Kinetics of Carbon Monoxide Migration and Binding in Solvated Myoglobin as Revealed by Molecular Dynamics Simulations and Quantum Mechanical Calculations

Benchmarking Rapid TLES Simulations of Gas Diffusion in Proteins: Mapping O2 Migration and Escape in Myoglobin as a Case Study

Standard molecular dynamics (MD) simulations of gas diffusion consume considerable computational time and resources even for small proteins. To combat this, temperature-controlled locally enhanced sampling (TLES) examines multiple diffusion trajectories per simulation by accommodating multiple noninteracting copies of a gas molecule that diffuse independently, while the protein and water molecules experience an average interaction from all copies. Furthermore, gas migration within a protein matrix can be accelerated without altering protein dynamics by increasing the effective temperature of the TLES copies. These features of TLES enable rapid simulations of gas diffusion within a protein matrix at significantly reduced (∼98%) computational cost. However, the results of TLES and standard MD simulations have not been systematically compared, which limits the adoption of the TLES approach. We address this drawback here by benchmarking TLES against standard MD in the simulation of O2 diffusion in myoglobin (Mb) as a case study since this model system has been extensively characterized. We find that 2 ns TLES and 108 ns standard simulations map the same network of diffusion tunnels in Mb and uncover the same docking sites, barriers, and escape portals. We further discuss the influence of simulation time as well as the number of independent simulations on the O2 population density within the diffusion tunnels and on the sampling of Mb's conformational space as revealed by principal component analysis. Overall, our comprehensive benchmarking reveals that TLES is an appropriate and robust tool for the rapid mapping of gas diffusion in proteins when the kinetic data provided by standard MD are not required. Furthermore, TLES provides explicit ligand diffusion pathways, unlike most rapid methods.

Uncovering a dynamically formed substrate access tunnel in carbon monoxide dehydrogenase/acetyl-CoA synthase

The transport of small ligands to active sites of proteins is the basis of vital processes in biology such as enzymatic catalysis and cell signaling, but also of more destructive ones including enzyme inhibition and oxidative damage. Here, we show how a diffusion-reaction model solved by means of molecular dynamics and density functional theory calculations provides novel insight into the transport of small ligands in proteins. In particular, we unravel the existence of an elusive, dynamically formed gas channel, which CO2 takes to diffuse from the solvent to the active site (C-cluster) of the bifunctional multisubunit enzyme complex carbon monoxide dehydrogenase/acetyl-CoA synthase (CODH/ACS). Two cavities forming this channel are temporarily created by protein fluctuations and are not apparent in the X-ray structures. The ligand transport is controlled by two residues at the end of this tunnel, His113 and His116, and occurs on the same time scale on which chemical binding to the active site takes place (0.1-1 ms), resulting in an overall binding rate on the second time scale. We find that upon reduction of CO2 to CO, the newly formed Fe-hydroxy ligand greatly strengthens the hydrogen-bond network, preventing CO from exiting the protein through the same way that CO2 takes to enter the protein. This is the basis for directional transport of CO from the production site (C-cluster of CODH subunit) to the utilization site (A-cluster of ACS subunit). In view of these results, a general picture emerges of how large proteins guide small ligands toward their active sites.

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.

Molecular dynamics study of hell's gate globin I (HGbI) from a methanotrophic extremophile: oxygen migration through a large cavity

Hell's gate globin I (HGbI), a heme-containing protein from the extremophile Methylacidiphilum infernorum, has fast oxygen-binding/slow release characteristics due to its distal residues Gln and Tyr. The combination of Gln/Tyr distal iron coordination, adaptation to extreme environmental conditions, and lack of a D helix suggests that ligand migration in HGbI differs from other previously studied globins. Locally enhanced molecular dynamics trajectories of oxygen migration indicate a large internal cavity. This may increase the tendency of oxygen to exit from portals other than the most direct exit from the space near the heme. Oxygen may reside transiently in shallow surface depressions around the exits. Such surface trapping may enhance both oxygen uptake by increasing contact time between molecules, and decrease release by increasing the probability of oxygen reentry from the vicinity of the portal.

