Molecular dynamics study of unfolding of lysozyme in water and its mixtures with dimethyl sulfoxide

Accepted Manuscript Title: Molecular dynamics study of unfolding of lysozyme in water and its mixtures with dimethyl sulfoxide Authors: Igor A. Sedov, Timur I. Magsumov PII: DOI: Reference:

S1093-3263(17)30233-4 http://dx.doi.org/doi:10.1016/j.jmgm.2017.07.032 JMG 6991

To appear in:

Journal of Molecular Graphics and Modelling

Received date: Revised date: Accepted date:

27-3-2017 28-7-2017 30-7-2017

Please cite this article as: Igor A.Sedov, Timur I.Magsumov, Molecular dynamics study of unfolding of lysozyme in water and its mixtures with dimethyl sulfoxide, Journal of Molecular Graphics and Modellinghttp://dx.doi.org/10.1016/j.jmgm.2017.07.032 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Molecular dynamics study of unfolding of lysozyme in water and its mixtures with dimethyl sulfoxide

Igor A. Sedov* and Timur I. Magsumov

Chemical Institute, Kazan Federal University, 420008, Kremlevskaya 18, Kazan, Russia * e-mail: [email protected] Phone: +79600503916

Graphical abstract

Highlights:

 Direct determination of protein unfolding times from MD simulation trajectories  DMSO accelerates lysozyme unfolding into random coil-like structures  Water preserves compact globular state even with disrupted native contacts and secondary structure  Increase in preferential solvation with DMSO during denaturation

Abstract All-atom explicit solvent molecular dynamics was used to study the process of unfolding of hen egg white lysozyme in water and mixtures of water with dimethyl sulfoxide at different compositions. We have determined the kinetic parameters of unfolding at a constant temperature 450 K. For each run, the time of disruption of the tertiary structure of lysozyme tu was defined as the moment when a certain structural criterion computed from the trajectory reaches its critical value. A good agreement is observed between the results obtained using several different criteria. The secondary structure according to DSSP calculations is found to be partially unfolded to the moment of disruption of tertiary structure, but some of its elements keep for a long time after that. The values of tu averaged over ten 30 ns-long trajectories for each solvent composition are shown to decrease very rapidly with addition of dimethyl sulfoxide, and rather small amounts of dimethyl sulfoxide are found to change the pathway of unfolding. In pure water, despite the loss of tertiary contacts and disruption of secondary structure elements, the protein preserves its compact globular state at least over 130 ns of simulation, while even at 5 mole percents of dimethyl sulfoxide it loses its compactness within 30 ns. The proposed methodology is a generally applicable tool to quantify the rate of protein unfolding in simulation studies.

Keywords: molecular dynamics; unfolding; lysozyme; tertiary structure; secondary structure; kinetics

1. Introduction

The rate and mechanism of denaturation of proteins may significantly vary with the changes in temperature, pressure, pH, ionic strength, and addition of various chemicals. Hen egg white lysozyme (HEWL) is a popular protein to study its denaturation under various conditions. Numerous works have been devoted to the thermodynamic and kinetic stability of lysozyme in pure water and in the presence of various additives and denaturants [1–5]. The significance of

these works is connected with the advantages of aqueous-organic solvents as media for enzymatic processes and search for the ways to improve the stability of proteins in solutions. Many common water-miscible organic solvents can lower the melting point of proteins. Dimethyl sulfoxide (DMSO, (CH3)2SO) is a low toxic solvent commonly used for solubilization of drugs and as a component of penetrating cryoprotectants for biological samples. Promotion of unfolding of lysozyme with DMSO was analyzed by means of differential scanning calorimetry (DSC) [6,7] in solution, which can provide the data on the temperature and enthalpy of denaturation and the heat capacities of the native and denatured forms of protein, and various spectroscopic techniques offering information on the changes in secondary and/or tertiary structure of protein upon unfolding. The maxima on DSC curves of HEWL corresponding to its melting point in solution steadily decrease with addition of growing amount of DMSO reaching room temperature at 35-50 mole percent of DMSO (depending on pH of the buffer). CD spectra indicate the loss of secondary and tertiary structure of lysozyme upon thermal unfolding in pure water [8]. The presence of DMSO leads to a strong absorption in the far UV region limiting the possibilities of this method. Small angle neutron scattering study of solution of lysozyme in the mixtures of pure water with DMSO at room temperature [9] has shown that it unfolds into a molten-globule like state with the loss of tertiary and partial preservation of the secondary structure in the range of DMSO mole fractions 0.37 to 0.7, while higher concentrations lead to complete unfolding into a random coil. Kinetics of thermal denaturation and renaturation of lysozyme in water has also been studied experimentally, and the possibility of intermediate formation was discussed. Some researchers suggest all-or-none model of lysozyme unfolding denying the existence of sufficiently stable intermediates [10], while others prove the existence of intermediates [11] or reversibly and irreversibly denatured forms in solution [12]. It is known that addition of organic solvents can alter the pathway of denaturation, and change the relative rates of disruption of secondary and tertiary structures [13]. The effect of particular denaturants on the mechanism of protein unfolding is still poorly known, and most of the experimental methods cannot provide a detailed information on it.

