KirkwoodâBuff-Derived Alcohol Parameters for Aqueous

Subscriber access provided by UNIV OF LOUISIANA

B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Kirkwood-Buff Derived Alcohol Parameters for Aqueous Carbohydrates and Their Application to Preferential Interaction Coefficient Calculations of Proteins Theresa Cloutier, Chaitanya Sudrik, Hasige A Sathish, and Bernhardt L Trout J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b07623 • Publication Date (Web): 14 Sep 2018 Downloaded from http://pubs.acs.org on September 19, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Kirkwood-Bu Derived Alcohol Parameters for Aqueous Carbohydrates and their Application to Preferential Interaction Coecient Calculations of Proteins †

Theresa Cloutier,

Chaitanya Sudrik,

†

Hasige A. Sathish,

‡

and Bernhardt L.

∗,†

Trout

†Department

of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

‡Formulation

Sciences, MedImmune LLC, Gaithersburg, MD, USA

E-mail: [email protected]

Phone: 617-258-5021

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The CHARMM36 carbohydrate parameter set did not adequately reproduce experimental thermodynamic data of carbohydrate interactions with water or proteins or carbohydrate self-association; thus a new nonbonded parameter set for carbohydrates was developed. The parameters were developed to reproduce experimental KirkwoodBu integral values, dened by the Kirkwood-Bu theory of solutions, and applied to simulations of glycerol, sorbitol, glucose, sucrose, and trehalose. Compared to the CHARMM36 carbohydrate parameters, these new Kirkwood-Bu based parameters reproduced accurately carbohydrate self-association and the trend of activity coecient derivative changes with concentration. When using these parameters, preferential interaction coecients calculated from simulations of these carbohydrates and the proteins lysozyme, bovine serum albumin, α-chymotrypsinogen A, and RNase A agreed well with experimental data, while use of the CHARMM36 parameters indicated preferential inclusion of the carbohydrates, in disagreement with experiment. Thus, calculating preferential interaction coecients from simulations requires using a force eld that accurately reproduces trends in the thermodynamic properties of binary excipient-water solutions, and in particular the trend in the activity coecient derivative. Finally, the carbohydrate-protein simulations using the new parameters indicated that the carbohydrate size was a major factor in the distribution of dierent carbohydrates around a protein surface.

Introduction Carbohydrates are an important class of molecules that interact with proteins, and they are generally considered to be kosmotropes and thus excluded from protein surfaces. 1,2 It would be advantageous to understand on the molecular level how they interact, but experimental methods can provide limited molecular-level information. On the other hand, molecular dynamics simulations can be used to examine the molecular-level interactions of excipients with proteins and also lead to insight into the mechanism of action of a carbohydrate with 2


Page 2 of 33

Page 3 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a protein. 3 The selection of an appropriate force eld is critical for simulating any given system, and one measure of accuracy is the reproduction of solute-solute, solute-water, and water-water interactions. The CHARMM36 force eld 46 contains parameters for proteins, carbohydrates, and water. Previous simulations of trehalose performed by Sapir and Harries found that too much self-association of trehalose occurred in simulations using the CHARMM35 force eld compared with experiment, 7 and we show here that the CHARMM36 force eld has a similar issue. Additionally, we tested several precursors to the CHARMM36 force eld, including that developed by John Brady's group 8 and the CSFF, 9 both of which, like the CHARMM36 force eld, showed preferential inclusion of carbohydrates around proteins at low (1 m) carbohydrate concentrations, whereas experiment indicates preferential exclusion. A previous study of urea by Weerasinghe and Smith found that preferential interaction coecient calculations from simulations required the force eld to predict accurately excipient self-association. 10 Thus, we desired a force eld that would predict accurately carbohydrate self-association for the study of preferential interactions. In developing the CHARMM36 force eld, the partial charges and Lennard-Jones parameters were determined by comparing simulation results to experimental data, with the general approach described by Yin and Mackerell 11 and the specics for carbohydrates described by Guvench et al. 5 The choice of experimental target data used in parameter development aects the nal parameter set, and numerous dierent carbohydrate force elds have been developed that each emphasize dierent experimental data. 12 Paul Smith's group developed a force eld parameterization procedure using Kirkwood-Bu (KB) integral values as the target experimental data. 1316 This approach emphasizes the correct balance of solute-solute, solute-water, and water-water interactions by using the KB integral values as the target experimental data. These values can be obtained from simulations from radial distribution functions 13 or from experiment from the activity coecient derivatives, isothermal compressibility, and partial molar volumes. 17 3



We used this KB approach for parameter determination to develop new nonbonded parameters for carbohydrates, performing simulations of aqueous glycerol, sorbitol, glucose, sucrose, and trehalose and comparing the results with experimental data. The nal parameter set, termed the KB based carbohydrate parameters (KBPs), reproduces KB integral values more accurately than the CHARMM36 parameters. The new parameters are compatible with the CHARMM36 force eld and TIP3P water model, which are extensively used in protein simulations. We then used this set of KBPs to calculate preferential interaction coecients for the ve carbohydrates with several small proteins (lysozyme, bovine serum albumin, α-chymotrypsinogen A, and ribonuclease A), with good agreement with experiment, and then examined the distribution of the carbohydrates around the protein. We expect that these parameters can be used in the study of preferential interactions of carbohydrates with other proteins to gain insight into the mechanism of action with proteins.

Methodology Molecular Dynamics Simulations Molecular dynamics simulations were performed using Gromacs 5.0.5 18 with parameters taken from the CHARMM36 force eld 4,5,19 or with our KBPs for carbohydrates. The TIP3P 20 model for water was used. Hydrogen bonds were constrained using the Lincs algorithm. 21 The Verlet cuto scheme was used for van der Waals interactions, with neighbor list and VdW cuto distances of 12 Å and forces smoothly switched to zero between 10 and 12 Å. Long range electrostatics were calculated using the particle-mesh Ewald method with a 12 Å cuto distance. The structures of α-chymotrypsinogen A (α-Cgn A, PDB code: 2cga), bovine serum albumin (BSA, PDB code: 4f5s), hen egg white lysozyme (PDB code: 1e81), and ribonuclease A (RNase A, PDB code: 1kf5) were obtained from the Protein Data Bank. 22 Simulations were performed in rectangular boxes using periodic boundary conditions, and 4


