An Approximate Method in Using Molecular Mechanics Simulations To Study Slow Protein Conformational Changes

Simulation Studies of Protein and Small Molecule Interactions and Reaction

Computational studies of protein and small molecule (protein-ligand/enzyme-substrate) interactions become more and more important in biological science and drug discovery. Computer modeling can provide molecular details of the processes such as conformational change, binding, and transportation of small molecules/proteins, which are not easily to be captured in experiments. In this chapter, we discussed simulation studies of both protein and small molecules from three aspects: conformation sampling, transportations of small molecules in enzymes, and enzymatic reactions involving small molecules. Both methodology developments and examples of simulation studies in this field were presented.

Linear Response Path Following: A Molecular Dynamics Method To Simulate Global Conformational Changes of Protein upon Ligand Binding

Molecular functions of proteins are often fulfilled by global conformational changes that couple with local events such as the binding of ligand molecules. High molecular complexity of proteins has, however, been an obstacle to obtain an atomistic view of the global conformational transitions, imposing a limitation on the mechanistic understanding of the functional processes. In this study, we developed a new method of molecular dynamics (MD) simulation called the linear response path following (LRPF) to simulate a protein's global conformational changes upon ligand binding. The method introduces a biasing force based on a linear response theory, which determines a local reaction coordinate in the configuration space that represents linear coupling between local events of ligand binding and global conformational changes and thus provides one with fully atomistic models undergoing large conformational changes without knowledge of a target structure. The overall transition process involving nonlinear conformational changes is simulated through iterative cycles consisting of a biased MD simulation with an updated linear response force and a following unbiased MD simulation for relaxation. We applied the method to the simulation of global conformational changes of the yeast calmodulin N-terminal domain and successfully searched out the end conformation. The atomistically detailed trajectories revealed a sequence of molecular events that properly lead to the global conformational changes and identified key steps of local-global coupling that induce the conformational transitions. The LRPF method provides one with a powerful means to model conformational changes of proteins such as motors and transporters where local-global coupling plays a pivotal role in their functional processes.

Increasing the sampling efficiency of protein conformational transition using velocity-scaling optimized hybrid explicit/implicit solvent REMD simulation

The application of temperature replica exchange molecular dynamics (REMD) simulation on protein motion is limited by its huge requirement of computational resource, particularly when explicit solvent model is implemented. In the previous study, we developed a velocity-scaling optimized hybrid explicit/implicit solvent REMD method with the hope to reduce the temperature (replica) number on the premise of maintaining high sampling efficiency. In this study, we utilized this method to characterize and energetically identify the conformational transition pathway of a protein model, the N-terminal domain of calmodulin. In comparison to the standard explicit solvent REMD simulation, the hybrid REMD is much less computationally expensive but, meanwhile, gives accurate evaluation of the structural and thermodynamic properties of the conformational transition which are in well agreement with the standard REMD simulation. Therefore, the hybrid REMD could highly increase the computational efficiency and thus expand the application of REMD simulation to larger-size protein systems.

Effect of Calcium Ion Removal, Ionic Strength, and Temperature on the Conformation Change in Calmodulin Protein at Physiological pH

The response of the calmodulin (CaM) protein as a function of calcium ion removal, ionic strength, and temperature at physiological pH condition was investigated using classical molecular dynamics simulations. Changing the ionic strength and temperature came out to be two of the possible routes for observing a conformation change in the protein. This behavior is similar to the conformation change observed in our previous study where a change in the pH was observed to trigger a conformation change in this protein. In the present study, as the calcium ions are removed from the protein, the protein is observed to acquire more flexibility. This flexibility is observed to be more prominent at a higher ionic strength. At a lower ionic strength of 150 mM with all the four calcium ions intact, the N- and C-lobes are observed to come close to a distance of 30 Å starting from an initial separation distance of 48 Å. This conformation change is observed to take place around 50 ns in a simulation of 100 ns. As a second parameter, temperature is observed to play a key role in the conformation change of the protein. With an increase in the temperature, the protein is observed to acquire a more compact form with the formation of different salt bridges between the residues of the N- and the C-lobes. The salt bridge formation leads to an overall lowering of the energy of the protein thus favoring the bending of the two lobes towards each other. The improper and dihedral terms show a significant shift thus leading to a more compact form on increasing the temperature. Another set of simulations is also performed at an increased temperature of 500 K to verify the reproducibility of the results. Thus a set of three possible alterations in the environmental conditions of the protein CaM are studied, with two of them giving rise to a conformation change and one adding flexibility to the protein.

