Studies of proton translocations in biological systems: simulating proton transport in carbonic anhydrase by EVB-based models

The Scope of the Applicability of Non-relativistic DFT Calculations of NMR Chemical Shifts in Pyridine-Metal Complexes for Applied Applications

Heavy metals are toxic, but it is impossible to stop using them. Considering the variety of molecular systems in which they can be present, the multicomponent nature and disorder of the structure of such systems, one of the most effective methods for studying them is NMR spectroscopy. This determines the need to calculate NMR chemical shifts for expected model systems. For elements beyond the third row of the periodic table, corrections for relativistic effects are necessary when calculating NMR parameters. Such corrections may be necessary even for light atoms due to the shielding effect of a neighboring heavy atom. This work examines the extent to which non-relativistic DFT calculations are able to reproduce experimental 15N and 113Cd NMR chemical shift tensors in pyridine-metal coordination complexes. It is shown that while for the calculation of 15N NMR chemical shift tensors there is no real need to consider relativistic corrections, for 113Cd, on the contrary, none of the tested calculation methods could reproduce the experimentally obtained tensor to any extent correctly.

Cooperative protein-solvent tuning of proton transfer energetics: carbonic anhydrase as a case study

We investigate the coupling between the proton transfer (PT) energetics and the protein-solvent dynamics using the intra-molecular PT in wild type (wt) human carbonic anhydrase II and its ten-fold faster mutant Y7F/N67Q as a test case. We calculate the energy variation upon PT, and from that we also calculate the PT reaction free energy, making use of a hybrid quantum mechanics/molecular dynamics approach. In agreement with the experimental data, we obtain that the reaction free energy is basically the same in the two systems. Yet, we show that the instantaneous PT energy is on average lower in the mutant possibly contributing to the faster PT rate. Analysis of the contribution to the PT energetics of the solvent and of each protein residue, also not in the vicinity of the active site, provides evidence for electrostatic tuning of the PT energy arising from the combined effect of the solvent and the protein environment. These findings open up a way to the more general task of the rational design of mutants with either enhanced or reduced PT rate.

Combined computational and experimental studies on cysteine-sulfadiazine adduct formation

The electrochemical characterization of sulfadiazine-cysteine (SD-CYS) adduct formation was performed in phosphate buffer (pH 7) on the basis of voltammetric current and peak potential measurements. Due to the association of cysteine with sulfadiazine, the reduction peak currents of mercuric and mercurous cysteine thiolates decreased and their peak potentials simultaneously shifted to less negative potentials. By using the current changes of mercurous cysteine thiolate, it was determined that cysteine and sulfadiazine are associated with a 1:1 stoichiometry with a conditional association constant of 1.99 ×104 M-1 . In addition to experimental studies, a computational approach was carried out to study the geometrical parameters, electron densities, and UV-Vis absorption spectra of sulfadiazine and SDCYS adduct in water. Calculated (B3LYP/6-311++G(d,p) level) and experimental UV-Vis absorption spectra of the compounds were found to be in good agreement in water. The computational study suggests that cysteine bound to the C(5) on the pyrimidine ring via SH-group nucleophilic attack. Computational results reveal that sulfadiazine and its derivatives effectively bind cysteine and may lead to new molecules/drugs to target cysteine.

On the control of the proton current in the voltage-gated proton channel Hv1

The nature of the action of voltage-activated proton transport proteins is a conundrum of great current interest. Here we approach this issue by exploring the action of Hv1, a voltage-gated proton channel found in different cells in humans and other organisms. Our study focuses on evaluating the free energy of transporting a proton through the channel, as well as the effect of the proton transfer through D112, in both the closed and open channel conformations. It is found that D112 allows a transported proton to bypass the electrostatic barrier of the open channel, while not being able to help in passing the barrier in the closed form. This reflects the change in position of the gating arginine residues relative to D112, upon voltage activation. Significantly, the effect of D112 accounts for the observed trend in selectivity by overcoming the electrostatic barrier at its highest point. Thus, the calculations provide a structure/function correlation for the Hv1 system. The present work also clarifies that the action of Hv1 is not controlled by a Grotthuss mechanism but, as is always the case, by the protein electrostatic potential at the rate-limiting barriers.

Hydronium Ions Accompanying Buried Acidic Residues Lead to High Apparent Dielectric Constants in the Interior of Proteins

Internal ionizable groups are known to play important roles in protein functions. A mystery that has attracted decades of extensive experimental and theoretical studies is the apparent dielectric constants experienced by buried ionizable groups, which are much higher than values expected for protein interiors. Many interpretations have been proposed, such as water penetration, conformational relaxation, local unfolding, protein intrinsic backbone fluctuations, etc. However, these interpretations conflict with many experimental observations. The virtual mixture of multiple states (VMMS) simulation method developed in our lab provides a direct approach for studying the equilibrium of multiple chemical states and can monitor p K_a values along simulation trajectories. Through VMMS simulations of staphylococcal nuclease (SNase) variants with internal Asp or Glu residues, we discovered that cations were attracted to buried deprotonated acidic groups and the presence of the nearby cations were essential to reproduce experimentally measured p K_a values. This finding, combined with structural analysis and validation simulations, suggests that the proton released from a deprotonation process stays near the deprotonated group inside proteins, possibly in the form of a hydronium ion. The existence of a proton near a buried charge has many implications in our understanding of protein functions.

