Treatment of Ionic Strength in Biomolecular Simulations of Charged Lipid Bilayers

Computational Study of the pH-Dependent Ionic Environment around β-Lactoglobulin

Ions are involved in multiple biological processes and may exist bound to biomolecules or may be associated with their surface. Although the presence of ions in nucleic acids has traditionally gained more interest, ion-protein interactions, often with a marked dependency on pH, are beginning to gather attention. Here we present a detailed analysis on the binding and distribution of ions around β-lactoglobulin using a constant-pH MD (CpHMD) method, at a pH range 3-8, and compare it with the more traditional Poisson-Boltzmann (PB) model and the existing experimental data. Most analyses used ion concentration maps built around the protein, obtained from either the CpHMD simulations or PB calculations. The requirements of approximate charge neutrality and ionic strength equal to bulk, imposed on the MD box, imply that the absolute value of the ion excess should be half the protein charge, which is in agreement with experimental observation on other proteins ( Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2015879118) and lends support to this protocol. In addition, the protein total charge (including territorially bound ions) estimated with MD is in excellent agreement with electrophoretic measurements. Overall, the CpHMD simulations show good agreement with the nonlinear form of the PB (NLPB) model but not with its linear form, which involves a theoretical inconsistency in the calculation of the concentration maps. In several analyses, the observed pH-dependent trends for the counterions and co-ions are those generally expected, and the ion concentration maps correctly converge to the bulk ionic strength as one moves away from the protein. Despite the overall similarity, the CpHMD and NLPB approaches show some discrepancies when analyzed in more detail, which may be related to an apparent overestimation of counterion excess and underestimation of co-ion exclusion by the NLPB model, particularly at short distances from the protein.

Increasing the Realism of in Silico pHLIP Peptide Models with a Novel pH Gradient CpHMD Method

The pH-low insertion peptides (pHLIP) are pH-dependent membrane inserting peptides, whose function depends on the cell microenvironment acidity. Several peptide variants have been designed to improve upon the wt-sequence, particularly the state transition kinetics and the selectivity for tumor pH. The variant 3 (Var3) peptide is a 27 residue long peptide, with a key titrating residue (Asp-13) that, despite showing a modest performance in liposomes (pK^ins ∼ 5.0), excelled in tumor cell experiments. To help rationalize these results, we focused on the pH gradient in the cell membrane, which is one of the crucial properties that are not present in liposomes. We extended our CpHMD-L method and its pH replica-exchange (pHRE) implementation to include a pH gradient and mimic the pHLIP-membrane microenvironment in a cell where the internal pH is fixed (pH 7.2) and the external pH is allowed to change. We showed that, by properly modeling the pH-gradient, we can correctly predict the experimentally observed loss and gain of performance in tumor cells experiments by the wt and Var3 sequences, respectively. In sum, the pH gradient implementation allowed for more accurate and realistic pK_a estimations and was a pivotal step in bridging the in silico data and the in vivo cell experiments.

Extending the Stochastic Titration CpHMD to CHARMM36m

The impact of pH on proteins is significant but often neglected in molecular dynamics simulations. Constant-pH Molecular Dynamics (CpHMD) is the state-of-the-art methodology to deal with these effects. However, it still lacks widespread adoption by the scientific community. The stochastic titration CpHMD is one of such methods that, until now, only supported the GROMOS force field family. Here, we extend this method's implementation to include the CHARMM36m force field available in the GROMACS software package. We test this new implementation with a diverse group of proteins, namely, lysozyme, Staphylococcal nuclease, and human and E. coli thioredoxins. All proteins were conformationally stable in the simulations, even at extreme pH values. The RMSE values (pK_a prediction vs experimental) obtained were very encouraging, in particular for lysozyme and human thioredoxin. We have also identified a few residues that challenged the CpHMD simulations, highlighting scenarios where the method still needs improvement independently of the force field. The CHARMM36m all-atom implementation was more computationally efficient when compared with the GROMOS 54A7, taking advantage of a shorter nonbonded interaction cutoff and a less frequent neighboring list update. The new extension will allow the study of pH effects in many systems for which this force field is particularly suited, i.e., proteins, membrane proteins, lipid bilayers, and nucleic acids.

