Proton affinity changes driving unidirectional proton transport in the bacteriorhodopsin photocycle

PIEZO2 Proton Affinity and Availability May Also Regulate Mechanical Pain Sensitivity, Drive Central Sensitization and Neurodegeneration

The current opinion manuscript posits that not only Piezo2 voltage block, but also proton affinity and availability in relation to Piezo2, a mechanically gated ion channel, may count in the mediation of pain and its sensitivity. Moreover, this paper argues that autonomously acquired Piezo2 channelopathy on somatosensory terminals is likely the initiating peripheral impaired input source that drives the central sensitization of spinal nociceptive neurons on the chronic path as being the autonomous pain generator. In parallel, impaired proprioception and the resultant progressive deficit in neuromuscular junctions of motoneurons might be initiated on the chronic path by the impairment of the proton-based ultrafast proprioceptive feedback to motoneurons due to disconnection through vesicular glutamate transporter 1. The irreversible form of this autonomously acquired Piezo2 ion channel microdamage, in association with genetic predisposition and/or environmental risk factors, is suggested to lead to progressive motoneuron death in addition to loss of pain sensation in amyotrophic lateral sclerosis. Furthermore, the impairment of the proton-based ultrafast long-range oscillatory synchronization to the hippocampus through vesicular glutamate transporter 2 may gain further importance in pain modulation and formation on the chronic path. Overall, this novel, unaccounted Piezo2-initiated protonic extrafast signaling, including both the protonic ultrafast proprioceptive and the rapid nociceptive ones, within the nervous system seems to be essential in order to maintain life. Hence, its microdamage promotes neurodegeneration and accelerates aging, while the complete loss of it is incompatible with life sustainment, as is proposed in amyotrophic lateral sclerosis.

Proton-Mediated PIEZO2 Channelopathy: Linking Oxaliplatin Treatment to Impaired Proprioception and Cognitive Deficits

Oxaliplatin induces acute neuropathy within a few hours post-treatment, with symptoms persisting for several days. Delayed onset muscle soreness also causes the delayed onset of mechanical pain sensation starting at about 6-8 h and lasting up to a week after exercise. Both conditions come with impaired proprioception and could be chronic if these bouts are repeated frequently. The involvement of PIEZO2 ion channels, as the principal mechanosensory channels responsible for proprioception, is theorized in both conditions as well. The current opinion manuscript is meant to explain how the minor stretch-related microdamage of PIEZO2 on Type Ia proprioceptive terminals could explain the aforementioned symptoms of impaired proprioception. This includes a platinum-induced proton affinity 'switch' on these proprioceptive endings with PIEZO2 content, resulting in this being the likely initiating cause. Furthermore, it postulates how the proton-based ultrafast long-range oscillatory synchronization to the hippocampus could be impaired due to this microdamage on Type Ia proprioceptive terminals. Finally, the manuscript provides insight into how the impairment of the PIEZO2-initiated ultrafast muscle-brain axis may contribute to chemobrain and its associated cognitive and memory deficits.

Quantifying Bacteriorhodopsin Activity as a Function of its Local Environment with a Raman-Based Assay

Bacteriorhodopsin (bR) is a transmembrane protein that functions as a light-driven proton pump in halophilic archaea. The bR photocycle has been well-characterized; however, these measurements almost exclusively measured purified bR, outside of its native membrane. To investigate what effect the cellular environment has on the bR photocycle, we have developed a Raman-based assay that can monitor the activity of the bR in a variety of conditions, including in its native membrane. The assay uses two continuous-wave lasers, one to initiate photochemistry and one to monitor bR activity. The excitation leads to the steady-state depletion of ground-state bR, which directly relates to the population of photocycle intermediate states. We have used this assay to monitor bR activity both in vitro and in vivo. Our in vitro measurements confirm that our assay is sensitive to bulk environmental changes reported in the literature. Our in vivo measurements show a decrease in bR activity with increasing extracellular pH for bR in its native membrane. The difference in activity with increasing pH indicates that the native membrane environment affects the function of bR. This assay opens the door to future measurements into understanding how the local environment of this transmembrane protein affects function.

Light-driven proton transfers and proton transport by microbial rhodopsins - A biophysical perspective

In the last twenty years, our understanding of the rules and mechanisms for the outward light-driven proton transport (and underlying proton transfers) by microbial rhodopsins has been changing dramatically. It transitioned from a very detailed atomic-level understanding of proton transport by bacteriorhodopsin, the prototypical proton pump, to a confounding variety of sequence motifs, mechanisms, directions, and modes of transport in its newly found homologs. In this review, we will summarize and discuss experimental data obtained on new microbial rhodopsin variants, highlighting their contribution to the refinement and generalization of the ideas crystallized in the previous century. In particular, we will focus on the proton transport (and transfers) vectoriality and their structural determinants, which, in many cases, remain unidentified.

Protein Motifs for Proton Transfers That Build the Transmembrane Proton Gradient

Biological membranes are barriers to polar molecules, so membrane embedded proteins control the transfers between cellular compartments. Protein controlled transport moves substrates and activates cellular signaling cascades. In addition, the electrochemical gradient across mitochondrial, bacterial and chloroplast membranes, is a key source of stored cellular energy. This is generated by electron, proton and ion transfers through proteins. The gradient is used to fuel ATP synthesis and to drive active transport. Here the mechanisms by which protons move into the buried active sites of Photosystem II (PSII), bacterial RCs (bRCs) and through the proton pumps, Bacteriorhodopsin (bR), Complex I and Cytochrome c oxidase (CcO), are reviewed. These proteins all use water filled proton transfer paths. The proton pumps, that move protons uphill from low to high concentration compartments, also utilize Proton Loading Sites (PLS), that transiently load and unload protons and gates, which block backflow of protons. PLS and gates should be synchronized so PLS proton affinity is high when the gate opens to the side with few protons and low when the path is open to the high concentration side. Proton transfer paths in the proteins we describe have different design features. Linear paths are seen with a unique entry and exit and a relatively straight path between them. Alternatively, paths can be complex with a tangle of possible routes. Likewise, PLS can be a single residue that changes protonation state or a cluster of residues with multiple charge and tautomer states.