Page 4 of 33

Page 5 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a list of simulation congurations is given in the supplementary information. Simulations containing a protein were set up with water extending a minimum of 14 Å beyond the protein and with a minimum side length of 75 Å, while simulations without proteins were performed in boxes with side lengths of at least 64 Å. The initial congurations were generated using Packmol. 23 The pH of the simulations was set by setting the protonation state of any amino acids present using PropKa. 24 Simulations of lysozyme and BSA were performed at pH 6, except for the simulation of lysozyme and trehalose, which was performed at pH 5.5. Simulations of RNase A with sorbitol were performed at pH 2, with sucrose at pH 3, and with trehalose at pH 5.5. Simulations of α-Cgn A with glucose were performed at pH 3.5 and with sucrose at pH 3. All systems were made charge neutral by the addition of sodium or chloride counterions, if necessary. The temperature of each simulation was set to 298 K using the V-rescale algorithm and the pressure was set to 1 atm using the Parrinello-Rahman algorithm. Simulations were rst energy minimized and then equilibrated for 15 ns. Congurations were saved every 10 ps. Following equilibration, the simulations used to calculate KB integral values were run for a minimum of 85 ns, and the simulations used to calculate preferential interactions were run for a minimum of 55 ns. Statistical error calculations were performed using the method of Allen and Tildesley. 25 All trajectory analysis was performed using the MDAnalysis Python package. 26,27

Kirkwood-Bu Theory Kirkwood-Bu theory can be used to relate the KB integrals to thermodynamic properties of a solution. 13,17,28 Briey, the KB integrals for a binary solution can be calculated from simulations according to 13

Gij = 4π

Z 0

∞

gijN pT (r) − 1 r2 dr

5


(1)


Page 6 of 33

N pT where Gij is the KB integral value for components i and j , gij is the radial distribution

function in the NpT ensemble, and r is the distance between the centers of masses of the two components. The simulation box was made large enough that the radial distribution function approached 1 past some distance R, allowing the integral to be evaluated from 0 to

R. The subscript 1 will be used to refer to water, 2 to protein, and 3 to excipient for all following equations. The KB integrals were related to the excipient partial molar volume, V¯3 , the isothermal compressibility, κT , and the activity coecient derivative, f33 , according to 13,17

1 + ρ1 (G11 − G31 ) ρ1 + ρ3 + ρ1 ρ3 (G11 + G33 − 2G31 )

(2)

1 1 + ρ1 G11 + ρ3 G33 + ρ1 ρ3 (G11 G33 − G231 ) RT ρ1 + ρ3 + ρ1 ρ3 (G11 + G33 − 2G31 )

(3)

V¯3 =

κT = f33 =

∂ ln f3 ∂ ln x3

!

=− p,T

ρ1 x3 (G11 + G33 − 2G31 ) 1 + ρ1 x3 (G11 + G33 − 2G31 )

(4)

where ρi is the molar density, R is the gas constant, fi is the mole fraction scale activity coecient, and xi is the mole fraction. Values were determined by the ensemble average over the trajectory following equilibration.

Clustering Carbohydrate molecules were dened as being in a cluster if they had at least one connecting hydrogen bond, where hydrogen bonds were dened as occurring between an alcohol O and an alcohol H if the donor and acceptor were within 3 Å and the angle between the donor, the hydrogen, and the acceptor heavy atom was greater than 150◦ . Clusters were identied at each saved trajectory conguration, and cluster size distributions and probabilities were determined by averaging over the course of the trajectory following equilibration.

6


Page 7 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Preferential Interaction Theory The preferential interaction coecient (Γ23 ), which is a measure of the relative concentrations of excipients in the local domain of the protein as compared to the bulk, was calculated from simulations according to 3,29

n3 − n3 (r, t) Γ23 (r, t) = n3 (r, t) − n1 (r, t) n1 − n1 (r, t)

!

(5)

where ni (r, t) refers to the number of molecules of type i within a distance r of the protein surface at time t and ni refers to the total number of molecules of type i in the simulation. The simulation average of Γ23 (r, t) was used for analysis. Past some distance R, Γ23 (r) converges to a constant value, and the value of R is often about 8 Å. The Γ23 (R) values, referred to as Γ23 , were compared to experimental data.

Experimental determination of Γ23 The Γ23 values of trehalose with lysozyme were obtained experimentally. Briey, a protein stock solution was prepared by dissolving lyophilized lysozyme from chicken egg white (Sigma catalog #L6876) in an aqueous buer of 25 mM histidine.HCl (pH 5.5), followed by dialysis with three buer exchanges against 25 mM histidine.HCl (pH 5.5) to remove impurities from the lyophilized powder. The nal concentration of lysozyme in the dialyzed solution was ascertained to be about 75 mg/mL. Trehalose (Sigma catalog #T9449) was dissolved in 25 mM histidine.HCl (pH 5.5) buer to obtain 10 stock solutions with concentrations in the range of roughly 0 to 1 molal. These stock solutions were then diluted roughly 2-fold, with either buer alone to obtain a binary series of solutions, or with the protein stock to obtain a ternary series of solutions. All solutions were prepared gravimetrically to obtain a more precise estimate of the concentration of trehalose. Next, a Wescor VAPRO 5600 vapor pressure osmometer was used to determine the osmolality of each solution at room temperature. Osmolality data for each solution were collected at least in triplicate to min7



imize experimental error in the estimation of preferential interaction. Using the osmolality data for the binary and ternary solutions, Γ23 for lysozyme with trehalose was estimated for trehalose concentrations in the range of roughly 0 to 0.5 molal, according to the procedure described in Hong et al. 30

Results and Discussion Parameter Determination For the purposes of studying preferential interactions of carbohydrates with proteins, it is necessary for the force eld parameters to reproduce accurately the experimental properties of carbohydrates in aqueous solutions at the concentrations used in protein formulations. The CHARMM36 carbohydrate parameters 5,6,19 were used as a starting point for parameter determination. The experimental target data used in the development of the CHARMM36 parameters included experimental heats of vaporization and molecular volumes of neat liquids. Guvench et al. noted that the CHARMM36 parameters greatly overpredict intermolecular hydrogen bonding for glycerol. 5 Thus, the CHARMM36 parameters, developed using target experimental data that includes pure carbohydrates, do not model aqueous carbohydrate solutions with sucient accuracy for the calculation of preferential interactions at the relatively low concentrations relevant for formulations. Therefore, we adjusted the carbohydrate parameters to reproduce experimental KB integral values for aqueous carbohydrate solutions of up to 2 m. The KB integral values were calculated from the radial distribution functions of carbohydrates and water according to equation 1, treating each molecule as a point at its center of mass. Figure S1 in the supplementary information shows the radial distribution functions

gij (r) and KB integral values Gij (r) for 1 m trehalose using the KBPs, which were calculated from the radial distribution functions using equation 1. The Gij values compared to experiment were obtained by averaging Gij (r) past 2 nm. 8