Proton Wire Dynamics in the Green Fluorescent Protein

Inside proteins, protons move on proton wires (PWs). Starting from the highest resolution X-ray structure available, we conduct a 306 ns molecular dynamics simulation of the (A-state) wild-type (wt) green fluorescent protein (GFP) to study how its PWs change with time. We find that the PW from the chromophore via Ser205 to Glu222, observed in all X-ray structures, undergoes rapid water molecule insertion between Ser205 and Glu222. Sometimes, an alternate Ser205-bypassing PW exists. Side chain rotations of Thr203 and Ser205 play an important role in shaping the PW network in the chromophore region. Thr203, with its bulkier side chain, exhibits slower transitions between its three rotameric states. Ser205 experiences more frequent rotations, slowing down when the Thr203 methyl group is close by. The combined states of both residues affect the PW probabilities. A random walk search for PWs from the chromophore reveals several exit points to the bulk, one being a direct water wire (WW) from the chromophore to the bulk. A longer WW connects the "bottom" of the GFP barrel with a "water pool" (WP1) situated below Glu222. These two WWs were not observed in X-ray structures of wt-GFP, but their analogues have been reported in related fluorescent proteins. Surprisingly, the high-resolution X-ray structure utilized herein shows that Glu222 is protonated at low temperatures. At higher temperatures, we suggest ion pairing between anionic Glu222 and a proton hosted in WP1. Upon photoexcitation, these two recombine, while a second proton dissociates from the chromophore and either exits the protein using the short WW or migrates along the GFP-barrel axis on the long WW. This mechanism reconciles the conflicting experimental and theoretical data on proton motion within GFP.

Coupling Protein Dynamics with Proton Transport in Human Carbonic Anhydrase II

The role of protein dynamics in enzyme catalysis is one of the most highly debated topics in enzymology. The main controversy centers around what may be defined as functionally significant conformational fluctuations and how, if at all, these fluctuations couple to enzyme catalyzed events. To shed light on this debate, the conformational dynamics along the transition path surmounting the highest free energy barrier have been herein investigated for the rate limiting proton transport event in human carbonic anhydrase (HCA) II. Special attention has been placed on whether the motion of an excess proton is correlated with fluctuations in the surrounding protein and solvent matrix, which may be rare on the picosecond and subpicosecond time scales of molecular motions. It is found that several active site residues, which do not directly participate in the proton transport event, have a significant impact on the dynamics of the excess proton. These secondary participants are shown to strongly influence the active site environment, resulting in the creation of water clusters that are conducive to fast, moderately slow, or slow proton transport events. The identification and characterization of these secondary participants illuminates the role of protein dynamics in the catalytic efficiency of HCA II.

Wide-dynamic-range kinetic investigations of deep proton tunnelling in proteins

Directional proton transport along 'wires' that feed biochemical reactions in proteins is poorly understood. Amino-acid residues with high pKa are seldom considered as active transport elements in such wires because of their large classical barrier for proton dissociation. Here, we use the light-triggered proton wire of the green fluorescent protein to study its ground-electronic-state proton-transport kinetics, revealing a large temperature-dependent kinetic isotope effect. We show that 'deep' proton tunnelling between hydrogen-bonded oxygen atoms with a typical donor-acceptor distance of 2.7-2.8 Å fully accounts for the rates at all temperatures, including the unexpectedly large value (2.5 × 10(9) s(-1)) found at room temperature. The rate-limiting step in green fluorescent protein is assigned to tunnelling of the ionization-resistant serine hydroxyl proton. This suggests how high-pKa residues within a proton wire can act as a 'tunnel diode' to kinetically trap protons and control the direction of proton flow.

Simulating the function of sodium/proton antiporters

The molecular basis of the function of transporters is a problem of significant importance, and the emerging structural information has not yet been converted to a full understanding of the corresponding function. This work explores the molecular origin of the function of the bacterial Na+/H+ antiporter NhaA by evaluating the energetics of the Na+ and H+ movement and then using the resulting landscape in Monte Carlo simulations that examine two transport models and explore which model can reproduce the relevant experimental results. The simulations reproduce the observed transport features by a relatively simple model that relates the protein structure to its transporting function. Focusing on the two key aspartic acid residues of NhaA, D163 and D164, shows that the fully charged state acts as an Na+ trap and that the fully protonated one poses an energetic barrier that blocks the transport of Na+. By alternating between the former and latter states, mediated by the partially protonated protein, protons, and Na+ can be exchanged across the membrane at 2:1 stoichiometry. Our study provides a numerical validation of the need of large conformational changes for effective transport. Furthermore, we also yield a reasonable explanation for the observation that some mammalian transporters have 1:1 stoichiometry. The present coarse-grained model can provide a general way for exploring the function of transporters on a molecular level.

