Understanding and Manipulating Electrostatic Fields at the Protein

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Feature Article

Understanding and Manipulating Electrostatic Fields at the Protein-Protein Interface Using Vibrational Spectroscopy and Continuum Electrostatics Calculations Andrew W Ritchie, and Lauren J. Webb J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b06888 • Publication Date (Web): 16 Sep 2015 Downloaded from http://pubs.acs.org on September 23, 2015

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The Journal of Physical Chemistry

Understanding and Manipulating Electrostatic Fields at the Protein-Protein Interface Using Vibrational Spectroscopy and Continuum Electrostatics Calculations Andrew W. Ritchie and Lauren J. Webb* Department of Chemistry, Center for Nano- and Molecular Science and Technology, and Institute for Cell and Molecular Biology The University of Texas at Austin 105 E. 24th Street STOP A5300, Austin, TX 78712 *

To whom correspondence should be addressed: [email protected]

Abstract Biological function emerges in large part from the interactions of biomacromolecules in the complex and dynamic environment of the living cell. For this reason, macromolecular interactions in biological systems are now a major focus of interest throughout the biochemical and biophysical communities. The affinity and specificity of macromolecular interactions are the result of both structural and electrostatic factors. Significant advances have been made in characterizing structural features of stable protein-protein interfaces through the techniques of modern structural biology, but much less is understand about how electrostatic factors promote and stabilize specific functional macromolecular interactions over all possible choices presented to a given molecule in a crowded environment. In this Feature Article, we describe how vibrational Stark effect (VSE) spectroscopy is being applied to measure electrostatic fields at protein-protein interfaces, focusing on measurements of guanosine triphosphate (GTP)-binding proteins of the Ras superfamily binding with structurally related but functionally distinct downstream effector proteins. In VSE spectroscopy, spectral shifts of a probe oscillator’s energy are related directly to that probe’s local electrostatic environment. By performing this

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experiment repeatedly throughout a protein-protein interface, an experimental map of measured electrostatic fields generated at that interface is determined. These data can be used to rationalize selective binding of similarly structured proteins in both an in vitro and in vivo environment. Furthermore, these data can be used to compare to computational predictions of electrostatic fields to explore the level of simulation detail that is necessary to accurately predict our experimental findings. Introduction Our research group is interested in understanding at the molecular level how large biomacromolecules such as proteins, which have three dimensional structure largely determined by their chemical sequence, interact through noncovalent mechanisms with other macromolecular structures to generate biological function. Most physiologically relevant biological function emerges from biomolecular interactions such as protein-protein docking. Protein interactions occur in the complex, anisotropic, dynamic, and crowded environment of the living cell, and yet have mechanisms for selecting particular interactions that are exquisitely sensitive to biological specificity and function. A large and growing list of crystal structures of docked protein-protein complexes have become available in the protein crystal structure database (PDB), and these structures reveal that docked proteins are almost exclusively held together through noncovalent interactions. In the absence of chemical bonding, long-range but weak electrostatic forces generate potential energies for docking, control the orientation and structure of the assembled complex, and determine the rate of binding and dissociation. There has been much recent interest in quantifying the magnitude of electrostatic fields present at protein-protein interfaces, and in understanding how such electrostatic forces affect structure and function of the resulting docked complexes. Although this Feature Article focuses on studies of protein-protein

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interfaces, the methodologies discussed here are in principle generalizable to essentially any macromolecular interaction of interest, whether biological or synthetic. The three dimensional structure of a folded protein places a large number of atomic partial charges into a confined and organized environment. This system of fluid charges creates a complex Coulombic landscape with a wide distribution of electrostatic potentials across the biomacromolecule. The position gradient of these potentials in turn leads to electrostatic fields distributed throughout the protein structure. In principle, these fields can be computed easily; in Figure 1, for example, the magnitude of the electrostatic field perpendicular to the protein surface is mapped onto the interface of a docked protein-protein complex, where the range of positive to negative fields are shown in a gradient of blue to red colors. The quantitative details of how such an image is produced are discussed in more detail below; however, an image like this is qualitatively interesting for three reasons. First, the magnitude of the field calculated to be present along the surface of the protein, up to 50 MV/cm or more in this example, is enormous: at least an order of magnitude greater than a field that could be supported in a high quality synthetic dielectric. Exposing molecular dipoles to these large fields has been postulated to be important for protein function, influencing protein folding, chemical reactivity, protein-protein interactions and other important processes.1-8 Second, this image reveals that protein electric fields are heterogeneously distributed over the surface of the protein. Experimental verification and study of these fields must therefore be done at the ångström level in order to be meaningful. Third, visual inspection of Figure 1 reveals regions of electrostatic complementarity on either side of the protein-protein interface. Such complementarity could provide a pattern recognition function in protein-protein docking that might enable two proteins to interact in a specific orientation in a crowded and dynamic environment. Such specificity of docking structure will

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surely be as important to the function of a docked protein-protein complex as to an individual protein, and is vital to understand and predict how noncovalent forces lead to these structures. Our research group has been interested in exploring the quantitative implications of this qualitative picture. This Feature Article discusses recent work in our laboratory in addressing two questions. 1) Can electric fields be experimentally measured at a protein-protein interface at the length scale that is relevant, and if so, can their functional importance be determined, tested, and manipulated? 2) With the help of experimental data, can calculation such as those used to generate Figure 1 be tested and improved for various experimental conditions? After reviewing these two questions, broader implications of the biological function of electrostatic fields at the protein-protein interface, both in a model system and in general, are discussed. Experimental Methods Vibrational Stark Effect Spectroscopy of Site-Specific Nitrile Probes: Many of the experimental methods used in this research have been extensively described by previous reports.9-13 To avoid repetition, these methods are reviewed here only in the context of the particular ways they are applied to protein surfaces and interfaces. Our primary experimental methodology is based on the vibrational Stark effect (VSE), described extensively by Boxer and coworkers, including in a recent Review.14 Briefly, VSE exploits differences between the ground and excited state dipole moments of harmonic oscillators; these can be quite large in certain cases, such as the nitrile group. This difference in ground and excited state dipole moments, ! ΔµCN , couples the oscillator’s absorption energy to local electrostatic fields. The change in

absorption energy of the nitrile oscillator, Δνobs, is related to the change in electrostatic field in the vicinity of the nitrile probe caused by the perturbation of the protein-protein interaction,