Page 8 of 33

Page 9 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


In our development of the KBPs, we only considered changes to the nonbonded parameters: the atomic partial charges and the Lennard-Jones parameters ε and σ . Direct scaling of the partial charges for carbohydrate molecules did not produce agreement with KB integral values. Instead, to address the overprediction of carbohydrate self-association by the CHARMM36 force eld, we reduced the magnitude of the alcohol partial charges, as the alcohol groups drive intermolecular interactions. In the CHARMM36 force eld, the partial charge of alcohol O is -0.65 and H is 0.42, while the KBPs have an alcohol O partial charge of -0.50 and an H charge of 0.18. In order to maintain a net charge of zero, carbon partial charges were slightly increased. The partial charges of the KBPs for glycerol, sorbitol, glucose, sucrose, and trehalose are shown in gure 1. Note that partial charges of the same types of carbon atoms were maintained across molecules. For example, the partial charges of carbons in trehalose are the same as those of corresponding carbons in glucose, except for C1 , due to the 1,1-glycosidic bond in trehalose. The Lennard-Jones parameters for the alcohol KBPs are shown in table 1. The σ parameters are identical to the CHARMM36 values. The KBPs dene two ε values for each atom, one for non-water interactions (general) and one specically for water interactions, with the water-specic ε added by specifying NBFIX terms. The CHARMM36 ε value for alcohol O is 0.804 kJ/mol and for alcohol H is 0.192 kJ/mol, and there is no separate value for water interactions. Generally, the KBPs made self-interactions less energetically favorable and carbohydrate-water interactions more energetically favorable. The CHARMM36 ε value for TIP3P water O is 0.636 kJ/mol, lower than that of alcohol oxygens, making alcohol self-interactions energetically more favorable than water interactions and contributing to the overprediction of G33 and underprediction of G31 values observed with the CHARMM36 force eld. Dening a separate ε value for alcohol interactions with water was necessary to achieve the appropriate balance of carbohydrate-carbohydrate and carbohydrate-water interactions. Alcohol-water interactions were made more favorable by using NBFIX terms to dene higher 9



Page 10 of 33

Table 1: Alcohol Lennard-Jones Parameters for KBPs

atom

interaction

ε (kJ/mol)

σ (nm)

O

general water

0.450 0.900

0.314

H

general water

0.120 0.300

0.040

ε values for alcohol interactions with water. Four NBFIX terms were dened, one for each combination of the two alcohol atoms and the two types water atoms. In each NBFIX term, the overall ε value was the geometric mean of the individual atom ε values (for water atoms, the value directly from the CHARMM force eld, and for the alcohol atoms, the value given for water interactions in table 1) and the overall σ value was the arithmetic mean of the individual atom σ values. Changes to σ had a noticeable impact on the KB integral values, in particular with increases in σ reducing G33 values, but the adjusted parameter set used the same σ values as the CHARMM36 force eld due to the appropriate choice of partial charge and ε values. The KB integral values for the carbohydrates with the CHARMM36 parameters and the KBPs are shown in gure 2, with each column showing plots of G11 , G33 , or G31 and each row showing results for one carbohydrate. These KB integral values were compared to experimental KB values calculated from experimental data using equations 2-4. The CHARMM36 parameters tended to overestimate G11 and G33 and underestimate G31 for all ve carbohydrates, as shown in gure 2. Interestingly, the CHARMM36 parameters often demonstrated the wrong trends for G33 and G31 , indicating a decrease in self-association of carbohydrates with increasing concentration, which is opposite of the experimental trends. Additionally, the G33 values using the CHARMM36 parameters were consistently greater than the experimental values, indicating excessive self-association compared with experiment. This observation is in agreement with the ndings of Guvench et al. with glycerol 5 and Sapir and Harries with trehalose. 7 The CHARMM36 parameters also consistently over-

10


Page 11 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


predicted G11 values, which is related to the overprediction of G33 and underprediction of

G31 values. Excessive carbohydrate self-association reduces carbohydrate-water interactions and thus increases water-water interactions. For all ve carbohydrates, the KBPs showed better agreement with experimental data for all three KB integral values compared to the CHARMM36 parameters, and in particular matched the experimental trends of increasing G33 and increasing G31 with increasing carbohydrate concentration. The KBPs showed very good agreement with the experimental results for G11 and G31 for all ve carbohydrates. The KBPs showed good agreement with experimental G33 values for sucrose and trehalose, and even though the KBPs slightly underestimated the magnitude of G33 for glycerol, sorbitol, and glucose, the results followed the experimental trend of increasing G33 with increasing carbohydrate concentration. In all cases, the results using the KBPs were closer to the experimental result than the results using the CHARMM36 parameters, indicating that the KBPs represent a signicant improvement over the CHARMM36 parameters in modeling aqueous behavior of these carbohydrates. Recalling that the KBPs were developed using experimental KB integral values for glycerol and trehalose, the ability of the new parameter set to generalize to other carbohydrate molecules was tested by evaluating the performance of the KBPs on sorbitol, glucose, and sucrose. The good agreement with experimental trends observed for these other carbohydrates, as shown in gure 2, indicated that the KBPs can be successfully applied to other carbohydrates. The density, partial molar volume, and activity coecient derivative data for the carbohydrates are shown in gure 3. Figure 3 indicates that both parameter sets predicted almost identical densities, which matched well with experimental data. Except for sorbitol, the experimental partial molar volume data matched reasonably well with the results using the CHARMM36 parameters. The V¯3 values from simulations using the KBPs tended to be higher than the experimental results, and, for sorbitol, glucose, and sucrose, were further from the experimental result than the values using the CHARMM36 parameters. Despite 11



