Stability of Proteins in Carbohydrates and Other Additives during

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Stability of Proteins in Carbohydrates and Other Additives During Freezing: The Human Growth Hormone as a Case Study Andrea Arsiccio, and Roberto Pisano J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05541 • Publication Date (Web): 22 Aug 2017 Downloaded from http://pubs.acs.org on August 22, 2017

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The Journal of Physical Chemistry

Stability of Proteins in Carbohydrates and Other Additives During Freezing: The Human Growth Hormone as a Case Study

Andrea Arsiccio and Roberto Pisano

∗

Department of Applied Science and Technology, Politecnico di Torino 24 corso Duca degli Abruzzi, Torino, 10129 Italy

E-mail: [email protected]

Phone: +39 011 0904679

1

ACS Paragon Plus Environment


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Abstract Molecular dynamics is here used to elucidate the mechanism of protein stabilization by carbohydrates and other additives during freezing. More specically, we used molecular dynamics simulations to obtain a quantitative estimation of the capability of various cryoprotectants to preserve a model protein, the human growth hormone, against freezing stresses. Three mechanisms were investigated, preferential exclusion, water replacement, and vitrication. Model simulations were nally validated upon experimental data in terms of excipients ability to prevent protein aggregation. Overall we found that the preferential exclusion and vitrication mechanisms are important during the whole freezing process, while water replacement becomes dominant only towards the end of the cryoconcentration phase. The disaccharides were found to be the most ecient excipients, as regards both preferential exclusion and water replacement. Moreover, sugars were in general more ecient than other excipients, such as glycine or sorbitol.

Introduction Protein-based therapeutics play an indispensable and increasing role in human health. In fact, they are used in the treatment of a wide number of high impact human diseases, such as diabetes, auto-immune diseases, metabolic disorders and several forms of cancer. 1,2 As most of protein-based drugs are unstable at liquid state, they have to be stabilized by drying. Unfortunately, conventional drying methodologies cannot be used because proteins are usually temperature-sensitive and, hence, denature at high temperature. By contrast, lyophilization is particularly suitable for protein-based drugs, because drying is carried out at very low temperature and pressure. 3 However, attention has to be paid to both process conditions and formulation in order to preserve proteins against stresses induced by freezing and drying, and impede their aggregation as well. 4 This is particularly true for freezing, which can promote stresses to proteins because of low temperature, cryoconcentration, formation of 2


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ice-water interface, pH changes, phase separation and, when most of water is frozen, stresses due to dehydration. 4 So, it is of the utmost importance to use a well-designed formulation in order to protect proteins from freezing stresses. One of the most widely accepted mechanisms at the basis of stabilization of proteins during freezing is the preferential exclusion. In fact, it has been observed that there is a deciency in the stabilizing co-solute molecules in the immediate vicinity of proteins, relative to the bulk solution, and that the protein molecule is preferentially hydrated. Thus, as described in Timashe, 5 the presence of these co-solutes in a protein solution creates a thermodynamically unfavorable situation, since the chemical potentials of both protein and additives are increased. Consequently, the native structure of proteins is stabilized because denaturation or dissociation would lead to a greater contact surface between protein and solvent and, therefore, augment this thermodynamically unfavorable eect. However, several other stabilization mechanisms were postulated and vitrication is one of the most important. Many cryoprotectants, such as polymers and sugars, can increase the viscosity of a solution, restricting diusion of reacting molecules. This phenomenon produces the formation of a very viscous system that slows down protein denaturation and unfolding. 6 Moreover, towards the end of the freezing process, most of the water has transformed into ice and therefore there is no sucient free water to satisfy the hydrogen bonding requirement of polar groups on the protein surface. So, another possible stabilization mechanism is the water replacement hypothesis, 7 which states that excipients preserve the native structure of proteins by serving as water substitutes. Among the possible stabilizers, sugars, polyols and amino acids are frequently used. 810 Their eciency as cryoprotectants has been experimentally tested and their stabilizing action has been hypothesized to be due to one or more of the mechanisms previously discussed. However, simulations at the molecular scale have never investigated in details the stabilizing eect of these excipients during freezing. In this paper, we present a molecular dynamics study of the stabilizing eects of excip-

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ients during freezing of pharmaceutical proteins, using human growth hormone (hGH) as a case study. Human growth hormone is an aggregation-prone protein widely studied in literature. 1115 It easily forms, during freezing and freeze-drying, both soluble and insoluble aggregates. Soluble aggregates can be determined using SEC-HPLC, while the insoluble ones can be separated through ltration (0.22 µm lters). 11,15 The relative ease with which hGH aggregation can be monitored makes this protein particularly suitable for research on stabilization mechanisms. In particular, we analyzed the cryoprotection mechanisms given by some of the most common pharmaceutical excipients, namely sucrose, trehalose, cellobiose, lactose, glucose, sorbitol and glycine. This study aims not only to validate theoretical hypotheses, but also to establish molecular dynamics as an eetive and economic tool, alternative to experimental campaigns, for testing the eciency of a molecule as a protectant.

