pH-dependent dynamics of complex RNA macromolecules

Understanding the adsorption of plasmid DNA and RNA molecules onto arginine-agarose chromatographic resin

Background

The production of nucleic acids (plasmid DNA or mRNA) in response to the development of new advanced vaccine platforms has greatly increased recently, mostly resulting from the pandemic situation. Due to the intended pharmaceutical use, nucleic acids preparations must fulfill all the required specifications in terms of purity and quality. Chromatography is a standard operation used to isolate these molecules from impurities, playing a central role in the manufacturing processes. However, the mechanism of nucleic acid adsorption in chromatographic resins is poorly understood, often leading to low adsorption capacities and a lack of specificity.

Methods and results

Here we investigated the adsorption of plasmid DNA and RNA molecules onto arginine-agarose, a resin with potential for large-scale application. Equilibrium batch studies were performed through pre-purified samples, using arginine-based ligands by varying the adsorption conditions in the pH value range from 6.0 to 9.0. Langmuir and Freundlich isotherm models were used to describe the adsorption equilibrium. The best fit for both nucleic acids was achieved using the Freundlich model. The correct choice of pH showed critical for controlling the efficacy of arginine-nucleic acid interaction, due to its influence on the nucleic acid structures. This type of analysis is necessary for the improvement of the selectivity and binding capacities of the resins used for plasmid DNA or mRNA purification.

Conclusions

The results presented here indicate that adsorption conditions can be tuned to enhance separation between pDNA and RNA, an important feature in the purification of nucleic acids for vaccine production.

Titration of Adenine in a GA Mismatch with Grand Canonical Simulations

Computational prediction of the pKa of ionizable groups remains a central challenge in biomolecular modeling. Although all-atom fixed-charge force fields could be accurate to describe the interaction network within the biomolecules, proper sampling techniques are required to obtain the thermodynamic information in the (de)protonation event. Sufficient sampling requires an ensemble of structures from simulations with proper treatments of the acid-base equilibria, and the grand canonical simulation technique could be used to model the growth/annihilation of hydrogen atoms by merging Hamiltonians of different protonation states into one simulation ensemble. The electrostatic feature of nucleotide systems is especially difficult to model, and the situation becomes more challenging when the ionizable site is highly perturbed. Although there are many successful predictions obtained from the grand canonical constant pH simulations, few reports focus on highly perturbed nucleotide systems with unconventional base-pair features. In this work, with the discrete constant pH method, we investigate the titration thermodynamics of an adenine in the catalytic triad in a 35-nucleotide single-stranded RNA hairpin, featuring an unconventional GA mismatch and a substantially shifted pKa value. Validation tests are performed with two system setups, both of which provide pKa predictions in good agreement with the experimental value. A single-configuration-based technique is used to calculate the pKa for comparison. The current success indicates the predictive power of the current nucleotide modeling framework.

Exploring pH Dependent Host/Guest Binding Affinities

When the electrostatic environment surrounding binding partners changes between unbound and bound states, the net uptake or release of a proton is possible by either binding partner. This process is pH-dependent in that the free energy required to uptake or release the proton varies with pH. This pH-dependence is typically not considered in conventional free energy methods where the use of fixed protonation states is the norm. In the present paper, we apply a simple two-step approach to calculate the pH-dependent binding free energy of a model cucubit[7]uril host/guest system. By use of λ-dynamics with an enhanced sampling protocol, adaptive landscape flattening, pK_a shifts and reference binding free energies upon complexation were determined. This information enables the construction of pH-dependent binding profiles that accurately capture the pK_a shifts and reproduce binding free energies at the different pH conditions that were observed experimentally. Our calculations illustrate a general framework for computing pH-dependent binding free energies but also point to some issues in modeling the molecular charge distributions within this series of molecules with CGenFF. However, by introducing some minor charge modifications to the CGenFF force field, we saw significant improvement in accuracy of the calculated pK_a shifts.

M2 amphipathic helices facilitate pH-dependent conformational transition in influenza A virus

The matrix-2 (M2) protein from influenza A virus is a tetrameric, integral transmembrane (TM) protein that plays a vital role in viral replication by proton flux into the virus. The His37 tetrad is a pH sensor in the center of the M2 TM helix that activates the channel in response to the low endosomal pH. M2 consists of different regions that are believed to be involved in membrane targeting, packaging, nucleocapsid binding, and proton transport. Although M2 has been the target of many experimental and theoretical studies that have led to significant insights into its structure and function under differing conditions, the main mechanism of proton transport, its conformational dynamics, and the role of the amphipathic helices (AHs) on proton conductance remain elusive. To this end, we have applied explicit solvent constant pH molecular dynamics using the multisite λ-dynamics approach (CpHMD^MSλD) to investigate the buried ionizable residues comprehensively and to elucidate their effect on the conformational transition. Our model recapitulates the pH-dependent conformational transition of M2 from closed to open state when the AH domain is included in the M2 construct, revealing the role of the amphipathic helices on this transition and shedding light on the proton-transport mechanism. This work demonstrates the importance of including the amphipathic helices in future experimental and theoretical studies of ion channels. Finally, our work shows that explicit solvent CpHMD^MSλD provides a realistic pH-dependent model for membrane proteins.

An IRMPD spectroscopic and computational study of protonated guanine-containing mismatched base pairs in the gas phase

Infrared multiple photon dissociation spectroscopy has been used to probe the structures of the three protonated base-pair mismatches containing 9-ethylguanine (9eG) in the gas phase. Some of these protonated base-pairs have been identified in RNA.