Effect of the Number of Methyl Groups on the Cation Affinity of Oxygen, Nitrogen, and Phosphorus Sites of Lewis Bases

The effect of number of CH₃ groups (n) on the cation (H⁺, Li⁺, Na⁺, Al⁺, CH₃⁺) affinity, polarizability, and dipole moment of 14 simple molecules was investigated. Linear correlations were observed between the polarizabilities and the number of methyl groups. The variations of the cation affinities and dipole moments with the number of methyl groups (n) were not linear, and a quadratic function was proposed for obtaining a good fit of the experimental data. Also, because the proton affinities (PA), lithium cation affinities (LCA), sodium cation affinities (SCA), aluminum cation affinity (AlCA), and methyl cation affinity (MCA) varied quadratically with polarizabilities (α), a formula of the form [cation affinities] = a + bα + cα² was proposed. After correction of the PAs, LCAs, SCAs, AlCA, and MCA for the dipole/charge interaction (E_μ), linear relationships were observed between the corrected cation affinities and n or α. The contribution of E_μ to PA and MCA was small (less than 20%), and its contribution to LCA and SCA was large (>50%). The electrostatic contribution to AlCA was considerable (20-50%); however, it was smaller than the electrostatic contribution to LCA and SCA.

Grotthuss mechanisms: from proton transport in proton wires to bioprotonic devices

In 1804, Theodore von Grotthuss proposed a mechanism for proton (H(+)) transport between water molecules that involves the exchange of a covalent bond between H and O with a hydrogen bond. This mechanism also supports the transport of OH(-) as a proton hole and is essential in explaining proton transport in intramembrane proton channels. Inspired by the Grotthuss mechanism and its similarity to electron and hole transport in semiconductors, we have developed semiconductor type devices that are able to control and monitor a current of H(+) as well as OH(-) in hydrated biopolymers. In this topical review, we revisit these devices that include protonic diodes, complementary, transistors, memories and transducers as well as a phenomenological description of their behavior that is analogous to electronic semiconductor devices.

SK. Structural exploration of acid sphingomyelinase at different physiological pH through molecular dynamics and docking studies

Acid sphingomyelinase (ASM) hydrolysis the sphingomyelin at physiological pH 5.0 and subsequently leads to ceramide production.

Halorhodopsin pumps Cl- and bacteriorhodopsin pumps protons by a common mechanism that uses conserved electrostatic interactions

Key mutations differentiate the functions of homologous proteins. One example compares the inward ion pump halorhodopsin (HR) and the outward proton pump bacteriorhodopsin (BR). Of the nine essential buried ionizable residues in BR, six are conserved in HR. However, HR changes three BR acids, D85 in a central cluster of ionizable residues, D96, nearer the intracellular, and E204, nearer the extracellular side of the membrane to the small, neutral amino acids T111, V122, and T230, respectively. In BR, acidic amino acids are stationary anions whose proton affinity is modulated by conformational changes, establishing a sequence of directed binding and release of protons. Multiconformation continuum electrostatics calculations of chloride affinity and residue protonation show that, in reaction intermediates where an acid is ionized in BR, a Cl(-) is bound to HR in a position near the deleted acid. In the HR ground state, Cl(-) binds tightly to the central cluster T111 site and weakly to the extracellular T230 site, recovering the charges on ionized BR-D85 and neutral E204 in BR. Imposing key conformational changes from the BR M intermediate into the HR structure results in the loss of Cl(-) from the central T111 site and the tight binding of Cl(-) to the extracellular T230 site, mirroring the changes that protonate BR-D85 and ionize E204 in BR. The use of a mobile chloride in place of D85 and E204 makes HR more susceptible to the environmental pH and salt concentrations than BR. These studies shed light on how ion transfer mechanisms are controlled through the interplay of protein and ion electrostatics.

Proton transfer-mediated GPCR activation

G-protein coupled receptors (GPCRs) play essential roles in signal transduction from the environment into the cell. While many structural features have been elucidated in great detail, a common functional mechanism on how the ligand-binding signal is converted into a conformational change on the cytoplasmic face resulting in subsequent activation of downstream effectors remain to be established. Based on available structural and functional data of the activation process in class-A GPCRs, we propose here that a change in protonation status, together with proton transfer via conserved structural elements located in the transmembrane region, are the key elements essential for signal transduction across the membrane.

ProBLM web server: protein and membrane placement and orientation package

The 3D structures of membrane proteins are typically determined without the presence of a lipid bilayer. For the purpose of studying the role of membranes on the wild type characteristics of the corresponding protein, determining the position and orientation of transmembrane proteins within a membrane environment is highly desirable. Here we report a geometry-based approach to automatically insert a membrane protein with a known 3D structure into pregenerated lipid bilayer membranes with various dimensions and lipid compositions or into a pseudomembrane. The pseudomembrane is built using the Protein Nano-Object Integrator which generates a parallelepiped of user-specified dimensions made up of pseudoatoms. The pseudomembrane allows for modeling the desolvation effects while avoiding plausible errors associated with wrongly assigned protein-lipid contacts. The method is implemented into a web server, the ProBLM server, which is freely available to the biophysical community. The web server allows the user to upload a protein coordinate file and any missing residues or heavy atoms are regenerated. ProBLM then creates a combined protein-membrane complex from the given membrane protein and bilayer lipid membrane or pseudomembrane. The user is given an option to manually refine the model by manipulating the position and orientation of the protein with respect to the membrane.

Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions

We investigate the influence of three common definitions of the solute/solvent dielectric boundary (DB) on the accuracy of the electrostatic solvation energy ΔG_el computed within the Poisson Boltzmann and the generalized Born models of implicit solvation. The test structures include small molecules, peptides and small proteins; explicit solvent ΔG_el are used as accuracy reference. For common atomic radii sets BONDI, PARSE (and ZAP9 for small molecules) the use of van der Waals (vdW) DB results, on average, in considerably larger errors in ΔG_el than the molecular surface (MS) DB. The optimal probe radius ρ_w for which the MS DB yields the most accurate ΔG_el varies considerably between structure types. The solvent accessible surface (SAS) DB becomes optimal at ρ_w ~ 0.2 Å (exact value is sensitive to the structure and atomic radii), at which point the average accuracy of ΔG_el is comparable to that of the MS-based boundary. The geometric equivalence of SAS to vdW surface based on the same atomic radii uniformly increased by ρ_w gives the corresponding optimal vdW DB. For small molecules, the optimal vdW DB based on BONDI + 0.2 Å radii can yield ΔG_el estimates at least as accurate as those based on the optimal MS DB. Also, in small molecules, pairwise charge-charge interactions computed with the optimal vdW DB are virtually equal to those computed with the MS DB, suggesting that in this case the two boundaries are practically equivalent by the electrostatic energy criteria. In structures other than small molecules, the optimal vdW and MS dielectric boundaries are not equivalent: the respective pairwise electrostatic interactions in the presence of solvent can differ by up to 5 kcal/mol for individual atomic pairs in small proteins, even when the total ΔG_el are equal. For small proteins, the average decrease in pairwise electrostatic interactions resulting from the switch from optimal MS to optimal vdW DB definition can be mimicked within the MS DB definition by doubling of the solute dielectric constant. However, the use of the higher interior dielectric does not eliminate the large individual deviations between pairwise interactions computed within the two DB definitions. It is argued that while the MS based definition of the dielectric boundary is more physically correct in some types of practical calculations, the choice is not so clear in some other common scenarios.

GPCR activation: protonation and membrane potential

GPCR proteins represent the largest family of signaling membrane proteins in eukaryotic cells. Their importance to basic cell biology, human diseases, and pharmaceutical interventions is well established. Many crystal structures of GPCR proteins have been reported in both active and inactive conformations. These data indicate that agonist binding alone is not sufficient to trigger the conformational change of GPCRs necessary for binding of downstream G-proteins, yet other essential factors remain elusive. Based on analysis of available GPCR crystal structures, we identified a potential conformational switch around the conserved Asp2.50, which consistently shows distinct conformations between inactive and active states. Combining the structural information with the current literature, we propose an energy-coupling mechanism, in which the interaction between a charge change of the GPCR protein and the membrane potential of the living cell plays a key role for GPCR activation.

Molecular mechanisms for generating transmembrane proton gradients

Membrane proteins use the energy of light or high energy substrates to build a transmembrane proton gradient through a series of reactions leading to proton release into the lower pH compartment (P-side) and proton uptake from the higher pH compartment (N-side). This review considers how the proton affinity of the substrates, cofactors and amino acids are modified in four proteins to drive proton transfers. Bacterial reaction centers (RCs) and photosystem II (PSII) carry out redox chemistry with the species to be oxidized on the P-side while reduction occurs on the N-side of the membrane. Terminal redox cofactors are used which have pKas that are strongly dependent on their redox state, so that protons are lost on oxidation and gained on reduction. Bacteriorhodopsin is a true proton pump. Light activation triggers trans to cis isomerization of a bound retinal. Strong electrostatic interactions within clusters of amino acids are modified by the conformational changes initiated by retinal motion leading to changes in proton affinity, driving transmembrane proton transfer. Cytochrome c oxidase (CcO) catalyzes the reduction of O2 to water. The protons needed for chemistry are bound from the N-side. The reduction chemistry also drives proton pumping from N- to P-side. Overall, in CcO the uptake of 4 electrons to reduce O2 transports 8 charges across the membrane, with each reduction fully coupled to removal of two protons from the N-side, the delivery of one for chemistry and transport of the other to the P-side.

Deprotonation of D96 in bacteriorhodopsin opens the proton uptake pathway

Despite extensive investigation, the precise mechanism controlling the opening of the cytoplasmic proton uptake pathway in bacteriorhodopsin (bR) has remained a mystery. From an analysis of the X-ray structure of the D96G/F171C/F219L triple mutant of bR and 60 independent molecular dynamics simulations of bR photointermediates, we report that the deprotonation of D96, a key residue in proton transfer reactions, serves two roles that occur sequentially. First, D96 donates a proton to the Schiff base. Subsequently, the deprotonation of D96 serves to "unlatch" the cytoplasmic side. The latching function of D96 appears to be remarkably robust, functioning to open hydration channels in all photointermediate structures. These results suggest that the protonation state of D96 may be the critical biophysical cue controlling the opening and closing of the cytoplasmic half-channel in bR. We suspect that this protonation-switch mechanism could also be utilized in other proton pumps to minimize backflow and reinforce directionality.

Protonation and pK changes in protein-ligand binding

Formation of protein-ligand complexes causes various changes in both the receptor and the ligand. This review focuses on changes in pK and protonation states of ionizable groups that accompany protein-ligand binding. Physical origins of these effects are outlined, followed by a brief overview of the computational methods to predict them and the associated corrections to receptor-ligand binding affinities. Statistical prevalence, magnitude and spatial distribution of the pK and protonation state changes in protein-ligand binding are discussed in detail, based on both experimental and theoretical studies. While there is no doubt that these changes occur, they do not occur all the time; the estimated prevalence varies, both between individual complexes and by method. The changes occur not only in the immediate vicinity of the interface but also sometimes far away. When receptor-ligand binding is associated with protonation state change at particular pH, the binding becomes pH dependent: we review the interplay between sub-cellular characteristic pH and optimum pH of receptor-ligand binding. It is pointed out that there is a tendency for protonation state changes upon binding to be minimal at physiologically relevant pH for each complex (no net proton uptake/release), suggesting that native receptor-ligand interactions have evolved to reduce the energy cost associated with ionization changes. As a result, previously reported statistical prevalence of these changes - typically computed at the same pH for all complexes - may be higher than what may be expected at optimum pH specific to each complex. We also discuss whether proper account of protonation state changes appears to improve practical docking and scoring outcomes relevant to structure-based drug design. An overview of some of the existing challenges in the field is provided in conclusion.

Understanding photosynthetic light-harvesting: a bottom up theoretical approach

We discuss a bottom up approach for modeling photosynthetic light-harvesting. Methods are reviewed for a full structure-based parameterization of the Hamiltonian of pigment-protein complexes (PPCs). These parameters comprise (i) the local transition energies of the pigments in their binding sites in the protein, the site energies; (ii) the couplings between optical transitions of the pigments, the excitonic couplings; and (iii) the spectral density characterizing the dynamic modulation of pigment transition energies and excitonic couplings by protein vibrations. Starting with quantum mechanics perturbation theory, we provide a microscopic foundation for the standard PPC Hamiltonian and relate the expressions obtained for its matrix elements to quantities that can be calculated with classical molecular mechanics/electrostatics approaches including the whole PPC in atomic detail and using charge and transition densities obtained with quantum chemical calculations on the isolated building blocks of the PPC. In the second part of this perspective, the Hamiltonian is utilized to describe the quantum dynamics of excitons. Situations are discussed that differ in the relative strength of excitonic and exciton-vibrational coupling. The predictive power of the approaches is demonstrated in application to different PPCs, and challenges for future work are outlined.