Mechanistic insight into the blocking of CO diffusion in [NiFe]-hydrogenase mutants through multiscale simulation

[NiFe]-hydrogenases are fascinating biological catalysts with potential application in biofuel cells. However, a severe problem in practical application is the strong sensitivity of hydrogenase to gaseous inhibitor molecules such as CO and O(2). Recently, a number of successful protein engineering studies have been reported that aimed at lowering the access of diatomic inhibitors to the active site pocket, but the molecular mechanism conferring increased resistance remained unclear. Here we use a multiscale simulation approach combining molecular dynamics with a master equation formalism to explain the steady drop in CO diffusion rate observed for the mutants V74M L122A, V74M L122M, and V74M of Desulfovibrio fructosovorans [NiFe]-hydrogenase. We find that diffusion in these variants is controlled by two gates, one between residues 74 and 476 and the other between residues 74 and 122. The existence of two control points in different locations explains why the reduction in the experimental diffusion rate does not simply correlate with the width of the main gas channel. We also find that in the more effective mutation (V74M) CO molecules are still able to reach the active site through transitions that are gated by the microsecond dihedral motions of the side chain of R476 and the thermal fluctuations of the width of the gas channel defined by M74 and L122. Reflecting on the molecular information gained from simulation, we discuss future mutation experiments that could further lower the diffusion rates of small ligands inhibiting [NiFe]-hydrogenase.

A microscopic model for gas diffusion dynamics in a [NiFe]-hydrogenase

We describe and apply a microscopic model for the calculation of gas diffusion rates in a [NiFe]-hydrogenase. This enzyme has attracted much interest for use as a H(2) oxidising catalyst in biofuel cells, but a major problem is their inhibition by CO and O(2). In our model, the diffusive hopping of gas molecules in the protein interior is coarse grained using a master equation approach with transition rates estimated from equilibrium and non-equilibrium pulling simulations. Propagating the rate matrix in time, we find that the probability for a gas molecule to reach the enzyme active site follows a mono-exponential increase. Fits to a phenomenological rate law give an effective diffusion rate constant for CO that is in very good agreement with experimental measurements. We find that CO prefers to move along the canonical 'hydrophobic' main channel towards the active site, in contrast to O(2) and H(2), which were previously shown to explore larger fractions of the protein. Differences in the diffusion of the three gases are discussed in light of recent efforts to engineer a gas selectivity filter in the enzyme.

Multiscale simulation reveals multiple pathways for H2 and O2 transport in a [NiFe]-hydrogenase

Hydrogenases are enzymes that catalyze the reversible conversion of hydrogen molecules to protons and electrons. The mechanism by which the gas molecules reach the active site is important for understanding the function of the enzyme and may play a role in the selectivity for hydrogen over inhibitor molecules. Here, we develop a general multiscale molecular simulation approach for the calculation of diffusion rates and determination of pathways by which substrate or inhibitor gases can reach the protein active site. Combining kinetic data from both equilibrium simulations and enhanced sampling, we construct a master equation describing the movement of gas molecules within the enzyme. We find that the time-dependent gas population of the active site can be fit to the same phenomenological rate law used to interpret experiments, with corresponding diffusion rates in very good agreement with experimental data. However, in contrast to the conventional picture, in which the gases follow a well-defined hydrophobic tunnel, we find that there is a diverse network of accessible pathways by which the gas molecules can reach the active site. The previously identified tunnel accounts for only about 60% of the total flux. Our results suggest that the dramatic decrease in the diffusion rate for mutations involving the residue Val74 could be in part due to the narrowing of the passage Val74-Arg476, immediately adjacent to the binding site, explaining why mutations of Leu122 had only a negligible effect in experiment. Our method is not specific to the [NiFe]-hydrogenase and should be generally applicable to the transport of small molecules in proteins.

Kinetics of carbon monoxide migration and binding in solvated neuroglobin as revealed by molecular dynamics simulations and quantum mechanical calculations

Neuroglobin (Ngb) is a globular protein that reversibly binds small ligands at the six coordination position of the heme. With respect to other globins similar to myoglobin, Ngb displays some peculiarities as the topological reorganization of the internal cavities coupled to the sliding of the heme, or the binding of the endogenous distal histidine to the heme in the absence of an exogenous ligand. In this Article, by using multiple (independent) molecular dynamics trajectories (about 500 ns in total), the migration pathways of photolized carbon monoxide (CO) within solvated Ngb were analyzed, and a quantitative description of CO migration and corresponding kinetics was obtained. MD results, combined with quantum mechanical calculations on the CO-heme binding-unbinding reaction step in Ngb, allowed construction of a quantitative model representing the relevant steps of CO migration and rebinding.

Rate theories for biologists

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein-protein and protein-DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.