Coarse-Grained Protein Models and Their Applications

Minimum action transition paths connecting minima on an energy surface

Dynamics is essential to the biological functions of many bio-molecules, yet our knowledge of dynamics remains fragmented. Experimental techniques for studying bio-molecules either provide high resolution information on static conformations of the molecule or provide low-resolution, ensemble information that does not shed light on single molecule dynamics. In parallel, bio-molecular dynamics occur at time scale that are not yet attainable through detailed simulation methods. These limitations are especially noticeable when studying transition paths. To address this issue, we report in this paper two methods that derive meaningful trajectories for proteins between two of their conformations. The first method, MinActionPath, uses approximations of the potential energy surface for the molecule to derive an analytical solution of the equations of motion related to the concept of minimum action path. The second method, RelaxPath, follows the same principle of minimum action path but implements a more sophisticated potential, including a mixed elastic potential and a collision term to alleviate steric clashes. Using this new potential, the equations of motion cannot be solved analytically. We have introduced a relaxation method for solving those equations. We describe both the theories behind the two methods and their implementations, focusing on the specific techniques we have used that make those implementations amenable to study large molecular systems. We have illustrated the performance of RelaxPath on simple 2D systems. We have also compared MinActionPath and RelaxPath to other methods for generating transition paths on a well suited test set of large proteins, for which the end points of the trajectories as well as an intermediate conformation between those end points are known. We have shown that RelaxPath outperforms those other methods, including MinActionPath, in its ability to generate trajectories that get close to the known intermediates. We have also shown that the structures along the RelaxPath trajectories remain protein-like. Open source versions of the two programs MinActionPath and RelaxPath are available by request.

The Renormalization Group and Its Applications to Generating Coarse-Grained Models of Large Biological Molecular Systems

Understanding the dynamics of biomolecules is the key to understanding their biological activities. Computational methods ranging from all-atom molecular dynamics simulations to coarse-grained normal-mode analyses based on simplified elastic networks provide a general framework to studying these dynamics. Despite recent successes in studying very large systems with up to a 100,000,000 atoms, those methods are currently limited to studying small- to medium-sized molecular systems due to computational limitations. One solution to circumvent these limitations is to reduce the size of the system under study. In this paper, we argue that coarse-graining, the standard approach to such size reduction, must define a hierarchy of models of decreasing sizes that are consistent with each other, i.e., that each model contains the information of the dynamics of its predecessor. We propose a new method, Decimate, for generating such a hierarchy within the context of elastic networks for normal-mode analysis. This method is based on the concept of the renormalization group developed in statistical physics. We highlight the details of its implementation, with a special focus on its scalability to large systems of up to millions of atoms. We illustrate its application on two large systems, the capsid of a virus and the ribosome translation complex. We show that highly decimated representations of those systems, containing down to 1% of their original number of atoms, still capture qualitatively and quantitatively their dynamics. Decimate is available as an OpenSource resource.

Combining the MARTINI and Structure-Based Coarse-Grained Approaches for the Molecular Dynamics Studies of Conformational Transitions in Proteins

The application of coarse-grained (CG) models in biology is essential to access large length and time scales required for the description of many biological processes. The ELNEDIN protein model is based on the well-known MARTINI CG force-field and incorporates additionally harmonic bonds of a certain spring constant within a defined cutoff distance between pairs of residues, in order to preserve the native structure of the protein. In this case, the use of unbreakable harmonic bonds hinders the study of unfolding and folding processes. To overcome this barrier we have replaced the harmonic bonds with Lennard-Jones interactions based on the contact map of the native protein structure as is done in Go̅-like models. This model exhibits very good agreement with all-atom simulations and the ELNEDIN. Moreover, it can capture the structural motion linked to particular catalytic activity in the Man5B protein, in agreement with all-atom simulations. In addition, our model is based on the van der Waals radii, instead of a cutoff distance, which results in a smaller contact map. In conclusion, we anticipate that our model will provide further possibilities for studying biological systems based on the MARTINI CG force-field by using advanced-sampling methods, such as parallel tempering and metadynamics.

Performance Comparison of Systematic Methods for Rigorous Definition of Coarse-Grained Sites of Large Biomolecules

Construction of coarse-grained (CG) models for large biomolecules used for multiscale simulations demands a rigorous definition of CG sites for them. Several coarse-graining methods such as the simulated annealing and steepest descent (SASD) based on the essential dynamics coarse-graining (ED-CG) or the stepwise local iterative optimization (SLIO) based on the fluctuation maximization coarse-graining (FM-CG), were developed to do it. However, the practical applications of these methods such as SASD based on ED-CG are subject to limitations because they are too expensive. In this work, we extend the applicability of ED-CG by combining it with the SLIO algorithm. A comprehensive comparison of optimized results and accuracy of various algorithms based on ED-CG show that SLIO is the fastest as well as the most accurate algorithm among them. ED-CG combined with SLIO could give converged results as the number of CG sites increases, which demonstrates that it is another efficient method for coarse-graining large biomolecules. The construction of CG sites for Ras protein by using MD fluctuations demonstrates that the CG sites derived from FM-CG can reflect the fluctuation properties of secondary structures in Ras accurately.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).

