changes indicate that cNMA is capable of generating conformational vectors considerably better at approximating conformational changes with contributions from both intrinsic flexibility and inter-molecular interactions than conventional NMA only considering intrinsic flexibility does. The empirical results also indicate that a straightforward application of conventional NMA to an encounter complex often does not improve upon NMA for an individual protein under study and intra- and inter-molecular interactions need to be differentiated properly. Moreover, in addition to induced motions of a protein under study, the induced motions of its binding partner and the coupling between the two sets of protein motions present in a near-native encounter complex lead to the improved performance. A study to isolate and assess the sole contribution of intermolecular interactions toward improvements against conventional NMA further validates the additional benefit from induced-fit effects. Taken together, these results provide new insights into molecular mechanisms underlying protein interactions and new tools for dimensionality reduction for flexible protein docking.Availability and implementation: Source codes are available upon request.Contact: yshen@tamu.edu

Analysis of conformational motions and related key residue interactions responsible for a specific function of proteins with elastic network model

Protein collective motions play a critical role in many biochemical processes. How to predict the functional motions and the related key residue interactions in proteins is important for our understanding in the mechanism of the biochemical processes. Normal mode analysis (NMA) of the elastic network model (ENM) is one of the effective approaches to investigate the structure-encoded motions in proteins. However, the motion modes revealed by the conventional NMA approach do not necessarily correspond to a specific function of protein. In the present work, a new analysis method was proposed to identify the motion modes responsible for a specific function of proteins and then predict the key residue interactions involved in the functional motions by using a perturbation approach. In our method, an internal coordinate that accounts for the specific function was introduced, and the Cartesian coordinate space was transformed into the internal/Cartesian space by using linear approximation, where the introduced internal coordinate serves as one of the axes of the coordinate space. NMA of ENM in this internal/Cartesian space was performed and the function-relevant motion modes were identified according to their contributions to the specific function of proteins. Then the key residue interactions important for the functional motions of the protein were predicted as the interactions whose perturbation largely influences the fluctuation along the internal coordinate. Using our proposed methods, the maltose transporter (MalFGK2) from E. Coli was studied. The functional motions and the key residue interactions that are related to the channel-gating function of this protein were successfully identified.

Conventional NMA as a better standard for evaluating elastic network models

Normal mode analysis (NMA) is an important tool for studying protein dynamics. Because of the complexity of conventional NMA that uses an all-atom model and a semi-empirical force field, many simplified NMA models have been developed, some of which are known as elastic network models. The quality of these simplified NMA models was assessed mostly by evaluating their predictions against experimental B-factors, and rarely by comparing them with the original NMA. In this work, we take the effort to create a publicly accessible dataset of proteins with their minimized structures, NMA modes, and mean-square fluctuations. Then, for the first time, we evaluate the quality of individual normal modes of several widely used elastic network models by comparing them with the conventional NMA. Our results demonstrate that the conventional NMA presents a better and more complete evaluation measure of the quality of elastic network models. This realization should be very helpful in improving current or designing new, higher quality elastic network models. Moreover, using the conventional NMA as the standard of evaluation, a number of interesting and significant insights into the elastic network models are gained.

Normal mode analysis of protein dynamics in a non-Eckart frame

Normal mode analysis, with the all-atom or coarse-grained elastic network model, represents the equilibrium fluctuation of protein molecule in the Eckart frame, where contributions from external motions (translation and rotation) of the entire protein molecule are eliminated. On the other hand, domain motion is frequently exhibited by the relative motion of one domain to the other. Such a representation of fluctuations in the non-Eckart frame cannot be achieved by conventional normal mode analysis. Here, we propose normal mode analysis in a non-Eckart frame, where the external degrees of freedom are fixed for any portion of the system. In this analysis, the covariance matrix in the Eckart frame is transformed into one in the non-Eckart frame. Using a molecular dynamics simulation, we have confirmed the validity of the transformation formula and discussed the physical implication of the formula.

Development of Chemical Bond based Elastic Network Model and its application in identifying functional motions in H5N1 highly pathogenic avian influenza viruses

Here we proposed a Chemical Bond based Elastic Network Model (CB-ENM) method, which was demonstrated with a better performance in representing functional movements, especially the local motions, than the conventional normal mode analysis. CB-ENM was applied in characterising functional motions in surface glycoprotein Haemagglutinin (HA) of H5N1 highly pathogenic avian influenza virus. Eleven local peaks were identified amongst HA fluctuation spectrum, and eight of these peaks were correlated with the reported five antigenic binding sites and Receptor Binding Sites (RBS) in influenza viruses. Our study showed that CB-ENM has a potential in identifying functional residues in protein structure.

Resonance between continuous spectra: Secular behavior of Alfvén waves in a flowing plasma

Conventional normal mode analysis often falls short in predicting a variety of transient phenomena in a non-self-adjoint (non-Hermitian) system. Laplace transform is capable of capturing all possible behavior in general systems. However, degenerate essential spectra require careful analysis. The Alfvén wave in a flowing plasma is an example in which the coalescence of the Alfvén singularities yields nonexponential growth of fluctuations. Invoking hyperfunction theory, rigorous expression of the Laplace transform leads to an accurate estimate of the asymptotic behavior of resonant singular modes.

Guiding mode analysis, a generalization of normal mode analysis

A new approach is presented to investigating collective periodic motion in molecules, analyzing the Fourier transforms of molecular dynamics simulation trajectories. Demanding that atoms vibrating together in some mode must oscillate in phase enables the corresponding collective coordinate to be deduced. We demonstrate that the method for purely harmonic potentials gives results identical to conventional normal mode analysis. It can, however, be applied to any molecular dynamics simulation trajectory, probing anharmonic regions of the potential, with solvent explicitly included, in non-equilibrium situations.