Tracking Proton Transfer through Titratable Amino Acid Side Chains in Adaptive QM/MM Simulations

QM/MM Free Energy Calculations of Long-Range Biological Protonation Dynamics by Adaptive and Focused Sampling

Water-mediated proton transfer reactions are central for catalytic processes in a wide range of biochemical systems, ranging from biological energy conversion to chemical transformations in the metabolism. Yet, the accurate computational treatment of such complex biochemical reactions is highly challenging and requires the application of multiscale methods, in particular hybrid quantum/classical (QM/MM) approaches combined with free energy simulations. Here, we combine the unique exploration power of new advanced sampling methods with density functional theory (DFT)-based QM/MM free energy methods for multiscale simulations of long-range protonation dynamics in biological systems. In this regard, we show that combining multiple walkers/well-tempered metadynamics with an extended system adaptive biasing force method (MWE) provides a powerful approach for exploration of water-mediated proton transfer reactions in complex biochemical systems. We compare and combine the MWE method also with QM/MM umbrella sampling and explore the sampling of the free energy landscape with both geometric (linear combination of proton transfer distances) and physical (center of excess charge) reaction coordinates and show how these affect the convergence of the potential of mean force (PMF) and the activation free energy. We find that the QM/MM-MWE method can efficiently explore both direct and water-mediated proton transfer pathways together with forward and reverse hole transfer mechanisms in the highly complex proton channel of respiratory Complex I, while the QM/MM-US approach shows a systematic convergence of selected long-range proton transfer pathways. In this regard, we show that the PMF along multiple proton transfer pathways is recovered by combining the strengths of both approaches in a QM/MM-MWE/focused US (FUS) scheme and reveals new mechanistic insight into the proton transfer principles of Complex I. Our findings provide a promising basis for the quantitative multiscale simulations of long-range proton transfer reactions in biological systems.

Solvent structure and dynamics over Brønsted acid MWW zeolite nanosheets

In the liquid phase of heterogeneous catalysis, solvent plays an important role and governs the kinetics and thermodynamics of a reaction. Although it is often difficult to quantify the role of the solvent, it becomes particularly challenging when a zeolite is used as the catalyst. This difficulty arises from the complex nature of the liquid/zeolite interface and the different solvation environments around catalytically active sites. Here, we use ab initio molecular dynamics simulations to probe the local solvation structure and dynamics of methanol and water over MWW zeolite nanosheets with varying Brønsted acidity. We find that the zeolite framework and the number and location of the acid sites in the zeolite influence the structure and dynamics of the solvent. In particular, methanol is more likely to be in the vicinity of the aluminum (Al3+) at the T4 site than at T1 due to easy accessibility. The methanol oxygen binds strongly to the Al at the T4 site, weakening the Al-O for the bridging acid site, which results in the formation of the silanol group, significantly reducing the acidity of the site. The behavior of methanol is in direct contrast to that of water, where protons can easily propagate from the zeolite to the solvent molecules regardless of the acid site location. Our work provides molecular-level insights into how solvent interacts with zeolite surfaces, leading to an improved understanding of the catalytic site in the MWW zeolite nanosheet.

A Vision for the Future of Multiscale Modeling

The rise of modern computer science enabled physical chemistry to make enormous progresses in understanding and harnessing natural and artificial phenomena. Nevertheless, despite the advances achieved over past decades, computational resources are still insufficient to thoroughly simulate extended systems from first principles. Indeed, countless biological, catalytic and photophysical processes require ab initio treatments to be properly described, but the breadth of length and time scales involved makes it practically unfeasible. A way to address these issues is to couple theories and algorithms working at different scales by dividing the system into domains treated at different levels of approximation, ranging from quantum mechanics to classical molecular dynamics, even including continuum electrodynamics. This approach is known as multiscale modeling and its use over the past 60 years has led to remarkable results. Considering the rapid advances in theory, algorithm design, and computing power, we believe multiscale modeling will massively grow into a dominant research methodology in the forthcoming years. Hereby we describe the main approaches developed within its realm, highlighting their achievements and current drawbacks, eventually proposing a plausible direction for future developments considering also the emergence of new computational techniques such as machine learning and quantum computing. We then discuss how advanced multiscale modeling methods could be exploited to address critical scientific challenges, focusing on the simulation of complex light-harvesting processes, such as natural photosynthesis. While doing so, we suggest a cutting-edge computational paradigm consisting in performing simultaneous multiscale calculations on a system allowing the various domains, treated with appropriate accuracy, to move and extend while they properly interact with each other. Although this vision is very ambitious, we believe the quick development of computer science will lead to both massive improvements and widespread use of these techniques, resulting in enormous progresses in physical chemistry and, eventually, in our society.