One-Dimensional Structural Properties of Proteins in the Coarse-Grained CABS Model

Despite the significant increase in computational power, molecular modeling of protein structure using classical all-atom approaches remains inefficient, at least for most of the protein targets in the focus of biomedical research. Perhaps the most successful strategy to overcome the inefficiency problem is multiscale modeling to merge all-atom and coarse-grained models. This chapter describes a well-established CABS coarse-grained protein model. The CABS (C-Alpha, C-Beta, and Side chains) model assumes a 2-4 united-atom representation of amino acids, knowledge-based force field (derived from the statistical regularities seen in known protein sequences and structures) and efficient Monte Carlo sampling schemes (MC dynamics, MC replica-exchange, and combinations). A particular emphasis is given to the unique design of the CABS force-field, which is largely defined using one-dimensional structural properties of proteins, including protein secondary structure. This chapter also presents CABS-based modeling methods, including multiscale tools for de novo structure prediction, modeling of protein dynamics and prediction of protein-peptide complexes. CABS-based tools are freely available at http://biocomp.chem.uw.edu.pl/tools.

Highly Flexible Protein-Peptide Docking Using CABS-Dock

Protein-peptide molecular docking is a difficult modeling problem. It is even more challenging when significant conformational changes that may occur during the binding process need to be predicted. In this chapter, we demonstrate the capabilities and features of the CABS-dock server for flexible protein-peptide docking. CABS-dock allows highly efficient modeling of full peptide flexibility and significant flexibility of a protein receptor. During CABS-dock docking, the peptide folding and binding process is explicitly simulated and no information about the peptide binding site or its structure is used. This chapter presents a successful CABS-dock use for docking a potentially therapeutic peptide to a protein target. Moreover, simulation contact maps, a new CABS-dock feature, are described and applied to the docking test case. Finally, a tutorial for running CABS-dock from the command line or command line scripts is provided. The CABS-dock web server is available from http://biocomp.chem.uw.edu.pl/CABSdock/ .

Comparative Normal Mode Analysis of the Dynamics of DENV and ZIKV Capsids

Key steps in the life cycle of a virus, such as the fusion event as the virus infects a host cell and its maturation process, relate to an intricate interplay between the structure and the dynamics of its constituent proteins, especially those that define its capsid, much akin to an envelope that protects its genomic material. We present a comprehensive, comparative analysis of such interplay for the capsids of two viruses from the flaviviridae family, Dengue (DENV) and Zika (ZIKV). We use for that purpose our own software suite, DD-NMA, which is based on normal mode analysis. We describe the elements of DD-NMA that are relevant to the analysis of large systems, such as virus capsids. In particular, we introduce our implementation of simplified elastic networks and justify their parametrization. Using DD-NMA, we illustrate the importance of packing interactions within the virus capsids on the dynamics of the E proteins of DENV and ZIKV. We identify differences between the computed atomic fluctuations of the E proteins in DENV and ZIKV and relate those differences to changes observed in their high resolution structures. We conclude with a discussion on additional analyses that are needed to fully characterize the dynamics of the two viruses.

Protein-peptide molecular docking with large-scale conformational changes: the p53-MDM2 interaction

Protein-peptide interactions are often associated with large-scale conformational changes that are difficult to study either by classical molecular modeling or by experiment. Recently, we have developed the CABS-dock method for flexible protein-peptide docking that enables large-scale rearrangements of the protein chain. In this study, we use CABS-dock to investigate the binding of the p53-MDM2 complex, an element of the cell cycle regulation system crucial for anti-cancer drug design. Experimental data suggest that p53-MDM2 binding is affected by significant rearrangements of a lid region - the N-terminal highly flexible MDM2 fragment; however, the details are not clear. The large size of the highly flexible MDM2 fragments makes p53-MDM2 intractable for exhaustive binding dynamics studies using atomistic models. We performed extensive dynamics simulations using the CABS-dock method, including large-scale structural rearrangements of MDM2 flexible regions. Without a priori knowledge of the p53 peptide structure or its binding site, we obtained near-native models of the p53-MDM2 complex. The simulation results match well the experimental data and provide new insights into the possible role of the lid fragment in p53 binding. The presented case study demonstrates that CABS-dock methodology opens up new opportunities for protein-peptide docking with large-scale changes of the protein receptor structure.

Coarse-Grained Simulations of Membrane Insertion and Folding of Small Helical Proteins Using the CABS Model

The CABS coarse-grained model is a well-established tool for modeling globular proteins (predicting their structure, dynamics, and interactions). Here we introduce an extension of the CABS representation and force field (CABS-membrane) to the modeling of the effect of the biological membrane environment on the structure of membrane proteins. We validate the CABS-membrane model in folding simulations of 10 short helical membrane proteins not using any knowledge about their structure. The simulations start from random protein conformations placed outside the membrane environment and allow for full flexibility of the modeled proteins during their spontaneous insertion into the membrane. In the resulting trajectories, we have found models close to the experimental membrane structures. We also attempted to select the correctly folded models using simple filtering followed by structural clustering combined with reconstruction to the all-atom representation and all-atom scoring. The CABS-membrane model is a promising approach for further development toward modeling of large protein-membrane systems.