Jessica M. J. Swanson

Revisiting Free Energy Calculations: A Theoretical Connection to MM/PBSA and Direct Calculation of the Association Free Energy

The prediction of absolute ligand-receptor binding affinities is essential in a wide range of biophysical queries, from the study of protein-protein interactions to structure-based drug design. End-point free energy methods, such as the Molecular Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) model, have received much attention and widespread application in recent literature. These methods benefit from computational efficiency as only the initial and final states of the system are evaluated, yet there remains a need for strengthening their theoretical foundation. Here a clear connection between statistical thermodynamics and end-point free energy models is presented. The importance of the association free energy, arising from one molecules loss of translational and rotational freedom from the standard state concentration, is addressed. A novel method for calculating this quantity directly from a molecular dynamics simulation is described. The challenges of accounting for changes in the protein conformation and its fluctuations from separate simulations are discussed. A simple first-order approximation of the configuration integral is presented to lay the groundwork for future efforts. This model has been applied to FKBP12, a small immunophilin that has been widely studied in the drug industry for its potential immunosuppressive and neuroregenerative effects.

Multiscale simulation reveals a multifaceted mechanism of proton permeation through the influenza A M2 proton channel

Significance The M2 channel in the influenza A virus is one of three commonly targeted proteins in the viral membrane. Proton permeation across the M2 channel acidifies the virion, releasing the viral RNA and core proteins. This work constitutes, to our knowledge, the first complete characterization of this process by multiscale computer simulation, and the results are in quantitative agreement with prior experimental measurements. The simulations confirm that the mechanism involves a “shuttling” of protons through the His37 tetrad and that the rate-limiting step is histidine deprotonation. The results also reveal several important features, including a large barrier for protons to reach the His37 tetrad and increased conductance for lower pH values due to channel broadening and increased solvent dynamics despite larger charge repulsion. The influenza A virus M2 channel (AM2) is crucial in the viral life cycle. Despite many previous experimental and computational studies, the mechanism of the activating process in which proton permeation acidifies the virion to release the viral RNA and core proteins is not well understood. Herein the AM2 proton permeation process has been systematically characterized using multiscale computer simulations, including quantum, classical, and reactive molecular dynamics methods. We report, to our knowledge, the first complete free-energy profiles for proton transport through the entire AM2 transmembrane domain at various pH values, including explicit treatment of excess proton charge delocalization and shuttling through the His37 tetrad. The free-energy profiles reveal that the excess proton must overcome a large free-energy barrier to diffuse to the His37 tetrad, where it is stabilized in a deep minimum reflecting the delocalization of the excess charge among the histidines and the cost of shuttling the proton past them. At lower pH values the His37 tetrad has a larger total charge that increases the channel width, hydration, and solvent dynamics, in agreement with recent 2D-IR spectroscopic studies. The proton transport barrier becomes smaller, despite the increased charge repulsion, due to backbone expansion and the more dynamic pore water molecules. The calculated conductances are in quantitative agreement with recent experimental measurements. In addition, the free-energy profiles and conductances for proton transport in several mutants provide insights for explaining our findings and those of previous experimental mutagenesis studies.

Hydrated Excess Protons Can Create Their Own Water Wires.

Grotthuss shuttling of an excess proton charge defect through hydrogen bonded water networks has long been the focus of theoretical and experimental studies. In this work we show that there is a related process in which water molecules move (“shuttle”) through a hydrated excess proton charge defect in order to wet the path ahead for subsequent proton charge migration. This process is illustrated through reactive molecular dynamics simulations of proton transport through a hydrophobic nanotube, which penetrates through a hydrophobic region. Surprisingly, before the proton enters the nanotube, it starts “shooting” water molecules into the otherwise dry space via Grotthuss shuttling, effectively creating its own water wire where none existed before. As the proton enters the nanotube (by 2–3 Å), it completes the solvation process, transitioning the nanotube to the fully wet state. By contrast, other monatomic cations (e.g., K+) have just the opposite effect, by blocking the wetting process and making the nanotube even drier. As the dry nanotube gradually becomes wet when the proton charge defect enters it, the free energy barrier of proton permeation through the tube via Grotthuss shuttling drops significantly. This finding suggests that an important wetting mechanism may influence proton translocation in biological systems, i.e., one in which protons “create” their own water structures (water “wires”) in hydrophobic spaces (e.g., protein pores) before migrating through them. An existing water wire, e.g., one seen in an X-ray crystal structure or MD simulations without an explicit excess proton, is therefore not a requirement for protons to transport through hydrophobic spaces.

Multiscale Reactive Molecular Dynamics for Absolute pKa Predictions and Amino Acid Deprotonation

Accurately calculating a weak acid’s pKa from simulations remains a challenging task. We report a multiscale theoretical approach to calculate the free energy profile for acid ionization, resulting in accurate absolute pKa values in addition to insights into the underlying mechanism. Importantly, our approach minimizes empiricism by mapping electronic structure data (QM/MM forces) into a reactive molecular dynamics model capable of extensive sampling. Consequently, the bulk property of interest (the absolute pKa) is the natural consequence of the model, not a parameter used to fit it. This approach is applied to create reactive models of aspartic and glutamic acids. We show that these models predict the correct pKa values and provide ample statistics to probe the molecular mechanism of dissociation. This analysis shows changes in the solvation structure and Zundel-dominated transitions between the protonated acid, contact ion pair, and bulk solvated excess proton.