Reshaping the QM Region On-the-Fly: Adaptive-Shape QM/MM Dynamic Simulations of a Hydrated Proton in Bulk Water

Adaptive quantum mechanics/molecular mechanics (QM/MM) reclassifies on-the-fly a molecule or molecular fragment as QM or MM during dynamics simulations without abrupt changes in the energy or forces. Notably, the permuted adaptive-partitioning (PAP) algorithms have been applied to simulate a hydrated proton, with a mobile QM zone anchored at a pseudoatom called a proton indicator. The position of the proton indicator approximates the location of the delocalized excess proton, yielding a smooth trajectory of the proton diffusing via the Grotthuss mechanism in aqueous solutions. The mobile QM zone, which has been taken to be a sphere with a preset radius, follows the proton wherever it goes. Although the simulations are successful, the use of a spherical QM zone has one disadvantage: A large preset radius must be utilized to minimize the chance of missing water molecules that are important to proton translocation. A large radius leads to a large QM zone, which is computationally expensive. In this work, we report a new way to set up the QM zone, where one includes only the water molecules important to proton transfer. The importance of a given water molecule is quantified by its "weight" that depends on its relation to the reaction path of proton transfer. The weight varies smoothly, ensuring that a water molecule gradually appears in or disappears from the QM zone without abrupt changes, as required by the PAP method. Consequently, the shape of the QM zone evolves on-the-fly, keeping the QM zone as small as possible and as large as necessary. Test simulations demonstrate that the new algorithm significantly improves the computation efficiency while maintaining the proper descriptions of proton transfer in bulk water.

Adaptive-Partitioning Multilayer Dynamics Simulations: 2. Implementations of the Permuted and Interpolated Adaptive-Partitioning Gradients

Recently, an adaptive-partitioning multilayer Q1/Q2/MM method was proposed, where Q1 and Q2 denote, respectively, two distinct quantum-mechanical levels of theory and MM, the molecular-mechanical force fields. Such a multilayer model resembles the ONIOM (our own N-layered integrated molecular orbital and molecular mechanics) model by Morokuma and co-workers, but it is distinguished by on-the-fly reclassifying atoms to be Q1, Q2, or MM in dynamics simulations. To smoothly blend the levels of descriptions of the atoms, buffer zones are introduced between adjacent layers, and the energy is smoothly interpolated. In particular, the Q1/Q2 interaction energy was expressed in two different formalisms: permuted and interpolated adaptive-partitioning (PAP and IAP), respectively. While the PAP energy is based on a weighted many-body expansion, the IAP energy is derived via alchemical quantum calculations with interpolated Fock and overlap matrices. In this article, we examine in-depth the irregularities in the IAP energy near the boundary between the buffer and Q2 zones, which were found prominent in some calculations. These irregularities are due to basis-set linear dependencies, which can be effectively suppressed using a cutoff for the weighted atomic orbital coefficients. Furthermore, we derived and implemented the gradients for both PAP and IAP. Test calculations on a series of water cluster models show perfectly smooth gradients in PAP, while a minor discontinuity occurs in IAP gradients at the buffer/Q2 boundary. The energy and gradient discontinuities in IAP become smaller when moving the buffer/Q2 boundary further away from the Q1 center and when increasing the size of the basis sets used. Overall, those discontinuities are controllable, and possible ways to further diminish them are discussed.