! ΔFdock , through equation 1:

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! ! ΔE = hcΔυ obs = −ΔµCN • ΔFdock

(1)

! where ΔµCN , also called the Stark tuning rate, has been previously measured. When the nitrile is ! introduced as a thiocyanate on the side chain of cysteine, ΔµCN = 0.7 cm-1 /(MV/cm).15 Because

this dipole vector points from the nitrogen atom to the carbon atom of the thiocyanate, a 1 MV/cm increase in the electrostatic field in the direction of the difference dipole upon docking will shift the absorption energy of the nitrile probe by -0.7 cm-1. This work is enabled by the extensive capabilities of modern biotechnology to place unnatural functionality into biomolecules. Our work uses four independent methods that we select from based on the needs of the experiment and the particular protein construct under investigation: 1) post-translational modification of genetically engineered cysteine residues to thiocyanate probes;15 2) synthesis of nitrile-containing analogs of ligands that are known to bind to proteins, such as nitrile-containing GTP molecules synthesized by our laboratory;16 3) semisynthesis of short peptides containing artificial amino acids;17-19 and 4) biosynthetic incorporation of nitrile containing amino acid side chains such as p-cyanophenylalanine during recombinant expression of the protein in E. coli.20-22 All of these methods are used interchangeably in our laboratory based on the protein and experiment being investigated. The experiments discussed in this Feature Article are primarily conducted at the protein surface, and so post-translational reaction of solvent-exposed cysteine mutations to thiocyanate (method 1) is a particularly useful method for introducing the nitrile probe and will dominate the experimental results discussed herein. Electrostatic Fields at the Ras-Effector Interface: Much of the early work in our research laboratory focused on building a good experimental system in which to test experimental methods and explore hypotheses of effective noncovalent interactions of proteins. Much of our

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work has focused on the guanosine triphosphatase (GTPase) p21Ras (hereafter referred to as Ras) and its analogs docked with their downstream effector proteins. Ras, the first so-called “oncoprotein,” was discovered in 1965 and mutations to the human isoforms of this protein are found in approximately 30% of human cancer tumors.23 Because of this, research on the structure and function of Ras have been central to the development of the field of molecular oncology for five decades, and there is significant biochemical understanding of this protein. Ras regulates the propagation of signal transduction cascades by switching between a GTPbound ON state and a guanosine diphosphate (GDP)-bound OFF state. In the ON state, Ras docks with several downstream effector proteins, including the Ras binding domain (RBD) of Raf (mitogen-activated protein (MAP)-kinase-kinase-kinase); this docking interaction initiates the MAP-kinase-kinase (MEK)/MAP-kinase (ERK) pathway, eventually resulting in a variety of changes to the cell, including initiating cell division. In order to control signal propagation pathways, Ras remains docked to a variety of proteins throughout its catalytic cycle (Figure 2), including GTPase activating proteins (GAPs), G-nucleotide dissociation inhibitors (GDIs), and G-nucleotide exchange factors (GEFs), that promote GTP hydrolysis, Ras inhibition, and Ras activation, respectively. The importance of Ras-effector interactions in Ras carcinogenic function was recognized early in Ras research, and much work on Ras has focused on the structure, kinetics, and function of Ras-effector docked complexes. There is therefore an extensive library of high quality crystallographic and NMR structures as well as simple kinetic assays of function to support further Ras-based research. There is an additional aspect to Ras that is particularly relevant to understanding the function of electrostatic fields at protein-protein interfaces. Ras is the canonical member of a large superfamily of GTPases, all of which have the same three-dimentional structure as shown

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in Figure 1, the same catalytic cycle shown in Figure 2, and all of which propagate signal transduction cascades throughout the cell. The specificity that directs which GTPase regulates which chemical cascade arises in part through the exact downstream effector each GTPase interacts with in its ON state.24-26 After nearly 50 years of intense study, no Ras-targeting drug has emerged from clinical trials, largely because of the structural similarity of the large number of GTPases in human cells which bind to GTP with high affinity. Any molecule that targets Ras with high enough affinity to outcompete GTP and be useful as a drug also targets other GTPases with high affinity, and is unacceptably toxic. However, if the specificity of Ras-based pathological responses is generated from the Ras-Raf interaction, learning how to target that protein-protein interface to the exclusion of other GTPase-effector interactions could possibly be transformational for the treatment of Ras-derived tumors. To explore this idea, our laboratory has focused on the GTPase Rap1a (hereafter referred to as Rap) in comparison to Ras. Structures of these proteins are shown in Figure 3. Rap and Ras have nearly identical tertiary structures; the root mean square (RMS) deviation for homologous residues is of 0.7 Å,27 and they both dock with the RBD of a downstream effector, Ral, that is itself highly similar in structure to Raf. However, the binding affinity of Ras for the RBD of Raf is nearly 100-fold greater than that of Ras for RBD of Ral (measured as a binding dissociation constant).28 Most importantly, this in vitro measurement is independent of cellular mechanisms for co-localization of the GTPase with the appropriate downstream effector, and represents a clear thermodynamic selection mechanism for the “appropriate” versus “inappropriate” downstream effector. Because of the high structural similarity of both GTPases and RBDs, the Ras-Raf versus Rap-Ral systems provide an ideal model for studying electrostatic

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contributions to protein interface formation for which structural factors are controlled for to the greatest extent possible. That has been the goal of our research laboratory. Measuring Electrostatic Fields With VSE: Because we are working with docked proteinprotein complexes for which there are good crystal structures, each experiment begins by identifying amino acid residues at and near the interfacial region for systematic mutation to cysteine and labeling to make the thiocyanate.27-31 The GTPase and downstream effector RBD proteins we have worked with have generally contained few wild type (WT) cysteines (as expected since cysteine is a rare residue) and no disulfide bonds. We first generate a “cysless” variant of the protein in which any WT cysteines have been mutated to alanine; this strategy has proven to be benign to protein expression, purification, and further handling. (To avoid confusion, these “cysless” constructs are referred to with the suffix “β:” i.e. Ralβ or Rafβ. Furthermore, the names Raf and Ral refer to the RBDs of those two proteins.) These constructs are then subjected to further mutagenesis to insert cysteine mutations at or near the surface region of interest in the protein. After expression and purification of the cysteine-containing mutant, the protein is exposed to bis-dithionitrobenzoic acid (DTNB) followed by potassium cyanide to form the cysteine thiocyanate vibrational probe.15 The absorption energy of this probe is measured on the monomeric protein in aqueous buffer. The protein is then exposed to the docking partner of interest, and the absorption energy is measured again. The change in vibrational absorption energy between the monomer and docked states is used in equation 1 to estimate the change in electric field the probe experiences between the solvated monomer and interfacially docked positions. This process is repeated in as many probe locations along the protein-protein interface as possible to assemble an experimental electrostatic map of the interfacial region.