A density functional and quantum Monte Carlo study of glutamic acid in vacuo and in a dielectric continuum medium

We present density functional theory (DFT) and quantum Monte Carlo (QMC) calculations of the glutamic acid and glutamate ion in vacuo and in various dielectric continuum media within the polarizable continuum model (PCM). In DFT, we employ the integral equation formalism variant of PCM while, in QMC, we use a PCM scheme we have developed to include both surface and volume polarization. We investigate the gas-phase protonation thermochemistry of the glutamic acid using a large set of structural conformations, and find that QMC is in excellent agreement with the best available theoretical and experimental results. For the solvated glutamic acid and glutamate ion, we perform DFT calculations for dielectric constants, ε, between 4 and 78. We find that the glutamate ion in the zwitterionic form is more stable than the non-zwitterionic form over the whole range of dielectric constants, while the glutamic acid is more stable in its non-zwitterionic form at ε = 4. The dielectric constant at which the two glutamic acid species have the same energy depends on the cavity size and lies between 5 and 12.5. We validate these results with QMC for the two limiting values of the dielectric constant, and find qualitative agreement with DFT even though the solvent polarization is less pronounced at the QMC level.

H++ 3.0: automating pK prediction and the preparation of biomolecular structures for atomistic molecular modeling and simulations

The accuracy of atomistic biomolecular modeling and simulation studies depend on the accuracy of the input structures. Preparing these structures for an atomistic modeling task, such as molecular dynamics (MD) simulation, can involve the use of a variety of different tools for: correcting errors, adding missing atoms, filling valences with hydrogens, predicting pK values for titratable amino acids, assigning predefined partial charges and radii to all atoms, and generating force field parameter/topology files for MD. Identifying, installing and effectively using the appropriate tools for each of these tasks can be difficult for novice and time-consuming for experienced users. H++ (http://biophysics.cs.vt.edu/) is a free open-source web server that automates the above key steps in the preparation of biomolecular structures for molecular modeling and simulations. H++ also performs extensive error and consistency checking, providing error/warning messages together with the suggested corrections. In addition to numerous minor improvements, the latest version of H++ includes several new capabilities and options: fix erroneous (flipped) side chain conformations for HIS, GLN and ASN, include a ligand in the input structure, process nucleic acid structures and generate a solvent box with specified number of common ions for explicit solvent MD.

Multi-dimensional characterization of electrostatic surface potential computation on graphics processors

BACKGROUND

Calculating the electrostatic surface potential (ESP) of a biomolecule is critical towards understanding biomolecular function. Because of its quadratic computational complexity (as a function of the number of atoms in a molecule), there have been continual efforts to reduce its complexity either by improving the algorithm or the underlying hardware on which the calculations are performed.

RESULTS

We present the combined effect of (i) a multi-scale approximation algorithm, known as hierarchical charge partitioning (HCP), when applied to the calculation of ESP and (ii) its mapping onto a graphics processing unit (GPU). To date, most molecular modeling algorithms perform an artificial partitioning of biomolecules into a grid/lattice on the GPU. In contrast, HCP takes advantage of the natural partitioning in biomolecules, which in turn, better facilitates its mapping onto the GPU. Specifically, we characterize the effect of known GPU optimization techniques like use of shared memory. In addition, we demonstrate how the cost of divergent branching on a GPU can be amortized across algorithms like HCP in order to deliver a massive performance boon.

CONCLUSIONS

We accelerated the calculation of ESP by 25-fold solely by parallelization on the GPU. Combining GPU and HCP, resulted in a speedup of at most 1,860-fold for our largest molecular structure. The baseline for these speedups is an implementation that has been hand-tuned SSE-optimized and parallelized across 16 cores on the CPU. The use of GPU does not deteriorate the accuracy of our results.

Charge state of the globular histone core controls stability of the nucleosome

Presented here is a quantitative model of the wrapping and unwrapping of the DNA around the histone core of the nucleosome that suggests a mechanism by which this transition can be controlled: alteration of the charge state of the globular histone core. The mechanism is relevant to several classes of posttranslational modifications such as histone acetylation and phosphorylation; several specific scenarios consistent with recent in vivo experiments are considered. The model integrates a description based on an idealized geometry with one based on the atomistic structure of the nucleosome, and the model consistently accounts for both the electrostatic and nonelectrostatic contributions to the nucleosome free energy. Under physiological conditions, isolated nucleosomes are predicted to be very stable (38 +/- 7 kcal/mol). However, a decrease in the charge of the globular histone core by one unit charge, for example due to acetylation of a single lysine residue, can lead to a significant decrease in the strength of association with its DNA. In contrast to the globular histone core, comparable changes in the charge state of the histone tail regions have relatively little effect on the nucleosome's stability. The combination of high stability and sensitivity explains how the nucleosome is able to satisfy the seemingly contradictory requirements for thermodynamic stability while allowing quick access to its DNA informational content when needed by specific cellular processes such as transcription.

Accelerating electrostatic surface potential calculation with multi-scale approximation on graphics processing units

Tools that compute and visualize biomolecular electrostatic surface potential have been used extensively for studying biomolecular function. However, determining the surface potential for large biomolecules on a typical desktop computer can take days or longer using currently available tools and methods. Two commonly used techniques to speed-up these types of electrostatic computations are approximations based on multi-scale coarse-graining and parallelization across multiple processors. This paper demonstrates that for the computation of electrostatic surface potential, these two techniques can be combined to deliver significantly greater speed-up than either one separately, something that is in general not always possible. Specifically, the electrostatic potential computation, using an analytical linearized Poisson-Boltzmann (ALPB) method, is approximated using the hierarchical charge partitioning (HCP) multi-scale method, and parallelized on an ATI Radeon 4870 graphical processing unit (GPU). The implementation delivers a combined 934-fold speed-up for a 476,040 atom viral capsid, compared to an equivalent non-parallel implementation on an Intel E6550 CPU without the approximation. This speed-up is significantly greater than the 42-fold speed-up for the HCP approximation alone or the 182-fold speed-up for the GPU alone.