Novel US-CpHMD Protocol to Study the Protonation-Dependent Mechanism of the ATP/ADP Carrier

We have designed a protocol combining constant-pH molecular dynamics (CpHMD) simulations with an umbrella sampling (US) scheme (US-CpHMD) to study the mechanism of ADP/ATP transport (import and export) by their inner mitochondrial membrane carrier protein [ADP/ATP carrier (AAC)]. The US scheme helped overcome the limitations of sampling the slow kinetics involved in these substrates' transport, while CpHMD simulations provided an unprecedented realism by correctly capturing the associated protonation changes. The import of anionic substrates along the mitochondrial membrane has a strong energetic disadvantage due to a smaller substrate concentration and an unfavorable membrane potential. These limitations may have created an evolutionary pressure on AAC to develop specific features benefiting the import of ADP. In our work, the potential of mean force profiles showed a clear selectivity in the import of ADP compared to ATP, while in the export, no selectivity was observed. We also observed that AAC sequestered both substrates at longer distances in the import compared to the export process. Furthermore, only in the import process do we observe transient protonation of both substrates when going through the AAC cavity, which is an important advantage to counteract the unfavorable mitochondrial membrane potential. Finally, we observed a substrate-induced disruption of the matrix salt-bridge network, which can promote the conformational transition (from the C- to M-state) required to complete the import process. This work unraveled several important structural features where the complex electrostatic interactions were pivotal to interpreting the protein function and illustrated the potential of applying the US-CpHMD protocol to other transport processes involving membrane proteins.

Approach to Study pH-Dependent Protein Association Using Constant-pH Molecular Dynamics: Application to the Dimerization of β-Lactoglobulin

Protein-protein association is often mediated by electrostatic interactions and modulated by pH. However, experimental and computational studies have often overlooked the effect of association on the protonation state of the protein. In this work, we present a methodological approach based on constant-pH molecular dynamics (MD), which aims to provide a detailed description of a pH-dependent protein-protein association, and apply it to the dimerization of β-lactoglobulin (BLG). A selection of analyses is performed using the data generated by constant-pH MD simulations of monomeric and dimeric forms of bovine BLG, in the pH range 3-8. First, we estimate free energies of dimerization using a computationally inexpensive approach based on the Wyman-Tanford linkage theory, calculated in a new way through the use of thermodynamically based splines. The individual free energy contribution of each titratable site is also calculated, allowing for identification of relevant residues. Second, the correlations between the proton occupancies of pairs of sites are calculated (using the Pearson coefficient), and extensive networks of correlated sites are observed at acidic pH values, sometimes involving distant pairs. In general, strongly correlated sites are also slow proton exchangers and contribute significantly to the pH-dependency of the dimerization free energy. Third, we use ionic density as a fingerprint of protein charge distribution and observe electrostatic complementarity between the monomer faces that form the dimer interface, more markedly at the isoionic point (where maximum dimerization occurs) than at other pH values, which might contribute to guide the association. Finally, the pH-dependent dimerization modes are inspected using PCA, among other analyses, and two states are identified: a relaxed state at pH 4-8 (with the typical alignment of the crystallographic structure) and a compact state at pH 3-4 (with a tighter association and rotated alignment). This work shows that an approach based on constant-pH MD simulations can produce rich detailed pictures of pH-dependent protein associations, as illustrated for BLG dimerization.

Lipid21: Complex Lipid Membrane Simulations with AMBER

We extend the modular AMBER lipid force field to include anionic lipids, polyunsaturated fatty acid (PUFA) lipids, and sphingomyelin, allowing the simulation of realistic cell membrane lipid compositions, including raft-like domains. Head group torsion parameters are revised, resulting in improved agreement with NMR order parameters, and hydrocarbon chain parameters are updated, providing a better match with phase transition temperature. Extensive validation runs (0.9 μs per lipid type) show good agreement with experimental measurements. Furthermore, the simulation of raft-like bilayers demonstrates the perturbing effect of increasing PUFA concentrations on cholesterol molecules. The force field derivation is consistent with the AMBER philosophy, meaning it can be easily mixed with protein, small molecule, nucleic acid, and carbohydrate force fields.