Explicit-solvent molecular dynamics simulations can reproduce temperature-induced unfolding of proteins in water at 400–500 K in nano- to microsecond timescale [14] and allow to observe directly the pathway of unfolding and its change with the change of various factors. Despite the difference in temperature from the experimental conditions, this approach is widely used and has led to many fruitful results agreeing with the experiments [15–17]. However, simulations of proteins in aqueous-organic media are still quite scarce. It should be noted that prior to such simulations, a model of organic solvent should be carefully parameterized to produce a good agreement with the experimental properties of its mixtures with water. In a recent work [18], simulations of lysozyme at 300 K in the mixtures of water with 0 to 40 mole percent of DMSO were reported, but no direct observation of unfolding is possible at such temperature and reasonable simulation times. In the present work, we study the influence of solvent composition on the rate of unfolding at different temperatures and obtain quantitative kinetic data by averaging the results of multiple simulations. The rates of disruption of tertiary and secondary structure in simulations are compared. Possible links with the tendencies learned from the previous experimental studies are discussed.

2. Methodology

Molecular dynamics simulations were conducted using Gromacs 5.1 software [19]. We used OPLS force field in conjunction with SPC/E water model. The molecule of DMSO was modeled using united atom approach with the partial charges on atoms, geometric and intermolecular interaction parameters taken from literature [20,21]. In the protein, all hydrogens were considered explicitly. During the simulations, all the bonds were kept rigid with the LINCS algorithm. A cutoff for short-range electrostatic and van der Waals interactions was 1.0 nm. The particle mesh Ewald method was used to compute long-range electrostatic interactions. The constant temperature was maintained by v-rescale algorithm. In constant-pressure simulations, a Parrinello-Rahman barostat was used.

The physical properties of DMSO + water binary mixtures with different compositions were calculated using standard Gromacs routines from 10 ns-long trajectories in NPT ensemble after 1 ns of preliminary equilibration. Each simulation cell contained a total of 10000 molecules of solvent, while the fraction of DMSO x1 was varied from 0 to 1. In Table 1, the experimental (interpolated from the literature data [22,23]) and simulated densities of the mixtures are compared. They are in good agreement with each other. The self-diffusion coefficients of the mixture components also show in agreement with experimental data (Fig. 1), and the concentration dependence of the enthalpy of mixing of water and DMSO at 298 K is qualitatively reproduced (Table 2). The positive deviations of the calculated enthalpies indicate slightly underestimated DMSO-water interactions in comparison with water-water and DMSODMSO interactions. The mixture does not separate into organic and aqueous phases during simulation at any of the considered compositions and temperatures. More values of the physical properties of DMSO + water mixtures calculated using this model have been compared with the experimental results in the work [20].