Coarse-grained dynamic RNA titration simulations

Electrostatic interactions play a pivotal role in many biomolecular processes. The molecular organization and function in biological systems are largely determined by these interactions. Owing to the highly negative charge of RNA, the effect is expected to be more pronounced in this system. Moreover, RNA base pairing is dependent on the charge of the base, giving rise to alternative secondary and tertiary structures. The equilibrium between uncharged and charged bases is regulated by the solution pH, which is therefore a key environmental condition influencing the molecule's structure and behaviour. By means of constant-pH Monte Carlo simulations based on a fast proton titration scheme, coupled with the coarse-grained model HiRE-RNA, molecular dynamic simulations of RNA molecules at constant pH enable us to explore the RNA conformational plasticity at different pH values as well as to compute electrostatic properties as local pK _a values for each nucleotide.

Evidence for Hidden Involvement of N3-Protonated Guanine in RNA Structure and Function

Charged nucleobases have been found to occur in several known RNA molecules and are considered essential for their structure and function. The mechanism of their involvement is however not yet fully understood. Revelation of the role of N7-protonated guanine, in modulating the geometry and stability of noncanonical base pairs formed through its unprotonated edges [Watson-Crick (WC) and sugar], has triggered the need to evaluate the feasibility of similar roles of other protonated nucleobases [Halder et al., Phys Chem Chem Phys, 2015, 17, 26249]. In this context, N3 protonation of guanine makes an interesting case as its influence on the charge distribution of the WC edge is similar to that of N7 protonation, though its thermodynamic cost of protonation is significantly higher. In this work, we have carried out structural bioinformatics analyses and quantum mechanics-based calculations to show that N3 protonation of guanine may take place in a cellular environment, at least in the G:C W:W Trans and G:G W:H Cis base pairs. Our results provide a reasonable starting point for future investigations in order to address the larger mechanistic question.

Single-Molecule Mechanical Folding and Unfolding of RNA Hairpins: Effects of Single A-U to A·C Pair Substitutions and Single Proton Binding and Implications for mRNA Structure-Induced -1 Ribosomal Frameshifting

A wobble A·C pair can be protonated at near physiological pH to form a more stable wobble A⁺·C pair. Here, we constructed an RNA hairpin (rHP) and three mutants with one A-U base pair substituted with an A·C mismatch on the top (near the loop, U22C), middle (U25C), and bottom (U29C) positions of the stem, respectively. Our results on single-molecule mechanical (un)folding using optical tweezers reveal the destabilization effect of A-U to A·C pair substitution and protonation-dependent enhancement of mechanical stability facilitated through an increased folding rate, or decreased unfolding rate, or both. Our data show that protonation may occur rapidly upon the formation of an apparent mechanical folding transition state. Furthermore, we measured the bulk -1 ribosomal frameshifting efficiencies of the hairpins by a cell-free translation assay. For the mRNA hairpins studied, -1 frameshifting efficiency correlates with mechanical unfolding force at equilibrium and folding rate at around 15 pN. U29C has a frameshifting efficiency similar to that of rHP (∼2%). Accordingly, the bottom 2-4 base pairs of U29C may not form under a stretching force at pH 7.3, which is consistent with the fact that the bottom base pairs of the hairpins may be disrupted by ribosome at the slippery site. U22C and U25C have a similar frameshifting efficiency (∼1%), indicating that both unfolding and folding rates of an mRNA hairpin in a crowded environment may affect frameshifting. Our data indicate that mechanical (un)folding of RNA hairpins may mimic how mRNAs unfold and fold in the presence of translating ribosomes.

Constant-pH Molecular Dynamics Simulations for Large Biomolecular Systems

An increasingly important endeavor is to develop computational strategies that enable molecular dynamics (MD) simulations of biomolecular systems with spontaneous changes in protonation states under conditions of constant pH. The present work describes our efforts to implement the powerful constant-pH MD simulation method, based on a hybrid nonequilibrium MD/Monte Carlo (neMD/MC) technique within the highly scalable program NAMD. The constant-pH hybrid neMD/MC method has several appealing features; it samples the correct semigrand canonical ensemble rigorously, the computational cost increases linearly with the number of titratable sites, and it is applicable to explicit solvent simulations. The present implementation of the constant-pH hybrid neMD/MC in NAMD is designed to handle a wide range of biomolecular systems with no constraints on the choice of force field. Furthermore, the sampling efficiency can be adaptively improved on-the-fly by adjusting algorithmic parameters during the simulation. Illustrative examples emphasizing medium- and large-scale applications on next-generation supercomputing architectures are provided.

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

pH is a critical parameter for biological and technological systems directly related with electrical charges. It can give rise to peculiar electrostatic phenomena, which also makes them more challenging. Due to the quantum nature of the process, involving the forming and breaking of chemical bonds, quantum methods should ideally by employed. Nevertheless, due to the very large number of ionizable sites, different macromolecular conformations, salt conditions, and all other charged species, the CPU time cost simply becomes prohibitive for computer simulations, making this a quite complex problem. Simplified methods based on Monte Carlo sampling have been devised and will be reviewed here, highlighting the updated state-of-the-art of this field, advantages, and limitations of different theoretical protocols for biomolecular systems (proteins and nucleic acids). Following a historical perspective, the discussion will be associated with the applications to protein interactions with other proteins, polyelectrolytes, and nanoparticles.

Fast coarse-grained model for RNA titration

A new numerical scheme for RNA (ribonucleic acid) titration based on the Debye-Hückel framework for the salt description is proposed in an effort to reduce the computational costs for further applications to study protein-RNA systems. By means of different sets of Monte Carlo simulations, we demonstrated that this new scheme is able to correctly reproduce the experimental titration behavior and salt pK_a shifts. In comparison with other theoretical approaches, similar or even better outcomes are achieved at much lower computational costs. The model was tested on the lead-dependent ribozyme, the branch-point helix, and the domain 5 from Azotobacter vinelandii Intron 5.