Methods Simulation The interactions between excipients, namely sucrose, trehalose, cellobiose, lactose, glucose, sorbitol and glycine, and human growth hormone (hGH) were evaluated during freezing using the molecular dynamics software GROMACS 16 (vers. 5.0.7). The hGH topology le was obtained from the RCSB Protein Data Bank (PDB 3hHR ). 17 The sucrose, trehalose, cellobiose, lactose, glucose, sorbitol and glycine topology les were obtained from the ATB database. 18 All simulations were conducted using a cubic box with periodic boundary conditions. 19 The simulation box was modeled with the Gromos 54A7 force eld, 20 using explicit SPC/E water. 21 The initial structures were energy minimized using the steepest descent algorithm, then equilibrated at the desired temperature using the velocity rescaling thermostat. 22 The long range electrostatics were calculated by the Particle Mesh Ewald technique 23 and the resulting conguration was equilibrated at 1 bar with the Parrinello-Rahman baro4


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stat. 24 The nal simulations were then conducted for 45 ns using 1 fs as time step and saving coordinates and velocities every 10 ps. A Lennard-Jones cut-o of 1.4 nm was used for all the simulations.

Design of simulations The study was aimed to verify at the molecular scale the validity of the preferential exclusion hypothesis, the vitrication theory and the water replacement mechanism. The simulations details are shown in Table 1, where c3 is the excipient molar concentration.

Table 1: Details of simulations performed to evaluate hGH-excipient interactions Simulation identier 1 2 3 4 5

c3 , mol l−1 0.38 1.15 2.5 0.38 0.77

box volume nm3 572 572 179 572 572

temperature K 258 272 233 272 272

duration, ns 45 45 45 45 45

Simulated conditions were chosen so as to reproduce stresses of the product being frozen. Simulation 1 corresponds to the conditions encountered by the formulation during cooling, close to the nucleation temperature. Simulations 2, 4 and 5, on the contrary, reproduce the environment encountered during freezing, when the product temperature is equal to the freezing equilibrium value and cryoconcentration occurs. Finally, simulation 3 corresponds to the situation encountered by the product at the end of freezing, when the asymptotic temperature value is reached. A scheme of the relationship between simulations and the freezing curve is reproduced in Figure 1. Simulations 1 to 3 were performed for each of the seven excipients considered. By contrast, simulations 4 and 5 were carried out for sucrose only and were aimed to verify the relative importance of dierent mechanisms upon variation of excipient concentration. Simulations were equilibrated for 45 ns before they were analyzed. 5


The excipients


°C

30

Temperature,

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20

# 2, 4, 5

10

# 3

0 -10 -20 -30

# 1

-40 0

1

2 Time,

h

3

4

5

Figure 1: Evolution of temperature during freezing of a solution. Conditions for simulations of Table 1 are also shown.

molecules were, at the beginning of simulations, mostly concentrated far away from the protein surface. However, thanks to diusion, they redistributed over the box volume during the equilibration time. The number of excipient molecules within 0.35 nm from the protein surface, n(0.35 nm), was monitored over time for all the simulations performed. This distance, i.e., 0.35 nm, was also used for the evaluation of preferential exclusion. To provide an example, the evolution of n(0.35 nm) for sucrose and in the case of simulations 1, 2 and 3 is shown in Figure 2. As it is possible to notice, n(0.35 nm) reached a plateau level after about 20 ns of equilibration for simulations 1 and 2 or even before for simulation 3. This means that 45 ns as equilibration time was more than enough to allow complete redistribution of excipient molecules within the box volume. Similar results were obtained for all the other excipients.