this, the results with the KBPs exhibited the proper trend for all ve carbohydrates, showing small increases in V¯3 with increasing carbohydrate concentration. This indicated that the KBPs, like the CHARMM36 parameters, appropriately modeled the changes in partial molar volume with concentration. Additionally, despite the general overprediction of the magnitudes of the partial molar volumes by the KBPs, the relative partial molar volumes were reasonably accurate. For example, both the experimental results and the KBP results indicated that sorbitol has a higher partial molar volume than glucose. The largest dierences between the two parameter sets was seen in the activity coecient derivative results. For all ve carbohydrates at concentrations below 2 m, the experimental results indicated that f33 increased slightly with increasing carbohydrate concentration, indicating increases in the activity coecient. The CHARMM36 parameters predicted negative f33 values, which correspond to decreases in the activity coecient with increasing concentration. The KBPs better matched the experimental f33 results, as they result in positive f33 values at all concentrations considered here, which agrees with experimental data. The best agreement with experiment was observed with sucrose and trehalose. However, even for glycerol, sorbitol, and glucose, the proper trend of increasing f33 with increasing carbohydrate concentration was observed, despite the magnitudes being slightly higher than experiment. This represents a signicant improvement over the CHARMM36 parameters and is particularly important for force elds used in calculating preferential interactions. Weerasinghe and Smith found that reproducing urea activity trends was necessary for modeling the preferential exclusion of urea from cavities. 10 Additionally, it is possible that other parameter sets not considered here would yield similar KB integral values. The sensitivity of the KB integral values for glycerol to changes in the nonbonded parameters is examined in the supplementary information. Alternatively, an approach involving using dierent Lennard-Jones mixing rules might also improve agreement with the KB integral values without modifying the parameters. Finally, the KBPs were developed specically to model these carbohydrates in aqueous 12


Page 12 of 33

Page 13 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


solution at concentrations below 2 m. Their ability to reproduce KB integral values at higher concentrations was not examined. However, for use in comparing these force eld parameters to others, some properties of pure carbohydrate systems were calculated, with the results in the supplementary information. Briey, compared to the CHARMM36 parameters, the KBPs are slightly less accurate in modeling the Cremer and Pople ring pucker parameter, Q, 42 for glucose. The experimental crystal unit cell volumes were generally better reproduced by the KBPs than the CHARMM36 parameters, although results for sucrose were much higher than experiment with both force elds. Pure component densities were generally lower than experiment when using either parameter set. However, for glucose, sucrose, and trehalose, results with the KBPs were slightly closer to the experimental result than results with the CHARMM36 parameters.

Clustering Some carbohydrate self-association, or clustering, was observed through alcohol hydrogen bonding interactions for all ve types of carbohydrates with either force eld. In general, more extensive clustering was observed using the CHARMM36 parameters as compared to the KBPs. In simulations using the KBPs, monomers accounted for approximately 15% more of the total clustered units compared to simulations using the CHARMM36 parameters. Additionally, the probability of nding a particular carbohydrate molecule in a monomer was higher with the KBPs, as shown in gure S2 for 1 m sucrose and 1 m sorbitol. Experimentally, self-association of monosaccharides and disaccharides in solution is observed, 43,44 and this is reproduced by the simulation results with the KBPs. Simulations of 1 m carbohydrate with the KBPs indicate that glycerol molecules spend about 6-8% of the simulation time hydrogen bound to other glycerol molecules, while sorbitol and glucose molecules spend 15-20% of the time hydrogen bound to other solute molecules, and sucrose and trehalose spend 30-35% of the time hydrogen bound to other solute molecules. The self-association of the carbohydrate molecules aects their distribution throughout the sim13



ulation and thus aects the preferential interaction coecient in simulations containing a protein.

Preferential Interaction Coecients The Γ23 results with the KBPs showed excellent agreement with experimental results for preferential interactions of the carbohydrates with small proteins at a variety of pHs. The small proteins used for this validation were lysozyme, BSA, α-Cgn A, and RNase A, chosen due to the availability of literature preferential interaction data with these carbohydrates. The preferential interaction coecients were calculated from simulations using equation 5. The results with the CHARMM36 parameters showed an increasing Γ23 value with increasing carbohydrate concentration for concentrations below 2 m for all combinations of carbohydrates and proteins examined, while the experimental results indicated that all carbohydrates were linearly excluded from all protein surfaces. The Γ23 values for glycerol with lysozyme and BSA at pH 6 are shown in gure 4. The results using the KBPs slightly overestimated the Γ23 value with lysozyme and slightly underestimated the values with BSA compared to the experimental results. 45 The Γ23 values for sorbitol with RNase A at pH 2 are shown in gure 5. The results with the KBPs almost exactly matched the experimental data. 46 The Γ23 values for glucose with lysozyme (pH 6), BSA (pH 6), and α-Cgn A (pH 3.5) are shown in gure 6. Good agreement with experimental results 45 was demonstrated for the KBPs for all three proteins, although the Γ23 values with BSA were slightly lower than experiment. Glucose was the only single-ringed sugar included in this study. The Γ23 values for sucrose with α-Cgn A and RNase A (pH 3) are shown in gure 7, with excellent agreement with experimental results. 1 The results for trehalose with lysozyme (pH 5.5) and RNase A (pH 5.5) are shown in gure 8, and again the results with the KBPs almost exactly matched the experimental results. 47 It can be clearly seen from the results of all carbohydrate and protein combinations 14


Page 14 of 33

Page 15 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


that the simulations with the KBPs predicted a linear decrease in Γ23 with increasing concentration, agreeing with the experimental trend, whereas the CHARMM36 parameter set resulted in the wrong trend. The better agreement of the KBPs with experiment compared to CHARMM36 was likely due to the better agreement with f33 values, since gure 3 shows that the major dierence between the CHARMM36 parameter results and the KBP results was that the experimental trend in f33 was better modeled using the KBPs. This agrees with a previous study of urea. 10 Table 2 compares the Γ23 values determined from experiment and from simulation with the KBPs for the small proteins. For BSA, both simulation and experiment agree that glucose is more excluded than glycerol, although the Γ23 values are not identical. The Γ23 values for lysozyme and RNase A are much closer in magnitude, with the experimental data indicating that the Γ23 values at 1 m carbohydrate are within 2 units, which is approaching the sensitivity of the simulations. Because the Γ23 values are so close for all the excipients with lysozyme and with RNase A, the simulations results do not dierentiate well between the exclusion of the carbohydrates with these two proteins.