The initial structure of HEWL was an X-ray structure from the Protein Data Bank (193L) [26]. It was placed together with 10000 molecules of water and 8 Cl– ions to make the total charge zero in a cubic simulation cell with the periodic boundary conditions. The system was minimized and equilibrated at 298.15 K and 1 bar pressure first for 100 ps with position restraints on heavy atoms of the protein, then for 1 ns without restraints. The resulting protein structure was cut and used in further simulations. The process of unfolding of lysozyme was studied in similar periodic cells containing in total 10000 molecules of solvent (both DMSO and water). The fraction of DMSO x1 was varied with the step 0.05 mole fraction units for x1 from 0 to 0.30, with the step 0.10 from 0.30 to 0.60, and with the step 0.20 from 0.60 to 1. At room or slightly elevated temperature, unfolding goes slowly and will take enormous amount of computational time. We conducted the simulations starting from the native structure at 450 K for all the mentioned concentrations of DMSO. According to Arrhenius equation, for a process with 100 kJ·mol–1 activation energy as reported

for lysozyme unfolding [27], a decrease in temperature from 450 to 400 K will lead to a 28-fold increase in average time of unfolding, which will become equal to hundreds of nanoseconds. Nevertheless, we also studied unfolding starting from a partially unfolded structure at 400 K and x1 from 0 to 0.20 with the step 0.05 (more details below). The temperature in our simulations is higher than the boiling point of SPC/E water at 1 bar pressure (397 K[28]). Even though the mixtures containing DMSO may not boil at simulation temperature and 1 bar pressure, their density decreases very significantly in comparison with that in real unfolding experiments at 330 – 350 K. An alternative is to keep the density the same as at low temperature by using NVT simulation box, but in this case the pressures are so large that they can influence the pathway of unfolding process[29]. Our approach offers a compromise between the high pressure and low density: each cell was minimized and heated up to 400 K in NPT ensemble at p = 1 bar for a short time (200 ps) with position restrained protein. Then the volume of the cell was fixed and it was heated up in NVT ensemble to 450 K (or left at 400 K in experiments with partially unfolded structure) and equilibrated at this temperature for 1 ns. After that, the position restraints were turned off and a production run under NVT conditions was performed. When the runs were repeated for the same system, we always started from the configuration obtained after NPT equilibration at 400 K.

3. Results and discussion

3.1. Choice of the methods to monitor unfolding

A general difference between unfolding in pure water and in its mixtures with DMSO is clearly seen even after visual inspection of trajectories. In all our simulations in mixtures (10 repetitions for each solvent composition), even at 5% of DMSO, the protein lost its tertiary structure in less than 30 ns and came to a state with significantly less dense packing. At higher concentrations of DMSO, 30 ns-long trajectories end with a structure resembling a random coil. In contrast, in all 10 simulations in water the compact structure of lysozyme kept over the whole

time of simulation, which was equal to 130 ns. However, the secondary structure and tertiary contacts became disrupted, but not as quickly as in the presence of DMSO. We tried to translate the results of simulations into the language of chemical kinetics by averaging the time until protein unfolding over a number of repetitive simulations for the same system, which allows to determine the rate constant given by k = 1/. There is a number of difficulties associated with such approach. The transition between folded and unfolded forms takes significant time and it is difficult to say exactly when the protein becomes unfolded. We can only tell when the changes become prominent using different assumptions and critical values of structural parameters. The tertiary and secondary structures may disappear with different rates. The secondary structure is often lost only partly (as in a molten globule state). It is disrupted with different rates for different parts of a molecule or for different types of structures, and certain elements often form again after their disruption. It should also be understood that the loss of compactness always means the loss of tertiary (but not secondary) structure, while the reverse is not true: the protein may loss tertiary contacts but remain in a globular state. To calculate the number of the elements of secondary structure in HEWL, we used DSSP algorithm. For the criterion of disruption of the tertiary structure, many different parameters can be suggested. We have compared several of them, namely total Cα-RMSD, radius of gyration Rg, hydrophobic SASA, and the fraction of native contacts (FNC). In addition, visual analysis of simulation trajectories shows that at the early stages of the process of unfolding in the binary mixtures the contact between two α-helices in HEWL molecule is lost (Fig. 2). This leads to a huge increase in the radius of gyration and SASA due to the loss of compactness, and soon unfolding of the helices. After this, the protein has a low probability to fold back. Thus, we can view the loss of contact between the residues 6 to 21 and 89 to 100 of HEWL as a critical event for transition from the globular state to the unfolded form. The distances d1 between the Cαatoms in His15 and Thr89 residues and d2 between the Cα-atoms in Arg21 and Ser100 residues were monitored during the simulations. Their sum D = d1 + d2 was chosen as another parameter to judge about the loss of the tertiary structure.