Preferential exclusion theory According to the notation of Scatchard 25 and Stockmayer, 26 water will be designated as component 1, protein as component 2 and the excipient as component 3. The preferential exclusion theory is based on the measurement of the so-called preferential interaction

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4 3

n (0.35 nm)

6

2 (a) Sim. 1 - 0.38 M

0

0

10

20 Time,

ns

30

40

14 10 8 3

n (0.35 nm)

12

6 (b) Sim. 2 - 1.15 M

4 0

10

20 Time,

ns

30

40

56 52 48 3

n (0.35 nm)

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44 40

(c) Sim. 3 - 2.5 M

0

10

20 Time,

ns

30

40

Figure 2: Evolution of n(0.35 nm) over time during equilibration for (a) simulation 1, (b) simulation 2 and (c) simulation 3. In all cases, the excipient considered is sucrose.

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parameter ξ3 27

ξ3 =

∂g 3

∂g2

= A3 − g3 A1

(1)

where gi is the concentration of component i (mass of i per unit mass of water), and Ai is the amount of component i interacting with the protein (mass of i per unit mass of protein). The interaction parameter ξ3 is a measure of the excess of component 3 in the immediate domain of the protein over its concentration in the bulk solvent. A positive value of this parameter indicates an excess of component 3; a negative value means a deciency of component 3, i.e., an excess of component 1, water, in the domain of the protein. The interaction parameter was evaluated by measuring with GROMACS the number of excipient and water molecules within a shell of radius 0.35 nm around the protein. The value of 0.35 nm was chosen because it corresponds to the rst minimum of the radial distribution function of SPC water; however, similar results can be obtained by changing the radius, provided that the shell considered is not too much bigger than the volume actually perturbed by the protein. There is another way to estimate preferential exclusion using molecular dynamics. This procedure is based on the use of the GROMACS utility gmx rdf , which can be employed to evaluate the cumulative radial distribution function. Such utility allows the estimation of the average number of excipient, n3 (r), and water, n1 (r), particles within a distance r from the protein. Thus, the preferential exclusion theory can be validated plotting the function:

β=

n3 (r)/n1 (r) n3 (∞)/n1 (∞)

(2)

If β is lower than 1 for small r, this means that the excipient is preferentially excluded from the protein. On the contrary, if β is greater than 1, the excipient interacts preferentially with the protein. This parameter is similar to that dened by Lerbret at al. 28

8


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Vitrication theory The vitrication theory was tested by measuring the viscosity of the solution for all simulations performed. The viscosity µ was calculated using the periodic perturbation method, which has been recognized as one of the most accurate. 29 The diusion coecient was also evaluated by mean of the GROMACS utility gmx msd, which derives the diusion coecient from the mean square displacement of the molecule. 19 The viscosity was also measured indirectly from the diusion coecient D of the protein, using the Stokes-Einstein equation:

D=

kB T 6πµRg

(3)

where kB is the Boltzmann constant, T the absolute temperature and Rg the radius of gyration of the protein.

Water replacement theory The water replacement mechanism arms that when the concentration of water is too low to satisfy the hydrogen bonding requirement of the protein, the excipient serves as a water substitute. That is, protein stabilization involves hydrogen bonding with the excipient. Thus, this hypothesis was veried by evaluating the relative contribution of hydrogen bonding between the protein and the excipient with respect to the contribution given by the hydrogen bonding between protein and water molecules. In particular, while in simulations 1 and 2 the number of water molecules is more than enough to satisfy the hydrogen bonding requirements of the protein, in simulation 3 the number of water molecules is too low to allow the formation of a complete hydration shell. Therefore, the variable χ3 , dened as

χ3 =

number of protein-excipient hydrogen bonds total number of protein-excipient and protein-water hydrogen bonds

9


(4)


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was evaluated to test the water-replacement hypothesis. We also tried to nd a correlation between the molecular properties of the excipients investigated, determined by mean of the open-source software VEGA ZZ, and their behaviour as water substitutes. For this purpose, we dened parameter γ3 as

γ3 = (total number of hydrogen bond donors/acceptors ) × Area/Volume

(5)

γ3 will be later on referred to as hydrogen bond propensity parameter.

Comparison with experimental data The results collected were validated upon experimental data obtained from the works by Salnikova et al. 15 and Costantino et al. 13 For validation, the dierent behaviour of excipients in preventing protein aggregation was compared to the excipients eciency predicted by simulations. Molecular explanations were thus proposed for empirical observations.