Carbohydrate-Protein Interactions with the KBPs Experimentally, Timashe found that the native state of proteins is often stabilized by many types of carbohydrates, which are excluded from the protein surface and raise the chemical potential of the protein, making unfolded forms less favorable. 2,47 The simulations with the KBPs capture this overall exclusion and allow the exclusion of the carbohydrate molecules from dierent regions of the protein surface to be examined for insight into carbohydrateprotein interactions. Local interactions of carbohydrates with the protein surface

Trends in the interaction of carbohydrates with lysozyme and RNase A were examined more closely. In general, very similar distribution patterns were observed for all carbohydrates 15



Table 2: Experimental and Simulation

Γ23

Page 16 of 33

Concentration Dependence

Γ23 a Carbohydrate

Experiment

Simulation

Lysozyme

Glycerol Glucose Trehalose

(−5.6 ± 0.5)m3 b (−4.4 ± 0.4)m3 b (−3.7 ± 0.4)m3 c

(−2.0 ± 0.5)m3 (−2.7 ± 1.0)m3 (−2.7 ± 0.9)m3

BSA

Glycerol Glucose

(−12.4 ± 0.5)m3 b (−17.5 ± 0.4)m3 b

(−20.4 ± 2.0)m3 (−24.4 ± 1.5)m3

α-Cgn A

Glucose Sucrose

(−4.4 ± 0.4)m3 b (−7.5 ± 0.4)m3 d

(−6.6 ± 0.7)m3 (−6.7 ± 1.0)m3

Sorbitol (−6.0 ± 0.5)m3 e (−5.1 ± 0.8)m3 d RNase A Sucrose (−6.2 ± 0.8)m3 (−6.4 ± 1.0)m3 Trehalose (−6.2 ± 0.4)m3 f (−6.5 ± 0.8)m3 a m represents the molal concentration of excipient. 3 b Experimental data for glycerol and glucose from ref 45. c Experimental data gathered according to methods section. d Experimental data for sucrose calculated from data in ref 1. e Experimental data calculated from data in ref 46. f Experimental data calculated from data in ref 47. with the same protein, as shown in gures 9-10. However, the magnitude of the interaction was dependent on the size of the carbohydrate molecule, with fewer carbohydrates within 5 Å for larger carbohydrates. It is interesting that similar distributions of carbohydrates over the protein surface are observed for dierent carbohydrate molecules. In particular, trehalose was found in several cases to be a better protein stabilizer than other sugars tested, 48 but the simulations showed that it does not distribute itself very dierently around the protein surface compared to the other carbohydrates. However, the simulations showed that there are fewer trehalose molecules within 5 Å of residues on the protein surfaces, which is attributable to the larger size of trehalose compared to that of the polyols or glucose. Sola-Penna and Meyer-Fernandes concluded that the larger hydrated volume of trehalose compared to that of other sugars was responsible for its eectiveness and found that, when sugar concentrations were corrected by the percentage of the occupied volume, trehalose was no more eective than sucrose, maltose, glucose, and fructose at stabilizing macromolecules. 48 This agrees with the simulation results 16


Page 17 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


that the dierences in interaction of the carbohydrates with the protein surface are primarily due to the carbohydrate size. In general, there were more carbohydrate molecules near highly exposed residues. When normalizing by the exposed surface areas of residues, simulations of carbohydrates with lysozyme indicated slightly more interactions with exposed ALA, ILE, and PHE residues (0.02-0.03 carbohydrate molecules within 6 Å/residue/Å2 ) compared to the other residues (0.01-0.02 carbohydrate molecules/residue/Å2 ). This indicated that the carbohydrates, although generally excluded from the lysozyme surface, were slightly less excluded from these particular hydrophobic residues. Interactions of a carbohydrate with an exposed hydrophobic residue replace unfavorable interactions of these hydrophobic residues with water, contributing to the increased stability of the protein. Local residence time of carbohydrate molecules

In general, individual carbohydrate molecules did not spend a very long time continuously within 6 Å of the protein surface unless interacting in depressions. Hydrogen bond lifetimes between protein residues and carbohydrate molecules tended to be very short, with an average of 0.02 ns. Occasionally, individual carbohydrate molecules were observed to spend a longer time near the protein surface, generally due to the shape of the protein surface. For example, lysozyme contains a pocket with several hydrophobic residues (ALA107, ILE57, ILE98, TRP63, TRP108). While individual molecules of each of the carbohydrates examined were observed to spend several nanoseconds near this region, the eects are most pronounced with glycerol due to its small molecular size. In the 85 ns simulation of lysozyme with 1 m glycerol, this pocket was occupied by a glycerol molecule for most of the simulation. One glycerol molecule spent 54.4 ns continuously in this pocket, and a snapshot of a glycerol molecule in this pocket is shown in gure 11. No protein-glycerol hydrogen bonds were observed for glycerol molecules in this pocket, and the long residence time observed was likely due to the more favorable interactions of the hydrophobic residues with glycerol 17



than with water molecules. Orientation of carbohydrates around protein surfaces

Steric eects appear to dictate the orientation of carbohydrate molecules around the protein surfaces. The polyols glycerol and sorbitol tended to be oriented around the proteins such that a terminal alcohol oxygen was closest to the protein surface. Glucose showed a preference for an orientation in which O6 was closest to the protein surface, as shown in gure 12, and O6 is separated from the ring by one carbon. Interestingly, sucrose did not show a preference for any orientation, while trehalose showed a preference for O3 and O4 being closest to the carbohydrate surface. These oxygens are part of the alcohol groups on the outside of the rings and thus the least sterically hindered.