Resolving sugar puckers in RNA excited states exposes slow modes of repuckering dynamics

Recent studies have shown that RNAs exist in dynamic equilibrium with short-lived low-abundance 'excited states' that form by reshuffling base pairs in and around non-canonical motifs. These conformational states are proposed to be rich in non-canonical motifs and to play roles in the folding and regulatory functions of non-coding RNAs but their structure proves difficult to characterize given their transient nature. Here, we describe an approach for determining sugar pucker conformation in RNA excited states through nuclear magnetic resonance measurements of C1΄ and C4΄ rotating frame spin relaxation (R1ρ) in uniformly 13C/15N labeled RNA samples. Application to HIV-1 TAR exposed slow modes of sugar repuckering dynamics at the μs and ms timescale accompanying transitions between non-helical (C2΄-endo) to helical (C3΄-endo) conformations during formation of two distinct excited states. In contrast, we did not obtain any evidence for slow sugar repuckering dynamics for nucleotides in a variety of structural contexts that do not undergo non-helical to helical transitions. Our results outline a route for significantly improving the conformational characterization of RNA excited states and suggest that slow modes of repuckering dynamics gated by transient changes in secondary structure are quite common in RNA.

CHARMM-GUI 10 years for biomolecular modeling and simulation

CHARMM-GUI, http://www.charmm-gui.org, is a web-based graphical user interface that prepares complex biomolecular systems for molecular simulations. CHARMM-GUI creates input files for a number of programs including CHARMM, NAMD, GROMACS, AMBER, GENESIS, LAMMPS, Desmond, OpenMM, and CHARMM/OpenMM. Since its original development in 2006, CHARMM-GUI has been widely adopted for various purposes and now contains a number of different modules designed to set up a broad range of simulations: (1) PDB Reader & Manipulator, Glycan Reader, and Ligand Reader & Modeler for reading and modifying molecules; (2) Quick MD Simulator, Membrane Builder, Nanodisc Builder, HMMM Builder, Monolayer Builder, Micelle Builder, and Hex Phase Builder for building all-atom simulation systems in various environments; (3) PACE CG Builder and Martini Maker for building coarse-grained simulation systems; (4) DEER Facilitator and MDFF/xMDFF Utilizer for experimentally guided simulations; (5) Implicit Solvent Modeler, PBEQ-Solver, and GCMC/BD Ion Simulator for implicit solvent related calculations; (6) Ligand Binder for ligand solvation and binding free energy simulations; and (7) Drude Prepper for preparation of simulations with the CHARMM Drude polarizable force field. Recently, new modules have been integrated into CHARMM-GUI, such as Glycolipid Modeler for generation of various glycolipid structures, and LPS Modeler for generation of lipopolysaccharide structures from various Gram-negative bacteria. These new features together with existing modules are expected to facilitate advanced molecular modeling and simulation thereby leading to an improved understanding of the structure and dynamics of complex biomolecular systems. Here, we briefly review these capabilities and discuss potential future directions in the CHARMM-GUI development project. © 2016 Wiley Periodicals, Inc.

Versatile RNA tetra-U helix linking motif as a toolkit for nucleic acid nanotechnology

RNA nanotechnology employs synthetically modified ribonucleic acid (RNA) to engineer highly stable nanostructures in one, two, and three dimensions for medical applications. Despite the tremendous advantages in RNA nanotechnology, unmodified RNA itself is fragile and prone to enzymatic degradation. In contrast to use traditionally modified RNA strands e.g. 2'-fluorine, 2'-amine, 2'-methyl, we studied the effect of RNA/DNA hybrid approach utilizing a computer-assisted RNA tetra-uracil (tetra-U) motif as a toolkit to address questions related to assembly efficiency, versatility, stability, and the production costs of hybrid RNA/DNA nanoparticles. The tetra-U RNA motif was implemented to construct four functional triangles using RNA, DNA and RNA/DNA mixtures, resulting in fine-tunable enzymatic and thermodynamic stabilities, immunostimulatory activity and RNAi capability. Moreover, the tetra-U toolkit has great potential in the fabrication of rectangular, pentagonal, and hexagonal NPs, representing the power of simplicity of RNA/DNA approach for RNA nanotechnology and nanomedicine community.

Polyelectrolyte pKa from experiment and molecular dynamics simulation

The pK_a of a polyelectrolyte has been determined experimentally by potentiometric titration and computed using Molecular Dynamics (MD) constant pH (CpH) methodology, which allows the pK_a of each titratable site along the polymer backbone.

All-Atom Continuous Constant pH Molecular Dynamics With Particle Mesh Ewald and Titratable Water

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Toward this goal recent years have witnessed the emergence of the so-called constant pH molecular dynamics methods. However, the accuracy and generality of these methods have been hampered by the use of implicit-solvent models or truncation-based electrostatic schemes. Here we report the implementation of the particle mesh Ewald (PME) scheme into the all-atom continuous constant pH molecular dynamics (CpHMD) method, enabling CpHMD to be performed with a standard MD engine at a fractional added computational cost. We demonstrate the performance using pH replica-exchange CpHMD simulations with titratable water for a stringent test set of proteins, HP36, BBL, HEWL, and SNase. With the sampling time of 10 ns per replica, most pK_a's are converged, yielding the average absolute and root-mean-square deviations of 0.61 and 0.77, respectively, from experiment. Linear regression of the calculated vs experimental pK_a shifts gives a correlation coefficient of 0.79, a slope of 1, and an intercept near 0. Analysis reveals inadequate sampling of structure relaxation accompanying a protonation-state switch as a major source of the remaining errors, which are reduced as simulation prolongs. These data suggest PME-based CpHMD can be used as a general tool for pH-controlled simulations of macromolecular systems in various environments, enabling atomic insights into pH-dependent phenomena involving not only soluble proteins but also transmembrane proteins, nucleic acids, surfactants, and polysaccharides.