NMR studies of active-site properties of human carbonic anhydrase II by using (15) N-labeled 4-methylimidazole as a local probe and histidine hydrogen-bond correlations

By using a combination of liquid and solid-state NMR spectroscopy, (15) N-labeled 4-methylimidazole (4-MI) as a local probe of the environment has been studied: 1) in the polar, wet Freon CDF3 /CDF2 Cl down to 130 K, 2) in water at pH 12, and 3) in solid samples of the mutant H64A of human carbonic anhydrase II (HCA II). In the latter, the active-site His64 residue is replaced by alanine; the catalytic activity is, however, rescued by the presence of 4-MI. For the Freon solution, it is demonstrated that addition of water molecules not only catalyzes proton tautomerism but also lifts its quasidegeneracy. The possible hydrogen-bond clusters formed and the mechanism of the tautomerism are discussed. Information about the imidazole hydrogen-bond geometries is obtained by establishing a correlation between published (1) H and (15) N chemical shifts of the imidazole rings of histidines in proteins. This correlation is useful to distinguish histidines embedded in the interior of proteins and those at the surface, embedded in water. Moreover, evidence is obtained that the hydrogen-bond geometries of His64 in the active site of HCA II and of 4-MI in H64A HCA II are similar. Finally, the degeneracy of the rapid tautomerism of the neutral imidazole ring His64 reported by Shimahara et al. (J. Biol. Chem.- 2007, 282, 9646) can be explained with a wet, polar, nonaqueous active-site conformation in the inward conformation, similar to the properties of 4-MI in the Freon solution. The biological implications for the enzyme mechanism are discussed.

Time-averaged distributions of solute and solvent motions: exploring proton wires of GFP and PfM2DH

Proton translocation pathways of selected variants of the green fluorescent protein (GFP) and Pseudomonas fluorescens mannitol 2-dehydrogenase (PfM2DH) were investigated via an explicit solvent molecular dynamics-based analysis protocol that allows for direct quantitative relationship between a crystal structure and its time-averaged solute-solvent structure obtained from simulation. Our study of GFP is in good agreement with previous research suggesting that the proton released from the chromophore upon photoexcitation can diffuse through an extended internal hydrogen bonding network that allows for the proton to exit to bulk or be recaptured by the anionic chromophore. Conversely for PfM2DH, we identified the most probable ionization states of key residues along the proton escape channel from the catalytic site to bulk solvent, wherein the solute and high-density solvent crystal structures of binary and ternary complexes were properly reproduced. Furthermore, we proposed a plausible mechanism for this proton translocation process that is consistent with the state-dependent structural shifts observed in our analysis. The time-averaged structures generated from our analyses facilitate validation of MD simulation results and provide a comprehensive profile of the dynamic all-occupancy solvation network within and around a flexible solute, from which detailed hydrogen-bonding networks can be inferred. In this way, potential drawbacks arising from the elucidation of these networks by examination of static crystal structures or via alternate rigid-protein solvation analysis procedures can be overcome. Complementary studies aimed at the effective use of our methodology for alternate implementations (e.g., ligand design) are currently underway.

Donor-Bridge-Acceptor Proton Transfer in Aqueous Solution

We use ab initio molecular dynamics to study proton transfer in a donor-bridge-acceptor system in which the bridge is a single water molecule and the entire system is embedded in aqueous solution. The results, based on a large number of proton transfer trajectories, demonstrate that the dominant charge-transfer pathway is a subpicosecond "through bridge" event in which the bridge adopts an Eigen-like (hydronium) structure. We also identify another state in which the bridge forms a Zundel-like configuration with the acceptor that appears to be a dead end for the charge transfer. The reaction coordinate is inherently multidimensional and, as we demonstrate, cannot be given in terms of either local structural parameters of the donor-bridge-acceptor system or local solvent coordination numbers.

Introducing titratable water to all-atom molecular dynamics at constant pH

Recent development of titratable coions has paved the way for realizing all-atom molecular dynamics at constant pH. To further improve physical realism, here we describe a technique in which proton titration of the solute is directly coupled to the interconversion between water and hydroxide or hydronium. We test the new method in replica-exchange continuous constant pH molecular dynamics simulations of three proteins, HP36, BBL, and HEWL. The calculated pKa values based on 10-ns sampling per replica have the average absolute and root-mean-square errors of 0.7 and 0.9 pH units, respectively. Introducing titratable water in molecular dynamics offers a means to model proton exchange between solute and solvent, thus opening a door to gaining new insights into the intricate details of biological phenomena involving proton translocation.

Catalytic mechanism of α-class carbonic anhydrases: CO2 hydration and proton transfer

The carbonic anhydrases (CAs; EC 4.2.1.1) are a family of metalloenzymes that catalyze the reversible hydration of carbon dioxide (CO2) and dehydration of bicarbonate (HCO3 (-)) in a two-step ping-pong mechanism: [Formula: see text] CAs are ubiquitous enzymes and are categorized into five distinct classes (α, β, γ, δ and ζ). The α-class is found primarily in vertebrates (and the only class of CA in mammals), β is observed in higher plants and some prokaryotes, γ is present only in archaebacteria whereas the δ and ζ classes have only been observed in diatoms.The focus of this chapter is on α-CAs as the structure-function relationship is best understood for this class, in particular for humans. The reader is referred to other reviews for an overview of the structure and catalytic mechanism of the other CA classes. The overall catalytic site structure and geometry of α-CAs are described in the first section of this chapter followed by the kinetic studies, binding of CO2, and the proton shuttle network.

