Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.</p

Combining Optimal Control Theory and Molecular Dynamics for Protein Folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages

Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results. © 2014 Das et al

Computational design of new Peptide inhibitors for amyloid Beta (aβ) aggregation in Alzheimer's disease: application of a novel methodology.

Alzheimer's disease is the most common form of dementia. It is a neurodegenerative and incurable disease that is associated with the tight packing of amyloid fibrils. This packing is facilitated by the compatibility of the ridges and grooves on the amyloid surface. The GxMxG motif is the major factor creating the compatibility between two amyloid surfaces, making it an important target for the design of amyloid aggregation inhibitors. In this study, a peptide, experimentally proven to bind Aβ40 fibrils at the GxMxG motif, was mutated by a novel methodology that systematically replaces amino acids with residues that share similar chemical characteristics and subsequently assesses the energetic favorability of these mutations by docking. Successive mutations are combined and reassessed via docking to a desired level of refinement. This methodology is both fast and efficient in providing potential inhibitors. Its efficiency lies in the fact that it does not perform all possible combinations of mutations, therefore decreasing the computational time drastically. The binding free energies of the experimentally studied reference peptide and its three top scoring derivatives were evaluated as a final assessment/valuation. The potential of mean forces (PMFs) were calculated by applying the Jarzynski's equality to results of steered molecular dynamics simulations. For all of the top scoring derivatives, the PMFs showed higher binding free energies than the reference peptide substantiating the usage of the introduced methodology to drug design

Some sampled conformations on the folding trajectory.

<p>Numbers indicate the folding step. H1 (red), H2 (purple) and H3 (green) denote the three helices of Villin headpiece.</p

One dimensional schematic of potential energy surfaces.

<p><i>U</i> is the harmonic CG potential; <i>E</i> is the protein's true potential. Native values are subtracted from both.</p

Components of the internal energy.

<p>Conformational energy (bonds, angles, dihedrals, and impropers), nonbonded energy (vdW and electrostatic energy), and total energy are compared. Nonbonded energy determines the general trend of the total energy.</p

Flowchart of the Methodology.

<p>Flowchart of the Methodology.</p

Grouping System and Hydrophobicity Index[39] Used in This Study.

<p>Grouping System and Hydrophobicity Index<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0066178#pone.0066178-Kyte1" target="_blank">[39]</a> Used in This Study.</p