AutoParams: An Automated Web-Based Tool To Generate Force Field Parameters for Molecular Dynamics Simulations

Many research questions benefit from molecular dynamics simulations to observe the motions and conformations of molecules over time, which rely on force fields that describe sets of common molecules by category. With the increase of importance for large data sets used in machine learning and growing computational efficiency, the ability to rapidly create large numbers of force field inputs is of high importance. Unusual molecules, such as nucleotide analogues, functionalized carbohydrates, and modified amino acids, are difficult to describe consistently using standard force fields, requiring the development of custom parameters for each unique molecule. While these parameters may be created by individual users, the process can become time-consuming or may introduce errors that may not be immediately apparent. We present an open-source automated parameter generation service, AutoParams, which requires minimal input from the user and creates useful Amber force field parameter sets for most molecules, particularly those that combine molecular types (e.g., a carbohydrate functionalized with a benzene). We include hierarchical atom-typing logic that makes it straightforward to expand with additional force fields and settings, and options for creating monomers in polymers, such as functionalized amino acids. It can be straightforwardly linked to any charge generation program and currently has interfaces to Psi4, PsiRESP, and TeraChem. It is open source and is available via GitHub. It includes error checking and testing protocols to ensure the parameters will be sufficient for subsequent molecular dynamics simulations and streamlines the creation of force field databases.

pH-dependence of the Plasmodium falciparum chloroquine resistance transporter is linked to the transport cycle

The chloroquine resistance transporter, PfCRT, of the human malaria parasite Plasmodium falciparum is sensitive to acidic pH. Consequently, PfCRT operates at 60% of its maximal drug transport activity at the pH of 5.2 of the digestive vacuole, a proteolytic organelle from which PfCRT expels drugs interfering with heme detoxification. Here we show by alanine-scanning mutagenesis that E207 is critical for pH sensing. The E207A mutation abrogates pH-sensitivity, while preserving drug substrate specificity. Substituting E207 with Asp or His, but not other amino acids, restores pH-sensitivity. Molecular dynamics simulations and kinetics analyses suggest an allosteric binding model in which PfCRT can accept both protons and chloroquine in a partial noncompetitive manner, with increased proton concentrations decreasing drug transport. Further simulations reveal that E207 relocates from a peripheral to an engaged location during the transport cycle, forming a salt bridge with residue K80. We propose that the ionized carboxyl group of E207 acts as a hydrogen acceptor, facilitating transport cycle progression, with pH sensing as a by-product.

Tracking the Delocalized Proton in Concerted Proton Transfer in Bulk Water

A solvated proton in water is often characterized as a charge or structural defect, and it is important to track its evolution on-the-fly in certain dynamics simulations. Previously, we introduced the proton indicator, a pseudo-atom, whose position approximates the location of the excess proton modeled as a structural defect. The proton indicator generally yields a smooth trajectory of a hydrated proton diffusing in aqueous solutions, including in the events of stepwise proton transfer via the Grotthuss mechanism; however, the proton indicator did not perform well in the events of concerted proton transfer, for which it occasionally yielded large position displacements between two successive time steps. To overcome this hurdle, we develop a new algorithm of a proton indicator with greatly enhanced performance for concerted proton transfer in bulk water. A protocol is proposed to exhaustively explore the hydrogen-bonding network of the water wires over which the excess proton is delocalized and to properly account for the contributions of the water molecules in this network as the geometry evolves. The new proton indicator (called Indicator 2.0) is assessed in dynamics simulations of an excess proton in bulk water and in specially constructed model systems of more complex architectures. The results demonstrate that the new indicator yields a smooth trajectory in both stepwise and concerted proton transfers.

