Quantitative analysis of ligand migration from transition networks

Ligand Binding Rate Constants in Heme Proteins Using Markov State Models and Molecular Dynamics Simulations

Computer simulation studies of the molecular basis for ligand migration in proteins allow the description of key events such as the transition between docking sites, displacement of existing ligands and solvent molecules, and open/closure of specific "gates", among others. In heme proteins, ligand migration from the solvent to the active site preludes the binding to the heme iron and triggers different functions. In this work, molecular dynamics simulations, a Markov State Model of migration and empirical kinetic equations are combined to study the migration of O₂ and NO in two truncated hemoglobins of Mycobacterium tuberculosis (Mt-TrHbN and Mt-TrHbO). For Mt-TrHbN, we show that the difference in the association constant in the oxy and deoxy states relies mainly in the displacement of water molecules anchored in the distal cavity in the deoxy form. The results here provide a valuable approach to study ligand migration in globins.

Implications of short time scale dynamics on long time processes

This review provides a comprehensive overview of the structural dynamics in topical gas- and condensed-phase systems on multiple length and time scales. Starting from vibrationally induced dissociation of small molecules in the gas phase, the question of vibrational and internal energy redistribution through conformational dynamics is further developed by considering coupled electron/proton transfer in a model peptide over many orders of magnitude. The influence of the surrounding solvent is probed for electron transfer to the solvent in hydrated I-. Next, the dynamics of a modified PDZ domain over many time scales is analyzed following activation of a photoswitch. The hydration dynamics around halogenated amino acid side chains and their structural dynamics in proteins are relevant for iodinated TyrB26 insulin. Binding of nitric oxide to myoglobin is a process for which experimental and computational analyses have converged to a common view which connects rebinding time scales and the underlying dynamics. Finally, rhodopsin is a paradigmatic system for multiple length- and time-scale processes for which experimental and computational methods provide valuable insights into the functional dynamics. The systems discussed here highlight that for a comprehensive understanding of how structure, flexibility, energetics, and dynamics contribute to functional dynamics, experimental studies in multiple wavelength regions and computational studies including quantum, classical, and more coarse grained levels are required.

Migration of small ligands in globins: Xe diffusion in truncated hemoglobin N

In heme proteins, the efficient transport of ligands such as NO or O₂ to the binding site is achieved via ligand migration networks. A quantitative assessment of ligand diffusion in these networks is thus essential for a better understanding of the function of these proteins. For this, Xe migration in truncated hemoglobin N (trHbN) of Mycobacterium Tuberculosis was studied using molecular dynamics simulations. Transitions between pockets of the migration network and intra-pocket relaxation occur on similar time scales (10 ps and 20 ps), consistent with low free energy barriers (1-2 kcal/mol). Depending on the pocket from where Xe enters a particular transition, the conformation of the side chains lining the transition region differs which highlights the coupling between ligand and protein degrees of freedom. Furthermore, comparison of transition probabilities shows that Xe migration in trHbN is a non-Markovian process. Memory effects arise due to protein rearrangements and coupled dynamics as Xe moves through it.

Binding and transport of ligands in proteins is essential, in particular in globular proteins which often exhibit internal cavities. In truncated Hemoglobin N (trHbN) these cavities are arranged as a network with particular connectivities. The present work supports the notion that ligand diffusion in trHbN is an active process and coupled to the protein dynamics. Furthermore, transition probabilities between neighboring pockets depend on the location from where the ligand entered the transition, which is typical for non-Markovian processes. Hence, ligand migration in trHbN exhibits memory effects due to dynamical coupling between the protein and ligand motion.

Markov state models of protein misfolding

Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity.