Results and discussion Molecular dynamics evidence of the preferential exclusion theory The stabilizing eect of seven dierent excipients during freezing was studied. More specifically, three combinations of temperature and concentration, which correspond to dierent points of a typical freezing curve, were simulated. The data collected were analysed with the aim to verify the preferential exclusion, vitrication and water replacement theories. Cold denaturation was monitored as well, but no signicant modication of the protein structure was observed. More specically, we evaluated the RMSD of the protein heavy atoms and the radius of gyration of the protein during simulation, but no signicant changes were observed. As regards the protein surface area, special care was taken in its analysis as this is a crucial parameter for hGH. In fact, Kasimova et al. 30 found that a large hydrophobic surface 10


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becomes exposed to the solvent in the partially folded conformation of hGH. We carried out some preliminary simulations, with protein and water only. In this case, we observed that the non-polar surface area of the protein signicantly increased during the simulations, possibly indicating a partial unfolding of the protein. However, when the excipients were added, the non-polar surface area of the protein remained almost constant. This suggests that the presence of the excipients prevented protein unfolding. In this section, the results about preferential exclusion are presented. As can be seen in Table 2, the interaction parameter ξ3 was positive at low excipient concentration, as in simulation 1. In this condition, sucrose showed the smallest value of the interaction parameter, followed by trehalose and glycine. Cellobiose, lactose and sorbitol had a similar behaviour, while glucose interacted the most with the protein. At intermediate concentration, simulation 2, only sucrose and lactose were characterized by negative ξ3 , while glucose, sorbitol and glycine still showed a quite large and positive value of the interaction parameter. Trehalose and cellobiose had an intermediate behavior. At high excipient molarity, as in simulation 3, the interaction parameter became negative for all excipients, indicating preferential exclusion. The disaccharides, in particular lactose, showed the highest preferential exclusion, while glucose, sorbitol and glycine were only weakly excluded. Simulations 2, 4 and 5 were performed at equal temperature, but varying sucrose concentration. By comparison of the results obtained, it is possible to see that the interaction parameter decreased by increasing excipient concentration. To sum up, sucrose was excluded from the hGH surface to a greater extent with respect to trehalose, while cellobiose and lactose were, at low concentration (simulation 1), the least excluded among disaccharides. However, the degree of exclusion of both lactose and cellobiose increased more sharply with concentration with respect to sucrose and trehalose. In fact, at the highest concentration tested, i.e., simulation 3, cellobiose and lactose were more excluded from the protein surface than sucrose and trehalose. Glucose, sorbitol and

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Table 2: Interaction parameter as evaluated by simulations Simulation identier

1

2

3

4 5

excipient

A3

g3

A1

ξ3

sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose sucrose

0.085 0.100 0.124 0.124 0.195 0.099 0.054 0.216 0.232 0.278 0.201 0.366 0.206 0.136 0.541 0.502 0.441 0.386 0.376 0.400 0.233 0.200 0.232

0.141 0.141 0.141 0.140 0.070 0.072 0.028 0.560 0.57 0.560 0.554 0.247 0.253 0.092 11.08 11.53 11.48 11.30 5.84 5.96 2.48 0.141 0.323

0.44 0.43 0.41 0.41 0.38 0.41 0.435 0.39 0.37 0.37 0.376 0.305 0.342 0.386 0.063 0.057 0.057 0.062 0.083 0.083 0.11 0.399 0.382

0.023 0.04 0.066 0.066 0.168 0.069 0.042 -0.002 0.020 0.072 -0.007 0.291 0.119 0.100 -0.16 -0.15 -0.22 -0.31 -0.11 -0.09 -0.04 0.145 0.108

glycine were characterized by a degree of preferential exclusion which was signicantly lower with respect to those of the disaccharides. Furthermore, when the concentration of water was very low, as in simulation 3, the protein was preferentially hydrated, no matter what excipients was employed. Finally, increasing excipient concentration had a positive eect on the interaction parameter. As regards the parameter β , Figure 3 shows its variations with the distance from the protein surface for all the simulations performed. This parameter was found to be smaller than 1, at short distance from the protein surface, for almost all the simulations performed, indicating that the excipient was preferentially excluded from the protein. This means that, even when the interaction parameter ξ3 is positive, there might be preferential exclusion. This 12


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is due to the fact that the parameter ξ3 measures the accumulation of excipient molecules within the volume perturbed by the protein. However, denition of this volume is not univocal and the results obtained depend on the choice made. On the contrary, the parameter