Improved Indicator Algorithms for Tracking a Hydrated Proton as A Local Structural Defect in Grotthuss Diffusion in Aqueous Solutions

Keeping track of a hydrated proton in dynamics simulations is important and nontrivial. Here, we report two revised algorithms for the proton indicator, a pseudo-atom whose position approximates the location of an excess proton diffusing via the Grotthuss mechanism in aqueous solution. The new methods describe the delocalized proton as a structural defect. Encouragingly, in test simulations of a hydrated proton in bulk water, the new algorithms substantially outperform the original scheme by significantly reducing large displacements in the indicator positions upon donor switch, yielding smoother trajectories that effectively track the movement of the solvated proton.

Adaptive-Partitioning Multilayer Dynamics Simulations: 1. On-the-Fly Switch between Two Quantum Levels of Theory

We propose to generalize the previously developed two-layer permuted adaptive-partitioning quantum-mechanics/molecular-mechanics (QM/MM), which reclassifies atoms as QM or MM on-the-fly in dynamics simulations, to multilayer adaptive-partitioning algorithms that enable multiple levels of theory. In this work, we formulate two new algorithms that smoothly interpolate the energy between two QM (Q1 and Q2) levels of theory. The first "permuted adaptive-partitioning" scheme is based on the weighted many-body expansion of the potential, as in the adaptive-partitioning QM/MM. Unconventional and potentially more efficient, the second "interpolated adaptive-partitioning" method employs alchemical QM calculations with Q1/Q2-mixed basis sets, Fock matrices, and overlap matrices. To our knowledge, this is the first time that such alchemical calculations are performed in QM, although they are routinely done in MM. Test calculations on water-cluster models show that both new algorithms indeed yield smooth energy curves when water molecules shift between Q1 and Q2.

Harder, better, faster, stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Tradeoffs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multiscale QM/MM or iterative approach. Limitations to both conventional density-functional theory and classical MM force fields remain for describing noncovalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e. electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.

Protein Motifs for Proton Transfers That Build the Transmembrane Proton Gradient

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

The molecular basis for the pH-dependent calcium affinity of the pattern recognition receptor langerin

The C-type lectin receptor langerin plays a vital role in the mammalian defense against invading pathogens. Langerin requires a Ca²⁺ cofactor, the binding affinity of which is regulated by pH. Thus, Ca²⁺ is bound when langerin is on the membrane but released when langerin and its pathogen substrate traffic to the acidic endosome, allowing the substrate to be degraded. The change in pH is sensed by protonation of the allosteric pH sensor histidine H294. However, the mechanism by which Ca²⁺ is released from the buried binding site is not clear. We studied the structural consequences of protonating H294 by molecular dynamics simulations (total simulation time: about 120 μs) and Markov models. We discovered a relay mechanism in which a proton is moved into the vicinity of the Ca²⁺-binding site without transferring the initial proton from H294. Protonation of H294 unlocks a conformation in which a protonated lysine side chain forms a hydrogen bond with a Ca²⁺-coordinating aspartic acid. This destabilizes Ca²⁺ in the binding pocket, which we probed by steered molecular dynamics. After Ca²⁺ release, the proton is likely transferred to the aspartic acid and stabilized by a dyad with a nearby glutamic acid, triggering a conformational transition and thus preventing Ca²⁺ rebinding. These results show how pH regulation of a buried orthosteric binding site from a solvent-exposed allosteric pH sensor can be realized by information transfer through a specific chain of conformational arrangements.

Proton transfer in bulk water using the full adaptive QM/MM method: integration of solute- and solvent-adaptive approaches

The quantum mechanical/molecular mechanical (QM/MM) method is a hybrid molecular simulation technique that increases the accessibility of local electronic structures of large systems. The technique combines the benefit of accuracy found in the QM method and that of cost efficiency found in the MM method. However, it is difficult to directly apply the QM/MM method to the dynamics of solution systems, particularly for proton transfer. As explained in the Grotthuss mechanism, proton transfer is a structural interconversion between hydronium ions and solvent water molecules. Hence, when the QM/MM method is applied, an adaptive treatment, namely on-the-fly revisions on molecular definitions, is required for both the solute and solvent. Although several solvent-adaptive methods have been proposed, a full adaptive framework, which is an approach that also considers adaptation for solutes, remains untapped. In this paper, we propose a new numerical expression for the coordinates of the excess proton and its control algorithm. Furthermore, we confirm that this method can stably and accurately simulate proton transfer dynamics in bulk water.