Conclusions It has been shown that selection of carbohydrate parameters to reproduce experimental KB integral values led to better reproduction of experimental solution properties compared to the use of the CHARMM36 carbohydrate parameters. The KBP values, determined based on simulations of glycerol and trehalose, also worked well for sorbitol, glucose, and sucrose, indicated by good agreement with experimental values and trends, and this suggests that they could potentially be used for other carbohydrates. The KBPs developed here addressed the overprediction of self-association of carbohydrates by the CHARMM36 parameters by modifying the partial charge distribution and reducing the ε values for alcohols for nonwater interactions, making self-association less energetically favorable. This led to a reduced frequency of carbohydrate clusters, both in binary carbohydrate-water simulations and in ternary carbohydrate-protein-water simulations. The KBPs more accurately reproduced experimental preferential interactions of carbohydrates with the small proteins lysozyme, BSA, α-Cgn A, and RNase A compared to the

18


Page 18 of 33

Page 19 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CHARMM36 parameters. Analysis of the simulations indicated that this result was due in part to the modied self-association of the carbohydrates. In particular, the accurate prediction of the value and trend in f33 is necessary for a parameter set to be used in Γ23 calculations. The KBPs are limited in that they have only been developed for solutions of 2 m or less, and may not perform as well at higher concentrations or for pure carbohydrate simulations. Other parameter sets might perform equally well as the KBPs identied here. A dierent combination of a reduction in alcohol partial charge magnitude, a reduction in general ε values, and an increase in water-specic ε values compared to the CHARMM36 parameters could also reproduce the KB integral values. Finally, molecular dynamics simulations of dierent carbohydrates with lysozyme and RNase A indicated that dierent carbohydrates had similar local concentrations around the protein surface, although the number of carbohydrate molecules within 5 Å of the protein surface was aected by the carbohydrate size. This suggests that carbohydrate size is a major factor in the dierences in preferential interaction coecients among carbohydrates.

Acknowledgement The authors thank MedImmune for supporting this study.

Supporting Information Available The following les are available free of charge. supportinginfo.pdf: Summary of MD simulations performed and additional information on Kirkwood-Bu integrals

19



Page 20 of 33

References (1) Lee, J. C.; Timashe, S. N. The Stabilization of Proteins by Sucrose. 1981,

J. Biol. Chem.

, 71937201.

256

(2) Gekko, K.; Timashe, S. N. Mechanism of Protein Stabilization by Glycerol: Preferential Hydration in Glycerol-Water Mixtures.

Biochemistry

1981,

, 46674676.

20

(3) Shukla, D.; Shinde, C.; Trout, B. L. Molecular Computations of Preferential Interaction Coecients of Proteins.

J. Phys. Chem. B

2009,

, 1254612554.

113

(4) Best, R. B.; Zhu, X.; Shim, J.; Lopes, P. E. M.; Mittal, J.; Feig, M.; MacKerell, A. D. Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone φ, ψ and Side-Chain χ1 and χ2 Dihedral Angles. Chem. Theory Comput.

2012,

J.

, 32573273.

8

(5) Guvench, O.; Greene, S. N.; Kamath, G.; Brady, J. W.; Venable, R. M.; Pastor, R. W.; Mackerell, A. D. Additive Empirical Force Field for Hexopyranose Monosaccharides. J. Comput. Chem.

2008,

, 25432564.

29

(6) Hatcher, E. R.; Guvench, O.; MacKerell, A. D. CHARMM Additive All-Atom Force Field for Acyclic Polyalcohols, Acyclic Carbohydrates, and Inositol. Comput.

2009,

J. Chem. Theory

, 13151327.

5

(7) Sapir, L.; Harries, D. Linking Trehalose Self-Association with Binary Aqueous Solution Equation of State.

J. Phys. Chem. B

2011,

, 624634.

115

(8) Ha, S. N.; Giammona, A.; Field, M.; Brady, J. W. A Revised Potential-Energy Surface for Molecular Mechanics Studies of Carbohydrates.

Carbohydr. Res.

1988,

, 207

180

221. (9) Kuttel, M.; Brady, J. W.; Naidoo, K. J. Carbohydrate Solution Simulations: Producing

20


Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


a Force Field with Experimentally Consistent Primary Alcohol Rotational Frequencies and Populations.

J. Comp

2002,

, 12361243.

23

(10) Weerasinghe, S.; Smith, P. E. Cavity Formation and Preferential Interactions in Urea Solutions: Dependence on Urea Aggregation.

J. Chem. Phys.

2003,

, 59015910.

118

(11) Yin, D.; Mackerell, A. D. Combined Ab Initio / Empirical Approach for Optimization of Lennard-Jones Parameters.

1998,

J. Comput. Chem.

, 334348.

19

(12) Foley, B. L.; Tessier, M. B.; Woods, R. J. Carbohydrate Force Fields. Wiley Rev.: Comput. Mol. Sci.

2012,

Interdiscip.

, 652697.

2

(13) Weerasinghe, S.; Smith, P. E. A Kirkwood-Bu Derived Force Field for Mixtures of Urea and Water.

2003,

J. Phys. Chem. B

, 38913898.

107

(14) Weerasinghe, S.; Smith, P. E. A Kirkwood-Bu Derived Force Field for Sodium Chloride in Water.

J. Chem. Phys.

2003,

, 1134211349.

119

(15) Ploetz, E. A.; Smith, P. E. A Kirkwood-Bu Force Field for the Aromatic Amino Acids. Phys. Chem. Chem. Phys.

2011,

, 1815467.

13

(16) Ploetz, E. A.; Bentenitis, N.; Smith, P. E. Developing Force Fields from the Microscopic Structure of Solutions.

Fluid Phase Equilib.

2010,

, 4347.

290

(17) Ben-Naim, A. Inversion of the Kirkwood-Bu Theory of Solutions: Application to the Water-Ethanol System.

J. Chem. Phys.

1977,

, 48844890.

67

(18) Abraham, M. J.; Murtola, T.; Schulz, R.; Pall, S.; Smith, J. C.; Hess, B.; Lindahl, E. GROMACS: High Performance Molecular Simulations Through Multi-level Parallelism from Laptops to Supercomputers.

SoftwareX

2015,

, 1925.

1-2

(19) Guvench, O.; Hatcher, E.; Venable, R. M.; Pastor, R. W.; MacKerell, A. D. CHARMM Additive All-Atom Force Field for Glycosidic Linkages Between Hexopyranoses. Chem. Theory Comput.

2009,

, 23532370.

5

21


J.


Page 22 of 33

(20) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983,

, 926935.

79

(21) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations.

J. Comput. Chem.

1997,

, 14631472.

18

(22) Berman, H. M.; Westbrook, J.; Feng, Z.; Gilliland, G.; Bhat, T. N.; Weissig, H.; Shindyalov, I. N.; Bourne, P. E. The Protein Data Bank.

Nucleic Acids Res.

2000,

, 235242.