Moderately strong phenols dissociate by forming an ion-pair kinetic intermediate

We show computational evidence that ground-state moderately strong hydroxyarenes (Ar-OH, pKa ∼ 0) dissociate by forming an ion-pair intermediate that lives for 3-5 ps. The concentration of this intermediate is approximately 2 times smaller than that of the un-ionized acid at pH ∼ 0.6 and is characterized by average C-O bond lengths (1.30 Å) that are intermediate between those of un-ionized (1.29 Å) and fully dissociated (1.34 Å) species. During the lifetime of the ion-pair intermediate the excess proton fluctuates between the oxygen atom of the phenolic moiety and those of water molecules in the first and second solvation shells on a subpicosecond time scale (∼100-300 fs).

Adenosine triphosphate hydrolysis mechanism in kinesin studied by combined quantum-mechanical/molecular-mechanical metadynamics simulations

Kinesin is a molecular motor that hydrolyzes adenosine triphosphate (ATP) and moves along microtubules against load. While motility and atomic structures have been well-characterized for various members of the kinesin family, not much is known about ATP hydrolysis inside the active site. Here, we study ATP hydrolysis mechanisms in the kinesin-5 protein Eg5 by using combined quantum mechanics/molecular mechanics metadynamics simulations. Approximately 200 atoms at the catalytic site are treated by a dispersion-corrected density functional and, in total, 13 metadynamics simulations are performed with their cumulative time reaching ~0.7 ns. Using the converged runs, we compute free energy surfaces and obtain a few hydrolysis pathways. The pathway with the lowest free energy barrier involves a two-water chain and is initiated by the Pγ-Oβ dissociation concerted with approach of the lytic water to PγO3-. This immediately induces a proton transfer from the lytic water to another water, which then gives a proton to the conserved Glu270. Later, the proton is transferred back from Glu270 to HPO(4)2- via another hydrogen-bonded chain. We find that the reaction is favorable when the salt bridge between Glu270 in switch II and Arg234 in switch I is transiently broken, which facilitates the ability of Glu270 to accept a proton. When ATP is placed in the ADP-bound conformation of Eg5, the ATP-Mg moiety is surrounded by many water molecules and Thr107 blocks the water chain, which together make the hydrolysis reaction less favorable. The observed two-water chain mechanisms are rather similar to those suggested in two other motors, myosin and F1-ATPase, raising the possibility of a common mechanism.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Carbonic anhydrase binding site parameterization in OPLS-AA force field

The parameterization of carbonic anhydrase binding site in OPLS-AA force field was performed using quantum chemistry calculations. Both OH2 and OH(-) forms of the binding site were considered, showing important differences in terms of atomic partial charges. Three different parameterization protocols were used, and the results obtained highlighted the importance of including an extended binding site in the charge calculation. The force field parameters were subsequently validated using standard molecular dynamics simulations. The results presented in this work should greatly facilitate the use of molecular dynamics simulations for studying the carbonic anhydrase, and more generally, the metallo-enzymes.

Dynamic mechanism of proton transfer in mannitol 2-dehydrogenase from Pseudomonas fluorescens: mobile GLU292 controls proton relay through a water channel that connects the active site with bulk solvent

The active site of mannitol 2-dehydrogenase from Pseudomonas fluorescens (PfM2DH) is connected with bulk solvent through a narrow protein channel that shows structural resemblance to proton channels utilized by redox-driven proton pumps. A key element of the PfM2DH channel is the "mobile" Glu(292), which was seen crystallographically to adopt distinct positions up and down the channel. It was suggested that the "down → up" conformational change of Glu(292) could play a proton relay function in enzymatic catalysis, through direct proton shuttling by the Glu or because the channel is opened for water molecules forming a chain along which the protons flow. We report evidence from site-directed mutagenesis (Glu(292) → Ala) substantiated by data from molecular dynamics simulations that support a role for Glu(292) as a gate in a water chain (von Grotthuss-type) mechanism of proton translocation. Occupancy of the up and down position of Glu(292) is influenced by the bonding and charge state of the catalytic acid base Lys(295), suggesting that channel opening/closing motions of the Glu are synchronized to the reaction progress. Removal of gatekeeper control in the E292A mutant resulted in a selective, up to 120-fold slowing down of microscopic steps immediately preceding catalytic oxidation of mannitol, consistent with the notion that formation of the productive enzyme-NAD(+)-mannitol complex is promoted by a corresponding position change of Glu(292), which at physiological pH is associated with obligatory deprotonation of Lys(295) to solvent. These results underscore the important role of conformational dynamics in the proton transfer steps of alcohol dehydrogenase catalysis.

Simulating electrostatic energies in proteins: perspectives and some recent studies of pKas, redox, and other crucial functional properties

Electrostatic energies provide what is arguably the most effective tool for structure-function correlation of biological molecules. Here, we provide an overview of the current state-of-the-art simulations of electrostatic energies in macromolecules, emphasizing the microscopic perspective but also relating it to macroscopic approaches. We comment on the convergence issue and other problems of the microscopic models and the ways of keeping the microscopic physics while moving to semi-macroscopic directions. We discuss the nature of the protein dielectric "constants" reiterating our long-standing point that the dielectric "constants" in semi-macroscopic models depend on the definition and the specific treatment. The advances and the challenges in the field are illustrated considering different functional properties including pK(a)'s, redox potentials, ion and proton channels, enzyme catalysis, ligand binding, and protein stability. We emphasize the microscopic overcharging approach for studying pK(a) 's of internal groups in proteins and give a demonstration of power of this approach. We also emphasize recent advances in coarse grained models with a physically based electrostatic treatment and provide some examples including further directions in treating voltage activated ion channels.

