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A Benchmark Study of Peptide-Biomineral Interactions Michael S. Pacella, and Jeffrey J. Gray Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b00109 • Publication Date (Web): 30 Nov 2017 Downloaded from http://pubs.acs.org on December 3, 2017
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Crystal Growth & Design
A Benchmarking Study of Peptide-Biomineral Interactions Michael S. Pacella1, Jeffrey J. Gray2,3* 1
Department of Biomedical Engineering, 2Department of Chemical and Biomolecular
Engineering, 3Program in Molecular Biophysics Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA KEYWORDS Biomineralization, crystal growth, molecular simulation, monte carlo docking, benchmark, inhibition
ABSTRACT
A longstanding goal in the field of biomineralization has been to achieve a molecularlevel mechanistic understanding of how proteins participate in the nucleation and growth of inorganic crystals (both in vitro and in vivo). Computational methods offer an approach to explore these interactions and propose mechanisms at the atomic scale; however, to have confidence in the predictions of a computational method, the method must first be validated against a benchmark experimental data set of protein-mineral interactions. Relatively little work has been done to test the ability of computation to reproduce experimental results on mineral
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systems with biologically relevant additives present. The goal of this work is to develop a standard and varied benchmark to test whether a computational method is able to match experimental results at the length and time scales of biomineral-peptide interactions.
We
compare the results of the RosettaSurface algorithm to an experimental benchmark of kinetic and thermodynamic measurements on peptide-biomineral interactions taken from atomic force microscopy. The RosettaSurface algorithm successfully identifies which mineral face and step edges will bind peptides the strongest; however, the algorithm struggles to predict the correct rank order of binding for multiple peptides to the same face or step edge.
INTRODUCTION Biological organisms use biomolecules in combination with compartmentalization and ion sequestering strategies to craft intricately structured hard tissues such as nacre, tooth, and bone. A molecular-level mechanistic understanding of these biomineralization processes would enable biomimetic strategies to synthesize custom nano-structured materials in an environmentally-friendly, safe, and cost-efficient manner. Additionally, a deeper mechanistic understanding of how organisms control crystal nucleation and growth would aid in developing treatments for biomineralization related diseases such as osteoporosis, osteomalacia, hypophosphotasia, kidney stones, and atherosclerosis. An ongoing challenge in the field of biomineralization has been the experimental determination of atomic structure at biomolecule-biomineral interfaces. Computational methods offer the ability to explore these interactions and propose mechanisms, and they can augment sparse experimental data.1-6 In order to successfully elucidate interactions at the atomic scale an algorithm must (1) sample candidate conformations effectively and (2) discriminate between
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low-energy conformations likely to be observed in nature and high-energy conformations unlikely to be observed. These challenges are known as the “sampling” and “scoring” problems, respectively. To assess the ability of a computational method to address these challenges, here we compare algorithm predictions to a benchmark set of experimental observations. The first goal of this work is to develop a standard and diverse benchmark set to test whether a computational method is sampling and scoring well enough to match experimental results at the length and time scales of biomineral-peptide interactions. We then compare the results of the RosettaSurface algorithm to this experimental benchmark of kinetic and thermodynamic measurements on peptide-biomineral interactions taken from atomic force microscopy. Recent work on benchmarking of computational methods to study biomineralization processes has focused on the development of energy functions to reproduce experimental results on bulk and interfacial properties of minerals in aqueous ionic solutions.7-9 Force fields have been optimized to reproduce bulk mineral properties such as lattice parameters and relative thermodynamic stabilities of crystalline polymorphs,7 interfacial properties such as surface energies and water contact angles,9 and solution properties such as equilibrium constants for ion pair and ion cluster formation.10 Developed independently of the aforementioned energy functions for minerals, energy functions for proteins in aqueous solution have been shown to, in some cases, predict three-dimensional structure with sub-angstrom accuracy.11-16 Independent parameters from protein and mineral energy functions may be combined using standard mixing rules to simulate biomineralization processes; however, without benchmarking simulation results against experimental measurements of peptide-biomineral interactions, the validity of these mixing rules remains dubious.17
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Some previous work has focused on the development and validation of energy functions specifically to model the interaction between peptides and surfaces. Latour’s group has developed a benchmark set of host-guest peptides interacting with self-assembled monolayers of varying chemistry.18 In their benchmark, peptide adsorption free energies were measured with surface plasmon resonance spectroscopy and compared to computational free energy calculations. Next, GolP is an energy function parameterized to reproduce density functional theory data on amino acid small molecule analogues interacting with gold surfaces, and it displays agreement with experimental adsorption isotherms.19-20 Freeman and coworkers have developed a method for deriving peptide-mineral interaction parameters from crystallographic data in which analogous peptide atom types are incorporated in the crystal lattice.21 Comparing simulation results with experimental observations of biomineralization processes is complicated by uncertainty in the surface structure of the mineral, the presence of hydration species, the relevant mineral face, and the mode of interaction between the peptide and the mineral. Despite these complications there are several “gold standard” experiments where these uncertainties can be minimized. The experimental observables in the literature on peptidebiomineral interactions are broadly composed of three groups: (1) structural constraints obtained from solid state NMR (ssNMR),22 (2) thermodynamic data on mineral face-specific adsorption free energies from single molecule force spectroscopy (SMFS),23 and (3) kinetic data on mineral step-specific velocity measurements in the presence of peptide additives from in situ atomic force microscopy (in situ AFM).24 In the recent literature, SMFS and in situ AFM studies far outnumber ssNMR studies. As a result, in the benchmark set developed here, we focus solely on SMFS and in situ AFM experimental observables. The benchmark set includes data on natural