Improved Protocol to Tackle the pH Effects on Membrane-Inserting Peptides

Many important biological pathways rely on membrane-interacting peptides or proteins, which can alter the biophysical properties of the cell membrane by simply adsorbing to its surface to undergo a full insertion process. To study these phenomena with atomistic detail, model peptides have been used to refine the current computational methodologies. Improvements have been made with force-field parameters, enhanced sampling techniques to obtain faster sampling, and the addition of chemical-physical properties, such as pH, whose influence dramatically increases at the water/membrane interface. The pH (low) insertion peptide (pHLIP) is a peptide that inserts across a membrane bilayer depending on the pH due to the presence of a key residue (Asp14) whose acidity-induced protonation triggers the whole process. The complex nature of these peptide/membrane interactions resulted in sampling limitations of the protonation and configurational space albeit using state-of-the-art methods such as the constant-pH molecular dynamics. To address this issue and circumvent those limitations, new simulations were performed with our newly developed pH-replica exchange method using wild-type (wt)-pHLIP in different 2-oleoyl-1-palmitoyl-sn-glycero-3-phosphocholine membrane sizes. This technique provided enhanced sampling and allowed for the calculation of more complete Asp14 pK_a profiles. The conformational heterogeneity derived from strong electrostatic interactions between Asp14 and the lipid phosphate groups was identified as the source of most pK_a variability. In spite of these persistent and harder-to-equilibrate phosphate interactions, the pK_a values at deeper regions (6.0-6.2) still predicted the experimental pK of insertion (6.0) since the electrostatic perturbation decays as the residue inserts further into the membrane. We also observed that reducing the system size leads to membrane deformations where it increasingly loses the ability to accommodate the pHLIP-induced perturbations. This indicates that large membrane patches, such as 256 or even 352 lipids, are needed to obtain stable and more realistic pHLIP/membrane systems. These results strengthen our method pK_a predictive and analytical capabilities to study the intricate play of electrostatic effects of the peptide/membrane interface, granting confidence for future applications in similar systems.

Improved GROMOS 54A7 Charge Sets for Phosphorylated Tyr, Ser, and Thr to Deal with pH-Dependent Binding Phenomena

Phosphorylation is a ubiquitous post-translational modification in proteins, and the phosphate group is present constitutively or transiently in most biological building blocks. These phosphorylated biomolecules are involved in many high-affinity binding/unbinding events that rely predominantly on electrostatic interactions. To build accurate models of these molecules, we need an improved description of the atomic partial charges for all relevant protonation states. In this work, we showed that the commonly used protocols to derive atomic partial charges using well-solvated molecules are inadequate to model the protonation equilibria in binding events. We introduced a protocol based on PB/MC calculations with a single representative conformation (of both protonation states) and used the resulting pK_a estimations to help manually curate the atomic partial charges. The final charge set, which is fully compatible with the GROMOS 54A7 force field, proved to be very effective in modeling the protonation equilibrium in different phosphorylated peptides in the free (tetrapeptides, pentapeptides, and pY1021) and protein-complexed forms (pY1021/PLC-γ1 complex). This was particularly important in the case of the pY1021 bound to the SH2 domain of PLC-γ1, where only our curated charge set captured the correct protonation equilibrium at the neutral to slightly acidic pH range. The binding/unbinding phenomena in that pH range are biologically relevant, and to improve our models, we need to go beyond the commonly used protocols and obtain revised force field parameters for these molecules.

Molecular Dynamics Studies on COX-2 Protein-tyrosine Analogue Complex and Ligand-based Computational Analysis of Halo-substituted Tyrosine Analogues

Background:

The quest for new drug entities and novel structural fragments with applications in therapeutic areas is always at the core of medicinal chemistry.

Methods:

As part of our efforts to develop novel selective cyclooxygenase-2 (COX-2) inhibitors containing tyrosine scaffold. The objective of this study was to identify potent COX-2 inhibitors by dynamic simulation, pharmacophore and 3D-QSAR methodologies. Dynamics simulation was performed for COX-2/tyrosine derivatives complex to characterise structure validation and binding stability. Certainly, Arg120 and Tyr355 residue of COX-2 protein formed a constant interaction with tyrosine inhibitor throughout the dynamic simulation phase. A four-point pharmacophore with one hydrogen bond acceptor, two hydrophobic and one aromatic ring was developed using the HypoGen algorithm. The generated, statistically significant pharmacophore model, Hypo 1 with a correlation coefficient of r2, 0.941, root mean square deviation, 1.15 and total cost value of 96.85.