Prechemistry versus preorganization in DNA replication fidelity

The molecular origin of nucleotide insertion catalysis and fidelity of DNA polymerases is explored by means of computational simulations. Special attention is paid to the examination of the validity of proposals that invoke prechemistry effects, checkpoints concepts, and dynamical effects. The simulations reproduce the observed fidelity in Pol β, starting with the relevant observed X-ray structures of the complex with the right (R) and wrong (W) nucleotides. The generation of free energy surfaces for the R and W systems also allowed us to analyze different proposals about the origin of the fidelity and to reach several important conclusions. It is found that the potential of mean force (PMF) obtained by proper sampling does not support QM/MM-based proposals of a large barrier before the prechemistry state. Furthermore, examination of dynamical proposals by the renormalization approach indicates that the motions from open to close configurations do not contribute to catalysis or fidelity. Finally we discuss and analyze the induced fit concept and show that, despite its importance, it does not explain fidelity. That is, the fidelity is apparently due to the change in the preorganization of the chemical site, as a result of the relaxation of the binding site upon binding of the incorrect nucleotide. Finally and importantly, since the issue is the barrier associated with the enzyme-substrate (ES)/DNA complex at the chemical transition state and not the path to this complex formation (unless this path involves rate determining steps), it is also not useful to invoke checkpoints while discussing fidelity.

Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems

Recent years have witnessed an explosion in computational power, leading to attempts to model ever more complex systems. Nevertheless, there remain cases for which the use of brute-force computer simulations is clearly not the solution. In such cases, great benefit can be obtained from the use of physically sound simplifications. The introduction of such coarse graining can be traced back to the early usage of a simplified model in studies of proteins. Since then, the field has progressed tremendously. In this review, we cover both key developments in the field and potential future directions. Additionally, particular emphasis is given to two general approaches, namely the renormalization and reference potential approaches, which allow one to move back and forth between the coarse-grained (CG) and full models, as these approaches provide the foundation for CG modeling of complex systems.

Intrinsic proton-donating power of zinc-bound water in a carbonic anhydrase active site model estimated by NMR

Using liquid-state NMR spectroscopy we have estimated the proton-donating ability of Zn-bound water in organometallic complexes designed as models for the active site of the metalloenzyme carbonic anhydrase (CA). This ability is important for the understanding of the enzyme reaction mechanism. The desired information was obtained by (1)H and (15)N NMR at 180 K of solutions of [Tp(Ph,Me)ZnOH] [1, Tp(Ph,Me) = tris(2-methyl-4-phenylpyrazolyl)hydroborate] in CD(2)Cl(2), in the absence and presence of the proton donors (C(6)F(5))(3)BOH(2) [aquatris(pentafluorophenyl)boron] and Col-H(+) (2,4,6-trimethylpyridine-H(+)). Col-H(+) forms a strong OHN hydrogen bond with 1, where the proton is located closer to nitrogen than to oxygen. (C(6)F(5))(3)BOH(2), which exhibits a pK(a) value of 1 in water, also forms a strong hydrogen bond with 1, where the proton is shifted slightly across the hydrogen-bond center toward the Zn-bound oxygen. Finally, a complex between Col and (C(6)F(5))(3)BOH(2) was identified, exhibiting a zwitterionic OHN hydrogen bond, where H is entirely shifted to nitrogen. The comparison with complexes of Col with carboxylic acids studied previously suggests that, surprisingly, the Zn-bound water exhibits in an aprotic environment a similar proton-donating ability as a carboxylic acid characterized in water by a pK(a) of 2.2 ± 0.6. This value is much smaller than the value of 9 found for [Zn(OH(2))(6)](2+) in water and those between 5 and 8 reported for different forms of CA. Implications for the biological function of CA are discussed.

Multiscale modeling of biological functions

Recent years have witnessed a tremendous explosion in computational power, which in turn has resulted in great progress in the complexity of the biological and chemical problems that can be addressed by means of all-atom simulations. Despite this, however, our computational time is not infinite, and in fact many of the key problems of the field were resolved long before the existence of the current levels of computational power. This review will start by presenting a brief historical overview of the use of multiscale simulations in biology, and then present some key developments in the field, highlighting several cases where the use of a physically sound simplification is clearly superior to a brute-force approach. Finally, some potential future directions will be discussed.