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These experiments involve placing an unnatural and polar probe molecule into the binding region of the protein-protein interface of interest. This probe might perturb or alter the very interaction we are therefore trying to study. There are two possible sources of error that the probe could introduce. First, amino acid mutagenesis and probe insertion could alter the structure of the interfacial area in some critical way, thus changing the structure, orientation, or free energy of the docked complex. We monitor these perturbations by measuring the dissociation constant, Kd, of protein-protein interface formation of all labeled protein constructs through a straightforward GTP fluorescence-based kinetic assay to determine if the mutation or probe itself has any significant impacts on the formation of the interface under investigation. In general this protein system has been very robust towards mutation and nitrile labeling, and significant differences in Kd have rarely been observed.27,29 Second, a nitrile-containing proteinprotein interface that forms with an equilibrium constant similar to the purely WT system could still have its measured electrostatic field altered systematically by the presence of the dipole moment of the polar nitrile. There is little experimental investigation of this effect, although previous work on nitrile-labeling of enzyme active sites has shown that the absorption energy of a single nitrile probe is not altered by the presence of additional nitrile labels.15 Our laboratory is currently exploring the universality of this finding, with results reported in a later manuscript. If the nitrile substantially alters the measured electrostatic field of the experiment, it will do so in a systematic manner that should still be reproduced by accurate electrostatics calculations, described below. For these reasons, experimentally determining interface-wide electrostatic fields through VSE spectroscopy of nitrle probes is appropriate. Molecular Dynamics Simulations: Because the relationship between the Stark tuning rate and the local electric field is through a dot product, it is important to know the position of the

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nitrile probe in the experimental sample in order to interpret experimental vibrational energy data. Understanding VSE spectroscopic data and the connections between experimental observations and computational predictions requires confidence in knowing the position and orientation of the nitrile oscillator within the protein-protein interface. Although our experiments are done on systems with good crystal structures, these structures are of constructs that do not contain the nitrile probe or other relevant mutations. Even if we did have crystal structures of our exact experimental constructs, a single structural snapshot often does not identify the range of accessible orientations that our nitrile might visit in the course of a steady-state experiment taking several minutes. Because of this, our experimental protocol is coupled with significant molecular dynamics (MD) simulations to aid with all aspects of data interpretation. It is particularly important for us to generate a Boltzmann-weighted ensemble of reasonable structures of the nitrile within the protein. There are many possible enhanced MD approaches that can be taken to achieve this goal; our group has focused on umbrella sampling with the weighted histogram analysis method (WHAM).32,33 There are several reasons for this selection: 1) It is embarrassingly parallel, making it much more efficient to generate long simulations than, for example, replica exchange methods. 2) We can make and test hypotheses about the most relevant degrees of freedom, which is particularly useful given that VSE is sensitive to the magnitude of the field along the vibrational chromophore difference dipole moment. 3) It is trivially implemented in the freely-available MD package GROMACS.34-36 We have used umbrella sampling with WHAM to bias both the χ2 dihedral angle (CαCβ-Sγ-Cδ) in one-dimensional (1D) sampling, as well as the χ1 (N-Cα-Cβ-Sγ) and χ2 dihedral angles in two-dimensional (2D) sampling. As shown in Figure 4A, these two torsional angles represent the full degrees of freedom of the nitrile probe about the peptide backbone. In 1D

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sampling, we performed six different biased simulations along the χ2 dihedral coordinate, each for 3 ns, resulting in a total of 18 ns of simulation. During each of the 3 ns trajectories, it was observed that little-to-no rotation was observed about the χ1 dihedral angle. This severely limited the possible orientations of the probe, information which is critical for correctly calculating vibrational absorption shifts due to external field perturbations. In 2D sampling, we performed 144 different biased simulations across 12 χ1 and 12 χ2 dihedral coordinate pairs, each for 400 ps, resulting in a total of 57.6 ns of simulation.37 Although each individual trajectory was much shorter than in the one-dimensional sampling, the gain of information about nitrile orientation was more significant than the possible loss of information about residues distant from the cyanocysteine. The overriding (if not surprising) observation from this sampling was that significantly probable pairs of χ1, χ2 dihedrals were characteristic of the least sterically hindered orientations of the alkane cyanocysteine. A representative example of this is shown in Figure 4B. All further computational studies by our group have therefore been conducted using 2D sampling. From the MD-generated ensemble of structures, we determine average statistical parameters of nitrile position and structure, the most useful of which is generally the angle that the nitrile oscillator makes with respect to the protein-protein interfacial plane. We have termed this the “azimuthal” angle, which is shown schematically in Figure 4C. In particular, the variance of highly probable angles in a given simulation tells us about how many different conformational environments the probe experiences, and any change in average angle going from the monomer to the docked complex could indicate steric occlusion presented by protein-protein docking. Examples of two cases, a nitrile which remains relatively stationary when docked to different GTPases, and one which assumes very different positions depending on which mutant it is

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docked to, are shown in Figure 4D. No matter what the result, both stationary and variable behavior can easily be investigated further by examining snapshots of representative structures generated in the MD trajectory. These Boltzmann-weighted trajectories form the basis for further electrostatics calculations, described below. Investigating the GTPase-Effector Interface: We have applied our concurrent experimental-computational analysis to two large-scale studies of protein-protein interactions: 1) SCN-labeled Ralβ binding with Ras and Rap;27,29 and 2) WT Ras binding with SCN-labeled Ralβ and Rafβ.28,31 These experiments explore interface formation through both sides of the binary interface, allowing us to study the GTPase-effector system from several different locations and perspectives. The aggregate of the information gleaned from this strategy addresses the true mission of our experiments. For example, the data shown in Figure 5 indicate that when a nitrile-labeled Ralβ downstream effector docks with either WT Ras (black) or WT Rap (gray), at some probe positions along the interface, the probe behaves in similar ways when it is docked to either of the two WT GTPases. However, at three positions, Ralβ N27CSCN, N29CSCN, and Y31CSCN, the probe experiences very different electrostatic fields upon docking to Ras or Rap, either in the magnitude of the change in absorption energy, Δνobs, or even in the direction of the shift. We hypothesized that these locations represented functional “hot spots” that could direct functional discrimination of the protein-protein docking event to the appropriate versus inappropriate GTPase. To test this hypothesis, we placed the nitrile probe at these three locations and then began making functional mutations to the Rap GTPase to revert it back to the chemical identity of Ras. Although Ras and Rap do not have excessive amino acid similarities (50% identity, 80% homology), amongst the approximately 20 amino acids that line the protein-protein interfacial