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and engineered peptide interactions with brushite, calcite, calcium oxalate monohydrate, and mica. The thermodynamic benchmark data come from single molecule force spectroscopy using AFM tips functionalized with proteins/peptides.23,
25-26
In these experiments, the single-
molecule free energy of adsorption to specific crystalline faces is determined by repeatedly pulling an adsorbed protein/peptide away from a mineral surface and applying either Jarzynski’s equality27 to relate the ensemble averaged work to the free energy change or by measuring the mean work across a range of loading rates and extrapolating to an infinitely slow loading rate.25 Friddle et al.25 have performed one of the only studies in the literature to directly measure the adsorption free energy of a peptide (a C-terminal fragment of amelogenin) on a biomineral surface (hydroxyapatite). Unfortunately, due to the small size and elongated morphology of hydroxyapatite crystals, Friddle et al. were only able to calculate the adsorption free energy on a single hydroxyapatite surface for the C-terminal amelogenin peptide. Without multiple measurements, a rank-order comparison of peptide binding energies (as this work seeks to accomplish) is not possible. Alternatively, single molecule force spectroscopy may be performed in the kinetic regime where adsorption/desorption is not reversible. This precludes calculation of free energies; however, the residence time of a peptide on a mineral surface is still expected to scale with the binding strength. The kinetic benchmark data for proteins/peptides on mineral surfaces come from in situ atomic force microscopy.28-31 In these experiments, propagation of atomic steps from dislocation hillocks are directly visualized and step speeds are measured in the presence and absence of impurities such as peptides or proteins. The benefit of in situ AFM is that the kinetic data on step speeds can be directly compared with mechanistic predictions, and thus a particular mechanism
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of interaction between a protein/peptide and a surface can be proposed and subsequently compared with computational predictions. However, an assumption must be made to compare calculated binding energies from simulation to inhibitory potential from in situ AFM experiments: stronger binding will correspond to stronger inhibitory potential. In principle, stronger binding corresponds to a higher density of peptides adsorbed on a step edge, which will reduce the average step length between peptides and force a smaller radius of curvature for the growing steps, resulting in inhibition of crystal growth. Two factors enable our goal of developing a standard and diverse benchmark set to test computational methods in biomineralization. First, over the last five years there has been a steady increase in the amount of both single molecule force spectroscopy AFM data and in situ AFM data available in the literature. Second, the speed of the RosettaSurface algorithm allows rapid generation of results for the approximately 30 peptide-biomineral systems contained in the benchmark set. Previous computational work25, 32-34 (including modeling studies accompanying the experimental work used in this benchmark30, 35-36) has often focused on only one or a handful of peptide-biomineral systems at a time. These computational models are often generated specifically for the peptide-biomineral system at hand and lack general applicability to an arbitrary biomineralization system. Utilizing the speed and modularity of the RosettaSurface algorithm, here we are able to generate computational results across a diverse benchmark set including approximately 30 different combinations of minerals, crystal faces, step edges, and peptides.
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METHODS
Algorithm Overview We used the RosettaSurface algorithm37 to predict binding energies and geometries of peptides on mineral surfaces and step edges. We modified the standard algorithm specifically for peptide structure prediction, as opposed to protein structure prediction, in one key way. Instead of using structural fragments obtained from the Protein Data Bank38 to assemble a peptide structure (which bias sampling towards previously observed structures), we implemented large conformational changes to the peptide by sampling from a two-body neighbor-dependent Ramachandran distribution for φ and ψ angles.39 Utilizing this sampling strategy, only interactions between neighboring residues bias sampling. Additionally, we modified the standard algorithm to account for the reduced symmetry of mineral step edges, as opposed to flat mineral surfaces. In the standard algorithm, periodic boundary conditions are imposed by performing a “symmetry move” that re-centers the peptide in two dimensions on the mineral surface slab by translating the peptide an integer number of surface unit cells. This treatment is mathematically equivalent to enforcing two-dimensional periodic boundary conditions. In the case of a mineral step edge, symmetry is maintained only with one-dimensional translations parallel to the step edge by an integer number of surface unit cells. Hence, our modified algorithm effectively imposes periodic boundary conditions parallel to the step edge but not orthogonal to it. If a peptide moves orthogonally away from a step edge by a distance exceeding 30 Å, it is asymmetrically re-centered back to the step edge. RosettaSurface carries out conformational sampling in two stages; a solution-state stage optimizes the protein’s internal degrees of freedom in implicit solvent, independent of the
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surface, then an adsorbed-state stage optimizes both the protein internal degrees of freedom and the rigid body degrees of freedom describing the relative orientation of the protein to the surface. For computational efficiency, we held the positions of mineral atoms fixed at their equilibrium lattice positions. Model generation is repeated 10,000 times to generate a large ensemble of candidate structures, or decoys, for both the solution and adsorbed states. A flow chart of the RosettaSurface algorithm is shown in Scheme 1. Scheme 1. A flow chart of the RosettaSurface algorithm (MCM = Monte Carlo plus Minimization). Further algorithm details are described in Ref 37.