Constant-pH Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulation Method

A computational method is developed to carry out explicit solvent simulations of complex molecular systems under conditions of constant pH. In constant-pH simulations, preidentified ionizable sites are allowed to spontaneously protonate and deprotonate as a function of time in response to the environment and the imposed pH. The method, based on a hybrid scheme originally proposed by H. A. Stern (J. Chem. Phys. 2007, 126, 164112), consists of carrying out short nonequilibrium molecular dynamics (neMD) switching trajectories to generate physically plausible configurations with changed protonation states that are subsequently accepted or rejected according to a Metropolis Monte Carlo (MC) criterion. To ensure microscopic detailed balance arising from such nonequilibrium switches, the atomic momenta are altered according to the symmetric two-ends momentum reversal prescription. To achieve higher efficiency, the original neMD-MC scheme is separated into two steps, reducing the need for generating a large number of unproductive and costly nonequilibrium trajectories. In the first step, the protonation state of a site is randomly attributed via a Metropolis MC process on the basis of an intrinsic pKa; an attempted nonequilibrium switch is generated only if this change in protonation state is accepted. This hybrid two-step inherent pKa neMD-MC simulation method is tested with single amino acids in solution (Asp, Glu, and His) and then applied to turkey ovomucoid third domain and hen egg-white lysozyme. Because of the simple linear increase in the computational cost relative to the number of titratable sites, the present method is naturally able to treat extremely large systems.

Diverse mixtures of 2,4-dihydroxy tautomers and O4 protonated conformers of uridine and 2'-deoxyuridine coexist in the gas phase

The gas-phase conformations of protonated uridine, [Urd+H](+), and its modified form, protonated 2'-deoxyuridine, [dUrd+H](+), generated by electrospray ionization are investigated using infrared multiple photon dissociation (IRMPD) action spectroscopy techniques. IRMPD action spectra of [Urd+H](+) and [dUrd+H](+) are measured over the IR fingerprint and hydrogen-stretching regions. [Urd+H](+) and [dUrd+H](+) exhibit very similar IRMPD spectral profiles. However, the IRMPD yields of [Urd+H](+) exceed those of [dUrd+H](+) in both the IR fingerprint and hydrogen-stretching regions. The measured spectra are compared to the linear IR spectra predicted for the stable low-energy structures of these species computed at the B3LYP/6-311+G(d,p) level of theory to determine the tautomeric conformations populated by electrospray ionization. Both B3LYP and MP2 methods find O4 and O2 protonated canonical as well as 2,4-dihydroxy tautomers among the stable low-energy structures of [Urd+H](+) and [dUrd+H](+). Comparison between the measured IRMPD and calculated linear IR spectra suggests that these species exist in their ring-closed forms and that both 2,4-dihydroxy tautomers as well as O4 protonated canonical conformers coexist in the population generated by electrospray ionization for both [Urd+H](+) and [dUrd+H](+). The 2'-deoxy modification of [dUrd+H](+) reduces the variety of 2,4-dihydroxy tautomers populated in the experiments vs. those of [Urd+H](+).

Coarse-grained modeling of RNA 3D structure

Functional RNA molecules depend on three-dimensional (3D) structures to carry out their tasks within the cell. Understanding how these molecules interact to carry out their biological roles requires a detailed knowledge of RNA 3D structure and dynamics as well as thermodynamics, which strongly governs the folding of RNA and RNA-RNA interactions as well as a host of other interactions within the cellular environment. Experimental determination of these properties is difficult, and various computational methods have been developed to model the folding of RNA 3D structures and their interactions with other molecules. However, computational methods also have their limitations, especially when the biological effects demand computation of the dynamics beyond a few hundred nanoseconds. For the researcher confronted with such challenges, a more amenable approach is to resort to coarse-grained modeling to reduce the number of data points and computational demand to a more tractable size, while sacrificing as little critical information as possible. This review presents an introduction to the topic of coarse-grained modeling of RNA 3D structures and dynamics, covering both high- and low-resolution strategies. We discuss how physics-based approaches compare with knowledge based methods that rely on databases of information. In the course of this review, we discuss important aspects in the reasoning process behind building different models and the goals and pitfalls that can result.

Ribozyme Catalysis with a Twist: Active State of the Twister Ribozyme in Solution Predicted from Molecular Simulation

We present results from molecular dynamics simulations and free energy calculations of the twister ribozyme at different stages along the reaction path to gain insight into its mechanism. The results, together with recent biochemical experiments, provide support for a mechanism involving general-acid catalysis by a conserved adenine residue in the active site. Although adenine has been previously implicated as a general acid acting through the N1 position in other ribozymes such as the hairpin and VS ribozymes, in the twister ribozyme there may be a twist. Biochemical experiments suggest that general acid catalysis may occur through the N3 position, which has never before been implicated in this role; however, currently, there is a lack of a detailed structural model for the active state of the twister ribozyme in solution that is consistent with these and other experiments. Simulations in a crystalline environment reported here are consistent with X-ray crystallographic data, and suggest that crystal packing contacts trap the RNA in an inactive conformation with U-1 in an extruded state that is incompatible with an in-line attack to the scissile phosphate. Simulations in solution, on the other hand, reveal this region to be dynamic and able to adopt a conformation where U-1 is stacked with G33. In this state, the nucleophile is in line with the scissile phosphate, and the N1 position of G33 and N3 position of A1 are poised to act as a general base and acid, respectively, as supported by mutational experiments. Free energy calculations further predict the electrostatic environment causes a shift of the microscopic pKa at the N3 position of A1 toward neutrality by approximately 5 pKa units. These results offer a unified interpretation of a broad range of currently available experimental data that points to a novel mode of general acid catalysis through the N3 position of an adenine nucleobase, thus expanding the repertoire of known mechanistic strategies employed by small nucleolytic ribozymes.

Anions in Nucleic Acid Crystallography

Nucleic acid crystallization buffers contain a large variety of chemicals fitting specific needs. Among them, anions are often solely considered for pH-regulating purposes and as cationic co-salts while their ability to directly bind to nucleic acid structures is rarely taken into account. Here we review current knowledge related to the use of anions in crystallization buffers along with data on their biological prevalence. Chloride ions are frequently identified in crystal structures but display low cytosolic concentrations. Hence, they are thought to be distant from nucleic acid structures in the cell. Sulfate ions are also frequently identified in crystal structures but their localization in the cell remains elusive. Nevertheless, the characterization of the binding properties of these ions is essential for better interpreting the solvent structure in crystals and consequently, avoiding mislabeling of electron densities. Furthermore, understanding the binding properties of these anions should help to get clues related to their potential effects in crowded cellular environments.