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region there are only three amino acid differences, at positions 27, 30, and 31. Most significantly, at position 31, Ras contains a Glu while Rap contains a Lys. This charge reversal difference has long been cited as a possible significant cause of differential binding behavior of these two GTPases. Indeed, previous work by Hermann et al.25,38 has determined that forming the Rap reversion mutation Rap E30D/K31E creates a construct with Kd values for Ral similar to that of WT Ras, work our laboratory reproduced when we began working with these nitrile-labeled mutations.27 We hypothesized that this charge reversal mutation affected the protein-protein interface by a purely electrostatic mechanism, and that this could be quantified by nitrile VSE probes sitting at positions Ralβ N27CSCN, N29CSCN, and Y31CSCN, along the protein interface. Observing a change in nitrile absorption energy upon Ralβ docking with Rap K31E or Rap E30D/K31E to a similar energy measured upon Ralβ docking with WT Ras would support this hypothesis. These results, summarized in Figure 6,27 indeed observed this similarity for two of the nitrile probe positions, Ralβ N27CSCN and N29CSCN. However, for the third position, Ralβ Y31CSCN, while there were large changes in nitrile absorption energy with the three Rap reversion mutants, there was no discernable pattern to these changes based on the chemical identity of the mutant. Close examination of the nitrile azimuthal angles, shown in Figure 6, revealed that for Ralβ N27CSCN and N29CSCN, the nitrile remained in the same position for all four GTPase constructs studied. However, for Ralβ Y31CSCN, the nitrile assumed dramatically different positions when bound to different mutants, thus creating very different chemical environments for the nitrile when docked to these various mutants. Because the nitrile absorption energy data are convoluted by contributions from both structure and electrostatics, it is not possible to interpret the nitrile vibrational energy shifts in a purely electrostatic manner

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suggested by our hypothesis. These results both inform our understanding of GTPase-effector docking and demonstrate explicitly the value of high quality structural calculations for interpreting experimental results. We then asked how WT Ras distinguished between two nitrile-labeled effectors, Rafβ and Ralβ in the binding interaction. Despite the structural similarities in the two downstream effectors Raf and Ral evident in Figure 3, there is a significant difference in the orientation of these two proteins when docked with the GTPase; Ral is tilted approximately 35˚ with respect to Raf.39 In order to understand the origin of this difference between two similar effectors, we have studied Ras binding to nitrile-labeled Rafβ in a complementary experiment to nitrile-labeled Ralβ discussed above. These studies presented a new challenge: how can experimental data collected from different sets of nitrile probe positions on different proteins be compared and interpreted when the important information is not the sequence position of the cyanocysteine side chain, but rather the point in three dimensional space in which the nitrile sits after the downstream effector has docked to WT Ras? In other words, which data should be compared to which? To address this challenge, as before, we have turned to MD simulations to define a unique position of every nitrile probe, whether on Rafβ or Ralβ, with respect to the interfacial plane formed by the GTPase-effector docked structure. This plane remains fixed no matter which downstream effector is docked, and the position and orientation of the nitrile oscillator is mapped onto a fixed position on that plane. This analysis therefore allows electrostatic contributions on similar positions of the Ras surface to be compared no matter what their contributing source. Results, shown in Figure 7, clearly reveal a pattern of vibrational energy shifts in concentric rings of larger and larger radius surrounding Ras’s GTP binding site that is matched by both Rafβ and Ralβ.28 This result suggests that the downstream effector binds to the GTPase in a

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manner that conserves a pattern of electric fields, a mechanism that accounts for the 35˚ tilt angle between the two downstream effectors when docked to WT Ras. We suggest that this is a general mechanism for Ras-effector, and by extension GTPase-effector, binding and are currently testing this hypothesis by investigating a third downstream effector, PI3Kγ.40 If our hypothesis is correct, we should be able to predict the structure of this interface a priori, significantly enhancing the ability of modeling and prediction to probe and understand this physiologically important protein-protein interface. Testing Continuum Electrostatics Computational Methodologies: Our comprehensive VSE data set, now composed of over 60 nitrile-labeled proteins, both in monomeric and docked states, provides a unique opportunity to compare experimentally determined electrostatic fields to the results of electrostatic calculations. Accurate and simple calculation of electrostatic fields in proteins is a subject of longstanding interest in the biophysical community. Continuum Poisson-Boltzmann (PB) models have been used to calculate pKa values for titratable amino acids.1,41-43 Changes in free energy and pKa values have been examined using the ProteinDipoles-Langevin-Dipoles (PDLD) model of Warshel and Levitt, which first introduced solvent polarization by mapping water dipoles to a Langevin grid and including protein dipoles, eliminating the use of a macroscopic dielectric constant in a microscopic system. Comparison to continuum models can be achieved by reintroduction of the concept of solute dielectric through the semi-macroscopic PDLD/S model and PDLD/S-LRA models, which suggest solute dielectrics of at least 2 should be used (higher when solute configurations are not wellconsidered).5,6,44 All-atom electrostatics using fixed charge force fields have also seen use in understanding protein electrostatics,45-47 specifically in the context of vibrational Stark effect spectroscopy (VSE), allowing for direct measurement of electrostatic fields in complicated

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systems. Models that include explicit atomic polarization, rather than molecular polarization like PDLD and its variants, have also been used to study protein electrostatics. The fully polarizable force field AMOEBA (atomic multipole optimized energetics for biomolecular applications) has been used for a variety of electrostatics applications, such as binding free energies48 and solvation energies.49,50 Schnieders et al.51 demonstrated that a polarizable multipole PoissonBoltzmann continuum model, built upon AMOEBA, reproduces protein dipole moments calculated with explicit solvent, suggesting it to be an efficient alternative to expensive solvent sampling for other electrostatics problems such as binding free energies and pKa prediction. Additionally, mixed QM/MM methods are also being used to investigate protein electrostatics.5254