Mineral Models We constructed a (010) brushite slab using CrystalMaker version 9.1 and brushite unit cell coordinates from Schofield et al.40 We chose the thickness of the slab (8.2 Å) to exceed the maximum interaction distance in the Rosetta energy function, and we chose the lengths and widths to be large enough to remove edge effects (60 Å x 60 Å). We generated step edges by removing a layer of atoms along the appropriate edge direction, yielding a step height of 7.6 Å,
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in agreement with in situ AFM data.29 Because brushite contains a layer of ordered water molecules within the crystal structure, we tested two potential surface terminations. Our first termination assumed that the ordered water layer will be penetrated by peptide adsorbates that remove these waters from the surface slab. Our second termination assumed that the ordered waters will remain on the surface slab in their bulk lattice positions, where they form strong hydrogen bonds with the phosphate groups and pack against adjacent calcium atoms. Given these strong interactions, the bulk lattice positions represent one reasonable configuration; however, many other ordered water structures are possible. Thus adsorbed peptides will interact with the mineral via the adsorbed water layer. We adapted atomic parameters for brushite from the hydroxyapatite model used by Masica and Gray.41 We constructed a calcite (104) slab in a similar fashion by taking unit cell coordinates from Graf,42 and we used atomic parameters from Raiteri et al.7 Acute and obtuse step edges were generated by removing a monolayer of ions along the appropriate step-edge direction. We generated calcium oxalate monohydrate (COM) (010) and (101) slabs by using unit cell coordinates from Tazzoli and Domeneghetti,43 and we used calcium parameters from Raiteri et al. along with default CHARMM 27 parameters for the oxalate group. We generated a mica slab from coordinates of Heinz et al.,9 and we used parameters from their INTERFACE force field.9
Peptide Models We constructed extended peptides from each of the published sequences with ideal bond lengths and angles.44 We adjusted the protonation states of both the amino and carboxy termini as well as side chains of titratable residues to reflect the experimental pH range of 5-6. All main chain φ/ψ torsion angles as well as side chain χ angles were flexible.
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Energy Function We calculated adsorption energies using the Rosetta Talaris-2013 energy function,45 which has been tested in wide contexts. Talaris-2013 includes a linear combination of terms for van der Waals energies ( ), hydrogen bonds ( ), electrostatics ( ), and solvation ( ) via an implicit-solvent Gaussian exclusion model (eqn. 1). Each energy term (E) is multiplied by its corresponding weight (W) and summed to give the total energy (Etotal). We combined default Rosetta parameters for peptide atoms with the aforementioned mineral parameters for each system using Lorentz-Berthelot mixing rules. The implicit water model enables direct interaction of peptides with mineral surfaces without the limitation of water drainage timescales, with the trade-off of necessarily omitting water-mediated hydrogen bonding and local structuring. = + + + (eqn. 1) RESULTS Here we present a comparison between RosettaSurface algorithm predictions and a benchmark set of four different experimental systems. For each system, we will summarize the available experimental data and relate them to expected computational results. Then we will discuss the calculated binding energies for each peptide-surface pair in the system. Finally, we will analyze low-energy structures and interpret the agreement or disagreement with experimental data.
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Benchmark System 1: Osteopontin and Amelogenin Peptides on Brushite Steps Recent in situ AFM studies from the Wang group28-29 analyzed the impact of three different biomineralization peptide sequences on step velocities on the (010) terrace of brushite (figure 1). In these studies, the authors employed phosphorylated and non-phosphorylated 14mer peptide sequences extracted from the mineral binding domain of osteopontin (referred to as 3popn and npp, respectively) as well as a 13-mer sequence extracted from amelogenin’s Cterminal mineral binding domain (referred to as amel; sequences shown in figure 1). There are two primary results from their kinetic data: (1) 3popn is the only peptide of the three to have a significant inhibitory effect on step velocities, (2) the inhibitory effect seen from 3popn is specific to the [100] step edge direction. The kinetic data for 3popn on the [100] step edge revealed a classical “step-pinning” mechanism, originally proposed by Cabrera and Vermilyea,46 wherein crystal growth is inhibited by adsorption of peptides to a specific step-edge on a growing crystal. Based on the kinetic data, we expect two results from our simulations: (1) 3popn should bind strongest on the [100] step edge vs the [101] and [101] step edges, (2) on the [100] step edge, 3popn should bind the strongest of the three peptides.