On-the-fly determination of active region centers in adaptive-partitioning QM/MM

Quantum mechanics/molecular mechanics (QM/MM) methods are widely used in molecular dynamics (MD) simulations of large systems. By partitioning the system into active and environmental regions and treating them with different levels of theory, QM/MM methods achieve accuracy and efficiency at the same time. Adaptive-partitioning (AP) QM/MM allows the partition of the system to change during the MD simulation, making it possible to simulate processes in which the active and environmental regions exchange atoms or molecules, such as processes in solutions or solids. AP-QM/MM methods usually partition the system according to distances to centers of active regions. For energy-conserving AP-QM/MM methods, these centers are chosen beforehand and remain fixed during the MD simulation, making it difficult to simulate processes in which active regions may occur or vanish. In this paper, I develop an adaptive-center (AC) method that allows on-the-fly determination of the centers of active regions according to any geometrical criterion or any criterion dependent on the potential energy. The AC method is compatible with all existing energy-conserving AP-QM/MM methods, and the resulting potential energy surface is smooth. The application of the AC method is demonstrated with two examples in solid systems.

Extending scaled-interaction adaptive-partitioning QM/MM to covalently bonded systems

Quantum mechanics/molecular mechanics (QM/MM) is the method of choice for atomistic simulations of large systems that can be partitioned into active and environmental regions. Adaptive-partitioning (AP) methods extend the applicability of QM/MM, allowing active regions to change during the simulation. AP methods achieve continuous potential energy surface (PES) by introducing buffer regions in which atoms have both QM and MM characters. Most of the existing AP-QM/MM methods require multiple QM calculations per time step, which can be expensive for systems with many atoms in buffer regions. Although one can lower the computational cost by grouping atoms into fragments, this may not be possible for all systems, especially for applications in covalent solids. The SISPA method [Field, J. Chem. Theory Comput., 2017, 13, 2342] differs from other AP-QM/MM methods by only requiring one QM calculation per time step, but it has the flaw that the QM charge density and wavefunction near the buffer/MM boundary tend to those of isolated atoms/fragments. Besides, regular QM/MM methods for treating covalent bonds cut by the QM/MM boundary are incompatible with SISPA. Due to these flaws, SISPA in its original form cannot treat covalently bonded systems properly. In this work, I show that a simple modification to the SISPA method improves the treatment of covalently bonded systems. I also study the effect of correcting the charge density in SISPA by developing a density-corrected pre-scaled algorithm. I demonstrate the methods with simple molecules and bulk solids.

Accurate Estimation of pKb Values for Amino Groups from Surface Electrostatic Potential (VS,min) Calculations: The Isoelectric Points of Amino Acids as a Case Study

Theoretical calculation of equilibrium dissociation constants is a very computationally demanding and time-consuming process since it requires an extremely accurate computation of the solvation free energy changes for each of the species involved. By correlating the minimum surface electrostatic potential (V_S,min) on the nitrogen atom of several aliphatic amino groups-calculated at the density functional theory (DFT) ωB97X-D/cc-pVDZ level of theory-we obtained regression models for each kind of substitution pattern from which we interpolate their corresponding pK_b values with remarkable accuracy: primary R² = 0.9519; secondary R² = 0.9112; and tertiary R² = 0.8172 (N = 20 for each family). These models were validated with tests sets (N = 5) with mean absolute error (MAE) values of 0.1213 (primary), 0.4407 (secondary), and 0.3057 (tertiary). Combining this ansatz with another previously reported by our group to estimate pK_a values [Caballero-García, G.; et al. Molecules 2019, 24(1), 79] we are able to reproduce the isoelectric points of 13 amino acids with no titrable side chains with MAE = 0.4636 pI units.