3.2. Time of unfolding of the tertiary contacts

To determine the time of (the beginning of significant) unfolding of the tertiary structure tu, we used the following critical values: 0.7 nm for Cα-RMSD, 1.6 nm for Rg, 36 nm2 for hydrophobic SASA, 3.15 nm for D, 0.75 for the fraction of native contacts. They are chosen to be approximately equal to the halves of the sum of the average values of those magnitudes for the native state and undoubtedly unfolded states after long simulation times. The critical value of D is chosen to be 2 times higher than the average sum of distances His15–Thr89 and Arg21– Ser100 in the native state. All the parameters were calculated each 2 ps and averaged over 200 ps to minimize random fluctuations. We also tried to quantify the time before unfolding of the tertiary structure by subjective visual analysis of trajectories. The plots of SASA and D against time often have a sharp increase at tu (see Fig. 3 for a good example), while other parameters usually have less pronounced changes. The absence of a well-pronounced jump should lead to a higher uncertainty in the values of tu. In addition, SASA shows less oscillating behavior than other parameters. The unfolding times determined using each method and averaged over 10 simulations for each solvent composition are given in Table 3. Results from different methods are in general agreement with each other and with visual analysis (see Fig. 4). The unfolding time decreases with DMSO fraction increasing up to 0.2–0.3 and does not change significantly in the mixtures with larger content of DMSO. It is interesting that this plot resembles the concentration dependence of self-diffusion coefficients of water in its mixtures with DMSO, at least below 80 mole % of DMSO (Fig. 1). In pure water, the rate and mechanism of unfolding are very different even from the mixture containing 5 mole % of DMSO. The critical values of SASA and Rg are not achieved even after 130 ns of simulation, because the globular structure of HEWL remains. The critical value of Cα-RMSD is reached at some point, resulting in an average tu = 57±22 ns, but this magnitude is sensitive to the changes in the structure of any part of the protein molecule,

including secondary structure. (See Fig. 5 for visual comparison of sample trajectories in different solvent media). Thus, it is more correct to judge about loss of tertiary contacts using the values of FNC or D that characterizes only two particular contacts. The critical values used for the mixtures with DMSO lead to the following average value of tu in water: 53±15 ns (FNC criterion) and 55±24 ns (D criterion). This is much higher than for any of the mixtures.

3.3. Unfolding of the secondary helical structure

The changes in secondary structure were analyzed using DSSP method. The total content of residues belonging to alpha- and 310-helices was monitored. The beta structures were not analyzed because their content is initially 2 times lower than that of helical structures, which makes the results much more sensitive to the fluctuations, and due to formation of non-native beta structures. Similar to the analysis of the tertiary structure parameters, the helix contents were averaged over 200 ps. The “half-life time” of the secondary helical structure tsec/2, which is the time when less than a half of the initial number (43) of residues belonging to helices remains in helical conformation, was calculated and averaged over all trajectories at the same solvent composition. In Fig. 6, the dependence of on the fraction of DMSO is plotted. In additions, for each trajectory the fraction of remaining helices fhel was calculated at the time tu (according to the critical value of hydrophobic SASA). These values were also averaged over repetitive runs. The dependence of on the mixture composition is shown in Fig. 7.

It is clear that in pure water the secondary structure is also disrupted much slower than in the presence of DMSO. The fraction of the helices at the time tu is slightly less at lower than at high DMSO contents. At any solvent composition we can say that a significant part of secondary structure remains after the start of unfolding of tertiary structure, and some of the elements may keep at least during the whole 30 ns of simulation.

3.4. Simulations starting from a partially unfolded structure

It is desirable to model the unfolding process at the lowest possible temperature because we get closer to the experimental conditions of unfolding. However, with decreasing temperature the time of unfolding and the computational time of simulations grow up. In order to justify the concentration dependence of the structural stability of lysozyme and to show that the tendencies observed at 450 K will keep at lower temperatures, we have studied the process of unfolding at 400 K starting from the partially unfolded structure of lysozyme (critical values of the unfolding criteria are not reached) from one of the previous simulations. This structure is shown in Fig. 9 in comparison with the starting structure used in simulations at 450 K. We conducted a series of 20 simulations with the length of 10 ns for the fractions of DMSO x1 from 0 to 0.20 with the step 0.05. The results are shown as a histogram of unfolding times determined using the FNC criterion (Fig. 10).