Results:

The QSAR results exhibited good internal (r2, 0.992) and external predictions (r2pred, 0.814). The results of this study concluded the COX-2 docked complex was stable and interactive like experimental protein structure. Also, it offered vital chemical features with geometric constraints responsible for the inhibition of the selective COX-2 enzyme by tyrosine derivatives.

Conclusion:

In principle, this work offers significant structural understandings to design and develop novel COX-2 inhibitors.

Role of Counterions in Constant-pH Molecular Dynamics Simulations of PAMAM Dendrimers

Electrostatic interactions play a pivotal role in the structure and mechanism of action of most biomolecules. There are several conceptually different methods to deal with electrostatics in molecular dynamics simulations. Ionic strength effects are usually introduced using such methodologies and can have a significant impact on the quality of the final conformation space obtained. We have previously shown that full system neutralization can lead to wrong lipidic phases in the 25% PA/PC bilayer (J. Chem. Theory Comput. 2014,10, 5483-5492). In this work, we investigate how two limit approaches to the ionic strength treatment (implicitly with GRF or using full system neutralization with either GRF or PME) can influence the conformational space of the second-generation PAMAM dendrimer. Constant-pH MD simulations were used to map PAMAM's conformational space at its full pH range (from 2.5 to 12.5). Our simulations clearly captured the coupling between protonation and conformation in PAMAM. Interestingly, the dendrimer conformational distribution was almost independent of the ionic strength treatment methods, which is in contrast to what we have observed in charged lipid bilayers. Overall, our results confirm that both GRF with implicit ionic strength and a fully neutralized system with PME are valid approaches to model charged globular systems, using the GROMOS 54A7 force field.

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.

Diphenylhexatriene membrane probes DPH and TMA-DPH: A comparative molecular dynamics simulation study

Fluorescence spectroscopy and microscopy have been utilized as tools in membrane biophysics for decades now. Because phospholipids are non-fluorescent, the use of extrinsic membrane probes in this context is commonplace. Among the latter, 1,6-diphenylhexatriene (DPH) and its trimethylammonium derivative (TMA-DPH) have been extensively used. It is widely believed that, owing to its additional charged group, TMA-DPH is anchored at the lipid/water interface and reports on a bilayer region that is distinct from that of the hydrophobic DPH. In this study, we employ atomistic MD simulations to characterize the behavior of DPH and TMA-DPH in 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and POPC/cholesterol (4:1) bilayers. We show that although the dynamics of TMA-DPH in these membranes is noticeably more hindered than that of DPH, the location of the average fluorophore of TMA-DPH is only ~3-4Å more shallow than that of DPH. The hindrance observed in the translational and rotational motions of TMA-DPH compared to DPH is mainly not due to significant differences in depth, but to the favorable electrostatic interactions of the former with electronegative lipid atoms instead. By revealing detailed insights on the behavior of these two probes, our results are useful both in the interpretation of past work and in the planning of future experiments using them as membrane reporters.

Simulation of lipid bilayer self-assembly using all-atom lipid force fields

In this manuscript we expand significantly on our earlier communication by investigating the bilayer self-assembly of eight different types of phospholipids in unbiased molecular dynamics (MD) simulations using three widely used all-atom lipid force fields. Irrespective of the underlying force field, the lipids are shown to spontaneously form stable lamellar bilayer structures within 1 microsecond, the majority of which display properties in satisfactory agreement with the experimental data. The lipids self-assemble via the same general mechanism, though at formation rates that differ both between lipid types, force fields and even repeats on the same lipid/force field combination. In addition to zwitterionic phosphatidylcholine (PC) and phosphatidylethanolamine (PE) lipids, anionic phosphatidylserine (PS) and phosphatidylglycerol (PG) lipids are represented. To our knowledge this is the first time bilayer self-assembly of phospholipids with negatively charged head groups is demonstrated in all-atom MD simulations.

