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

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.

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.

A Fast and Interpretable Deep Learning Approach for Accurate Electrostatics-Driven pKa Predictions in Proteins

Existing computational methods for estimating pK_a values in proteins rely on theoretical approximations and lengthy computations. In this work, we use a data set of 6 million theoretically determined pK_a shifts to train deep learning models, which are shown to rival the physics-based predictors. These neural networks managed to infer the electrostatic contributions of different chemical groups and learned the importance of solvent exposure and close interactions, including hydrogen bonds. Although trained only using theoretical data, our pKAI+ model displayed the best accuracy in a test set of ∼750 experimental values. Inference times allow speedups of more than 1000× compared to physics-based methods. By combining speed, accuracy, and a reasonable understanding of the underlying physics, our models provide a game-changing solution for fast estimations of macroscopic pK_a values from ensembles of microscopic values as well as for many downstream applications such as molecular docking and constant-pH molecular dynamics simulations.

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.

Co-delivery of gefitinib and hematoporphyrin by aptamer-modified fluorinated dendrimer for hypoxia alleviation and enhanced synergistic chemo-photodynamic therapy of NSCLC

Although epidermal growth factor receptor tyrosine kinase inhibitors (EGFR-TKIs)-based molecular targeted therapy are proved to be effective in the treatment of non-small cell lung cancer (NSCLC) with EGFR mutation, its efficacy is limited by the acquired drug resistance. The combination of EGFR-TKIs with photodynamic therapy (PDT) has been explored to combat NSCLC with promising synergistic results. However, hypoxic tumor microenvironment is associated with the development of EGFR-TKIs resistance and severely limits the efficacy of PDT. Here, we synthesized an aptamer modified fluorinated dendrimer (APF) as a drug carrier and prepared nanocomplexes APFHG by encapsulation of gefitinib (Gef) and hematoporphyrin (Hp). APF has good oxygen-carrying capacity, high drug entrapment efficiency, and could release Gef and Hp in response to intracellular pH. APF can specifically recognize EGFR-positive NSCLC cells and effectively improve the tumor hypoxic microenvironment due to the targeting effect of aptamer and the good oxygen-carrying capacity of the fluorinated dendrimer. Under the laser irradiation, APFHG can significantly increase the production of the intracellular reactive oxygen species and produce a synergistic therapeutic effect in inhibition of cellular growth and induction of cell cycle arrest and apoptosis on both Gef-sensitive and Gef-resistant EGFR-mutant NSCLC cells through PDT/molecular targeted therapy. This work indicates that fluorinated dendrimer could be a potent drug delivery platform to overcome hypoxia-related resistance and the co-delivery of EGFR-TKI and photosensitizer by the fluorinated dendrimer could be a promising therapeutic approach for reversal of EGFR-TKIs resistance in EGFR mutation-positive NSCLC.

Monte Carlo simulations of weak polyampholyte microgels: pH-dependence of conformation and ionization

We performed Metropolis Monte Carlo simulations to investigate the impact of varying acid and base dissociation constants on the pH-dependent ionization and conformation of weak polyampholyte microgels under salt-free conditions and under explicit consideration of the chemical ionization equilibria of the acidic and basic groups and their electrostatic interaction. Irrespective of their relative acid and base dissociation constant, all of the microgels undergo a pH-dependent charge reversal from positive to negative with a neutral charge at the isoelectric point. This charge reversal is accompanied by a U-shaped swelling transition of the microgels with a minimum of their size at the point of charge neutrality. The width of the U-shaped swelling transition, however, is found to depend on the chosen relative acid and base dissociation constants through which the extent of the favorable electrostatic intramolecular interaction of the ionized acidic and basic groups is altered. The pH-dependent swelling transition of the microgels is found to become broader, the stronger the intramolecular electrostatic interaction of the oppositely charged ionized species is. In addition, the intramolecular charge compensation of the acidic and basic groups of the microgels allows their counterions to abandon the microgel and the associated gain in translational entropy further amplifies the broadening of the pH-dependent swelling transition. The analysis of the radial ionization profiles of the acidic and basic groups of the differently composed microgels reveals a variety of radial ionization patterns with a dependence on the overall charge of the microgels.

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.

Titratable Martini model for constant pH simulations

In this work, we deliver a proof of concept for a fast method that introduces pH effects into classical coarse-grained (CG) molecular dynamics simulations. Our approach is based upon the latest version of the popular Martini CG model to which explicit proton mimicking particles are added. We verify our approach against experimental data involving several different molecules and different environmental conditions. In particular, we compute titration curves, pH dependent free energies of transfer, and lipid bilayer membrane affinities as a function of pH. Using oleic acid as an example compound, we further illustrate that our method can be used to study passive translocation in lipid bilayers via protonation. Finally, our model reproduces qualitatively the expansion of the macromolecule dendrimer poly(propylene imine) as well as the associated pKa shift of its different generations. This example demonstrates that our model is able to pick up collective interactions between titratable sites in large molecules comprising many titratable functional groups.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Membrane-Induced p Ka Shifts in wt-pHLIP and Its L16H Variant

The pH (low) insertion peptides (pHLIPs) is a family of peptides that are able to insert into a lipid bilayer at acidic pH. The molecular mechanism of pHLIPs insertion, folding, and stability in the membrane at low pH is based on multiple protonation events, which are challenging to study at the molecular level. More specifically, the relation between the experimental p K of insertion (p K^exp) of pHLIPs and the p K_a of the key residues is yet to be clarified. We carried out a computational study, complemented with new experimental data, and established the influence of (de)protonation of titrable residues on the stability of the peptide membrane-inserted state. Constant-pH molecular dynamics simulations were employed to calculate the p K_a values of these residues along the membrane normal. In the wt-pHLIP, we identified Asp14 as the key residue for the stability of the membrane-inserted state, and its p K_a value is strongly correlated with the experimental p K^exp measured in thermodynamics studies. Also, in order to narrow down the pH range at which pHLIP is stable in the membrane, we designed a new pHLIP variant, L16H, where Leu in the 16th position was replaced by a titrable His residue. Our results showed that the L16H variant undergoes two transitions. The calculated p K_a and experimentally observed p K^exp values are in good agreement. Two distinct p K^exp values delimit a pH range where the L16H peptide is stably inserted in the membrane, while, outside this range, the membrane-inserted state is destabilized and the peptide exits from the bilayer. pHLIP peptides have been successfully used to target cancer cells for the delivery of diagnostics and therapeutic agents to acidic tumors. The fine-tuning of the stability of the pHLIP inserted state and its restriction to a narrow well-defined pH range might allow the design of new peptides, able to discriminate between tissues with different extracellular pH values.