Statistics and physical origins of pK and ionization state changes upon protein-ligand binding

This work investigates statistical prevalence and overall physical origins of changes in charge states of receptor proteins upon ligand binding. These changes are explored as a function of the ligand type (small molecule, protein, and nucleic acid), and distance from the binding region. Standard continuum solvent methodology is used to compute, on an equal footing, pK changes upon ligand binding for a total of 5899 ionizable residues in 20 protein-protein, 20 protein-small molecule, and 20 protein-nucleic acid high-resolution complexes. The size of the data set combined with an extensive error and sensitivity analysis allows us to make statistically justified and conservative conclusions: in 60% of all protein-small molecule, 90% of all protein-protein, and 85% of all protein-nucleic acid complexes there exists at least one ionizable residue that changes its charge state upon ligand binding at physiological conditions (pH = 6.5). Considering the most biologically relevant pH range of 4-8, the number of ionizable residues that experience substantial pK changes (DeltapK > 1.0) due to ligand binding is appreciable: on average, 6% of all ionizable residues in protein-small molecule complexes, 9% in protein-protein, and 12% in protein-nucleic acid complexes experience a substantial pK change upon ligand binding. These changes are safely above the statistical false-positive noise level. Most of the changes occur in the immediate binding interface region, where approximately one out of five ionizable residues experiences substantial pK change regardless of the ligand type. However, the physical origins of the change differ between the types: in protein-nucleic acid complexes, the pK values of interface residues are predominantly affected by electrostatic effects, whereas in protein-protein and protein-small molecule complexes, structural changes due to the induced-fit effect play an equally important role. In protein-protein and protein-nucleic acid complexes, there is a statistically significant number of substantial pK perturbations, mostly due to the induced-fit structural changes, in regions far from the binding interface.

An analytical approach to computing biomolecular electrostatic potential. I. Derivation and analysis

Analytical approximations to fundamental equations of continuum electrostatics on simple shapes can lead to computationally inexpensive prescriptions for calculating electrostatic properties of realistic molecules. Here, we derive a closed-form analytical approximation to the Poisson equation for an arbitrary distribution of point charges and a spherical dielectric boundary. The simple, parameter-free formula defines continuous electrostatic potential everywhere in space and is obtained from the exact infinite-series (Kirkwood) solution by an approximate summation method that avoids truncating the infinite series. We show that keeping all the terms proves critical for the accuracy of this approximation, which is fully controllable for the sphere. The accuracy is assessed by comparisons with the exact solution for two unit charges placed inside a spherical boundary separating the solute of dielectric 1 and the solvent of dielectric 80. The largest errors occur when the source charges are closest to the dielectric boundary and the test charge is closest to either of the sources. For the source charges placed within 2 A from the boundary, and the test surface located on the boundary, the root-mean-square error of the approximate potential is less than 0.1 kcal/mol/mid R:emid R: (per unit test charge). The maximum error is 0.4 kcal/mol/mid R:emid R:. These results correspond to the simplest first-order formula. A strategy for adopting the proposed method for realistic biomolecular shapes is detailed. An extensive testing and performance analysis on real molecular structures are described in Part II that immediately follows this work as a separate publication. Part II also contains an application example.

An analytical approach to computing biomolecular electrostatic potential. II. Validation and applications

An ability to efficiently compute the electrostatic potential produced by molecular charge distributions under realistic solvation conditions is essential for a variety of applications. Here, the simple closed-form analytical approximation to the Poisson equation rigorously derived in Part I for idealized spherical geometry is tested on realistic shapes. The effects of mobile ions are included at the Debye-Huckel level. The accuracy of the resulting closed-form expressions for electrostatic potential is assessed through comparisons with numerical Poisson-Boltzmann (NPB) reference solutions on a test set of 580 representative biomolecular structures under typical conditions of aqueous solvation. For each structure, the deviation from the reference is computed for a large number of test points placed near the dielectric boundary (molecular surface). The accuracy of the approximation, averaged over all test points in each structure, is within 0.6 kcal/mol/mid R:emid R: approximately kT per unit charge for all structures in the test set. For 91.5% of the individual test points, the deviation from the NPB potential is within 0.6 kcal/mol/mid R:emid R:. The deviations from the reference decrease with increasing distance from the dielectric boundary: The approximation is asymptotically exact far away from the source charges. Deviation of the overall shape of a structure from ideal spherical does not, by itself, appear to necessitate decreased accuracy of the approximation. The largest deviations from the NPB reference are found inside very deep and narrow indentations that occur on the dielectric boundaries of some structures. The dimensions of these pockets of locally highly negative curvature are comparable to the size of a water molecule; the applicability of a continuum dielectric models in these regions is discussed. The maximum deviations from the NPB are reduced substantially when the boundary is smoothed by using a larger probe radius (3 A) to generate the molecular surface. A detailed accuracy analysis is presented for several proteins of various shapes, including lysozyme whose surface features a functionally relevant region of negative curvature. The proposed analytical model is computationally inexpensive; this strength of the approach is demonstrated by computing and analyzing the electrostatic potential generated by a full capsid of the tobacco ring spot virus at atomic resolution (500 000 atoms). An analysis of the electrostatic potential of the inner surface of the capsid reveals what might be a RNA binding pocket. These results are generated with the modest computational power of a desktop personal computer.

Investigating the mechanisms of photosynthetic proteins using continuum electrostatics

Computational methods based on continuum electrostatics are widely used in theoretical biochemistry to analyze the function of proteins. Continuum electrostatic methods in combination with quantum chemical and molecular mechanical methods can help to analyze even very complex biochemical systems. In this article, applications of these methods to proteins involved in photosynthesis are reviewed. After giving a short introduction to the basic concepts of the continuum electrostatic model based on the Poisson-Boltzmann equation, we describe the application of this approach to the docking of electron transfer proteins, to the comparison of isofunctional proteins, to the tuning of absorption spectra, to the analysis of the coupling of electron and proton transfer, to the analysis of the effect of membrane potentials on the energetics of membrane proteins, and to the kinetics of charge transfer reactions. Simulations as those reviewed in this article help to analyze molecular mechanisms on the basis of the structure of the protein, guide new experiments, and provide a better and deeper understanding of protein functions.