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Ca(HPO4) • (H2O)2
Figure 1. In situ AFM surface micrograph of a triangular dislocation hillock on a brushite (010) terrace (top left). Molecular model of a step-edge in the [100] direction (right). Calcium atoms are shown in green, phosphorous in orange, oxygen in red, and hydrogen in white, Amino acid sequences of the three peptides used in the kinetic study (bottom). To calculate the adsorption energy of each peptide on each of the three step edges, we used the RosettaSurface algorithm as described in the methods section of this paper. Briefly, we generated a model of the bulk crystal using unit cell coordinates from Schofield et al.40 Using CrystalMaker software we removed atoms to expose a (010) surface. We then generated a stepedge by removing a layer of atoms along the appropriate edge direction. We created starting structures for each system by positioning a fully extended peptide model above the appropriately terminated step-edge slab. Next we used the RosettaSurface algorithm to search for low-energy structures by exploring ~107 conformations using a multi-start Monte Carlo-plus-minimization
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algorithm.47 Lowest energy structures were then selected for comparison between peptidesurface systems. The calculated adsorption energies (shown in figure 2) can be compared with the kinetic data. Adsorption energies are shown in “Rosetta Energy Units” (REUs), where one REU is approximately equivalent to one kcal/mol of energy. Since an REU is not exactly equivalent to kcal/mol, we seek qualitative rank-order agreement between our results and experimental measurements, not quantitative agreement of binding energies. On the [101] and [101] step edges, calculated binding energies do not significantly exceed the calculated binding energies for peptides on a flat brushite (010) surface, in agreement with the experimental observation of no significant inhibition for any of the three peptides on the [101] and [101] step edges. All three peptides bind strongest on the [100], in agreement with our expectation from kinetic data. However, on the [100] step edge, the non-phosphorylated peptide, npp, has the strongest calculated adsorption energy, in contrast to expectations from the kinetic data that 3popn should be the strongest binder.
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40
30
peptides 3popn amel npp
20
10
0 [100]
[101]
[101]
flat surface
step direction on (010) terrace
Figure 2. Step-specific peptide binding energies on brushite. Calculated adsorption energies for each of the three peptides on each of the three brushite step edges on the (010) terrace and the flat terrace are shown. Error bars represent one standard deviation. A possible explanation for this discrepancy can be seen by inspection of the lowest energy structures predicted for both 3popn and npp on the brushite [100] step edge (figure 3). Both peptides adopt an extended structure along the step edge, with alternating residues orientated towards and away from the step edge as in a beta strand structure. This geometry results in roughly half of the residues (~ 7 residues) making strong contacts with the step edge. Based on the kinetic data, we expect a strong interaction between the phosphorylated residues of the 3popn peptide and the exposed calcium ions on the [100] step edge. However, the predicted lowest energy structure of 3popn orients the phosphorylated residues of the peptide away from the exposed calciums on the step-edge. Energetic analysis of the 3popn structure by the RosettaSurface energy function indicates that solvation of the hydrophilic phosphorylated residues is favored over direct electrostatic interactions with the step. This result suggests that
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rebalancing the solvation and electrostatic components of the energy function may be necessary to improve accuracy. Alternatively, adjustment of brushite atom partial charges could also affect the electrostatic energy and alter its balance with solvation.
Figure 3. Calculated lowest energy structures for 3popn (top, yellow sticks) and npp (bottom, cyan sticks). Both peptides adopt an extended structure along the step edge, orienting half of their residues towards the step edge and half away from the step. Phosphoryl groups (orange phosphorous atom with three attached red oxygens) on the 3popn peptide are observed to be oriented away from the step edge instead of interacting with the exposed calcium atoms as expected from the kinetic data.
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Benchmark System 2: Calcite Step-Edges Affected by Polyaspartate in a Length-Dependent Fashion. An in situ AFM study from De Yoreo’s group48 determined the effect of polyaspartate peptides of varying length on step velocities on the rhombohedral (104) terrace of calcite. A schematic of the calcite (104) terrace is shown in figure 4. On each side of the c-glide plane a pair of “obtuse” and “acute” step edges exist, so named for the angle the carbonate plane makes with the terrace plane (in figure 4 the acute and obtuse steps are denoted by ‘-‘ and ‘+’ signs, respectively, at the end of the crystallographic direction).