Calmodulin readily switches conformation upon protonating high pKa acidic residues

We investigate protonation as a possible route for triggering conformational change in proteins by focusing on the calmodulin (CaM) example. Two hundred nanosecond molecular dynamics (MD) simulations are performed on both the extended and compact forms of calcium loaded CaM. The stability of both structures is confirmed under prevailing conditions. Protonation of nine acidic residues with upshifted pK(a) values leads to a large conformational change in less than 100 ns. The structure attained is consistent with fluorescence resonance energy transfer experimental results as well as structures from an ensemble compatible with NMR data. Analysis of the MD trajectories summing up to one microsecond implies that the key events leading to the completion of the conformational change begins with an initial formation of a salt bridge between the N-lobe and the linker, followed by the bending of the C-lobe and the organization of a stabilizing hydrophobic patch between the lobes. We find that CaM utilizes its Ca(2+) ions to harden/soften different regions so as to achieve various conformations. Thus, barrier crossing between extended and compact forms of CaM which is normally a rare event due to the repulsive electrostatic interactions between the two lobes is facilitated by protonation of high pK(a) residues. The results delineate how pH changes might be utilized in the cell to achieve different conformation-related functions.

Efficient and Unbiased Sampling of Biomolecular Systems in the Canonical Ensemble: A Review of Self-Guided Langevin Dynamics

This review provides a comprehensive description of the self-guided Langevin dynamics (SGLD) and the self-guided molecular dynamics (SGMD) methods and their applications. Example systems are included to provide guidance on optimal application of these methods in simulation studies. SGMD/SGLD has enhanced ability to overcome energy barriers and accelerate rare events to affordable time scales. It has been demonstrated that with moderate parameters, SGLD can routinely cross energy barriers of 20 kT at a rate that molecular dynamics (MD) or Langevin dynamics (LD) crosses 10 kT barriers. The core of these methods is the use of local averages of forces and momenta in a direct manner that can preserve the canonical ensemble. The use of such local averages results in methods where low frequency motion "borrows" energy from high frequency degrees of freedom when a barrier is approached and then returns that excess energy after a barrier is crossed. This self-guiding effect also results in an accelerated diffusion to enhance conformational sampling efficiency. The resulting ensemble with SGLD deviates in a small way from the canonical ensemble, and that deviation can be corrected with either an on-the-fly or a post processing reweighting procedure that provides an excellent canonical ensemble for systems with a limited number of accelerated degrees of freedom. Since reweighting procedures are generally not size extensive, a newer method, SGLDfp, uses local averages of both momenta and forces to preserve the ensemble without reweighting. The SGLDfp approach is size extensive and can be used to accelerate low frequency motion in large systems, or in systems with explicit solvent where solvent diffusion is also to be enhanced. Since these methods are direct and straightforward, they can be used in conjunction with many other sampling methods or free energy methods by simply replacing the integration of degrees of freedom that are normally sampled by MD or LD.

Application of nonlinear dimensionality reduction to characterize the conformational landscape of small peptides

The automatic classification of the wealth of molecular configurations gathered in simulation in the form of a few coordinates that help to explain the main states and transitions of the system is a recurring problem in computational molecular biophysics. We use the recently proposed ScIMAP algorithm to automatically extract motion parameters from simulation data. The procedure uses only molecular shape similarity and topology information inferred directly from the simulated conformations, and is not biased by a priori known information. The automatically recovered coordinates prove as excellent reaction coordinates for the molecules studied and can be used to identify stable states and transitions, and as a basis to build free-energy surfaces. The coordinates provide a better description of the free energy landscape when compared with coordinates computed using principal components analysis, the most popular linear dimensionality reduction technique. The method is first validated on the analysis of the dynamics of an all-atom model of alanine dipeptide, where it successfully recover all previously known metastable states. When applied to characterize the simulated folding of a coarse-grained model of beta-hairpin, in addition to the folded and unfolded states, two symmetric misfolding crossings of the hairpin strands are observed, together with the most likely transitions from one to the other.