Analysis of basic clustering algorithms for numerical estimation of statistical averages in biomolecules

In statistical mechanics, the equilibrium properties of a physical system of particles can be calculated as the statistical average over accessible microstates of the system. In general, these calculations are computationally intractable since they involve summations over an exponentially large number of microstates. Clustering algorithms are one of the methods used to numerically approximate these sums. The most basic clustering algorithms first sub-divide the system into a set of smaller subsets (clusters). Then, interactions between particles within each cluster are treated exactly, while all interactions between different clusters are ignored. These smaller clusters have far fewer microstates, making the summation over these microstates, tractable. These algorithms have been previously used for biomolecular computations, but remain relatively unexplored in this context. Presented here, is a theoretical analysis of the error and computational complexity for the two most basic clustering algorithms that were previously applied in the context of biomolecular electrostatics. We derive a tight, computationally inexpensive, error bound for the equilibrium state of a particle computed via these clustering algorithms. For some practical applications, it is the root mean square error, which can be significantly lower than the error bound, that may be more important. We how that there is a strong empirical relationship between error bound and root mean square error, suggesting that the error bound could be used as a computationally inexpensive metric for predicting the accuracy of clustering algorithms for practical applications. An example of error analysis for such an application-computation of average charge of ionizable amino-acids in proteins-is given, demonstrating that the clustering algorithm can be accurate enough for practical purposes.

An extended dead-end elimination algorithm to determine gap-free lists of low energy states

Proteins are flexible systems and commonly populate several functionally important states. To understand protein function, these states and their energies have to be identified. We introduce an algorithm that allows the determination of a gap-free list of the low energy states. This algorithm is based on the dead-end elimination (DEE) theorem and is termed X-DEE (extended DEE). X-DEE is applicable to discrete systems whose state energy can be formulated as pairwise interaction between sites and their intrinsic energies. In this article, the computational performance of X-DEE is analyzed and discussed. X-DEE is implemented to determine the lowest energy protonation states of proteins, a problem to which DEE has not been applied so far. We use X-DEE to calculate a list of low energy protonation states for two bacteriorhodopsin structures that represent the first proton transfer step of the bacteriorhodopsin photocycle.

Suppression of the back proton-transfer from Asp85 to the retinal Schiff base in bacteriorhodopsin: A theoretical analysis of structural elements

The transfer of a proton from the retinal Schiff base to the nearby Asp85 protein group is an essential step in the directional proton-pumping by bacteriorhodopsin. To avoid the wasteful back reprotonation of the Schiff base from Asp85, the protein must ensure that, following Schiff base deprotonation, the energy barrier for back proton-transfer from Asp85 to the Schiff base is larger than that for proton-transfer from the Schiff base to Asp85. Here, three structural elements that may contribute to suppressing the back proton-transfer from Asp85 to the Schiff base are investigated: (i) retinal twisting; (ii) hydrogen-bonding distances in the active site; and (iii) the number and location of internal water molecules. The impact of the pattern of bond twisting on the retinal deprotonation energy is dissected by performing an extensive set of quantum-mechanical calculations. Structural rearrangements in the active site, such as changes of the Thr89:Asp85 distance and relocation of water molecules hydrogen-bonding to the Asp85 acceptor group, may participate in the mechanism which ensures that following the transfer of the Schiff base proton to Asp85 the protein proceeds with the subsequent photocycle steps, and not with back proton transfer from Asp85 to the Schiff base.

Simulation of the Electron Transfer between the Tetraheme Subunit and the Special Pair of the Photosynthetic Reaction Center Using a Microstate Description

Charge transfer through biological macromolecules is essential for many biological processes such as, for instance, photosynthesis and respiration. Protons or electrons are transferred between titratable residues or redox-active cofactors, respectively. Transfer rates between these sites depend on the current charge configuration of neighboring sites. Here, we formulate the kinetics of charge-transfer systems in a microstate formalism. A unique transfer rate constant can be assigned to the interconversion of microstates. Mutual interactions between sites participating in the transfer reactions are naturally taken into account. The formalism is applied to the kinetics of electron transfer in the tetraheme subunit and the special pair of the reaction center of Blastochloris viridis. It is shown that continuum electrostatic calculations can be used in combination with an existing empirical rate law to obtain electron-transfer rate constants. The re-reduction kinetics of the photo-oxidized special pair simulated in a microstate formalism is shown to be in good agreement with experimental data. A flux analysis is used to follow the individual electron-transfer steps.

Model for Proton Transport Coupled to Protein Conformational Change: Application to Proton Pumping in the Bacteriorhodopsin Photocycle

A modeling method is presented for protein systems in which proton transport is coupled to conformational change, as in proton pumps and in motors driven by the proton-motive force. Previously developed methods for calculating pKa values in proteins using a macroscopic dielectric model are extended beyond the equilibrium case to a master-equation model for the time evolution of the system through states defined by ionization microstate and a discrete set of conformers. The macroscopic dielectric model supplies free energy changes for changes of protonation microstate, while the method for obtaining the energetics of conformational change and the relaxation rates, the other ingredients needed for the master equation, are system dependent. The method is applied to the photoactivated proton pump, bacteriorhodopsin, using conformational free energy differences from experiment and treating relaxation rates through three adjustable parameters. The model is found to pump protons with an efficiency relatively insensitive to parameter choice over a wide range of parameter values, and most of the main features of the known photocycle from very early M to the return to the resting state are reproduced. The boundaries of these parameter ranges are such that short-range proton transfers are faster than longer-range ones, which in turn are faster than conformational changes. No relaxation rates depend on conformation. The results suggest that an "accessibility switch", while not ruled out, is not required and that vectorial proton transport can be achieved through the coupling of the energetics of ionization and conformational states.