28

(23) Martinez, L.; Andrade, R.; Birgin, E. G.; Martinez, J. M. PACKMOL: A Package for Building Initial Congurations for Molecular Dynamics Simulations. J. Comput. Chem. 2009,

, 21572164.

30

(24) Dolinsky, T. J.; Czodrowski, P.; Li, H.; Nielsen, J. E.; Jensen, J. H.; Klebe, G.; Baker, N. A. PDB2PQR: Expanding and Upgrading Automated Preparation of Biomolecular Structures for Molecular Simulations.

Nucleic Acids Res.

2007,

,

35

W522525. (25) Allen, M.; Tildesley, D. Computer Simulation of Liquids ; Oxford University Press: New York, 1987; pp 191195. (26) Michaud-Agrawal, N.; Denning, E. J.; Woolf, T. B.; Beckstein, O. MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.

J. Comput. Chem.

2011,

, 23192327.

32

(27) Gowers, R. J.; Linke, M.; Barnoud, J.; Reddy, T. J. E.; Melo, M. N.; Seyler, S. L.; Domanski, J.; Dotson, D. L.; Buchoux, S.; Kenney, I. M. et al. MDAnalysis: A Python Package for the Rapid Analysis of Molecular Dynamics Simulations. Proc. of the 15th Python in Science Conf. Austin, TX., 2016; pp 102109.

22


Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(28) Kirkwood, J. G.; Bu, F. P. The Statistical Mechanical Theory of Solutions. I. J. Chem. Phys.

1951,

, 774777.

19

(29) Baynes, B. M.; Trout, B. L. Proteins in Mixed Solvents:Â A Molecular-Level Perspective.

The Journal of Physical Chemistry B

2003,

, 1405814067.

107

(30) Hong, J.; Capp, M. W.; Anderson, C. F.; Saecker, R. M.; Felitsky, D. J.; Anderson, M. W.; Record, M. T. Preferential Interactions of Glycine Betaine and of Urea with DNA: Implications for DNA Hydration and for Eects of These Solutes on DNA Stability.

Biochemistry

2004,

, 1474414758.

43

(31) Marcus, Y. Some Thermodynamic and Structural Aspects of Mixtures of Glycerol with Water.

Phys. Chem. Chem. Phys.

2000,

, 48914896.

2

(32) Cristancho, D. M.; Delgado, D. R.; Martínez, F.; Fakhree, M. A. A.; Jouyban, A. Volumetric Properties of Glycerol + Water Mixtures at Several Temperatures and Correlation with the Jouyban-Acree Model.

Rev. Colomb. Cienc. Quim.-Farm.

2011,

,

40

92115. (33) Bonner, O. Osmotic and Activity Coecients of Sodium Chloride-Sorbitol and Potassium Chloride-Sorbitol Solutions at 25°.

J. Solution Chem.

1982,

, 315324.

11

(34) DiPaola, G.; Belleau, B. Polyol-Water Interactions. Apparent Molal Heat Capacities and Volumes of Aqueous Polyol Solutions.

Can. J. Chem.

1977,

, 38253830.

55

(35) Banipal, T.; Sharma, S.; Lark, B.; Banipal, P. Thermodynamic and Transport Properties of Sorbitol and Mannitol in Water and in Mixed Aqueous Solutions. Chem.

1999,

Indian J.

, 11061115.

38A

(36) Fucaloro, A. F.; Pu, Y.; Cha, K.; Williams, A.; Conrad, K. Partial Molar Volumes and Refractions of Aqueous Solutions of Fructose, Glucose, Mannose, and Sucrose at 15.00, 20.00, and 25.00°C.

J. Sol. Chem.

2007,

, 6180.

36

23



Page 24 of 33

(37) Miyajima, K.; Sawada, M.; Nakagaki, M. Studies on Aqueous Solutions of Saccharides. I. Activity Coecients of Monosaccharides in Aqueous Solutions at 25°C. Soc. Jpn.

1983,

Bull. Chem.

, 16201623.

56

(38) Sangster, J.; Teng, T.-T.; Lenzi, F. Molal Volumes of Sucrose in Aqueous Solutions of NaCl, KCl, or Urea at 25°C.

J. Solution Chem.

1976,

, 575585.

5

(39) Robinson, R.; Stokes, R. Activity Coecients in Aqueous Solutions of Sucrose, Mannitol and their Mixtures at 25°.

J. Phys. Chem.

1961,

, 19541958.

65

(40) Elias, M.; Elias, A. Trehalose + Water Fragile System: Properties and Glass Transition. J. Mol. Liq.

1999,

, 303310.

83

(41) Banipal, T.; Kaur, D.; Singh, G.; Larrk, B.; Banipal, P. Partial Molar Volumes of Transfer of Some Disaccharides from Water to Aqueous Guanidine Hydrochloride Solutions at 298.15 K.

Indian J. Chem.

2002,

, 11311138.

41A

(42) Cremer, D.; Pople, J. A general denition of ring puckering coordinates. Soc.

1974,

J. Am. Chem.

, 13541358.

97

(43) Sidebottom, D. L. Ultraslow Relaxation of Hydrogen-bonded Dynamic Clusters in Glass-forming Aqueous Glucose Solutions: A Light Scattering Study. 2007,

Phys. Rev. E

, 011505.

76

(44) Sidebottom, D. L.; Tran, T. D. Universal Patterns of Equilibrium Cluster Growth in Aqueous Sugars Observed by Dynamic Light Scattering.

Phys. Rev. E

2010,

,

82

051904. (45) Schneider, C. P.; Trout, B. L. Investigation of Cosolute-Protein Preferential Interaction Coecients: New Insight into the Mechanism by Which Arginine Inhibits Aggregation. J. Phys. Chem. B

2009,

, 20502058.

113

24


Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(46) Xie, G.; Timashe, S. N. Mechanism of the Stabilization of Ribonuclease A by Sorbitol: Preferential Hydration is Greater for the Denatured than for the Native Protein. Protein Sci.

1997,

, 211221.

6

(47) Xie, G.; Timashe, S. N. The Thermodynamic Mechanism of Protein Stabilization by Trehalose.

Biophys. Chem.

1997,

, 2543.

64

(48) Sola-Penna, M.; Meyer-Fernandes, J. R. Stabilization Against Thermal Inactivation Promoted by Sugars on Enzyme Structure and Function: Why Is Trehalose More Effective Than Other Sugars?