β provides a more unambiguous estimation of preferential exclusion. In any case, we decided to measure ξ3 as well, because it reproduces fairly well the trend of excipient eciency which could be deduced from β , and has the advantage of allowing an easier comparison of dierent excipients. As can be seen, for simulations 1 and 2 only the disaccharides showed exclusion from the protein surface, while in the case of simulation 3 all excipients were almost equally excluded. In general, the disaccharides had a quite similar behaviour, even if sucrose seemed to be the most high-performing as regards preferential exclusion. The other excipients, such as glucose, sorbitol and glycine, were characterized by a signicantly poorer eciency as cryo-protectants, especially at low concentrations. Again, by comparing the β parameter for simulations 2, 4 and 5 it is evident that increasing sucrose concentration had a positive eect on preferential exclusion from the protein surface. From this analysis, it emerged that the cryoprotectant force eld could eectively predict preferential exclusion of the excipients from the protein surface. Moreover, it could also predict the well-known increase in preferential exclusion upon increasing excipient concentration. 31

Molecular dynamics evidence of the vitrication theory Simulations were here used to verify the vitrication theory, using the viscosity of the solution as benchmark. More specically, we were mainly interested in the viscosity change upon temperature and excipient concentration. Table 3 shows the viscosity µ of the solution, relative to the viscosity µw,0 of water at 300 K and 1 bar, as measured for all the conditions dened in Figure 1, using the periodic perturbation method (PP) and the Stokes-Einstein equation (SE). The diusion coecient, as measured from protein mean square displacement, and the radius of gyration of the protein are listed as well. 13



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2.5

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

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0.5

(a) Sim. 1 - 0.38 M

0

1

r,

(b) Sim. 2 - 1.15 M

2

0

nm

2.5

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

1

r,

2

nm

(d) Sim. 4, 5, 2 (c) Sim. 3 - 2.5 M

0

1

r,

sucrose 0.38, 0.77, 1.15 M

2

0

nm

1

r,

2

nm

Figure 3: (a, b, c)Plot of β parameter vs distance from the protein for simulations 1 (a), 2 (b) and 3 (c) for sucrose (), trehalose (- - -), cellobiose( ), lactose (O), glucose ( 4), sorbitol () and glycine (N). (d) Plot of β parameter vs distance from the protein for simulations 4 (), 5 ( ) and 2 (4) (0.38, 0.77 and 1.15 M sucrose solutions).

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Table 3: Viscosity of the solutions as evaluated by simulations. Comparison between values of sucrose and trehalose viscosity as obtained by simulations or by Genotelle equation (GE) 32 is also shown. Coecients of Genotelle equation were obtained from Longinotti at al. 33 Simulation Id.

1

2

3

4 5

excipient sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose sucrose

µ/µw,0 (PP) 6.57 7.05 7.07 7.28 5.13 5.27 4.75 14.32 14.58 18.88 19.2 4.85 6.55 3.35 1298 1410 1837 1870 438 638 303 4.18 6.78

D, m2 s−1 8.0· 9.5· 1.3· 9.6· 3.0· 1.3· 3.5· 1.6· 8.1· 2.0 · 9.0· 1.1· 1.6· 5.1· 1.6· 2.4· 1.9 · 2.8· 8.8· 1.9· 8.0· 1.1· 3.6·

10−12 10−12 10−11 10−12 10−11 10−11 10−11 10−12 10−13 10−12 10−13 10−11 10−11 10−11 10−13 10−13 10−13 10−13 10−13 10−13 10−13 10−11 10−12

Rg , nm 1.74 1.75 1.74 1.75 1.75 1.71 1.75 1.73 1.74 1.76 1.74 1.75 1.73 1.74 1.62 1.63 1.64 1.61 1.64 1.66 1.64 1.75 1.75

µ/µw,0 (SE) 15.2 13 9.37 12.9 4.68 9.37 3.51 85 165 64 149 13 8.4 2.3 763 509 650 436 137 638 152 12 36.3

µ/µw,0 (GE) 6.3 7.6

12.8 15.1

3.1 5.8

We found that the viscosity of the solution increased with the excipient concentration, which became higher and higher as a result of cryoconcentration. The increase in viscosity was highly non-linear, and we could observe that the disaccharides showed higher values of viscosity than those of glucose and glycine, especially at the highest concentration tested. Furthermore, the viscosity of sorbitol was intermediate between those of disaccharides and glucose or glycine. It is not easy to nd accurate values of viscosity for the systems that were simulated in this work. However, there are several correlations describing the concentration and temper15