Computation of pH-dependent binding free energies

Protein-ligand binding accompanies changes in the surrounding electrostatic environments of the two binding partners and may lead to changes in protonation upon binding. In cases where the complex formation results in a net transfer of protons, the binding process is pH-dependent. However, conventional free energy computations or molecular docking protocols typically employ fixed protonation states for the titratable groups in both binding partners set a priori, which are identical for the free and bound states. In this review, we draw attention to these important yet largely ignored binding-induced protonation changes in protein-ligand association by outlining physical origins and prevalence of the protonation changes upon binding. Following a summary of various theoretical methods for pKa prediction, we discuss the theoretical framework to examine the pH dependence of protein-ligand binding processes.

Conformational Dynamics and Binding Free Energies of Inhibitors of BACE-1: From the Perspective of Protonation Equilibria

BACE-1 is the β-secretase responsible for the initial amyloidogenesis in Alzheimer’s disease, catalyzing hydrolytic cleavage of substrate in a pH-sensitive manner. The catalytic mechanism of BACE-1 requires water-mediated proton transfer from aspartyl dyad to the substrate, as well as structural flexibility in the flap region. Thus, the coupling of protonation and conformational equilibria is essential to a full in silico characterization of BACE-1. In this work, we perform constant pH replica exchange molecular dynamics simulations on both apo BACE-1 and five BACE-1-inhibitor complexes to examine the effect of pH on dynamics and inhibitor binding properties of BACE-1. In our simulations, we find that solution pH controls the conformational flexibility of apo BACE-1, whereas bound inhibitors largely limit the motions of the holo enzyme at all levels of pH. The microscopic pK_a values of titratable residues in BACE-1 including its aspartyl dyad are computed and compared between apo and inhibitor-bound states. Changes in protonation between the apo and holo forms suggest a thermodynamic linkage between binding of inhibitors and protons localized at the dyad. Utilizing our recently developed computational protocol applying the binding polynomial formalism to the constant pH molecular dynamics (CpHMD) framework, we are able to obtain the pH-dependent binding free energy profiles for various BACE-1-inhibitor complexes. Our results highlight the importance of correctly addressing the binding-induced protonation changes in protein-ligand systems where binding accompanies a net proton transfer. This work comprises the first application of our CpHMD-based free energy computational method to protein-ligand complexes and illustrates the value of CpHMD as an all-purpose tool for obtaining pH-dependent dynamics and binding free energies of biological systems.

Formation of insoluble amyloid plaques in the vascular and hippocampal areas of the brain characterizes Alzheimer’s disease, a devastating neurodegenerative disorder causing dementia. Site-specific hydrolytic catalysis of β-secretase, or BACE-1, is responsible for production of oligomerative amyloid β-peptide. As the catalytic activity of BACE-1 is pH-dependent and its structural dynamics are intrinsic to the catalysis, we examine the dependence of dynamics of BACE-1 on solution pH and its implications on the catalytic mechanism of BACE-1. Also, we highlight the importance of accurate description of protonation states of the titratable groups in computer-aided drug discovery targeting BACE-1. We hope the understanding of pH dependence of the dynamics and inhibitor binding properties of BACE-1 will aid the structure-based inhibitor design efforts against Alzheimer’s disease.

Membrane environment modulates the pKa values of transmembrane helices

In this work, we apply the recently developed constant pH molecular dynamics technique to study protonation equilibria of titratable side chains in the context of simple transmembrane (TM) helices and explore the effect of pH on their configurations in membrane bilayers. We observe that, despite a significant shift toward neutral states, considerable population of different side chains stay in the charged state that give rise to pK_a values around 9.6 for Asp and Glu and 4.5 to 6 for His and Lys side chains, respectively. These charged states are highly stabilized by favorable interactions between head groups, water molecules, and the charged side chains that are facilitated by substantial changes in the configuration of the peptides. The pH dependent configurations and the measured pK_a values are in good agreement with relatively recent solid state NMR measurements. Our results presented here demonstrate that all-atom constant pH molecular dynamics can be applied to membrane proteins and peptides to obtain reliable pK_a values and pH dependent behavior for these systems.

pH-dependent transient conformational states control optical properties in cyan fluorescent protein

A recently engineered mutant of cyan fluorescent protein (WasCFP) that exhibits pH-dependent absorption suggests that its tryptophan-based chromophore switches between neutral (protonated) and charged (deprotonated) states depending on external pH. At pH 8.1, the latter gives rise to green fluorescence as opposed to the cyan color of emission that is characteristic for the neutral form at low pH. Given the high energy cost of deprotonating the tryptophan at the indole nitrogen, this behavior is puzzling, even if the stabilizing effect of the V61K mutation in proximity to the protonation/deprotonation site is considered. Because of its potential to open new avenues for the development of optical sensors and photoconvertible fluorescent proteins, a mechanistic understanding of how the charged state in WasCFP can possibly be stabilized is thus important. Attributed to the dynamic nature of proteins, such understanding often requires knowledge of the various conformations adopted, including transiently populated conformational states. Transient conformational states triggered by pH are of emerging interest and have been shown to be important whenever ionizable groups interact with hydrophobic environments. Using a combination of the weighted-ensemble sampling method and explicit-solvent constant pH molecular dynamics (CPHMD(MSλD)) simulations, we have identified a solvated transient state, characterized by a partially open β-barrel where the chromophore pKa of 6.8 is shifted by over 20 units from that of the closed form (6.8 and 31.7, respectively). This state contributes a small population at low pH (12% at pH 6.1) but becomes dominant at mildly basic conditions, contributing as much as 53% at pH 8.1. This pH-dependent population shift between neutral (at pH 6.1) and charged (at pH 8.1) forms is thus responsible for the observed absorption behavior of WasCFP. Our findings demonstrate the conditions necessary to stabilize the charged state of the WasCFP chromophore (namely, local solvation at the deprotonation site and a partial flexibility of the protein β-barrel structure) and provide the first evidence that transient conformational states can control optical properties of fluorescent proteins.