Water also poses a significant challenge in understanding and calculating protein electrostatics. Hydration water55-58 is known to behave differently than bulk water; it is less mobile, has a lower dielectric constant,59 and can play a role in stabilizing protein-protein and protein-ligand interactions.60,61 Calculations show that the ordered first and second hydration shells have a significant effect on the electrostatic potential energies of solvated proteins which are inadequately addressed by a purely implicit model, particularly when looking at both positively and negatively charged atoms.62 It has also been shown that these solvation shell effects, and therefore agreement between implicit and explicit solvent models, can be improved by optimizing atomic radii and accounting for charging the solvent in an explicit solvent system.62 Alternatively, a new implicit solvent model, semi-explicit assembly (SEA), has been developed, which differentiates between bulk and structural water and has been shown to approach implicit solvent calculation speeds with the accuracy of explicit solvent models.63 Hydrogen bonding to vibrational chromophores is another difficulty in electrostatics

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calculations. It has been shown that using ab initio absorption frequency calculations on various water clusters and performing a multivariate fit to the calculated electrostatics, can then be used with standard molecular dynamics to yield good agreement with experimentally measured absorption frequencies of small molecules in water clusters.54,64,65 Corcelli et al.66 does this by finding Stark tuning rates for each x, y, z vector components of the calculated electrostatic field and summing these components, while Choi et al. uses a weighted sum of electrostatic potentials around the vibrational chromophore.64,65 In a QM/MM study of a thiocyanate vibrational chromophore in the enzyme ketosteroid isomerase (KSI), Layfield et al. also demonstrated that the explicit consideration of the water molecule nearest to the vibrational probe is important for capturing solvent polarization effects, and therefore calculating vibrational Stark shifts.52 In the pKa Cooperative’s 2011 test of electrostatics calculation methods, scientists were challenged to calculate protein pKa values on a blind protein sample using their computational methods of choice. In the presentation of this challenge, the pKa Cooperative’s leaders summarized that “accounting for the heterogeneous response of proteins is generally considered the chief difficulty in modeling pKa values in proteins.”67 This statement can be generalized for all experimentally-measured electrostatic properties in proteins. While many electrostatic field calculations have been shown to work well for solvated small molecules,47 there is an enormous difference in the number of degrees of freedom between a small (7 atom) methyl thiocyanate in a water cluster and the number of degrees of freedom in a protein, which significantly complicate the protein calculations.37,45,46,68 Obtaining a good ensemble of structures is therefore much more computationally intense for a solvated protein system than for a solvated small molecule. Our data set of vibrational absorption energies measured on systems for which we have extensive structural information from MD provides a unique opportunity to test the accuracy of

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various computational outputs. We have two goals of this work. First, we want to understand the strengths and weaknesses of a variety of computational platforms for accurately predicting our data set: a collection of vibrational absorption energies. All computational methods yield results which are physically reasonable, yet in a single system, or even a single MD snapshot, results can vary significantly depending on how they were calculated. We are interested in determining the amount of physical rigor and computational expense required to obtain in silico electrostatic fields that are well correlated to the equivalent in vitro vibrational absorption frequencies and to compare the output of different methods. Second, full integration of computational information into our measurements will enhance our ability to interpret experimental observations and design new experiments in a way that enhances molecular-level understanding of our system. Ultimately, high confidence in electrostatics calculations methods would eliminate the need for VSE measurements in the first place. Our efforts in this area have focused on solving the Poisson-Boltzmann equation (PBE) to calculate electric fields at the midpoint of the nitrile bond. PB-based computational strategies are common in the biophysical literature because of their speed and ease of implementation, but have been criticized for their nonphysical implementation of an electrostatic continuum on a heterogeneous and anisotropic system (a protein). However, given their extensive use throughout the community, it is critical to understand the conditions under which PB-based strategies are appropriate and reliable. For all continuum electrostatics calculations, we have used the freely available software Adaptive Poisson-Boltzmann Solver (APBS),69 which can use both finite-element70,71 as well as multigrid methods72,73 to solve the linear PBE, equation 2:

∇ ⋅ε ( r ) ∇φ ( r ) = ε ( r )κ 2φ ( r ) − 4πρ ( r )

(2)

where φ(r) is the electrostatic potential at a point r, ε(r) is a position-dependent dielectric, κ 2 is 18


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the ion accessibility coefficient, and ρ(r) is the charge distribution. We have focused on solving the PBE using multigrid methods that employ a two-stage focusing protocol where a coarse solution is used as the boundary condition for a significantly finer solution centered on or near the vibrational probe. Regardless of the calculation method chosen, using the linear PBE will always require determining a numerical solution to a second order differential equation and because of this, is subject to numerical errors. To minimize these errors, we have used the strategy shown schematically in Figure 8. First, we placed a series of chargeless, massless dummy atoms along the nitrile bond, then solved for the numeric solvent reaction field potential (SRF), described in equation 3, at each position:

SRF = φ ( r )εsolute ≠εsolvent − φ ( r )εsolute =εsolvent

(3)

where each φ(r) is a solution to the PBE at different solvent dielectric. The SRF was determined from the difference between the PBE solution for the solvated potential and the PBE solution for the reference potential, illustrated in Figure 8A. The solvated potential, φ(r) solute ε

≠ε

solvent

,

represented by the leftmost image in Figure 8A, was calculated for a solute with dielectric εsolute solvated in a continuum of dielectric εsolvent. The reference electrostatic potential, φ(r) solute= solvent, ε

ε

represented by the middle image in Figure 8A, is calculated from the same solute with dielectric

εsolute solvated in a continuum also having a dielectric εsolute. Removing the reference potential from the solvated potential results in only the potential generated by the solvent polarizing about the solute, represented by the rightmost image in Figure 8A, the SRF. Second, we independently calculated the analytic Coulomb field of the solute. Third and finally, we added this Coulomb field to the negative gradient of the SRF. This result, which we refer to as the reaction field method (RFM), is shown equation 4:

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RFM = −∇ ( SRF ) +

1 1 N atoms qi ∑ 4π ε0 εsolute i ri2

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(4)

Here, ε0 is the vacuum permittivity, εsolute is the dielectric of the solute, qi is the charge on atom i, and ri is the distance between the location of interest and atom i.37,61 Figure 8B shows the SRF (leftmost image) result being added to the analytical solution to the Coulomb field for all protein atoms in a dielectric εsolute, (middle image), resulting in a total field which uses a numeric solution for the contribution of the implicit solvent and an analytic solution for the contribution of the explicit solute. In this way, numerical errors in the final result are reduced by only solving for part of the system (the solvent) numerically. This strategy also decreases the sensitivity of the calculation to input parameters such as box size, grid spacing, box location, charge mapping method, or other factors. In total, this strategy requires two numeric PBE solutions and one analytic Coulomb solution for each system. For solutions using the adaptive finite element solver, the “lrpbe” keyword in APBS solves for the SRF directly without requiring a reference calculation. All calculated fields were compared to experimentally measured vibrational absorption energies for the corresponding system. Different computational schemes were compared to each other on the basis of their correlation to the experimental absorption energies. We compared the RFM to the purely numerical solutions to the PBE and found two major conclusions. First, electrostatic fields calculated using the RFM were typically better correlated to experimentally measured vibrational absorption energies than fields calculated through the purely numerical method. Second, when looking at differences in calculated fields and comparing them to differences in measured vibrational absorption energies, the purely numeric solutions tended to be better correlated to experiment. When looking at the difference between a reference and a perturbation calculated using the numerical PBE solutions, a total of two numerically-error-probe 20


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PBE solutions are present in the final result, while when looking at the difference using the RFM, a total of four PBE solutions are present. The cancellation of error from taking one PBE solution and subtracting another is negated by the addition of another PBE solution pair. For the rest of this discussion, unless otherwise specified, all references to absolute fields use fields calculated via the RFM, while all references to difference fields use fields calculated from the solvated, numerical potentials only. PB calculations used to determine the electrostatic components of binding free energies often use a grid spacing of 0.5 Å/grid point or more,74 but a recent study by Harris et al.75 has demonstrated that this leads to errors in free energy calculations that are unacceptably large in comparison to the magnitudes of its contributing terms. Since we are interested in the electrostatic field at a point, which is the negative gradient of the electrostatic potential at that point, we have also examined how changing the grid spacing affects the calculated values and its correlations to experimental values. Unsurprisingly, we saw the calculated electrostatic field at a point converges to a single value as the number of grid points increases. In fact, this is the one of the distinct advantages of using a two-stage focusing strategy; a cheap calculation can be performed to find the boundary condition for a second, more expensive calculation focused on the location of interest, such as an enzyme’s active site.41 By using this two-stage focusing strategy, we are able to solve the PB equation for a very fine grid at the vibrational chromophore to obtain an electrostatic field with small numerical errors. We examined how second-stage box size, grid spacing, and box position affects the calculated electrostatic fields, shown in Figure 9. The top and middle plot in Figure 9 show the calculated field (y-axis) plotted against the experimental absorption frequency (x-axis) for six different nitrile probe locations on Ral in the monomeric state and docked to WT Ral. Each

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color represents a different second-stage box location. As previously mentioned, calculated fields converge on a value as the grid point density increases, and as such the coarser calculations were either less correlated to experiment than the finer calculation for a given box or not appreciably different. We also saw that these sorts of calculations were sensitive to the second-stage box size and the box position, as seen in the different box positions (represented by different colors) having different correlations in Figure 9. Furthermore, relative to the larger box, the smaller second-stage box was extremely sensitive to the box position. This is troubling—the accuracy of these calculations depends greatly on these tuning parameters in a way that is not predictable. We also looked at the field difference between the monomer and docked complexes compared against the vibrational absorption frequency difference between the monomer and docked complexes, which we refer to as the difference calculation, shown as the bottom plot in Figure 9. In this way, we examined change in field at the protein interface upon docking. Typically we saw an improvement in correlation with experimental vibrational absorption frequencies upon taking the difference relative to the absolute field calculations, particularly when using the purely numeric electrostatic field. For example, in calculation shown in red on Figure 9 (second-stage box centered on the nitrile), the correlation coefficients are -0.172 and 0.565 for the monomer and dock complex, respectively. Taking the difference between the two and plotting against the difference in measured absorption frequencies increases the magnitude of the correlation coefficient to -0.684. By taking the differences, whatever is nonphysical in the solutions to the Poisson-Boltzmann equation appear to cancel out, resulting in a much stronger correlation with experimental results than the absolute field calculations. As previously mentioned, when using the RFM and taking the difference, we don’t see this same cancellation of error due to the introduction of two additional numeric solution terms to the PBE.37

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One of the advantages of a continuum model is the ability to choose the solute dielectric value (although this becomes a disadvantage if used unwisely). Additionally, because the electrostatic field scales inversely with the solute dielectric constant, this can be assigned in postprocessing to best-recreated experimental values. This leads to a calibrated virtual Stark tuning rate (VSTR), which we have shown typically ranges from 2 to 40 and is in agreement with previous studies.76 However, this sort of practice overgeneralizes the heterogeneous nature of a protein with a homogenous dielectric. In fact, a dielectric constant is simply a bulk-material property governed by atomic polarizabilities which can be accounted for by explicitly modeling electronic polarizability in addition to structural rearrangement.5,77 We are interested in eliminating this parameter through the use of polarizable force fields such as AMOEBA, and this is now a significant focus of our research.49,51 This ability to compare calculations to two independent experimental measurements shows the power of VSE energy data when comparing to the output of electrostatics calculations. The Effect of Explicit Water Molecules in Simulations: As previously mentioned, nitrile absorption frequencies are inseparably intertwined with water. To that end, we experimented with including explicit tip3p78 water molecules as part of the PB solute in three different schemes; 1) all water within 5 Å of the nitrile nitrogen, 2) the water molecule closest to the nitrile nitrogen, and 3) any water molecule hydrogen-bonding to the nitrile. Based on the work of Layfield et al.,52 we hypothesized that the explicit inclusion of at least one water molecule would yield additional information about the electrostatic field as observed by the vibrational chromophore and increase the predictive capability of our model. We chose to look at three different methods of water-selection so that we could look at the result observed by Layfield et al. in that the explicit inclusion of the nearest water molecule is vital for information about