Chemical rescue of enzymes: proton transfer in mutants of human carbonic anhydrase II

In human carbonic anhydrase II (HCA II), the mutation of position 64 from histidine to alanine (H64A) disrupts the rate limiting proton transfer (PT) event, resulting in a reduction of the catalytic activity of the enzyme as compared to the wild-type. Potential of mean force (PMF) calculations utilizing the multistate empirical valence bond (MS-EVB) methodology for H64A HCA II yields a PT free energy barrier significantly higher than that found in the wild-type enzyme. This high barrier, determined in the absence of exogenous buffer and assuming no additional ionizable residues in the PT pathway, indicates the likelihood of alternate enzyme pathways that utilize either ionizable enzyme residues (self-rescue) and/or exogenous buffers (chemical rescue). It has been shown experimentally that the catalytic activity of H64A HCA II can be chemically rescued to near wild-type levels by the addition of the exogenous buffer 4-methylimidazole (4MI). Crystallographic studies have identified two 4MI binding sites, yet site-specific mutations intended to disrupt 4MI binding have demonstrated these sites to be nonproductive. In the present work, MS-EVB simulations show that binding of 4MI near Thr199 in the H64A HCA II mutant, a binding site determined by NMR spectroscopy, results in a viable chemical rescue pathway. Additional viable rescue pathways are also identified where 4MI acts as a proton transport intermediary from the active site to ionizable residues on the rim of the active site, revealing a probable mode of action for the chemical rescue pathway.

Kinetic and crystallographic studies of the role of tyrosine 7 in the active site of human carbonic anhydrase II

The rate limiting step in catalysis of bicarbonate dehydration by human carbonic anhydrase II (HCA II) is an intramolecular proton transfer from His64 to the zinc-bound hydroxide. We have examined the role of Tyr7 using site-specific mutagenesis and measuring catalysis by the ¹⁸O exchange method using membrane inlet mass spectrometry. The side chain of Tyr7 in HCA II extends into the active-site cavity about 7 Å from the catalytic zinc atom. Replacement of Tyr7 with eight other amino acids had no effect on the interconversion of bicarbonate and CO₂, but in some cases caused enhancements in the rate constant of proton transfer by nearly 10-fold. The variant Y7I HCA II enhanced intramolecular proton transfer approximately twofold; its structure was determined by X-ray crystallography at 1.5 Å resolution. No changes were observed in the ordered solvent structure in the active-site cavity or in the conformation of the side chain of the proton shuttle His64. However, the first 11 residues of the amino-terminal chain in Y7I HCA II assumed an alternate conformation compared with the wild type. Differential scanning calorimetry showed variants at position 7 had a melting temperature approximately 8 °C lower than that of the wild type.

A computational study of ultrafast acid dissociation and acid-base neutralization reactions. I. The model

Ultrafast, time-resolved investigations of acid-base neutralization reactions have recently been performed using systems containing the photoacid 8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt (HPTS) and various Bronsted bases. Two conflicting neutralization mechanisms have been formulated by Mohammed et al. [Science 310, 83 (2005)] and Siwick et al. [J. Am. Chem. Soc. 129, 13412 (2007)] for the same acid-base system. Herein an ab initio molecular dynamics based computational model is formulated, which is able to investigate the validity of the proposed mechanisms in the general context of ground-state acid-base neutralization reactions. Our approach consists of using 2,4,6-tricyanophenol (exp. pKa congruent with 1) as a model for excited-state HPTS( *) (pKa congruent with 1.4) and carboxylate ions for the accepting base. We employ our recently proposed dipole-field/quantum mechanics (QM) treatment [P. Maurer and R. Iftimie, J. Chem. Phys. 132, 074112 (2010)] of the proton donor and acceptor molecules. This approach allows one to tune the free energy of neutralization to any desired value as well as model initial nonequilibrium hydration effects caused by a sudden increase in acidity, making it possible to achieve a more realistic comparison with experimental data than could be obtained via a full-QM treatment of the entire system. It is demonstrated that the dipole-field/QM model reproduces correctly key properties of the 2,4,6-tricyanophenol acid molecule including gas-phase proton dissociation energies and dipole moments, and condensed-phase hydration structure and pKa values.

At the dawn of the 21st century: Is dynamics the missing link for understanding enzyme catalysis?

Enzymes play a key role in almost all biological processes, accelerating a variety of metabolic reactions as well as controlling energy transduction, the transcription, and translation of genetic information, and signaling. They possess the remarkable capacity to accelerate reactions by many orders of magnitude compared to their uncatalyzed counterparts, making feasible crucial processes that would otherwise not occur on biologically relevant timescales. Thus, there is broad interest in understanding the catalytic power of enzymes on a molecular level. Several proposals have been put forward to try to explain this phenomenon, and one that has rapidly gained momentum in recent years is the idea that enzyme dynamics somehow contributes to catalysis. This review examines the dynamical proposal in a critical way, considering basically all reasonable definitions, including (but not limited to) such proposed effects as "coupling between conformational and chemical motions," "landscape searches" and "entropy funnels." It is shown that none of these proposed effects have been experimentally demonstrated to contribute to catalysis, nor are they supported by consistent theoretical studies. On the other hand, it is clarified that careful simulation studies have excluded most (if not all) dynamical proposals. This review places significant emphasis on clarifying the role of logical definitions of different catalytic proposals, and on the need for a clear formulation in terms of the assumed potential surface and reaction coordinate. Finally, it is pointed out that electrostatic preorganization actually accounts for the observed catalytic effects of enzymes, through the corresponding changes in the activation free energies.