Interpretation of pH-activity profiles for acid-base catalysis from molecular simulations

The measurement of reaction rate as a function of pH provides essential information about mechanism. These rates are sensitive to the pK(a) values of amino acids directly involved in catalysis that are often shifted by the enzyme active site environment. Experimentally observed pH-rate profiles are usually interpreted using simple kinetic models that allow estimation of "apparent pK(a)" values of presumed general acid and base catalysts. One of the underlying assumptions in these models is that the protonation states are uncorrelated. In this work, we introduce the use of constant pH molecular dynamics simulations in explicit solvent (CpHMD) with replica exchange in the pH-dimension (pH-REMD) as a tool to aid in the interpretation of pH-activity data of enzymes and to test the validity of different kinetic models. We apply the methods to RNase A, a prototype acid-base catalyst, to predict the macroscopic and microscopic pK(a) values, as well as the shape of the pH-rate profile. Results for apo and cCMP-bound RNase A agree well with available experimental data and suggest that deprotonation of the general acid and protonation of the general base are not strongly coupled in transphosphorylation and hydrolysis steps. Stronger coupling, however, is predicted for the Lys41 and His119 protonation states in apo RNase A, leading to the requirement for a microscopic kinetic model. This type of analysis may be important for other catalytic systems where the active forms of the implicated general acid and base are oppositely charged and more highly correlated. These results suggest a new way for CpHMD/pH-REMD simulations to bridge the gap with experiments to provide a molecular-level interpretation of pH-activity data in studies of enzyme mechanisms.

Role of the active site guanine in the glmS ribozyme self-cleavage mechanism: quantum mechanical/molecular mechanical free energy simulations

The glmS ribozyme catalyzes a self-cleavage reaction at the phosphodiester bond between residues A-1 and G1. This reaction is thought to occur by an acid-base mechanism involving the glucosamine-6-phosphate cofactor and G40 residue. Herein quantum mechanical/molecular mechanical free energy simulations and pKa calculations, as well as experimental measurements of the rate constant for self-cleavage, are utilized to elucidate the mechanism, particularly the role of G40. Our calculations suggest that an external base deprotonates either G40(N1) or possibly A-1(O2'), which would be followed by proton transfer from G40(N1) to A-1(O2'). After this initial deprotonation, A-1(O2') starts attacking the phosphate as a hydroxyl group, which is hydrogen-bonded to deprotonated G40, concurrent with G40(N1) moving closer to the hydroxyl group and directing the in-line attack. Proton transfer from A-1(O2') to G40 is concomitant with attack of the scissile phosphate, followed by the remainder of the cleavage reaction. A mechanism in which an external base does not participate, but rather the proton transfers from A-1(O2') to a nonbridging oxygen during nucleophilic attack, was also considered but deemed to be less likely due to its higher effective free energy barrier. The calculated rate constant for the favored mechanism is in agreement with the experimental rate constant measured at biological Mg(2+) ion concentration. According to these calculations, catalysis is optimal when G40 has an elevated pKa rather than a pKa shifted toward neutrality, although a balance among the pKa's of A-1, G40, and the nonbridging oxygen is essential. These results have general implications, as the hammerhead, hairpin, and twister ribozymes have guanines at a similar position as G40.

Molecular modeling of nucleic Acid structure: electrostatics and solvation

This unit presents an overview of computer simulation techniques as applied to nucleic acid systems, ranging from simple in vacuo molecular modeling techniques to more complete all-atom molecular dynamics treatments that include an explicit representation of the environment. The third in a series of four units, this unit focuses on critical issues in solvation and the treatment of electrostatics. UNITS 7.5 & 7.8 introduced the modeling of nucleic acid structure at the molecular level. This included a discussion of how to generate an initial model, how to evaluate the utility or reliability of a given model, and ultimately how to manipulate this model to better understand its structure, dynamics, and interactions. Subject to an appropriate representation of the energy, such as a specifically parameterized empirical force field, the techniques of minimization and Monte Carlo simulation, as well as molecular dynamics (MD) methods, were introduced as a way of sampling conformational space for a better understanding of the relevance of a given model. This discussion highlighted the major limitations with modeling in general. When sampling conformational space effectively, difficult issues are encountered, such as multiple minima or conformational sampling problems, and accurately representing the underlying energy of interaction. In order to provide a realistic model of the underlying energetics for nucleic acids in their native environments, it is crucial to include some representation of solvation (by water) and also to properly treat the electrostatic interactions. These subjects are discussed in detail in this unit.

Effects of system net charge and electrostatic truncation on all-atom constant pH molecular dynamics

Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here, we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: (1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? (2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force-shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK(a) values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via cotitrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle mesh Ewald, considering the known artifacts due to charge-compensating background plasma.

Protocols utilizing constant pH molecular dynamics to compute pH-dependent binding free energies

In protein–ligand binding, the electrostatic environments of the two binding partners may vary significantly in bound and unbound states, which may lead to protonation changes upon binding. In cases where ligand binding results in a net uptake or release of protons, the free energy of binding is pH-dependent. Nevertheless, conventional free energy calculations and molecular docking protocols typically do not rigorously account for changes in protonation that may occur upon ligand binding. To address these shortcomings, we present a simple methodology based on Wyman’s binding polynomial formalism to account for the pH dependence of binding free energies and demonstrate its use on cucurbit[7]uril (CB[7]) host–guest systems. Using constant pH molecular dynamics and a reference binding free energy that is taken either from experiment or from thermodynamic integration computations, the pH-dependent binding free energy is determined. This computational protocol accurately captures the large pK_a shifts observed experimentally upon CB[7]:guest association and reproduces experimental binding free energies at different levels of pH. We show that incorrect assignment of fixed protonation states in free energy computations can give errors of >2 kcal/mol in these host–guest systems. Use of the methods presented here avoids such errors, thus suggesting their utility in computing proton-linked binding free energies for protein–ligand complexes.