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solvent polarization (scheme 2), only water molecules hydrogen-bonding to the nitrile are sufficiently structural and unlike bulk to be approximated as such (scheme 3), and the first solvation shell is structural water and sufficiently unlike bulk (scheme 1). Of the three schemes tested, only the 5 Å water sphere around the nitrile showed significantly different fields from the purely implicit calculations. Furthermore, only probes on the monomeric protein showed significant improvement, with explicit water in the dock complexes showing negligible or detrimental affects on computational efficacy. It was hypothesized that the improvement only for monomeric probes was due to water sampling—the smaller monomer systems were sampled for the same amount of time as the larger docked complex systems and the difference in simulation time was sufficient for the water is the monomeric systems to be well sampled, while the docked complexes were not. In the former case, the explicit solvent should give comparable results as implicit solvent, and if structural water is significant, the explicit water should do a better job of capturing those effects. If the sampling is insufficient, then the explicit solvent would give poor results due to an incomplete ensemble, while the implicit solvent model would yield a good “average” solvent reaction field potential, and thus be better representative of experimental measurements. The same arguments can be used as to why the water molecule closest to the nitrile nitrogen and the water molecule hydrogen-bonding to the nitrile did not yield significantly different results from the implicit solvent model. Once again, if the water is poorly sampled and water is either showing insignificant hydrogen bonding to the probe or a lack of consistent structure near the probe, the additional water molecule in the calculation is simply random noise which, on average, should cancel out, which is essentially what we saw. Current works have addressed this sampling question and we are in the process of analyzing the results.

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In general, our work has demonstrated a computational method of qualitatively predicting experimentally-measured vibrational absorption frequency, and therefore the electrostatic field at given location in a protein using out-of-the-box APBS with minimal parameterization (unnatural amino acids) and zero optimization. It is trivially performed on other systems—there is nothing system-specific about our methods. This makes it easily adapted to other systems in which electrostatic information is desired. For quantitative prediction, calibration experiments are currently required to semi-empirically determine a virtual Stark tuning rate. We are currently exploring other calculation methods, such as those employing a polarizable (as opposed to fixed-charge) force field, or incorporating quantum mechanical approaches into at least a portion of the electrostatics calculation. Our goal is to quantify, against a common comprehensive data set, levels of computational detail that need to be simulated in order to model and understand an experimental result. It is likely that different levels of simulation detail will be required to ask different questions about the protein. For example, a free energy calculation may require significant physical detail in the simulation, while a difference map of electric fields may be reliably done through a simple PBE approach. The question is not which calculation is “better,” but which is more appropriate for what problems. As this methodology is demonstrated to quantitatively and reliably predict and explain experimental data, then calculations at protein-protein interfaces can inform and direct experimental efforts, perhaps even dropping the nitrile probe from the experiment entirely. Conclusion and Future Work We are using VSE spectroscopy to study the role of electrostatic fields in mediating noncovalent interactions at protein-protein interfaces. Key discoveries in the last few years include that key residues along the surface of the effector Ral appear to distinguish alternative

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GTPases (Ras and Rap) through an electrostatic mechanism, and that two downstream effectors (Raf and Ral) dock differently with the same GTPase (Ras) in order to preserve a pattern of electric fields. We are using these experimental data to test and refine electrostatics computational strategies, as well as to ask a number of mechanistic questions about GTPase function, carcinogenic activity, docking mechanism, and even protein-protein interface druggability. The emphasis on connecting experiment and calculation in this work will make it possible to generalize discoveries made on the GTPase-effector interaction to other proteinprotein interfaces of interest to the community. Acknowledgements The work described in this Feature Article has been generously funded by The Welch Foundation (Grant No. F-1722), the Burroughs Wellcome Fund (Grant No. 1007207), the Alfred P. Sloan Foundation, and OpenEye Scientific Software. The authors gratefully acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing high-performance computing resources that have contributed to the results reported within this paper.

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Figure 1. Structure (left) and electrostatic representation (right) of protein surfaces of a GTPase (top) and downstream effector (bottom) when docked in a protein-protein complex. Electrostatic potentials are mapped onto the protein surface by solving the Poisson-Boltzmann equation using APBS with the multigrid method at a solute dielectric of 1, solvent dielectric of 78, and 0.15 M monovalent ion concentration with Amber03 partial charges.

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Figure 2. Lifecycle of Ras-like GTPases. While bound to GTP, Ras is in the ON state and binds to downstream effectors to propagate signal transduction cascades. GTPase activating proteins (GAPs) then bind to Ras to promote GTP hydrolysis. Ras is kept in the GDP-bound OFF state by binding to G-nucleotide dissociation inhibitors (GDIs). Ras is returned to the ON state by interacting with G-nucleotide exchange factors (GEFs), which promote the replacement of GDP with GTP.

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Ras / Rap

GDPNP Mg

2

+

Raf / Ral

Figure 3. Crystal structure of Ras (blue, with mutation E31K) bound to the Ras binding domain of Ral (green, 1LFD)79 overlaid with the crystal structure of Rap (gray, with mutation K31E) bound to the Ras binding domain of Raf (salmon, 1GUA).38 Reprinted with permission from Reference 29 (Stafford, A. J.; Ensign, D. L.; Webb, L. J. Vibrational Stark Effect Spectroscopy at the Interface of Ras and Rap1A Bound to the Ras Binding Domain of RalGDS Reveals an Electrostatic Mechanism for Protein-Protein Interaction. J. Phys. Chem. B 2010, 114, 1533115344). Copywrite 2010 American Chemical Society.

