UMMS: constrained harmonic and anharmonic analyses of macromolecules based on elastic network models

A mass weighted chemical elastic network model elucidates closed form domain motions in proteins

An elastic network model (ENM), usually Cα coarse-grained one, has been widely used to study protein dynamics as an alternative to classical molecular dynamics simulation. This simple approach dramatically saves the computational cost, but sometimes fails to describe a feasible conformational change due to unrealistically excessive spring connections. To overcome this limitation, we propose a mass-weighted chemical elastic network model (MWCENM) in which the total mass of each residue is assumed to be concentrated on the representative alpha carbon atom and various stiffness values are precisely assigned according to the types of chemical interactions. We test MWCENM on several well-known proteins of which both closed and open conformations are available as well as three α-helix rich proteins. Their normal mode analysis reveals that MWCENM not only generates more plausible conformational changes, especially for closed forms of proteins, but also preserves protein secondary structures thus distinguishing MWCENM from traditional ENMs. In addition, MWCENM also reduces computational burden by using a more sparse stiffness matrix.

DNA nanotube formation based on normal mode analysis

Ever since its inception, a popular DNA motif called the cross tile has been recognized to self-assemble into addressable 2D templates consisting of periodic square cavities. Although this may be conceptually correct, in reality certain types of cross tiles can only form planar lattices if adjacent tiles are designed to bind in a corrugated manner, in the absence of which they roll up to form 3D nanotube structures. Here we present a theoretical study on why uncorrugated cross tiles self-assemble into counterintuitive 3D nanotube structures and not planar 2D lattices. Coarse-grained normal mode analysis of single and multiple cross tiles within the elastic network model was carried out to expound the vibration modes of the systems. While both single and multiple cross tile simulations produce results conducive to tube formations, the dominant modes of a unit of four cross tiles (one square cavity), termed a quadruplet, fully reflect the symmetries of the actual nanotubes found in experiments and firmly endorse circularization of an array of cross tiles.

Iterative cluster-NMA: A tool for generating conformational transitions in proteins

Computational models provide insight into the structure-function relationship in proteins. These approaches, especially those based on normal mode analysis, can identify the accessible motion space around a given equilibrium structure. The large magnitude, collective motions identified by these methods are often well aligned with the general direction of the expected conformational transitions. However, these motions cannot realistically be extrapolated beyond the local neighborhood of the starting conformation. In this article, the iterative cluster-NMA (icNMA) method is presented for traversing the energy landscape from a starting conformation to a desired goal conformation. This is accomplished by allowing the evolving geometry of the intermediate structures to define the local accessible motion space, and thus produce an appropriate displacement. Following the derivation of the icNMA method, a set of sample simulations are performed to probe the robustness of the model. A detailed analysis of beta1,4-galactosyltransferase-T1 is also given, to highlight many of the capabilities of icNMA. Remarkably, during the transition, a helix is seen to be extended by an additional turn, emphasizing a new unknown role for secondary structures to absorb slack during transitions. The transition pathway for adenylate kinase, which has been frequently studied in the literature, is also discussed.

Group theory of icosahedral virus capsid vibrations: a top-down approach

We explore the use of a top-down approach to analyse the dynamics of icosahedral virus capsids and complement the information obtained from bottom-up studies of viral vibrations available in the literature. A normal mode analysis based on protein association energies is used to study the frequency spectrum, in which we reveal a universal plateau of low-frequency modes shared by a large class of Caspar-Klug capsids. These modes break icosahedral symmetry and are potentially relevant to the genome release mechanism. We comment on the role of viral tiling theory in such dynamical considerations.

Twenty-four near-instabilities of Caspar-Klug viruses

Group theoretical arguments combined with normal mode analysis techniques are applied to a coarse-grained approximation of icosahedral viral capsids which incorporates areas of variable flexibility. This highlights a remarkable structure of the low-frequency spectrum in this approximation, namely, the existence of a plateau of 24 near zero modes with universal group theory content.

Evolutionary conservation of protein vibrational dynamics

The aim of the present work is to study the evolutionary divergence of vibrational protein dynamics. To this end, we used the Gaussian Network Model to perform a systematic analysis of normal mode conservation on a large dataset of proteins classified into homologous sets of family pairs and superfamily pairs. We found that the lowest most collective normal modes are the most conserved ones. More precisely, there is, on average, a linear correlation between normal mode conservation and mode collectivity. These results imply that the previously observed conservation of backbone flexibility (B-factor) profiles is due to the conservation of the most collective modes, which contribute the most to such profiles. We discuss the possible roles of normal mode robustness and natural selection in the determination of the observed behavior. Finally, we draw some practical implications for dynamics-based protein alignment and classification and discuss possible caveats of the present approach.

Thorough validation of protein normal mode analysis: a comparative study with essential dynamics

The deformation patterns of a large set of representative proteins determined by essential dynamics extracted from atomistic simulations and coarse-grained normal mode analysis are compared. Our analysis shows that the deformational space obtained with both approaches is quite similar when taking into account a representative number of modes. The results provide not only a comprehensive validation of the use of a low-frequency modal spectrum to describe protein flexibility, but also a complete picture of normal mode limitations.

MinActionPath: maximum likelihood trajectory for large-scale structural transitions in a coarse-grained locally harmonic energy landscape

The non-linear problem of simulating the structural transition between two known forms of a macromolecule still remains a challenge in structural biology. The problem is usually addressed in an approximate way using 'morphing' techniques, which are linear interpolations of either the Cartesian or the internal coordinates between the initial and end states, followed by energy minimization. Here we describe a web tool that implements a new method to calculate the most probable trajectory that is exact for harmonic potentials; as an illustration of the method, the classical Calpha-based Elastic Network Model (ENM) is used both for the initial and the final states but other variants of the ENM are also possible. The Langevin equation under this potential is solved analytically using the Onsager and Machlup action minimization formalism on each side of the transition, thus replacing the original non-linear problem by a pair of linear differential equations joined by a non-linear boundary matching condition. The crossover between the two multidimensional energy curves around each state is found numerically using an iterative approach, producing the most probable trajectory and fully characterizing the transition state and its energy. Jobs calculating such trajectories can be submitted on-line at: http://lorentz.dynstr.pasteur.fr/joel/index.php.