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ature dependence of viscosity of disaccharides. Some of these correlations were investigated in detail in the work by Longinotti at al. 33 In this work, the experimental viscosity of aqueous solutions of sucrose and trehalose was analyzed over a wide range of concentrations and temperatures, covering the normal liquid and supercooled liquid regions. In this way, the authors obtained, for example, tting parameters to be employed in the empirical correlation by Genotelle. 32 We decided to use this correlation, in its range of validity, for validating the results obtained by simulations. Thus, in the last column of Table 3 we list some values of sucrose or trehalose viscosity, obtained using Genotelle equation (GE). 32 As can be seen comparing the values by Genotelle equation and by simulations, the change in viscosity upon concentration and temperature was fairly well predicted by Molecular Dynamics. Moreover, the periodic perturbation method was much more accurate than the Stokes-Einstein equation. This is not surprising, since the Stokes-Einstein equation is an approximate formula, which works well for spherical solutes at innite dilution only. 34

Molecular dynamics evidence of the water replacement theory Finally, the hydrogen bond network within simulation boxes was analysed so as to validate the water replacement theory. As evident from Table 4, the relative contribution of hydrogen bonding between hGH and excipient increased with increasing excipient concentration. In particular, it was small when the number of water molecules was suciently high, simulations 1, 2, 4 and 5, while it became predominant when the number of water molecules was no more sucient for a complete protein hydration, simulation 3. These data clearly demonstrate that water replacement is dominant in the solid state, when all water has been removed, while preferential exclusion is the prevailing mechanism in the liquid state. In any case, it was possible to observe that trehalose formed hydrogen bonds with the protein to a greater extent with respect to sucrose, and sucrose in its turn was more ecient than lactose as water substitute. Cellobiose was as ecient as trehalose in substituting water molecules. However, this also means that cellobiose and trehalose were excluded from 16


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Table 4: Water replacement parameter as evaluated by simulations Simulation identier

1

2

3

4 5

excipient

χ3 ,%

sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose trehalose cellobiose lactose glucose sorbitol glycine sucrose sucrose

10 13 13 9 20 11 5 16 19 20 15 31 23 16 64 68 67 63 60 59 46 13 14

the protein surface to a lesser extent with respect to sucrose, in line with the previous observations. Finally, glucose, sorbitol and glycine were less ecient than disaccharides as water substitutes. As will be shown later, these results can be correlated with molecular properties of excipients, such as the hydrogen bond propensity parameter γ3 . This nding is extremely interesting, as it could allow easy identication of new excipients, suitable for formulations to be freeze-dried. The results obtained allow an easy and fast choice of the most suitable excipient, which satises the desired requirements of preferential exclusion, vitrication and water replacement. So far, the design of a proper formulation was mainly driven by empirical observations. 17



Thanks to the simulations performed, this choice can now be guided by a deep understanding of phenomena involved.

Eect of cryoconcentration on stabilization mechanisms The stress induced by cryoconcentration on human growth hormone was also investigated in the case of sucrose as cryoprotectant. As can be seen in Figure 4, the increase in the concentration of sucrose had a positive eect on all the stabilization mechanisms, i.e. preferential exclusion, water replacement and vitrication. More specically, the preferential interaction parameter ξ3 decreased at high concentrations. Furthermore, although sucrose was more excluded from the protein surface, the water replacement parameter χ3 increased with increasing sucrose molarity. Finally, the viscosity of the solution became greater as a consequence of cryoconcentration. Thus, it can be concluded that the increase in excipient concentration has a positive eect on protein stability. 15 0.16

16 12 15

9

0.08

w,0

0.12

/

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Page 18 of 30

14

0.04

13

0.00

6 3 0

0.4

0.8

1.2 -1

c , mol l 3

Figure 4: Evolution of ξ3 ( ), χ3 () and viscosity (4) upon increasing sucrose concentration (simulations 4, 5 and 2). Viscosity was measured using the periodic perturbation method.

18


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Comparison with experimental data The results obtained are in good agreement with the preferential exclusion, vitrication and water replacement theories. Moreover, they seem to conrm the results obtained by Salnikova et al., 15 who observed, for the hGH/sucrose formulation, a smaller amount of insoluble aggregate formation after freeze-drying with respect to the hGH/trehalose formulation, as shown in Table 5.