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Figure 4. A. Structure of the cyanocysteine side chain showing the χ1 and χ2 torsional angles. B. Example of Boltzmann-weighted probability distribution of χ1 and χ2 torsional angles for N54CSCN docked with WT Ras. C. Schematic of the so-called “azimuthal” angle of a nitrile group on a cyanocysteine residue at the GTPase-effector interface. D. Example of azimuthal angles for two SCN-labeled Ralβ mutants, G28CSCN and K32CSCN, docked with four different GTPases. Angles > 0˚ represent nitriles pointed away from Ralβ, while angles < 0˚ represent nitriles pointed into Ralβ. The shaded area represents the variance of the angle from the Boltzmann-weighted distribution. Reprinted with permission from Reference 37 (Ritchie, A. W.; Webb, L. J. Optimizing Electrostatic Field Calculations with the Adaptive Poisson−Boltzmann Solver to Predict Electric Fields at Protein− Protein Interfaces. I. Sampling and Focusing. J. Phys. Chem. B 2013, 117, 11473-11489). Copyright 2013 American Chemical Society. Reprinted with permission from Reference 45 (Ensign, D. L.; Webb, L. J. Factors determining

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electrostatic fields in molecular dynamics simulations of the Ras/effector interface. Proteins 2011, 79, 3511-3524). Copywrite 2011 John Wiley and Sons. Reprinted with permission from Reference 27 (Ragain, C. M.; Newberry, R. W.; Ritchie, A. W.; Webb, L. J. Role of Electrostatics in Differential Binding of RalGDS to Rap Mutations E30D and K31E Investigated by Vibrational Spectroscopy of Thiocyanate Probes. J. Phys. Chem. B 2012, 116, 9326-9336). Copywrite 2012 American Chemical Society.

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Figure 5. Change in absorption energy, Δνobs, of a nitrile probe on SCN-labeled Ralβ mutants when bound to WT Ras (black) or WT Rap (gray), where Δνobs = 0 represents no change from the thiocyanate absorption energy in labeling buffer. Reprinted with permission from Reference 29 (Stafford, A. J.; Ensign, D. L.; Webb, L. J. Vibrational Stark Effect Spectroscopy at the Interface of Ras and Rap1A Bound to the Ras Binding Domain of RalGDS Reveals an Electrostatic Mechanism for Protein-Protein Interaction. J. Phys. Chem. B 2010, 114, 1533115344). Copywrite 2010 American Chemical Society.

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Figure 6. Left: Change in absorption energy of nitrile probes on SCN-labeled Ralβ mutants when bound with WT Ras and Rap mutants compared to when bound to WT Rap. Right: Azimuthal angle of side chains at position 31 of WT Rap and Rap mutants when docked with three SCN-labeled Ralβ mutants. Reprinted with permission from Reference 27 (Ragain, C. M.; Newberry, R. W.; Ritchie, A. W.; Webb, L. J. Role of Electrostatics in Differential Binding of RalGDS to Rap Mutations E30D and K31E Investigated by Vibrational Spectroscopy of Thiocyanate Probes. J. Phys. Chem. B 2012, 116, 9326-9336). Copywrite 2012 American Chemical Society.

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Figure 7. VSE and MD results for Rafβ and Ralβ overlaid on the binding interface of WT Ras (cyan ribbon diagram). Circles represent Boltzmann-weighted averages of the location of the nitrile midpoint projected on the Ras surface plane. Blue circles represent Δνobs > 0, and red circles represent Δνobs < 0 upon binding to WT Ras. The symbol within each circle represents the azimuthal angle of the nitrile with respect to the binding plane. Lines: nitrile probe is parallel (±15˚) with respect to the Ras binding plane; X: nitrile probe is pointed away from Ras (>15˚); •: nitrile probe is pointed into Ras (>15˚) and thus into the effector. Reproduced from Reference 28 (Walker, D. M.; Wang, R.; Webb, L. J. Conserved electrostatic fields at the Ras–effector interface measured through vibrational Stark effect spectroscopy explain the difference in tilt angle in the Ras binding domains of Raf and RalGDS. Phys. Chem. Chem. Phys. 2014, 16, 20047-20060) with permission from the PCCP Owner Societies.

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Figure 8. A schematic diagram of the reaction field method (RFM). A) Method for solving the solvent reaction field potential numerically using the Poisson-Boltzmann equation. Top left: The solvated electrostatic potential. Top middle: The reference electrostatic potential. Top right: The reference electrostatic potential is removed from the solvated electrostatic potential, leaving only the electrostatic potential due to solvent—the solvent reaction field potential. B) Method for combining the numerical solution to the solvent reaction field potential to the analytic coulomb field. Bottom left: The numeric solvent reaction field potential. Bottom middle: The analytic field obtained from Coulomb’s Law. Bottom right: The total electrostatic field is the sum of the numeric solvent reaction field and the analytic coulomb field.

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Figure 9. Absolute (top and middle) and difference (bottom) calculated fields compared to experimental vibrational frequency data calculated by APBS for three box locations around the surface of a thiocyanate-labeled Ral (top) or docked GTPase-Ral (middle and bottom) complex for one box size (10 Å, grid points every 0.052 Å) and three box locations: centered on the thiocyanate (red), moved toward the center of mass of Ral (blue); or moved toward the center of mass of the GTPase-Ral system (green). Correlations between experiment and theory (r) are shown in the corresponding color in each box. Reprinted with permission from Reference 37 (Ritchie, A. W.; Webb, L. J. Optimizing Electrostatic Field Calculations with the Adaptive Poisson−Boltzmann Solver to Predict Electric Fields at Protein− Protein Interfaces. I. Sampling

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and Focusing. J. Phys. Chem. B 2013, 117, 11473-11489). Copyright 2013 American Chemical Society.

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Andrew Ritchie obtained his bachelor's degree in chemistry from Baylor University in 2010. Immediately following his B.S. degree, he joined Lauren Webb's research group at the University of Texas at Austin, where he obtained his Ph.D. in physical chemistry in 2015 studying computational methods for modeling and quantifying electrostatic fields at protein interfaces using classical electrostatics.

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Lauren J. Webb is an associate professor of chemistry at The University of Texas at Austin. She obtained her A.B. in chemistry (music minor) from Bowdoin College in 2000. She entered graduate school at the California Institute of Technology and earned her Ph.D. in chemistry in 2005. She did her graduate work in the laboratory of Dr. Nathan Lewis, where she studied chemical and electronic properties of functionalized silicon(111) surfaces. From 2005 to 2008 she was a postdoctoral fellow in the laboratory of Dr. Steven Boxer in the Department of Chemistry at Stanford University. Her research focused on quantifying electrostatic fields in proteins using vibrational Stark effect spectroscopy. Dr. Webb moved to UT-Austin in 2008, where she has developed a research program based on her training in both surface and biological chemistry. Her research interests are centered on understanding and manipulating the mechanisms of interaction, organization, and self- assembly of biological macromolecules in both natural and artificial environments.

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Understanding and Manipulating Electrostatic Fields at the Protein

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