Arch. Biochem. Biophys.

25


1998,

, 1014.

360


Graphical TOC Entry G33 (cm3 /mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 33

1000 Expt. CHARMM36 KBP

0 1000 0.0

0.5 1.0 1.5 Trehalose concentration (m)

26

2.0


Page 27 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1: The KBP partial charges for glycerol, glucose, sorbitol, sucrose, and trehalose. The partial charge of alkyl H (not shown) is +0.09 for all molecules.

27



20

glucose

0.0

G33 (cm3 /mol)

150 100 50 0

sucrose

trehalose G33 (cm3 /mol)

150 100 50 0

G33 (cm3 /mol)

20 10 0 10 20

0.5

1.0 1.5 Concentration (m)

2.0

G31 (cm3 /mol)

300 0 300 600

sorbitol

glucose

400 0 400

glucose

80 120 160

sucrose

trehalose

1000 0 1000 0.0

80 120 160 200

sucrose

1000 500 0 500 1000

G31 (cm3 /mol)

0

60 70 80 90

sorbitol G31 (cm3 /mol)

G33 (cm3 /mol)

20

glycerol

G31 (cm3 /mol)

sorbitol

glycerol

100 0 100 200 300

G31 (cm3 /mol)

Expt. CHARMM36 KBP

G33 (cm3 /mol)

5 10 15 20

G11 (cm3 /mol)

G11 (cm3 /mol)

G11 (cm3 /mol)

G11 (cm3 /mol)

glycerol

G11 (cm3 /mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 33

0.5


2.0

100 200 300 400 trehalose

100 200 300 400 0.0

0.5


2.0

Figure 2: KB integral values for aqueous carbohydrates with CHARMM36 parameters (crosses) and KBPs (solid circles). Lines represent experimental data for glycerol, 7,31,32 sorbitol, 3335 glucose, 36,37 sucrose, 38,39 and trehalose. 7,40,41

28


glycerol

glycerol

V3 (cm3 /mol)

Density (g/cm3 )

1.20 1.05 0.90

90 f33

80 70 sorbitol

160 120

140 f33

120 100 sucrose

280 240

f33

V3 (cm3 /mol) V3 (cm3 /mol)

glucose

200

0.2 0.0 0.2 0.4

sucrose

0.8 0.4 0.0 0.4

trehalose


2.0

trehalose 0.4

280 240

f33

1.0

0.5

0.0 0.4

trehalose V3 (cm3 /mol)

Density (g/cm3 )

Density (g/cm3 )

sucrose

1.2 0.8 0.0

sorbitol

glucose

1.20 1.05 0.90

1.4

0.2 0.1 0.0 0.1 0.2 0.4

140

glucose

1.4 1.2 1.0 0.8

glycerol

f33

Expt. CHARMM36 KBP

V3 (cm3 /mol)

1.3 1.2 1.1 1.0

sorbitol

Density (g/cm3 )

0.0 0.4

200 0.0

0.5


2.0

0.0

0.5


2.0

23 : lysozyme

Figure 3: Density, partial molar volume and activity coecient derivatives as functions of carbohydrate concentration. Experimental data from sources in caption of gure 2.

23 : BSA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Density (g/cm3 )

Page 29 of 33

10 0 10 Expt. CHARMM36 KBP

20 0 20 40 0.0

0.5


2.0

Figure 4: Γ23 for glycerol with lysozyme (pH 6) and BSA (pH 6) as calculated using equation 5. Experimental data from Schneider and Trout. 45

29


Page 30 of 33

Expt. CHARMM36 KBP

10 0 10 0.0

0.5


2.0

23 : lysozyme

Figure 5: Γ23 for sorbitol with RNase A (pH 2), with experimental data from Xie and Timashe. 46

16 8 0

23 :

Cgn A

23 : BSA

8 30 15 0 15 30

Expt. CHARMM36 KBP

10 0 10 0.0

0.5


2.0

23 :

Cgn A

Figure 6: Γ23 for glucose with lysozyme (pH 6), BSA (pH 6), and α-Cgn A (pH 3.5), with experimental data from Schneider and Trout. 45

23 : RNase A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

23 : RNase A


16 8 0 8 16 10

Expt. CHARMM36 KBP

0 10 0.0

0.5


2.0

Figure 7: Γ23 for sucrose with α-Cgn A (pH 3) and RNase A (pH 3), with experimental data from Lee and Timashe. 1 30


23 : RNase A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23 : lysozyme

Page 31 of 33

16

Expt. CHARMM36 KBP

8 0

8 10 0 10 0.0

0.5


2.0

Figure 8: Γ23 for trehalose with lysozyme (pH 5.5), with experimental data gathered as described in the methods section, and for RNase A (pH 5.5), with experimental data from Xie and Timashe. 47

Glycerol

0.65 0.15

Glucose

Trehalose

Figure 9: Each lysozyme residue is colored by the average molality of glycerol, glucose, or trehalose within 5 Å of the residue surface in a simulation with 0.5 m carbohydrate. Similar distributions of carbohydrate around the protein surface are observed for all three carbohydrates. 31



Sorbitol

0.65 0.15

Sucrose

Trehalose

Figure 10: Each RNase A residue is colored by the average molality of sorbitol, sucrose, or trehalose within 5 Å of the residue surface in a simulation with 0.5 m carbohydrate. All three carbohydrates interact most strongly with similar domains on the protein surface.

32


Page 32 of 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 11: A glycerol molecule in a pocket on the surface of lysozyme (top) and the residues making up the pocket (ALA107, ILE57, ILE98, TRP63, and TRP108) (below). Snapshot from a simulation of lysozyme in 1 m glycerol.

Lysozyme in 0.5 m glucose

1.2 0.8

O1 O2 O3 O4 O6

g(r)

Page 33 of 33

0.4 0.0

0

2

4

6 r (Å)

8

10

12

Figure 12: Glucose showed a slight preference for the orientation around lysozyme such that O6, which is separated from the ring by one carbon, is closest to lysozyme. Data from a simulation of lysozyme in 0.5 m glucose using the KBPs.

33


KirkwoodâBuff-Derived Alcohol Parameters for Aqueous

Recommend Documents

KirkwoodâBuff-Derived Alcohol Parameters for Aqueous