Table 5: Comparison of sucrose and trehalose as excipients for hGH. Data from Salnikova et al. 15 Formulation

hGH/sucrose hGH/trehalose

% insoluble aggregates after freeze-drying 0.35±0.04 5.0 ±0.2

Rate of insoluble aggregate formation in the solid state√ (% insoluble aggregate/ week) 2.38 ± 0.01 1.97± 0.06

The smaller amount of high order aggregates in the sucrose-based formulation, immediately after freeze-drying, may be correlated with the greater extent of the preferential exclusion of sucrose from the protein surface. We can hypothesize that the greater extent of preferential exclusion exhibited by sucrose likely determined stronger destabilization of the unfolded protein with respect to the native one, thus lowering the extent of insoluble aggregate formation. However, as regards stability in the solid state, the preferential exclusion theory does not apply any more and the mechanism of water replacement becomes active. Thus, according to the results obtained in this paper, trehalose should be more eective in avoiding protein aggregation in the solid state and this is conrmed by the experimental observations by Salnikova et al., 15 who observed, for the sucrose formulation in the solid state, a higher rate of aggregate formation, see Table 5. Salnikova et al. 15 did not analyze the eects of cellobiose and lactose, but according to our results cellobiose should lead to an extent of aggregate formation similar to that observed for trehalose, while lactose should be less eective than cellobiose and trehalose as a protectant, having behaviour more similar to that of sucrose. These results are consistent with the 19



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work by Costantino et al., 13 who experimentally showed the great eciency of cellobiose and trehalose as protectants and the worse eciency of lactose, especially in the solid state, see Table 6.

Table 6: Psuedo rst-order rate constants for deterioration of hGH when lyophilized in the presence of various excipients. Data from Costantino et al. 13 Excipient trehalose cellobiose lactose sorbitol

Psuedo rst-order rate constant for deterioration (x10−3 days−1 ) 0.4±0.2 0±0.2 1.3±0.2 3.5±0.3

Costantino et al. analyzed the stabilizing eects of sorbitol as well, and they concluded that it was less ecient than disaccharides, which is in good agreement with our results. Thus, it is possible to write the following eciency classications: 1) eciency in the liquid state (preferential exclusion), sucrose, lactose > trehalose, cellobiose > glucose, sorbitol, glycine, 2) eciency as aggregation kinetic retarders (vitrication theory), disaccharides > sorbitol > glucose, glycine, 3) eciency in the solid state (water replacement), trehalose, cellobiose > sucrose, lactose > glucose, sorbitol >> glycine. The disaccharides were the most ecient excipients, both in the liquid and solid state. Moreover, sugars were in general more ecient than other excipients, as evident from the greater eciency of disaccharides and glucose with respect to glycine.

Correlating molecular properties of excipients with eciency as water substitutes We tried to nd a correlation between the molecular properties of the sugars investigated, determined by mean of the open-source software VEGA ZZ, and their eciency as water substitutes. As can be seen from Table 7, all the disaccharides investigated in this study had the same number of hydrogen bond donors and acceptors, but slightly dierent molecular 20


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Page 21 of 30

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surface areas and volumes. A deeper analysis of these molecular properties revealed that the area to volume ratio seemed to correlate with the degree of the disaccharide eciency in replacing water molecules. In particular, the higher the area to volume ratio was, the higher the disaccharide eciency in replacing water molecules was and, thus, the higher its eciency as a protectant was. This result could be explained considering that with a higher specic surface area the possibility to interact with the protein is enhanced, given that the number of hydrogen bond donors/acceptors is the same for all the molecules considered. In order to extend our observation to molecules with a dierent number of hydrogen bond donors/acceptors, such as glucose, sorbitol or glycine, we introduced the parameter γ3 , see Equation 5. This parameter seemed to correlate with the degree of eciency as water substitutes not only for disaccharides, but also for monosaccharides, such as glucose, and amino acids, such as glycine.

Table 7: Molecular properties of the excipients investigated

sucrose trehalose cellobiose lactose glucose sorbitol glycine

H-bond donors 8 8 8 8 5 6 2

H-bond acceptors 11 11 11 11 6 6 3

Area Å2 339.2 350.6 351.7 332.7 199.3 209.1 100.4

Volume Å3 282.5 281.6 283.1 279.2 155.5 160.9 68.1

Area/Volume Å−1 1.201 1.245 1.242 1.192 1.281 1.300 1.474

γ3 Å−1 22.8 23.7 23.6 22.6 14.1 15.6 7.37

A phenomenological model explaining this result can be derived assuming that the number of hydrogen bonds, N , between a species and the protein is directly proportional to the number, n(rV ), of the species molecules within the volume perturbed by the protein and the molecular parameter γ previously dened. Thus, considering water, component 1, and the

21



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Page 22 of 30

excipient, component 3, it is possible to write,

N1 ∝ n1 (rV )γ1

(6)

N3 ∝ n3 (rV )γ3

(7)

and thus assuming that the proportionality coecient is the same for both water and excipient,