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values.

Uncovering pH-dependent transient states of proteins with buried ionizable residues

The role of pH in regulating biological activity is ubiquitous, and understanding pH-mediated activity has traditionally relied on analyzing static biomolecular structures of highly populated ground states solved near physiological pH. However, recent advances have shown the increasing importance of transiently populated states, the characterization of which is extremely challenging but made plausible with the development of techniques such as relaxation dispersion NMR spectroscopy. To unlock the pH dependence of these transient states with atomistic-level details, we applied the recently developed explicit solvent constant pH molecular dynamics (CPHMD(MSλD)) framework to a series of staphylococcal nuclease (SNase) mutants with buried ionizable residues and probed their dynamics in different pH environments. Among our key findings is the existence of open states in all SNase mutants containing "buried" residues with highly shifted pKa's, where local solvation around the protonation site was observed. The calculated pKa demonstrated good agreement with experimental pKa's, with a low average unsigned error of 1.3 pKa units and correlation coefficient R(2) = 0.78. Sampling both open and closed states in their respective pH range, where they are expected to be dominant, was necessary to reproduce experimental pKa's, and in the most extreme examples of pKa shifts measured, it can be interpreted that the open-state structures are transient at physiological pH, contributing a small population of 1-2%. This suggests that buried ionizable residues can trigger conformational fluctuations that may be observed as transient-state structures at physiological pH. Furthermore, the coupled relationship of both open and closed states and their role in recapitulating macroscopic experimental observables suggest that structural analysis of buried residues may benefit from looking at structural pairs, as opposed to the conventional approach of looking at a single static ground-state conformation.

Recent development and application of constant pH molecular dynamics

Solution pH is a critical environmental factor for chemical and biological processes. Over the last decade, significant efforts have been made in the development of constant pH molecular dynamics (pHMD) techniques for gaining detailed insights into pH-coupled dynamical phenomena. In this article we review the advancement of this field in the past five years, placing a special emphasis on the development of the all-atom continuous pHMD technique. We discuss various applications, including the prediction of pK_a shifts for proteins, nucleic acids and surfactant assemblies, elucidation of pH-dependent population shifts, protein-protein and protein-RNA binding, as well as the mechanisms of pH-dependent self-assembly and phase transitions of surfactants and peptides. We also discuss future directions for the further improvement of the pHMD techniques.

Energetic and structural details of the trigger-loop closing transition in RNA polymerase II

An evolutionarily conserved element in RNA polymerase II, the trigger loop (TL), has been suggested to play an important role in the elongation rate, fidelity of selection of the matched nucleoside triphosphate (NTP), catalysis of transcription elongation, and translocation in both eukaryotes and prokaryotes. In response to NTP binding, the TL undergoes large conformational changes to switch between distinct open and closed states to tighten the active site and avail catalysis. A computational strategy for characterizing the conformational transition pathway is presented to bridge the open and closed states of the TL. Information from a large number of independent all-atom molecular dynamics trajectories from Hamiltonian replica exchange and targeted molecular dynamics simulations is gathered together to assemble a connectivity map of the conformational transition. The results show that with a cognate NTP, TL closing should be a spontaneous process. One major intermediate state is identified along the conformational transition pathway, and the key structural features are characterized. The complete pathway from the open TL to the closed TL provides a clear picture of the TL closing.

Hierarchy of RNA functional dynamics

RNA dynamics play a fundamental role in many cellular functions. However, there is no general framework to describe these complex processes, which typically consist of many structural maneuvers that occur over timescales ranging from picoseconds to seconds. Here, we classify RNA dynamics into distinct modes representing transitions between basins on a hierarchical free-energy landscape. These transitions include large-scale secondary-structural transitions at >0.1-s timescales, base-pair/tertiary dynamics at microsecond-to-millisecond timescales, stacking dynamics at timescales ranging from nanoseconds to microseconds, and other "jittering" motions at timescales ranging from picoseconds to nanoseconds. We review various modes within these three different tiers, the different mechanisms by which they are used to regulate function, and how they can be coupled together to achieve greater functional complexity.

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

pH is a ubiquitous regulator of biological activity, including protein-folding, protein-protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH-dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi-site λ-dynamics (CPHMD(MSλD)). In the CPHMD(MSλD) framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi-site λ-dynamics, and designed novel biasing potentials to ensure that the physical end-states are predominantly sampled. We show that explicit solvent CPHMD(MSλD) simulations model realistic pH-dependent properties of proteins such as the Hen-Egg White Lysozyme (HEWL), binding domain of 2-oxoglutarate dehydrogenase (BBL) and N-terminal domain of ribosomal protein L9 (NTL9), and the pKa predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pKa units. With the recent development of the explicit solvent CPHMD(MSλD) framework for nucleic acids, accurate modeling of pH-dependent properties of both major class of biomolecules-proteins and nucleic acids is now possible.