Figure 4. Schematic of a rhombohedral calcite (104) hillock. The c-glide plane is shown with a dashed line, each side of the glide plane exhibits a pair of acute and obtuse step edges denoted by ‘-‘ and ‘+’ signs, respectively. There are two primary results from their kinetic data: (1) the inhibitory effect of the peptides on both acute and obtuse step velocities increases with increasing length of the polyaspartate peptides, (2) at a polyaspartate peptide length of 2, the inhibition switches from being specific to the acute step to specific to the obtuse step. Based on these data we expect two results from our binding energy calculations: (1) binding energy on both step edges should increase with increasing polyaspartate length, (2) binding should be stronger on the acute step
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edge for peptides of length 1 (single amino acids) and stronger on the obtuse step for peptides of length 3 and higher. The calculated binding energies (shown in figure 5) agree with the experimental data. For both the acute and the obtuse step edges, the binding energy increases with increasing polyaspartate length, in agreement with experiment. Additionally, at a polyaspartate length of 2 residues there is a switch in the rank order of binding energies from favoring the acute step edge to favoring the obtuse step edge, also in agreement with the in situ AFM data. Additionally, with the exception of the single amino acid case, all calculated step edge binding energies significantly exceed the calculated flat surface binding energies for calcite (104).
binding energy (negative REU ~kcal/mol)
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step edge acute obtuse flat surface 5
0 Asp1
Asp2
Asp4
Asp5
Asp6
peptide identity
Figure 5. Polyaspartate length dependence of step-specific binding energies on calcite (104). Binding energies for each length of polyaspartate peptides are shown for both the acute and the obtuse step edge on the calcite (104) hillock and on the flat (104) terrace itself. Error bars represent one standard deviation.
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Inspection of the predicted lowest energy structures (figure 6) for Asp1 (a single amino acid) and Asp2 (a dipeptide) reveals a potential mechanistic explanation for the switch in step edge specificity. As seen in the top left panel of figure 6, hydrogen bonding on the acute step is more favorable than on the obtuse step due to the orientation of the carbonate oxygens relative to the acute step edge. For a single amino acid on the acute step edge, a lone hydrogen bond to the surface can be formed while minimally desolvating both the peptide and the surface. Due to the orientation of the carbonate oxygens on the obtuse edge this geometry is not possible and the amino acid has no interactions with the surface, instead allowing full solvation of both the step edge and the amino acid. Thus, binding on the acute step edge is more favorable than the obtuse edge for a single amino acid. In a dipeptide (and all subsequently longer peptides), the original position of one of the C-terminal carboxyl oxygens is replaced by an amine group that is electrostatically complementary to carbonates it is aligned with the on the step edge, providing a better geometrical match than that found on the acute step edge.
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Figure 6. Calculated lowest energy structures of a single aspartic acid (top) and an aspartic acid dipeptide on both acute and obtuse step edges on the calcite (104) terrace. In the single amino acid case a lone hydrogen bond can be formed from the amino group of the amino acid to the carbonate ion along the acute step edge (left) while minimally desolvating the amino acid and the step edge, thus favoring adsorption on the acute step edge. In the dipeptide case, the addition of a backbone amine group allows for a better geometrical match to the obtuse step edge.
Benchmark System 3: Calcium Oxalate Monohydrate Growth Inhibition by Polyaspartate Enantiomers Another in situ AFM study from De Yoreo’s group35 analyzed the effect of polyaspartate enantiomers on growth inhibition of calcium oxalate monohydrate. In this study, two polyaspartate peptides of length 6 were used, with one composed of amino acid subunits with Lchirality (L-Asp6) and the other composed of amino acid subunits with D-chirality (D-Asp6), making the two polyaspartate polymers non-superimposable mirror images of one another. There were two primary results from the kinetic data here: (1) inhibition of step velocities is stronger for both L-Asp6 and D-Asp6 on the (101) vs the (010) face, (2) inhibition of step velocities on the (010) face is slightly stronger for D-Asp6 vs L-Asp6. Based on these data, we expect two results from our simulations: (1) binding of both L-Asp6 and D-Asp6 will be stronger on the (101) face vs the (010) face (since there is a mirror plane in the (101) surface, binding energies of
D-
and L-Asp6 should be equivalent on (101) but different on (010), and (2) on the (010)
face, D-Asp6 should bind slightly stronger than L-Asp6.
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The calculated binding energies for both L-Asp6 and D-Asp6 on COM (101) and (010) are shown in figure 7. Partial agreement with experiment is obtained in this benchmark system. Binding energies for both L-Asp6 and D-Asp6 are stronger on the (101) face compared to the (010) face, in agreement with experiment. This result is also in agreement with computational work on calcium oxalate dihydrate (COD) from Parvaneh (cite) that demonstrates that a factor of two difference in binding energies on the (101) and (100) surfaces of COD is sufficient to observe preferential inhibition in growth experiments. However, on the (010) face, the binding energies for
L-Asp6
and
D-Asp6
are equivalent within standard deviation, in contrast to
experimental observations that D-Asp6 should be the stronger inhibitor on this face.