Acid activation mechanism of the influenza A M2 proton channel

Significance The influenza A M2 channel (AM2) transports protons into the influenza virus upon acid activation. It is an important pharmacological target as well as a prototypical case to study proton conduction through biological channels. The current work provides the most complete computational characterization to date of the physical basis for the acid activation mechanism of the AM2 proton channel. Our results show that lowering the pH value gradually opens the Trp41 gate and decreases the deprotonation barrier of the His37 tetrad, leading to channel activation. Our result also demonstrates that the C-terminal amphipathic helix does not significantly change the proton conduction mechanism in the AM2 transmembrane domain. The homotetrameric influenza A M2 channel (AM2) is an acid-activated proton channel responsible for the acidification of the influenza virus interior, an important step in the viral lifecycle. Four histidine residues (His37) in the center of the channel act as a pH sensor and proton selectivity filter. Despite intense study, the pH-dependent activation mechanism of the AM2 channel has to date not been completely understood at a molecular level. Herein we have used multiscale computer simulations to characterize (with explicit proton transport free energy profiles and their associated calculated conductances) the activation mechanism of AM2. All proton transfer steps involved in proton diffusion through the channel, including the protonation/deprotonation of His37, are explicitly considered using classical, quantum, and reactive molecular dynamics methods. The asymmetry of the proton transport free energy profile under high-pH conditions qualitatively explains the rectification behavior of AM2 (i.e., why the inward proton flux is allowed when the pH is low in viral exterior and high in viral interior, but outward proton flux is prohibited when the pH gradient is reversed). Also, in agreement with electrophysiological results, our simulations indicate that the C-terminal amphipathic helix does not significantly change the proton conduction mechanism in the AM2 transmembrane domain; the four transmembrane helices flanking the channel lumen alone seem to determine the proton conduction mechanism.

Multiscale simulations reveal key features of the proton-pumping mechanism in cytochrome c oxidase

Significance The long-studied proton-pumping mechanism in cytochrome c oxidase (CcO) continues to be a source of debate. This work provides a comprehensive computational characterization of the internal proton transport dynamics, while explicitly including Grotthuss shuttling, that lead to both pumping and catalysis. Focusing on the first steps of oxidation of the fully reduced enzyme, our results show that the transfer of the pumped and chemical protons are thermodynamically driven by electron transfer, and explain how proton back-leakage is avoided by large back-leak barriers and kinetic gating. This work also explicitly characterizes the coupling of proton transport with hydration changes in the hydrophobic cavity and D-channel, thus advancing our understanding of proton transport in biomolecules in general. Cytochrome c oxidase (CcO) reduces oxygen to water and uses the released free energy to pump protons across the membrane. We have used multiscale reactive molecular dynamics simulations to explicitly characterize (with free-energy profiles and calculated rates) the internal proton transport events that enable proton pumping during first steps of oxidation of the fully reduced enzyme. Our results show that proton transport from amino acid residue E286 to both the pump loading site (PLS) and to the binuclear center (BNC) are thermodynamically driven by electron transfer from heme a to the BNC, but that the former (i.e., pumping) is kinetically favored whereas the latter (i.e., transfer of the chemical proton) is rate-limiting. The calculated rates agree with experimental measurements. The backflow of the pumped proton from the PLS to E286 and from E286 to the inside of the membrane is prevented by large free-energy barriers for the backflow reactions. Proton transport from E286 to the PLS through the hydrophobic cavity and from D132 to E286 through the D-channel are found to be strongly coupled to dynamical hydration changes in the corresponding pathways and, importantly, vice versa.

Multiscale Simulations Reveal Key Aspects of the Proton Transport Mechanism in the ClC-ec1 Antiporter

Multiscale reactive molecular dynamics simulations are used to study proton transport through the central region of ClC-ec1, a widely studied ClC transporter that enables the stoichiometric exchange of 2 Cl(-) ions for 1 proton (H(+)). It has long been known that both Cl(-) and proton transport occur through partially congruent pathways, and that their exchange is strictly coupled. However, the nature of this coupling and the mechanism of antiporting remain topics of debate. Here multiscale simulations have been used to characterize proton transport between E203 (Glu(in)) and E148 (Glu(ex)), the internal and external intermediate proton binding sites, respectively. Free energy profiles are presented, explicitly accounting for the binding of Cl(-) along the central pathway, the dynamically coupled hydration changes of the central region, and conformational changes of Glu(in) and Glu(ex). We find that proton transport between Glu(in) and Glu(ex) is possible in both the presence and absence of Cl(-) in the central binding site, although it is facilitated by the anion presence. These results support the notion that the requisite coupling between Cl(-) and proton transport occurs elsewhere (e.g., during proton uptake or release). In addition, proton transport is explored in the E203K mutant, which maintains proton permeation despite the substitution of a basic residue for Glu(in). This collection of calculations provides for the first time, to our knowledge, a detailed picture of the proton transport mechanism in the central region of ClC-ec1 at a molecular level.