The EVB as a quantitative tool for formulating simulations and analyzing biological and chemical reactions

Recent years have seen dramatic improvements in computer power, allowing ever more challenging problems to be approached. In light of this, it is imperative to have a quantitative model for examining chemical reactivity, both in the condensed phase and in solution, as well as to accurately quantify physical organic chemistry (particularly as experimental approaches can often be inconclusive). Similarly, computational approaches allow for great progress in studying enzyme catalysis, as they allow for the separation of the relevant energy contributions to catalysis. Due to the complexity of the problems that need addressing, there is a need for an approach that can combine reliability with an ability to capture complex systems in order to resolve long-standing controversies in a unique way. Herein, we will demonstrate that the empirical valence bond (EVB) approach provides a powerful way to connect the classical concepts of physical organic chemistry to the actual energies of enzymatic reactions by means of computation. Additionally, we will discuss the proliferation of this approach, as well as attempts to capture its basic chemistry and repackage it under different names. We believe that the EVB approach is the most powerful tool that is currently available for studies of chemical processes in the condensed phase in general and enzymes in particular, particularly when trying to explore the different proposals about the origin of the catalytic power of enzymes.

Role of protein motions on proton transfer pathways in human carbonic anhydrase II

We report here a theoretical study on the formation of long-range proton transfer pathways in proteins due to side chain conformational fluctuations of amino acid residues and reorganization of interior hydration positions. The proton transfer pathways in such systems may be modeled as fluctuating hydrogen-bonded networks with both short- and long-lived connections between the networked nodes, the latter being formed by polar protein atoms and water molecules. It is known that these fluctuations may extend over several decades of time ranging from a few femtoseconds to a few milliseconds. We have shown in this article how the use of a variety of theoretical methods may be utilized to detect a generic set of pathways and assess the feasibility of forming one or more transient connections. We demonstrate the application of these methods to the enzyme human carbonic anhydrase II and its mutants. Our results reveal several alternative pathways in addition to the one mediated by His-64. We also probe at length the mechanism of key conformational fluctuations contributing to the formation of the detected pathways.

Proton transport in carbonic anhydrase: Insights from molecular simulation

This article reviews the insights gained from molecular simulations of human carbonic anhydrase II (HCA II) utilizing non-reactive and reactive force fields. The simulations with a reactive force field explore protein transfer and transport via Grotthuss shuttling, while the non-reactive simulations probe the larger conformational dynamics that underpin the various contributions to the rate-limiting proton transfer event. Specific attention is given to the orientational stability of the His64 group and the characteristics of the active site water cluster, in an effort to determine both of their impact on the maximal catalytic rate. The explicit proton transfer and transport events are described by the multistate empirical valence bond (MS-EVB) method, as are alternative pathways for the excess proton charge defect to enter/leave the active site. The simulation results are interpreted in light of experimental results on the wild-type enzyme and various site-specific mutations of HCA II in order to better elucidate the key factors that contribute to its exceptional efficiency.

Proton transfer in catalysis and the role of proton shuttles in carbonic anhydrase

The undisputed role of His64 in proton transfer during catalysis by carbonic anhydrases in the alpha class has raised questions concerning the details of its mechanism. The highly conserved residues Tyr7, Asn62, and Asn67 in the active-site cavity function to fine tune the properties of proton transfer by human carbonic anhydrase II (HCA II). For example, hydrophobic residues at these positions favor an inward orientation of His64 and a low pK(a) for its imidazole side chain. It appears that the predominant manner in which this fine tuning is achieved in rate constants for proton transfer is through the difference in pK(a) between His64 and the zinc-bound solvent molecule. Other properties of the active-site cavity, such as inward and outward conformers of His64, appear associated with the change in DeltapK(a); however, there is no strong evidence to date that the inward and outward orientations of His64 are in themselves requirements for facile proton transfer in carbonic anhydrase.

Simulating the electrostatic guidance of the vectorial translocations in hexameric helicases and translocases

The molecular origin of the action of helicases is explored, starting with a model built based on the different X-ray structures of the large tumor antigen (LTag) hexameric helicase and a simplified model containing the ionized phosphate backbones of a single-strand DNA. The coupling between the protein structural changes and the translocation process is quantified using an effective electrostatic free-energy surface for the protein/DNA complex. This surface is then used in Langevin dynamics simulations of the time dependence of the translocation process. Remarkably, the simulated motion along the free-energy surface results in a vectorial translocation of the DNA, consistent with the biological process. The electrostatic energy of the system appears to reproduce the directionality of this process. Thus, we are able to provide a consistent structure-based molecular description of the energetic and dynamics of the translocation process. This analysis may have general implications for relating structural models to translocation directionality in helicases and other DNA translocases.

Free energy for the permeation of Na(+) and Cl(-) ions and their ion-pair through a zwitterionic dimyristoyl phosphatidylcholine lipid bilayer by umbrella integration with harmonic fourier beads

Understanding the mechanism of ion permeation across lipid bilayers is key to controlling osmotic pressure and developing new ways of delivering charged, drug-like molecules inside cells. Recent reports suggest ion-pairing as the mechanism to lower the free energy barrier for the ion permeation in disagreement with predictions from the simple electrostatic models. In this paper we quantify the effect of ion-pairing or charge quenching on the permeation of Na(+) and Cl(-) ions across DMPC lipid bilayer by computing the corresponding potentials of mean force (PMFs) using fully atomistic molecular dynamics simulations. We find that the free energy barrier to permeation reduces in the order Na(+)-Cl(-) ion-pair (27.6 kcal/mol) > Cl(-) (23.6 kcal/mol) > Na(+) (21.9 kcal/mol). Furthermore, with the help of these PMFs we derive the change in the binding free energy between the Na(+) and Cl(-) with respect to that in water as a function of the bilayer permeation depth. Despite the fact that the bilayer boosts the Na(+)-Cl(-) ion binding free energy by as high as 17.9 kcal/mol near its center, ion-pairing between such hydrophilic ions as Na(+) and Cl(-) does not assist their permeation. However, based on a simple thermodynamic cycle, we suggest that ion-pairing between ions of opposite charge and solvent philicity could enhance ion permeation. Comparison of the computed permeation barriers for Na(+) and Cl(-) ions with available experimental data supports this notion. This work establishes general computational methodology to address ion-pairing in fluid anisotropic media and details the ion permeation mechanism on atomic level.