Structural Plasticity in Globins: Role of Protein Dynamics in Defining Ligand Migration Pathways

Globins are a family of proteins characterized by the presence of the heme prosthetic group and involved in variety of biological functions in the cell. Due to their biological relevance and widespread distribution in all kingdoms of life, intense research efforts have been devoted to disclosing the relationships between structural features, protein dynamics, and function. Particular attention has been paid to the impact of differences in amino acid sequence on the topological features of docking sites and cavities and to the influence of conformational flexibility in facilitating the migration of small ligands through these cavities. Often, tunnels are carved in the interior of globins, and ligand exchange is regulated by gating residues. Understanding the subtle intricacies that relate the differences in sequence with the structural and dynamical features of globins with the ultimate aim of rationalizing the thermodynamics and kinetics of ligand binding continues to be a major challenge in the field. Due to the evolution of computational techniques, significant advances into our understanding of these questions have been made. In this review we focus our attention on the analysis of the ligand migration pathways as well as the function of the structural cavities and tunnels in a series of representative globins, emphasizing the synergy between experimental and theoretical approaches to gain a comprehensive knowledge into the molecular mechanisms of this diverse family of proteins.

Understanding the kinetics of ligand binding to globins with molecular dynamics simulations: the necessity of multiple state models

Residue conformational changes and internal cavity migration processes play a key role in regulating the kinetics of ligand migration and binding events in globins. Molecular dynamics simulations have demonstrated their value in the study of these processes in different haemoglobins, but derivation of kinetic data demands the use of more complex techniques like enhanced sampling molecular dynamics methods. This review discusses the different methodologies that are currently applied to study the ligand migration process in globins and highlight those specially developed to derive kinetic data.

A comparative analysis of clustering algorithms: O2 migration in truncated hemoglobin I from transition networks

The ligand migration network for O2-diffusion in truncated Hemoglobin N is analyzed based on three different clustering schemes. For coordinate-based clustering, the conventional k-means and the kinetics-based Markov Clustering (MCL) methods are employed, whereas the locally scaled diffusion map (LSDMap) method is a collective-variable-based approach. It is found that all three methods agree well in their geometrical definition of the most important docking site, and all experimentally known docking sites are recovered by all three methods. Also, for most of the states, their population coincides quite favourably, whereas the kinetics of and between the states differs. One of the major differences between k-means and MCL clustering on the one hand and LSDMap on the other is that the latter finds one large primary cluster containing the Xe1a, IS1, and ENT states. This is related to the fact that the motion within the state occurs on similar time scales, whereas structurally the state is found to be quite diverse. In agreement with previous explicit atomistic simulations, the Xe3 pocket is found to be a highly dynamical site which points to its potential role as a hub in the network. This is also highlighted in the fact that LSDMap cannot identify this state. First passage time distributions from MCL clusterings using a one- (ligand-position) and two-dimensional (ligand-position and protein-structure) descriptor suggest that ligand- and protein-motions are coupled. The benefits and drawbacks of the three methods are discussed in a comparative fashion and highlight that depending on the questions at hand the best-performing method for a particular data set may differ.

Identification of Mutational Hot Spots for Substrate Diffusion: Application to Myoglobin

The pathways by which small molecules (substrates or inhibitors) access active sites are a key aspect of the function of enzymes and other proteins. A key problem in designing or altering such proteins is to identify sites for mutation that will have the desired effect on the substrate transport properties. While specific access channels have been invoked in the past, molecular simulations suggest that multiple routes are possible, complicating the analysis. This complexity, however, can be captured by a Markov State Model (MSM) of the ligand diffusion process. We have developed a sensitivity analysis of the resulting rate matrix, which identifies the locations where mutations should have the largest effect on the diffusive on rate. We apply this method to myoglobin, which is the best characterized example both from experiment and simulation. We validate the approach by translating the sensitivity parameter obtained from this method into the CO binding rates in myoglobin upon mutation, resulting in a semi-quantitative correlation with experiments. The model is further validated against an explicit simulation for one of the experimental mutants.