Isosteric and nonisosteric base pairs in RNA motifs: molecular dynamics and bioinformatics study of the sarcin-ricin internal loop

The sarcin-ricin RNA motif (SR motif) is one of the most prominent recurrent RNA building blocks that occurs in many different RNA contexts and folds autonomously, that is, in a context-independent manner. In this study, we combined bioinformatics analysis with explicit-solvent molecular dynamics (MD) simulations to better understand the relation between the RNA sequence and the evolutionary patterns of the SR motif. A SHAPE probing experiment was also performed to confirm the fidelity of the MD simulations. We identified 57 instances of the SR motif in a nonredundant subset of the RNA X-ray structure database and analyzed their base pairing, base-phosphate, and backbone-backbone interactions. We extracted sequences aligned to these instances from large rRNA alignments to determine the frequency of occurrence for different sequence variants. We then used a simple scoring scheme based on isostericity to suggest 10 sequence variants with a highly variable expected degree of compatibility with the SR motif 3D structure. We carried out MD simulations of SR motifs with these base substitutions. Nonisosteric base substitutions led to unstable structures, but so did isosteric substitutions which were unable to make key base-phosphate interactions. The MD technique explains why some potentially isosteric SR motifs are not realized during evolution. We also found that the inability to form stable cWW geometry is an important factor in the case of the first base pair of the flexible region of the SR motif. A comparison of structural, bioinformatics, SHAPE probing, and MD simulation data reveals that explicit solvent MD simulations neatly reflect the viability of different sequence variants of the SR motif. Thus, MD simulations can efficiently complement bioinformatics tools in studies of conservation patterns of RNA motifs and provide atomistic insight into the role of their different signature interactions.

Protonation of trimethylamine N-oxide (TMAO) is required for stabilization of RNA tertiary structure

The osmolyte trimethylamine N-oxide (TMAO) stabilizes the tertiary but not the secondary structures of RNA. However, molecular dynamics simulations performed on the PreQ1 riboswitch showed that TMAO destabilizes the tertiary riboswitch structure, leading us to hypothesize that the presence of RNA could result in enhanced population of the protonated form, TMAOP. Constant pH replica exchange simulations showed that a percentage of TMAO is indeed protonated, thus contributing to the stability of the tertiary but not the secondary structure of PreQ1. TMAOP results in an unfavorable dehydration of phosphodiester backbone, which is compensated by electrostatic attraction between TMAOP and the phosphate groups. In addition, TMAOP interacts with specific sites in the tertiary RNA structure, mimicking the behavior of positively charged ions and of the PreQ1 ligand in stabilizing RNA. Finally, we predict that TMAO-induced stabilization of RNA tertiary structures should be strongly pH dependent.

Polymeric Surfactants: Novel Agents with Exceptional Properties

This article presents recent progress in the field of polymeric surfactants made of permanently amphiphilic block copolymers or of stimulus-sensitive ones. We highlight key points in the design of amphiphilic macromolecules, to yield polymer surfactants with tailor-made properties, as well as recently developed and still challenging application fields for this new class of surfactants. The efficiency boosting of amphiphilic block copolymers as co-surfactants in microemulsions is discussed, as are surface modification by polymer surfactants, and stabilization of dispersions. Moreover, the use of block copolymers in nanosciences is presented, for instance as a tool for nanomaterial fabrication, or for biomedical and cosmetic applications in bio-nanotechnology. Finally, self-assembly and applications of some newly developed “exotic” amphiphilic block copolymer structures as new surface-active materials will be highlighted.

Characterizing the protonation state of cytosine in transient G·C Hoogsteen base pairs in duplex DNA

G·C Hoogsteen base pairs can form transiently in duplex DNA and play important roles in DNA recognition, replication, and repair. G·C Hoogsteen base pairs are thought to be stabilized by protonation of cytosine N3, which affords a second key hydrogen bond, but experimental evidence for this is sparse because the proton cannot be directly visualized by X-ray crystallography and nuclear magnetic resonance spectroscopy. Here, we combine NMR and constant pH molecular dynamics simulations to directly investigate the pKa of cytosine N3 in a chemically trapped N1-methyl-G·C Hoogsteen base pair within duplex DNA. Analysis of NMR chemical shift perturbations and NOESY data as a function of pH revealed that cytosine deprotonation is coupled to a syn-to-anti transition in N1-methyl-G, which results in a distorted Watson-Crick geometry at pH >9. A four-state analysis of the pH titration profiles yields a lower bound pKa estimate of 7.2 ± 0.1 for the G·C Hoogsteen base pair, which is in good agreement with the pKa value (7.1 ± 0.1) calculated independently using constant pH MD simulations. Based on these results and pH-dependent NMR relaxation dispersion measurements, we estimate that under physiological pH (pH 7-8), G·C Hoogsteen base pairs in naked DNA have a population of 0.02-0.002%, as compared to 0.4% for A·T Hoogsteen base pairs, and likely exist primarily as protonated species.

Towards Accurate Prediction of Protonation Equilibrium of Nucleic Acids

The role of protonated nucleotides in modulating the pH-dependent properties of nucleic acids is one of the emerging frontiers in the field of nucleic acid biology. The recent development of a constant pH molecular dynamics simulation (CPHMD^MSλD) framework for simulating nucleic acids has provided a tool for realistic simulations of pH-dependent dynamics. We enhanced the CPHMD^MSλD framework with pH-based replica exchange (pH-REX), which significantly improves the sampling of both titration and spatial coordinates. The results from our pK_a calculations for the GAAA tetraloop, which was predicted with lower accuracy previously due to sampling challenges, demonstrates that pH-REX reduces the average unsigned error (AUE) to 0.7 pK_a units, and the error of the most poorly predicted residue A17 was drastically reduced from 2.9 to 1.2 pK_a unit. Lastly, we show that pH-REX CPHMD^MSλD simulations can be used to identify the dominant conformation of nucleic acid structures in alternate pH environments. This work suggests that pH-REX CPHMD^MSλD simulations provide a practical tool for predicting nucleic acid protonation equilibrium from first-principles, and offering structural and mechanistic insight into the study of pH-dependent properties of nucleic acids.

Molecular modeling of nucleic acid structure: electrostatics and solvation

This unit presents an overview of computer simulation techniques as applied to nucleic acid systems, ranging from simple in vacuo molecular modeling techniques to more complete all-atom molecular dynamics treatments that include an explicit representation of the environment. The third in a series of four units, this unit focuses on critical issues in solvation and the treatment of electrostatics.