Characterizing Protein Protonation Microstates Using Monte Carlo Sampling

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Modeling pH-Dependent Biomolecular Photochemistry

The tuning mechanism of pH can be extremely challenging to model computationally in complex biological systems, especially with respect to the photochemical properties. This article reports a protocol aimed at modeling pH-dependent photodynamics using a combination of constant-pH molecular dynamics and semiclassical nonadiabatic molecular dynamics simulations. With retinal photoisomerization in Anabaena sensory rhodopsin (ASR) as a testbed, we show that our protocol produces pH-dependent photochemical properties, such as the isomerization quantum yield or decay rates. We decompose our results into single-titrated residue contributions, identifying some key tuning amino acids. Additionally, we assess the validity of the single protonation state picture to represent the system at a given pH and propose the most populated protein charge state as a compromise between cost and accuracy.

Computing the Relative Affinity of Chlorophylls a and b to Light-Harvesting Complex II

In plants and algae, the primary antenna protein bound to photosystem II is light-harvesting complex II (LHCII), a pigment-protein complex that binds eight chlorophyll (Chl) a molecules and six Chl b molecules. Chl a and Chl b differ only in that Chl a has a methyl group (-CH3) on one of its pyrrole rings, while Chl b has a formyl group (-CHO) at that position. This blue-shifts the Chl b absorbance relative to Chl a. It is not known how the protein selectively binds the right Chl type at each site. Knowing the selection criteria would allow the design of light-harvesting complexes that bind different Chl types, modifying an organism to utilize the light of different wavelengths. The difference in the binding affinity of Chl a and Chl b in pea and spinach LHCII was calculated using multiconformation continuum electrostatics and free energy perturbation. Both methods have identified some Chl sites where the bound Chl type (a or b) has a significantly higher affinity, especially when the protein provides a hydrogen bond for the Chl b formyl group. However, the Chl a sites often have little calculated preference for one Chl type, so they are predicted to bind a mixture of Chl a and b. The electron density of the spinach LHCII was reanalyzed, which, however, confirmed that there is negligible Chl b in the Chl a-binding sites. It is suggested that the protein chooses the correct Chl type during folding, segregating the preferred Chl to the correct binding site.

Quantum Computer Simulation of Protein Protonation

In attempts to simulate the protonation of proteins, a major challenge is that the number of protonation states grows rapidly as a function (2N) of the number of protonation sites (N). Expression on the free energy of the protonation state as an N-site Ising model ─ using an empirical Generalized-Born model ─ allows a quantum computer to efficiently determine the important states at a given pH value and subsequently reconstruct the pH titration process at all sites. Compared with the exact results painstakingly obtained with classical computers, the results obtained using quantum computers show good agreement for staphylococcal nuclease and excellent agreement for α-lactalbumin. This work illustrates the effectiveness of quantum computers in sampling important physical states, which may be useful in attacking challenging biomolecular problems.

Tools for analyzing protonation states and for tracing proton transfer pathways with examples from the Rb. sphaeroides photosynthetic reaction centers

Protons participate in many reactions. In proteins, protons need paths to move in and out of buried active sites. The vectorial movement of protons coupled to electron transfer reactions establishes the transmembrane electrochemical gradient used for many reactions, including ATP synthesis. Protons move through hydrogen bonded chains of waters and hydroxy side chains via the Grotthuss mechanism and by proton binding and release from acidic and basic residues. MCCE analysis shows that proteins exist in a large number of protonation states. Knowledge of the equilibrium ensemble can provide a rational basis for setting protonation states in simulations that fix them, such as molecular dynamics (MD). The proton path into the Q_B site in the bacterial reaction centers (RCs) of Rb. sphaeroides is analyzed by MD to provide an example of the benefits of using protonation states found by the MCCE program. A tangled web of side chains and waters link the cytoplasm to Q_B. MCCE analysis of snapshots from multiple trajectories shows that changing the input protonation state of a residue in MD biases the trajectory shifting the proton affinity of that residue. However, the proton affinity of some residues is more sensitive to the input structure. The proton transfer networks derived from different trajectories are quite robust. There are some changes in connectivity that are largely restricted to the specific residues whose protonation state is changed. Trajectories with Q_B^•- are compared with earlier results obtained with Q_B [Wei et. al Photosynthesis Research volume 152, pages153-165 (2022)] showing only modest changes. While introducing new methods the study highlights the difficulty of establishing the connections between protein conformation.

AMOEBA Force Field Trajectories Improve Predictions of Accurate pKa Values of the GFP Fluorophore: The Importance of Polarizability and Water Interactions

Precisely quantifying the magnitude, direction, and biological functions of electric fields in proteins has long been an outstanding challenge in the field. The most widely implemented experimental method to measure such electric fields at a particular residue in a protein has been through changes in pKa of titratable residues. While many computational strategies exist to predict these values, it has been difficult to do this accurately or connect predicted results to key structural or mechanistic features of the molecule. Here, we used experimentally determined pKa values of the fluorophore in superfolder green fluorescent protein (GFP) with amino acid mutations made at position Thr 203 to evaluate the pKa prediction ability of molecular dynamics (MD) simulations using a polarizable force field, AMOEBA. Structure ensembles from AMOEBA were used to calculate pKa values of the GFP fluorophore. The calculated pKa values were then compared to trajectories using a conventional fixed charge force field (Amber03 ff). We found that the position of water molecules included in the pKa calculation had opposite effects on the pKa values between the trajectories from AMOEBA and Amber03 force fields. In AMOEBA trajectories, the inclusion of water molecules within 35 Å of the fluorophore decreased the difference between the predicted and experimental values, resulting in calculated pKa values that were within an average of 0.8 pKa unit from the experimental results. On the other hand, in Amber03 trajectories, including water molecules that were more than 5 Å from the fluorophore increased the differences between the calculated and experimental pKa values. The inaccuracy of pKa predictions determined from Amber03 trajectories was caused by a significant stabilization of the deprotonated chromophore's free energy compared to the result in AMOEBA. We rationalize the cutoffs for explicit water molecules when calculating pKa to better predict the electrostatic environment surrounding the fluorophore buried in GFP. We discuss how the results from this work will assist the prospective prediction of pKa values or other electrostatic effects in a wide variety of folded proteins.

Electrostatics in Computational Biophysics and Its Implications for Disease Effects

This review outlines the role of electrostatics in computational molecular biophysics and its implication in altering wild-type characteristics of biological macromolecules, and thus the contribution of electrostatics to disease mechanisms. The work is not intended to review existing computational approaches or to propose further developments. Instead, it summarizes the outcomes of relevant studies and provides a generalized classification of major mechanisms that involve electrostatic effects in both wild-type and mutant biological macromolecules. It emphasizes the complex role of electrostatics in molecular biophysics, such that the long range of electrostatic interactions causes them to dominate all other forces at distances larger than several Angstroms, while at the same time, the alteration of short-range wild-type electrostatic pairwise interactions can have pronounced effects as well. Because of this dual nature of electrostatic interactions, being dominant at long-range and being very specific at short-range, their implications for wild-type structure and function are quite pronounced. Therefore, any disruption of the complex electrostatic network of interactions may abolish wild-type functionality and could be the dominant factor contributing to pathogenicity. However, we also outline that due to the plasticity of biological macromolecules, the effect of amino acid mutation may be reduced, and thus a charge deletion or insertion may not necessarily be deleterious.