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peptides D-Asp6 L-Asp6 10
0 (010)
(101)
COM surface
Figure 7. Calculated binding energies for both L-Asp6 and D-Asp6 peptides on COM (101) and (010) surfaces. Error bars represent one standard deviation.
An examination of the predicted lowest energy structures (shown in figure 8) confirms, as expected, that L-Asp6 and D-Asp6 bind in nearly mirror image orientations on the (101) surface.
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Additionally, the reason for stronger peptide binding on the (101) face vs the (010) face is the exposure of the negatively charged oxalate groups on the (010) face, repelling the negatively charged polyaspartate peptides. The reason for the discrepancy between simulation and experiment on the (010) face is difficult to discern from these structures, as both peptides form relatively weak interactions with the (010) face.
Figure 8. Calculated low energy structures for both L-Asp6 and D-Asp6 on COM (101) and (010) surfaces. A mirror symmetry plane on the COM (101) face (shown with a dashed line) facilitates mirror image binding of the two enantiomeric peptides. On COM (010) the exposure of negatively charged oxalate groups repels the negatively charged polyaspartate peptides.
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Benchmark System 4: Alanine Scanning Mutants of Phage-Display Selected Mica Binding Peptide Recent work from the Reches group36 used single molecule force spectroscopy to investigate the interactions of peptides with mica surfaces. In this study, the peptides were a series of alanine scan mutations of a peptide selected to bind mica using a phage display method. Single molecule force spectroscopy was performed in the kinetic regime, where the loading rate of force to remove the peptide from the surface is prohibitively high to facilitate a reversible process and calculation of adsorption free energy. However, in this regime calculation of kinetic parameters such as barrier height, barrier position, and surface residence time is possible using an appropriate kinetic model such as Bell-Evans.49 The experimental observable of interest is surface residence time: we expect to see a correlation between calculated binding energies of each peptide on mica and the experimentally observed residence time. A table of calculated binding energy vs. mica surface residence time for 5 of the 7 peptides investigated in the study is shown in table 1. (Two peptides that displayed anomalous behavior in the experimental study have been excluded from our benchmark comparison.) No significant correlation is observed, indicating disagreement between simulation results and SMFS measurements.
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residence time
binding energy
(seconds)
(REU)
QPAASRY
0.124
11.3
QPASARY
0.092
11.0
QPASSAY
0.18
11.5
QPASSRA
0.277
10.8
QPASSRY
0.122
10.4
peptide sequence
Table 1. Table of calculated binding energy vs mica surface residence time for each of the five peptides considered. No significant correlation is observed, indicating disagreement between computational and experimental results. Examination of the calculated low energy structures for each peptide reveals a potential explanation for the observed discrepancy. As shown in an example structure in figure 9, all peptides display relatively weak interactions with the mica surface and make almost no direct contact with the surface. One potential explanation is that the Lennard Jones well depths and radii prescribed by the INTERFACE force field are incompatible with the well depths and radii prescribed by the RosettaSurface energy function. In this case, the standard Lorentz Berthelot mixing rules cannot be applied to combine the mineral and protein parameters in this system.
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Figure 9. An example low energy structure of an alanine mutant peptide adsorbed on mica. Potassium ions are shown in purple, oxygen in red, and silicon in tan. Minimal direct contacts between the peptide and the mineral are observed. This may indicate an incompatibility between the Lennard Jones well depths and radii used by the INTERFACE force field and the RosettaSurface energy function. DISCUSSION A summary of each benchmark system, the experimental observables, and the comparisons to simulation are shown in Table 2. For example, in the brushite benchmark system, the algorithm correctly predicts that the [100] step edge direction is favored for all three of the peptides tested. In that same system, the algorithm is unable to correctly predict that the phosphorylated osteopontin peptide will bind stronger than the non-phosphorylated variant. In total, there are three cases where either face or step edge specificity are tested: (1) the preference of the phosphorylated osteopontin peptide for the [100] step edge over the [101] and [101] step edges on the brushite (010) terrace, (2) the switch in preference from acute to obtuse step edges on calcite (104) for the polyAsp peptides as length increases, (3) preference of both L and D polyAsp 6mer peptides on COM (101) vs COM (010). Because the calcite case involves a
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series of five peptides (each of which is predicted correctly), and the COM case involves two enantiomers (each of which is predicted correctly) a total of eight preferences are correctly predicted out of eight total predictions for face or edge specificity. In contrast, the performance predicting the rank ordering of peptide binding on a given step edge or face is less accurate. Of the four possible rank order predictions for peptide binding on a step edge or face, RosettaSurface predicts the correct order in only the calcite benchmark test. Thus, across this benchmark set, the RosettaSurface algorithm successfully predicts which mineral face and step edges will bind peptides the strongest; however, the algorithm struggles to predict the correct rank order of binding for multiple peptides to the same face or step edge. The inability of RosettaSurface to correctly predict the rank order binding affinity of peptides on a given step edge or surface could suggest that peptide flexibility and conformational entropy, which are neglected