Role of hydrophilic residues in proton transfer during catalysis by human carbonic anhydrase II

Catalysis by the zinc metalloenzyme human carbonic anhydrase II (HCA II) is limited in maximal velocity by proton transfer between His64 and the zinc-bound solvent molecule. Asn62 extends into the active site cavity of HCA II adjacent to His64 and has been shown to be one of several hydrophilic residues participating in a hydrogen-bonded solvent network within the active site. We compared several site-specific mutants of HCA II with replacements at position 62 (Ala, Val, Leu, Thr, and Asp). The efficiency of catalysis in the hydration of CO 2 for the resulting mutants has been characterized by (18)O exchange, and the structures of the mutants have been determined by X-ray crystallography to 1.5-1.7 A resolution. Each of these mutants maintained the ordered water structure observed by X-ray crystallography in the active site cavity of wild-type HCA II; hence, this water structure was not a variable in comparing with wild type the activities of mutants at residue 62. Crystal structures of wild-type and N62T HCA II showed both an inward and outward orientation of the side chain of His64; however, other mutants in this study showed predominantly inward (N62A, N62V, N62L) or predominantly outward (N62D) orientations of His64. A significant role of Asn62 in HCA II is to permit two conformations of the side chain of His64, the inward and outward, that contributes to maximal efficiency of proton transfer between the active site and solution. The site-specific mutant N62D had a mainly outward orientation of His64, yet the difference in p K a between the proton donor His64 and zinc-bound hydroxide was near zero, as in wild-type HCA II. The rate of proton transfer in catalysis by N62D HCA II was 5% that of wild type, showing that His64 mainly in the outward orientation is associated with inefficient proton transfer compared with His64 in wild type which shows both inward and outward orientations. These results emphasize the roles of the residues of the hydrophilic side of the active site cavity in maintaining efficient catalysis by carbonic anhydrase.

Simulating the proton transfer in gramicidin A by a sequential dynamical Monte Carlo method

The large interest in long-range proton transfer in biomolecules is triggered by its importance for many biochemical processes such as biological energy transduction and drug detoxification. Since long-range proton transfer occurs on a microsecond time scale, simulating this process on a molecular level is still a challenging task and not possible with standard simulation methods. In general, the dynamics of a reactive system can be described by a master equation. A natural way to describe long-range charge transfer in biomolecules is to decompose the process into elementary steps which are transitions between microstates. Each microstate has a defined protonation pattern. Although such a master equation can in principle be solved analytically, it is often too demanding to solve this equation because of the large number of microstates. In this paper, we describe a new method which solves the master equation by a sequential dynamical Monte Carlo algorithm. Starting from one microstate, the evolution of the system is simulated as a stochastic process. The energetic parameters required for these simulations are determined by continuum electrostatic calculations. We apply this method to simulate the proton transfer through gramicidin A, a transmembrane proton channel, in dependence on the applied membrane potential and the pH value of the solution. As elementary steps in our reaction, we consider proton uptake and release, proton transfer along a hydrogen bond, and rotations of water molecules that constitute a proton wire through the channel. A simulation of 8 mus length took about 5 min on an Intel Pentium 4 CPU with 3.2 GHz. We obtained good agreement with experimental data for the proton flux through gramicidin A over a wide range of pH values and membrane potentials. We find that proton desolvation as well as water rotations are equally important for the proton transfer through gramicidin A at physiological membrane potentials. Our method allows to simulate long-range charge transfer in biological systems at time scales, which are not accessible by other methods.

A theoretical study on the detection of proton transfer pathways in some mutants of human carbonic anhydrase II

Structural and kinetic studies of mutants can give much insight into the function of an enzyme. We report the detection of possible proton transfer pathways into the active site of a number of mutants of the enzyme human carbonic anhydrase II (HCA II). Using a recently developed method of path search in the protein conformational space, we identify hydrogen-bonded networks (or proton paths) that can dynamically connect the protein surface to the active site through fluctuations in protein structure and hydration. The feasibility of establishing such dynamical connectivities is assessed by computing the change in free energy of conformational fluctuations and compared to those identified earlier in the wild type enzyme. It is found that the point mutation facilitates or suppresses one or more of the alternative pathways. Our results allow the use of a generic set of pathways to correlate qualitatively the residual activity in the mutants to the molecular mechanism of proton transfer in the absence of His at position 64. We also demonstrate how the detected pathways may be used to compare the efficiencies of the mutants His-64-Ala/Asn-62-His and His-64-Ala/Asn-67-His using the empirical valence bond theory.

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.