Constant-pH Molecular Dynamics Study of Kyotorphin in an Explicit Bilayer

To our knowledge, we present the first constant-pH molecular dynamics study of the neuropeptide kyotorphin in the presence of an explicit lipid bilayer. The overall conformation freedom of the peptide was found to be affected by the interaction with the membrane, in accordance with previous results using different methodologies. Analysis of the interactions between the N-terminus amine group of the peptide and several lipid atoms shows that the membrane is able to stabilize both ionized and neutral forms of kyotorphin, resulting in a pKa value that is similar to the one obtained in water. This illustrates how a detailed molecular model of the membrane leads to rather different results than would be expected from simply regarding it as a low-dielectric slab.

Molecular-level insight into the interactions of DNA with phospholipid bilayers: barriers and triggers

A zwitterionic phospholipid bilayer represents a repulsive barrier for DNA binding; this barrier can be overcome through adsorption of divalent cations to the bilayer surface.

pH-Responsive Self-Assembly of Polysaccharide through a Rugged Energy Landscape

Self-assembling polysaccharides can form complex networks with structures and properties highly dependent on the sequence of triggering cues. Controlling the emergence of such networks provides an opportunity to create soft matter with unique features; however, it requires a detailed understanding of the subtle balance between the attractive and repulsive forces that drives the stimuli-induced self-assembly. Here we employ all-atom molecular dynamics simulations on the order of 100 ns to study the mechanisms of the pH-responsive gelation of the weakly basic aminopolysaccharide chitosan. We find that low pH induces a sharp transition from gel to soluble state, analogous to pH-dependent folding of proteins, while at neutral and high pH self-assembly occurs via a rugged energy landscape, reminiscent of RNA folding. A surprising role of salt is to lubricate the conformational search for the thermodynamically stable states. Although our simulations represent the early events in the self-assembly process of chitosan, which may take seconds or minutes to complete, the atomically detailed insights are consistent with recent experimental observations and provide a basis for understanding how environmental conditions modulate the structure and mechanical properties of the self-assembled polysaccharide systems. The ability to control structure and properties via modification of process conditions will aid in the technological efforts to create complex soft matter with applications ranging from bioelectronics to regenerative medicine.

Microsecond Simulations of the Diphtheria Toxin Translocation Domain in Association with Anionic Lipid Bilayers

Diphtheria toxin translocation (T) domain undergoes conformational changes in acidic solution and associates with the lipid membranes, followed by refolding and transmembrane insertion of two nonpolar helices. This process is an essential step in delivery of the toxic catalytic domain of the diphtheria toxin to the infected cell, yet its molecular determinants are poorly characterized and understood. Therefore, an atomistic model of the T-domain-membrane interaction is needed to help characterize factors responsible for such association. In this work, we present atomistic model structures of T-domain membrane-bound conformations and investigate structural factors responsible for T-domain affinity with the lipid bilayer in acidic solution using all-atom molecular dynamics (MD) simulations. The initial models of the protein conformations and protein-membrane association that serve as starting points in the present work were developed using atomistic simulations of partial unfolding of the T-domain in acidic solution (Kurnikov, I. V.; et al. J. Mol. Biol. 2013, 425, 2752-2764), and coarse-grained simulations of the T-domain association with the membranes of various compositions (Flores-Canales, J. C.; et al. J. Membr. Biol. 2015, 248, 529-543). In this work we present atomistic level modeling of two distinct configurations of the T-domain in association with the anionic lipid bilayer. In microsecond-long MD simulations both conformations retain their compact structure and gradually penetrate deeper into the bilayer interface. One membrane-bound conformation is stabilized by the protein contacts with the lipid hydrophobic core. The second modeled conformation is initially inserted less deeply and forms multiple contacts with the lipid at the interface (headgroup) region. Such contacts are formed by the charged and hydrophilic groups of partially unfolded terminal helixes and loops. Neutralization of the acidic residues at the membrane interface allows for deeper insertion of the protein and reorientation of the protein at the membrane interface, which corroborates that acidic residue protonation as well as presence of the anionic lipids may play a role in the membrane association and further membrane insertion of the T-domain as implicated in experiments. All simulations reported in this work were performed using AMBER force-field on Anton supercomputer. To perform these reported simulations, we developed and carefully tested a force-field for the anionic 1-palmitoyl-2-oleoyl-phosphatidyl-glycerol (POPG) lipid, compatible with the Amber 99SB force-field and stable in microsecond-long MD simulations in isothermal-isobaric ensemble.