Influence of the Membrane Potential on the Protonation of Bacteriorhodopsin: Insights from Electrostatic Calculations into the Regulation of Proton Pumping

Proton binding and release are elementary steps for the transfer of protons within proteins, which is a process that is crucial in biochemical catalysis and biological energy transduction. Local electric fields in proteins affect the proton binding energy compared to aqueous solution. In membrane proteins, also the membrane potential affects the local electrostatics and can thus be crucial for protein function. In this paper, we introduce a procedure to calculate the protonation probability of titratable sites of a membrane protein in the presence of a membrane potential. In the framework of continuum electrostatics, we use a modified Poisson-Boltzmann equation to include the influence of the membrane potential. Our method considers that in a transmembrane protein each titratable site is accessible for protons from only one side of the membrane depending on the hydrogen bond pattern of the protein. We show that the protonation of sites receiving their protons from different sides of the membrane is differently influenced by the membrane potential. In addition, the effect of the membrane potential is combined with the effect of the pH gradient resulting from proton pumping. Our method is applied to bacteriorhodopsin, a light-activated proton pump. We find that the proton pumping of this protein might be regulated by Asp115, a conserved residue for which no function has been identified yet. According to our calculations, the interaction of Asp115 with Asp85 leads to the protonation of the latter if the pH gradient or the membrane potential becomes too large. Since Asp85 is the primary proton acceptor in the photocycle, bacteriorhodopsin molecules in which Asp85 is protonated cannot pump protons. Furthermore, we estimate how the membrane potential affects the energetics of the individual proton-transfer reactions of the photocycle. Most reactions, except the initial proton transfer from the Schiff base to Asp85, are influenced. Our calculations give new insights into the mechanism with which bacteriorhodopsin senses the membrane potential and the pH gradient and how the proton pumping is regulated by these parameters.

Calculated proton uptake on anaerobic reduction of cytochrome C oxidase: is the reaction electroneutral?

Cytochrome c oxidase is a transmembrane proton pump that builds an electrochemical gradient using chemical energy from the reduction of O(2). Ionization states of all residues were calculated with Multi-Conformation Continuum Electrostatics (MCCE) in seven anaerobic oxidase redox states ranging from fully oxidized to fully reduced. One long-standing problem is how proton uptake is coupled to the reduction of the active site binuclear center (BNC). The BNC has two cofactors: heme a(3) and Cu(B). If the protein needs to maintain electroneutrality, then 2 protons will be bound when the BNC is reduced by 2 electrons in the reductive half of the reaction cycle. The effective pK(a)s of ionizable residues around the BNC are evaluated in Rhodobacter sphaeroides cytochrome c oxidase. At pH 7, only a hydroxide coordinated to Cu(B) shifts its pK(a) from below 7 to above 7 and so picks up a proton when heme a(3) and Cu(B) are reduced. Glu I-286, Tyr I-288, His I-334, and a second hydroxide on heme a(3) all have pK(a)s above 7 in all redox states, although they have only 1.6-3.5 DeltapK units energy cost for deprotonation. Thus, at equilibrium, they are protonated and cannot serve as proton acceptors. The propionic acids near the BNC are deprotonated with pK(a)s well below 7. They are well stabilized in their anionic state and do not bind a proton upon BNC reduction. This suggests that electroneutrality in the BNC is not maintained during the anaerobic reduction. Proton uptake on reduction of Cu(A), heme a, heme a(3), and Cu(B) shows approximately 2.5 protons bound per 4 electrons, in agreement with prior experiments. One proton is bound by a hydroxyl group in the BNC and the rest to groups far from the BNC. The electrochemical midpoint potential (E(m)) of heme a is calculated in the fully oxidized protein and with 1 or 2 electrons in the BNC. The E(m) of heme a shifts down when the BNC is reduced, which agrees with prior experiments. If the BNC reduction is electroneutral, then the heme a E(m) is independent of the BNC redox state.

Design principles of proton-pumping haem-copper oxidases

Transmembrane electrochemical proton gradients are used to store free energy in biological systems, and to drive the synthesis of biomolecules and transmembrane transport. These gradients are maintained by membrane-bound proton transporters that employ free energy provided by, for example, electron transfer or light. In recent years, the structures of several membrane proteins involved in proton translocation have been determined, and indicate that both protein-bound water molecules and protonatable amino acid residues play central roles in transmembrane proton conduction. From these structures, in combination with functional studies, have emerged general principles of proton transfer across membranes and control mechanisms for such reactions, in particular with regard to the electron-transfer-driven proton pump cytochrome c oxidase.

A simple clustering algorithm can be accurate enough for use in calculations of pKs in macromolecules

Structure and function of macromolecules depend critically on the ionization states of their acidic and basic groups. Most current structure-based theoretical methods that predict pK of ionizable groups in macromolecules include, as one of the key steps, a computation of the partition sum (Boltzmann average) over all possible protonation microstates. As the number of these microstates depends exponentially on the number of ionizable groups present in the molecule, direct computation of the sum is not realistically feasible for many typical proteins that may have tens or even hundreds of ionizable groups. We have tested a simple and robust approximate algorithm for computing these partition sums for macromolecules. The method subdivides the interacting sites into independent clusters, based upon the strength of site-site electrostatic interaction. The resulting partition function is factorizable into computationally manageable components. Two variants of the approach are presented and validated on a representative test set of 602 proteins, by comparing the pK(1/2) values computed by the proposed method with those obtained by the standard Monte Carlo approach used as a reference. With 95% confidence, the relative error introduced by the more accurate of the two methods is less than 0.25 pK units. The algorithms are one to two orders of magnitude faster than the Monte Carlo method, with the typical settings. A graphical representation is introduced that visualizes the clusters of strong site-site interactions in the context of the three-dimensional (3D) structure of the macromolecule, facilitating identification of functionally important clusters of ionizable groups; the approach is exemplified on two proteins, bacteriorhodopsin and myoglobin.

Factors influencing the energetics of electron and proton transfers in proteins. What can be learned from calculations

A protein structure should provide the information needed to understand its observed properties. Significant progress has been made in developing accurate calculations of acid/base and oxidation/reduction reactions in proteins. Current methods and their strengths and weaknesses are discussed. The distribution and calculated ionization states in a survey of proteins is described, showing that a significant minority of acidic and basic residues are buried in the protein and that most of these remain ionized. The electrochemistry of heme and quinones are considered. Proton transfers in bacteriorhodopsin and coupled electron and proton transfers in photosynthetic reaction centers, 5-coordinate heme binding proteins and cytochrome c oxidase are highlighted as systems where calculations have provided insight into the reaction mechanism.