in RosettaSurface, play a significant role in binding to biominerals. Differences in conformational entropy between peptides would affect the rank order binding of peptides on a given face but would be less likely to affect which step edge will bind peptides the strongest, which matches the pattern of discrepancies observed in the benchmark set. Another trend revealed in the benchmark data is the importance of properly balancing implicit solvation and electrostatic contributions to the energy function. For instance, in the brushite system, the algorithm incorrectly orients the phosphorylated serine residues away from the exposed calcium atoms on the brushite step edge, solvating the hydrophilic phosphate groups at the expense of favorable electrostatic interactions with the step edge. The accuracy of both the protein and mineral energy function parameters, and the validity of using standard mixing rules to combine them, is a potential source of error in the benchmark set. If structural details of the peptide-mineral interactions in a benchmark set were known, it
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would be possible to diagnose a scoring problem by identifying predicted structures that were similar to the experimental structure but were not low-scoring. Because the structural details of the interactions in our benchmark set (or any peptide-mineral system) are not known, we are forced to assess the accuracy of the energy function parameters while assuming complete sampling of relevant conformational space. Although the Rosetta Talaris-2013 energy function is used throughout the benchmark set to describe the protein component of each system, the source of the mineral energy function parameters is variable (custom Raiteri force field,7 CHARMM,13 INTERFACE9). Thus, the quality of the energy function parameters may not be uniform across all mineral systems in the benchmark. One clue can be seen in the magnitudes of our energies: the energy for binding brushite (Fig. 6) is in the 1-2 kcal/mol range, but previous [experiments/calculations] suggest that the binding of Asp to a solvated Ca atom is around 1.5 kcal/mol.[cite] Since the binding of a solvated ion should be stronger than the binding to a Ca atom on a mineral surface, these data suggest that our binding energies may be overestimated. Parvenah et al.’s calculations[cite] of binding acetate on COD are in the same order of magnitude (-3 to -6 kcal/mol) but also somewhat less than the values Rosetta produces for each group on COM (~y kcal/mol). Development of the varied and large-scale benchmark set of peptide-biomineral interactions used in this study is a vital step in improving the accuracy of computational models in the biomineralization field. With an objective measure of accuracy, meaningful comparisons between different sampling and scoring strategies can be discussed within the community. Standard benchmarking datasets are nearly ubiquitous in other computational fields. For instance, an objective comparison of antibody structure prediction tools was recently made possible by employing a standard benchmark set.50 Additionally, the bioinformatics field has
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benefitted from a standard benchmark set associating specific point mutations with loss of protein function.51-53 To facilitate comparison with the results of other computational methods, here we provide the starting coordinates and the coordinates of the calculated lowest energy structure for each benchmark system as supplementary files (Supplementary Data S1). The computational results presented in this paper represent the largest benchmarking study of biomineralization systems to date. Previous computational work25,
32-34
(including
modeling studies accompanying the experimental work used in this benchmark30, 35-36) has often focused on only one or a handful of peptide-biomineral systems at a time. These computational models are often generated specifically for the peptide-biomineral system at hand and may only involve a local sampling of candidate structures. In some cases, these models are custom-built to provide a plausible mechanistic explanation for observed experimental data. In contrast, the RosettaSurface algorithm uses a global sampling strategy that requires no user input aside from the peptide sequence and the crystallographic face or step edge to dock with. Speed is another major advantage of the RosettaSurface algorithm and is the main reason it was possible to generate computational results for such a large benchmark system. A weakness of explicit solvent models in biomineralization systems is that the timescale of the simulation must exceed the timescale for water drainage away from the relevant mineral surface. In work from Sahai’s group,54 an examination of the potential of mean force for peptide adsorption on hydroxyapatite reveals a global free energy minimum when the peptide is in direct contact with the surface; however, this global minimum is separated from the solvated peptide state by an energy barrier corresponding to the desorption of structured waters at the hydroxyapatite surface. As discussed in work from Gale’s group,55 water residence times near calcite step edges are on the order of tens of nanoseconds, a potentially prohibitively long
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timescale for current molecular dynamics methods unless an explicit accelerating treatment of the water dynamics is considered (for instance, including a biasing potential). It remains uncertain whether all peptides actually remove ordered waters from mineral surfaces and step edges over the timescales relevant to biomineral-peptide interactions. Further work is needed for a detailed comparison between molecular dynamics and RosettaSurface and to explore potential routes to combine the two techniques. One route forward would be to seed explicit solvent molecular dynamics simulations with adsorbed peptide structures predicted using RosettaSurface. Using this method, large peptide conformational changes could be modeled efficiently with RosettaSurface while water-mediated interactions with the mineral surface could be captured using explicit solvent molecular dynamics (as done in Ref.