Computationally Efficient Multiscale Reactive Molecular Dynamics to Describe Amino Acid Deprotonation in Proteins

An important challenge in the simulation of biomolecular systems is a quantitative description of the protonation and deprotonation process of amino acid residues. Despite the seeming simplicity of adding or removing a positively charged hydrogen nucleus, simulating the actual protonation/deprotonation process is inherently difficult. It requires both the explicit treatment of the excess proton, including its charge defect delocalization and Grotthuss shuttling through inhomogeneous moieties (water and amino residues), and extensive sampling of coupled condensed phase motions. In a recent paper (J. Chem. Theory Comput.2014, 10, 2729−273725061442), a multiscale approach was developed to map high-level quantum mechanics/molecular mechanics (QM/MM) data into a multiscale reactive molecular dynamics (MS-RMD) model in order to describe amino acid deprotonation in bulk water. In this article, we extend the fitting approach (called FitRMD) to create MS-RMD models for ionizable amino acids within proteins. The resulting models are shown to faithfully reproduce the free energy profiles of the reference QM/MM Hamiltonian for PT inside an example protein, the ClC-ec1 H+/Cl– antiporter. Moreover, we show that the resulting MS-RMD models are computationally efficient enough to then characterize more complex 2-dimensional free energy surfaces due to slow degrees of freedom such as water hydration of internal protein cavities that can be inherently coupled to the excess proton charge translocation. The FitRMD method is thus shown to be an effective way to map ab initio level accuracy into a much more computationally efficient reactive MD method in order to explicitly simulate and quantitatively describe amino acid protonation/deprotonation in proteins.

The Origin of Coupled Chloride and Proton Transport in a Cl-/H+ Antiporter

The ClC family of transmembrane proteins functions throughout nature to control the transport of Cl– ions across biological membranes. ClC-ec1 from Escherichia coli is an antiporter, coupling the transport of Cl– and H+ ions in opposite directions and driven by the concentration gradients of the ions. Despite keen interest in this protein, the molecular mechanism of the Cl–/H+ coupling has not been fully elucidated. Here, we have used multiscale simulation to help identify the essential mechanism of the Cl–/H+ coupling. We find that the highest barrier for proton transport (PT) from the intra- to extracellular solution is attributable to a chemical reaction, the deprotonation of glutamic acid 148 (E148). This barrier is significantly reduced by the binding of Cl– in the “central” site (Cl–cen), which displaces E148 and thereby facilitates its deprotonation. Conversely, in the absence of Cl–cen E148 favors the “down” conformation, which results in a much higher cumulative rotation and deprotonation barrier that effectively blocks PT to the extracellular solution. Thus, the rotation of E148 plays a critical role in defining the Cl–/H+ coupling. As a control, we have also simulated PT in the ClC-ec1 E148A mutant to further understand the role of this residue. Replacement with a non-protonatable residue greatly increases the free energy barrier for PT from E203 to the extracellular solution, explaining the experimental result that PT in E148A is blocked whether or not Cl–cen is present. The results presented here suggest both how a chemical reaction can control the rate of PT and also how it can provide a mechanism for a coupling of the two ion transport processes.

Proton movement and coupling in the POT family of peptide transporters

Significance The uptake of nutrients from the environment is an essential process that is achieved in most cells through the use of secondary active transporters. The POT family of proton-coupled peptide transporters are one of the most diverse nutrient uptake systems, recognizing amino acids, peptides, nitrate, and seed-defense compounds. A long-standing question is how this family achieves such ligand diversity. A high-resolution crystal structure combined with multiscale molecular dynamics simulations demonstrate water molecules are able to shuttle protons using a Grotthuss-type mechanism, suggesting a separation of ligand recognition from proton movement. This would have clear advantages for a transporter family that must accommodate chemically diverse ligands while retaining the ability to couple transport to the proton electrochemical gradient. POT transporters represent an evolutionarily well-conserved family of proton-coupled transport systems in biology. An unusual feature of the family is their ability to couple the transport of chemically diverse ligands to an inwardly directed proton electrochemical gradient. For example, in mammals, fungi, and bacteria they are predominantly peptide transporters, whereas in plants the family has diverged to recognize nitrate, plant defense compounds, and hormones. Although recent structural and biochemical studies have identified conserved sites of proton binding, the mechanism through which transport is coupled to proton movement remains enigmatic. Here we show that different POT transporters operate through distinct proton-coupled mechanisms through changes in the extracellular gate. A high-resolution crystal structure reveals the presence of ordered water molecules within the peptide binding site. Multiscale molecular dynamics simulations confirm proton transport occurs through these waters via Grotthuss shuttling and reveal that proton binding to the extracellular side of the transporter facilitates a reorientation from an inward- to outward-facing state. Together these results demonstrate that within the POT family multiple mechanisms of proton coupling have likely evolved in conjunction with variation of the extracellular gate.