Full kinetics of CO entry, internal diffusion, and exit in myoglobin from transition-path theory simulations

We use Markovian milestoning molecular dynamics (MD) simulations on a tessellation of the collective variable space for CO localization in myoglobin to estimate the kinetics of entry, exit, and internal site-hopping. The tessellation is determined by analysis of the free-energy surface in that space using transition-path theory (TPT), which provides criteria for defining optimal milestones, allowing short, independent, cell-constrained MD simulations to provide properly weighted kinetic data. We coarse grain the resulting kinetic model at two levels: first, using crystallographically relevant internal cavities and their predicted interconnections and solvent portals; and second, as a three-state side-path scheme inspired by similar models developed from geminate recombination experiments. We show semiquantitative agreement with experiment on entry and exit rates and in the identification of the so-called "histidine gate" at position 64 through which ≈90% of flux between solvent and the distal pocket passes. We also show with six-dimensional calculations that the minimum free-energy pathway of escape through the histidine gate is a "knock-on" mechanism in which motion of the ligand and the gate are sequential and interdependent. In total, these results suggest that such TPT simulations are indeed a promising approach to overcome the practical time-scale limitations of MD to allow reliable estimation of transition mechanisms and rates among metastable states.

Coupled protein-ligand dynamics in truncated hemoglobin N from atomistic simulations and transition networks

BACKGROUND

The nature of ligand motion in proteins is difficult to characterize directly using experiment. Specifically, it is unclear to what degree these motions are coupled.

METHODS

All-atom simulations are used to sample ligand motion in truncated Hemoglobin N. A transition network analysis including ligand- and protein-degrees of freedom is used to analyze the microscopic dynamics.

RESULTS

Clustering of two different subsets of MD trajectories highlights the importance of a diverse and exhaustive description to define the macrostates for a ligand-migration network. Monte Carlo simulations on the transition matrices from one particular clustering are able to faithfully capture the atomistic simulations. Contrary to clustering by ligand positions only, including a protein degree of freedom yields considerably improved coarse grained dynamics. Analysis with and without imposing detailed balance agree closely which suggests that the underlying atomistic simulations are converged with respect to sampling transitions between neighboring sites.

CONCLUSIONS

Protein and ligand dynamics are not independent from each other and ligand migration through globular proteins is not passive diffusion.

GENERAL SIGNIFICANCE

Transition network analysis is a powerful tool to analyze and characterize the microscopic dynamics in complex systems. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Ligand migration through hemeprotein cavities: insights from laser flash photolysis and molecular dynamics simulations

The presence of cavities and tunnels in the interior of proteins, in conjunction with the structural plasticity arising from the coupling to the thermal fluctuations of the protein scaffold, has profound consequences on the pathways followed by ligands moving through the protein matrix. In this perspective we discuss how quantitative analysis of experimental rebinding kinetics from laser flash photolysis, trapping of unstable conformational states by embedding proteins within the nanopores of silica gels, and molecular simulations can synergistically converge to gain insight into the migration mechanism of ligands. We show how the evaluation of the free energy landscape for ligand diffusion based on the outcome of computational techniques can assist the definition of sound reaction schemes, leading to a comprehensive understanding of the broad range of chemical events and time scales that encompass the transport of small ligands in hemeproteins.

Oxygen migration pathways in NO-bound truncated hemoglobin

Atomistic simulations of dioxygen (O(2)) dynamics and migration in nitric oxide-bound truncated Hemoglobin N (trHbN) of Mycobacterium tuberculosis are reported. From more than 100 ns of simulations the connectivity network involving the metastable states for localization of the O(2) ligand is built and analyzed. It is found that channel I is the primary entrance point for O(2) whereas channel II is predominantly an exit path although access to the protein active site is also possible. For O(2) a new site compared to nitric oxide, from which reaction with the heme group can occur, was found. As this site is close to the heme iron, it could play an important role in the dioxygenation mechanism as O(2) can remain there for hundreds of picoseconds after which it can eventually leave the protein, while NO is localized in Xe2. The present study supports recent experimental work which proposed that O(2) docks in alternative pockets than Xe close to the reactive site. Similar to other proteins, a phenylalanine residue (Phe62) plays the role of a gate along the access route in channel I. The most highly connected site is the Xe3 pocket which is a "hub" and free energy barriers between the different metastable states are ≈1.5 kcal mol(-1) which allows facile O(2) migration within the protein.