54
) Additionally, the results from RosettaSurface here suggest that peptide binding
preferences for particular crystal faces could be assessed rapidly and accurately with RosettaSurface. Thus, RosettaSurface could be used to identify relevant mineral surfaces and step edges for more detailed (and more computationally expensive) explicit solvent molecular dynamics simulations. A second route forward would be to perform RosettaSurface simulations with a semiexplicit solvent treatment. Some recent methods56-57 allow structured waters present at the mineral surface to be modeled explicitly and to remain static or be sampled using a Monte Carlo move set, thus allowing for water-mediated hydrogen bonding between the peptide and the surface. Additionally, an implicit treatment of solvent with directional dependence could be used to capture water mediated interactions with RosettaSurface.58-59
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We are at the beginning of using simulation to decipher the mechanisms by which peptides control biomineral nucleation and growth. At present, potentially crucial physical details are overlooked in order to perform benchmarking simulations with current computing resources. Physical details missing from RosettaSurface include explicit water molecules and counter-ions, polarizability of both peptide and mineral atoms, motion of surface atoms or lattice defects, and an energetic model for the stability of the mineral surface. Without these details, developing models for some biomineralization systems may not be possible. For instance, recent work from Rimer’s group indicates that some positively charged proteins are capable of enhancing the rate of crystal growth by up to 20%.60 Additionally, Elhadj et al. has observed that the negatively charged polyaspartate peptides employed in benchmark systems 2 can also enhance the rate of crystal growth at low concentrations.48 Any model of this phenomenon will need to incorporate both how proteins assist in the transport of ions to the growing step edge as well as how proteins disrupt the structure of water surrounding a step edge. Using quantum chemical calculations on a small molecule system, one recent study suggested that interactions between adsorbates and mineral surfaces can strain mineral atoms away from their equilibrium lattice positions and destabilize the mineral phase,61 leading to negative growth rates in systems that are supersaturated. A detailed energetic model for the stability of the mineral surface would be needed to capture these kind of effects computationally. Work from Wallace et al.8 on nucleation suggests that liquid-liquid separation may be an important step in the development of an amorphous mineral phase as a precursor to nucleation. Any model of liquid-liquid separation and amorphous phases will require explicit water and mineral ions accounting for all degrees of freedom. Computational work from these groups is beginning to demonstrate how these physical
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details can be captured. Unfortunately, the cost of including these details in all of the benchmark systems described in this work is still prohibitive. At least in the near future, the path toward deciphering these more complex biomineralization mechanisms will be to coarse-grain and exclude some level of physical detail, as done in RosettaSurface. By analyzing the results of more detailed simulations on small model systems, coarse-graining parameters for larger systems may be developed. The creation of a peptide-biomineral simulation benchmark is a significant step in this endeavor because it provides a standard by which to objectively compare the accuracy of a computational method at reproducing experimental results at length and time scales relevant to biomineral-peptide interactions. With an objective measure of accuracy, the validity of excluding physical details (such as explicit water or polarizability) may be assessed and optimal values for coarse-graining parameters can be determined. Additionally, the advantages and disadvantages of particular sampling and scoring methods can be discussed within the community, guiding further improvements to existing methods and assisting in the development of new methods.
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Table 2. Benchmark summary.
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SUPPORTING MATERIALS A zipped archive containing PDB-formatted starting structures for all peptide/mineral benchmark systems described in this study is provided as supporting material. Additionally, this zipped archive contains PDB-formatted lowest-energy structures predicted by the RosettaSurface algorithm for each peptide/mineral benchmark system described in this study. AUTHOR INFORMATION Corresponding Author *E-mail:
[email protected] Telephone: 410-516-5313
Author Contributions The manuscript was written through contributions of all authors. All authors have approved the final version of the manuscript. Funding Sources NSF BMAT Award #1507736 ACKNOWLEDGMENT This research was supported by an NSF BMAT award (#1507736). Computational resources were provided by the Maryland Advanced Research Computing Center (MARCC) and the Texas Advanced Computing Center (TACC). We wish to acknowledge Jason Labonte, Shourya Sonkar Roy Burman, Joseph Lubin, Rebecca Alford, and Kayvon Tabrizi for helpful discussions and feedback on the manuscript. ABBREVIATIONS AFM, atomic force microscope; SMFS, single molecule force spectroscopy; ssNMR, solid state nuclear magnetic resonance spectroscopy;
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FOR TABLE OF CONTENTS USE ONLY MANUSCRIPT TITLE: A Benchmark Study of Peptide-Biomineral Interactions AUTHOR LIST: Michael S. Pacella, Jeffrey J. Gray TOC GRAPHIC:
SYNOPSIS: We compare the results of the RosettaSurface algorithm to an experimental benchmark of kinetic and thermodynamic measurements on peptide-biomineral interactions taken from atomic force microscopy. The RosettaSurface algorithm successfully identifies which mineral face and step edges will bind peptides the strongest; however, the algorithm struggles to predict the correct rank order of binding for multiple peptides to the same face or step edge.
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