Photoinduced Surface Potential Change of Bacteriorhodopsin Mutant D96N Measured by Scanning Surface Potential Microscopy

We report the direct measurement of photoinduced surface potential differences of wild-type (WT) and mutant D96N bacteriorhodopsin (BR) membranes at pH 7 and 10.5. Atomic force microscopy (AFM) and scanning surface potential microscopy (SSPM) were used to measure the BR membrane with the extracellular side facing up. We present AFM and SSPM images of WT and mutant D96N in which the light-dark transition occurred in the mid-scan of a single BR membrane. Photosteady-state populations of the M state were generated to facilitate measurement in each sample. The photoinduced surface potential of D96N is 63 mV (peak to valley) at pH 10.5 and is 48 mV at pH 7. The photoinduced surface potential of WT is 37 mV at pH 10.5 and approximately 0 at pH 7. Signal magnitudes are proportional to the amount of M produced at each pH. The results indicated that the surface potentials were generated by photoformation of surface charges on the extracellular side of the membrane. Higher surface potential correlated with a longer lifetime of the charges. A mechanistic basis for these signals is proposed, and it is concluded that they represent a steady-state measurement of the B2 photovoltage.

Time-resolved thermodynamic profiles for CO photolsysis from the mixed valence form of bovine heart cytochrome c oxidase

Photoacoustic calorimetry has been utilized to probe the thermodynamics accompanying photodissociation of the CO mixed valence form of bovine heart cytochrome c oxidase (COMV CcO). At pH's below 9 photolysis of the COMV CcO results in three kinetic phases with the first phase occurring faster than the time resolution of the instrument (i.e., < approximately 50 ns), a second phase occurring with a lifetime of approximately 100 ns and a third phase occurring with a lifetime of approximately 2 micros. The corresponding volume and enthalpy changes for these processes are: DeltaH1, DeltaV1 = +79 +/- 10 kcal mol(-1), +9 +/- 1 mL mol(-1); DeltaH2, DeltaV2 = -79 +/- 5 kcal mol(-1), -9 +/- 2 mL mol(-1); DeltaH3, DeltaV3 = +54 +/- 7 kcal mol(-1), +8 +/- 1 mL mol(-1). At pH's above 9 only one phase is observed, a prompt phase occurring in < 50 ns. The overall volume change is negligible above pH 9 and the enthalpy change is +29 +/- 5 kcal mol(-1). The data are consistent with the prompt phase being associated with CO-Fe(a3) bond cleavage, CO-CuB+ bond formation, Fe(a3) low-spin to high-spin transition and fast electron transfer (ET) from heme a3 to heme a followed by proton transfer from Glu242 to Arg38 on an approximately 100 ns timescale. The slow phase is likely a combination of CO thermal dissociation from CuB and additional ET between heme a3 to heme a. Interestingly, this phase is not evident above pH 9 suggesting linkage between CO dissociation/ET and the protonation state of a group or groups near the binuclear center.

Two conformational states of Glu242 and pKas in bovine cytochrome c oxidase

Cytochrome c oxidase (CcO) is the terminal enzyme in the respiratory electron transport chain of aerobic organisms. It catalyses the reduction of atmospheric oxygen to water, and couples this reaction to proton pumping across the membrane; this process generates the electrochemical gradient that subsequently drives the synthesis of ATP. The molecular details of the mechanism by which electron transfer is coupled to proton pumping in CcO is poorly understood. Recent calculations from our group indicate that His291, a ligand of the Cu(B) center of the enzyme, may play the role of the pumping element. In this paper we describe calculations in which a DFT/continuum electrostatic method is used to explore the coupling of the conformational changes of Glu242 residue, the main proton donor of both chemical and pump protons, to its pKa, and the pKa of His291, a putative proton loading site of our pumping model. The computations are done for several redox states of metal centers, different protonation states of Glu242 and His291, and two well-defined conformations of the Glu242 side chain. Thus, in addition to equilibrium redox/protonation states of the catalytic cycle, we also examine the transient and intermediate states. Different dielectric models are employed to investigate the robustness of the results, and their viability in the light of the proposed proton pumping mechanism of CcO. The main results are in agreement with the experimental measurements and support the proposed pumping mechanism. Additionally, the present calculations indicate a possibility of gating through conformational changes of Glu242; namely, in the pumping step, we find that Glu242 needs to be reprotonated before His291 can eject a proton to the P-site of membrane. As a result, the reprotonation of Glu can control proton release from the proton loading site.

Theoretical investigation of the behavior of titratable groups in proteins

This paper presents a theoretical analysis of the titration behavior of strongly interacting titratable residues in proteins. Strongly interacting titratable residues exist in many proteins such as for instance bacteriorhodopsin, cytochrome c oxidase, cytochrome bc(1), or the photosynthetic reaction center. Strong interaction between titratable groups can lead to irregular titration behavior. We analyze under which circumstances titration curves can become irregular. We demonstrate that conformational flexibility alone can not lead to irregular titration behavior. Strong interaction between titratable groups is a necessary, but not sufficient condition for irregular titration curves. In addition, the two interacting groups also need to titrate in the same pH-range. These two conditions together lead to irregular titration curves. The mutation of a single residue within a cluster of interacting titratable residues can influence the titration behavior of the other titratable residues in the cluster. We demonstrate this effect on a cluster of four interacting residues. This example underlines that mutational studies directed at identifying the role of a certain titratable residue in a cluster of interacting residues should always be accompanied by an analysis of the effect of the mutation on the titration behavior of the other residues.

Molecular dynamics simulations of proteins in lipid bilayers

With recent advances in X-ray crystallography of membrane proteins promising many new high-resolution structures, molecular dynamics simulations will become increasingly valuable for understanding membrane protein function, as they can reveal the dynamic behavior concealed in the static structures. Dramatic increases in computational power, in synergy with more efficient computational methodologies, now allow us to carry out molecular dynamics simulations of any structurally known membrane protein in its native environment, covering timescales of up to 0.1 micros. At the frontiers of membrane protein simulations are ion channels, aquaporins, passive and active transporters, and bioenergetic proteins.