χ3 =

N3 1 = γ V) N1 + N3 1 + γ31 nn13 (r (rV )

(8)

The values of n1 (rV ) and n3 (rV ) have been evaluated in this work using molecular dynamics, but they are also experimentally accessible; in fact, they can be obtained from the interaction parameter ξ3 (9)

ξ3 = A3 − g3 A1 V

= v3 n3 (rV ) + v1 n1 (rV )

A3 M3 n3 (rV ) = n1 (rV ) A1 M1

(10) (11)

where V is the volume of liquid perturbed by the protein, v is the molecular volume, and M is the molar mass. Combining Equations 9 to 11, it is possible to obtain

n3 (rV ) = n1 (rV )

V M3 v3 M2

v1 M3 v3 M1

V M3 v3 M2

+ g3

− ξ3

−

v1 M3 M1 v3 M1 M3

(12)

which, substitued in Equation 8, allows the evaluation of χ3 . Figure 5 shows the model tting of simulations data. As can be seen from the graph, the χ3 values obtained with GROMACS t fairly well with those predicted by the model. This is an important result considering the simplicity of the model and the total absence of tting parameters. 22


Page 23 of 30

0.8

, gromacs

0.6

y = x 0.4

0.2

3

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


0.0 0.0

0.2

0.4

0.6

0.8

, model

3

Figure 5: Model tting of simulations data. On the x- and y-axis the parameter χ3 as evaluated by the model and by simulations with gromacs is shown, respectively.

Finally, using the model it was possible to calculate a contour plot showing χ3 values upon modication of dierent variables. For example, Figure 6 shows the χ3 variation when the interaction parameter ξ3 and the excipient concentration g3 are changed for both sucrose and glycine. As general guideline, a large number of hydrogen bond donors and acceptors is an important requirement for an excipient, especially in the solid state. However, this is not sucient, since these hydrogen bond sites must also be available for bonding with the protein. All these aspects are condensed in the parameter γ3 , which should be as high as possible for a good lyoprotectant. This parameter can be easily evaluated, without performing time-consuming experiments or simulations. Thus, it could eciently guide the choice of a suitable protectant. As regards preferential exclusion, drawing similar conclusions is more dicult, but future work will address this problem as well. In any case, our work conrms that disaccharides are the most eective excipients, both in the liquid and solid state.

23



0.3

(a) sucrose

0.2

80 3

60

0.1 3

1

40

0 2

20

-0.1 3 -0.2 0

5

10

g3

0.3

(b) glycine

0.2

0 80 3

60

0.1 2 3

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 24 of 30

40 01 20

3

-0.1 -0.2

0 0

5

g3

10

Figure 6: Contour plot showing the variation of χ3 (colour bar) as evaluated by the model, upon modication of ξ3 and g3 for (a) sucrose and (b) glycine. The points indicated with 1, 2 and 3 correspond to the three dierent simulations performed for each excipient, see Table 1.

24


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Conclusions In this paper, molecular dynamics was used to better understand the phenomena at the basis of protein stabilization during freezing. Simulations made it possible to study the eects of various excipients, including sugars, polyols and amino acids, on the freezing stability of human growth hormone. We tested the validity of the preferential exclusion, vitrication and water replacement theories, using an approach based on molecular simulations. Moreover, our results seem to be in line with experimental observations. Simulations were found to provide insight into cryo-protection mechanisms and allowed validation of the most important theories hypothesized in the literature. This study has furthermore demonstrated the possibility to use molecular dynamics as an eective and economic tool for testing the eciency of an excipient as a cryoprotectant, without need of experimental campaign. This would allow a signicant saving of time. Moreover, we found a molecular parameter, easy to evaluate, which seems to correlate with the eciency of the excipient as a water substitute. Future work will use the systematic approach here developed in order to nd and explain at molecular level the rules governing the choice of an appropriate formulation. The objective is that of discovering, using an economic and rational approach, the most suitable formulation for biopharmaceuticals. This would be a signicant achievement, especially considering the increasing importance of protein drugs as therapeutics for human diseases.

Acknowledgement The authors thank the hpc@polito team, which provided the computational resources for simulations (http://www.hpc.polito.it).

25



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Graphical TOC Entry In this paper, molecχ3 ular dynamics is used to investigate the role of excipients, particularly carbohydrates, in protein stabilization during freezing. Using hGH as model protein, γ3 we show that molecular simulations can be an eective tool for testing the eciency of excipients.

ξ3

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

30


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Stability of Proteins in Carbohydrates and Other Additives during

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