The tendency to decrease of the unfolding time with addition of DMSO is reproduced. While only one from 20 runs led to unfolding of HEWL in water, at 5 percents of DMSO it started to unfold within 10 ns in 13 cases. The number of runs in which the protein starts to unfold in less than 4 ns grows up from 5 to 13 when the fraction of DMSO increases from 5 to 20 mole percents.

3.5. Further discussion

The most obvious distinction of simulations in pure water is, of course, preservation of the compact state of HEWL even after breakup of the tertiary contacts. In the presence of DMSO, degradation of secondary structure and destabilization of tertiary contacts lead to soon disruption of the globule. The difference in the pathways can be clearly shown using property space histograms. These histograms can be constructed by plotting the negative logarithm of the number of frames  ln N ( p1 ,.., pi ) within a simulation trajectory(-ies) for which certain

structural parameters p1 ,.., pi of the protein lie in the range [ p1 , p1  p1;...; pi , pi  pi ] , where

p1 ,..., pi are parameter bin sizes, against the values of parameters p1 ,.., pi , resulting in an i+1dimensional histogram. We binned the values of FNC and SASA parameters taken each 2ps from all the simulations at the same concentration of DMSO. The resulting plots with the values of  ln N shown in color scale are given in Fig. 10. We see that the pathways of unfolding in pure water and in the presence of DMSO are different, while an increase in concentration of DMSO results in speeding up the unfolding process without the change of the pathway.

It is known from the experiment that thermally denatured state of lysozyme has a value of Rg not less than 1.8 nm [29,30], which is much larger than that we obtained for the globules in simulations in pure water. Thus, we have observed a kinetically stable intermediate, which should lose compactness after some more time. When we tried to perform a simulation of unfolding in water at 600 K, the protein unfolded into random coil-like states with large Rg after 5 ns. Previous simulations of thermal unfolding of HEWL in water have also shown the relative stability of a globule and disruption of significant part of the helical structure during 10 ns in NPT ensemble at 500 K and 1 atm using CHARMM force field [30]. However, the final values of Rg (1.52–1.68 nm) were significantly larger than in our study. The difference is likely to be explained by a larger kinetic stability of the native state in OPLS force field [14]. GROMOS force fields promote unfolding even more than CHARMM, resulting in an increase of Rg of HEWL up to 1.6 nm even after 100 ps of simulation at 500 K [31,32]. On the other hand, simulations of chemical denaturation of lysozyme in 8M urea (CHARMM force field) [33] have shown a quick loss of the compact state even at 310 K. Experimental studies of kinetics of thermal or chemical unfolding of HEWL are not numerous. In the study of time dependence of viscosity of aqueous lysozyme solutions, which is directly dependent on the radius of gyration of a protein, it took several hours for the viscosity to begin to rise even at the temperatures 5–10 degrees above the melting point of HEWL in water[35]. This fact is in agreement with our conclusion about kinetically stable globular

unfolding intermediate in water. Thermodynamic DSC and spectroscopic studies indicate that the thermal stability of lysozyme as measured by its melting point steadily decreases when the concentration of DMSO increases [6,7]. A correlation between the rate constants of unfolding and the melting points was reported[36]. The rate constants of unfolding ku estimated from the experiments using this correlation will grow up with increasing fraction of DMSO, which means a decrease in the times of unfolding. The most straightforward explanation of higher stability of a globule in water than in the presence of DMSO is that its destruction increases the hydrophobic surface area, which is unfavorable, while DMSO can preferentially solvate the hydrophobic side chains. An increase in preferential solvation of transition state in the process of unfolding with DMSO molecules in comparison with the initial native state may also explain its unfolding acceleration effect. The growth of amount of DMSO in solvation shell of lysozyme upon heat denaturation in DMSO + water mixtures was observed experimentally using scanning microcalorimetry technique [37]. We have compared the compositions of solvation shells of a native state, a partially unfolded state (shown in Fig. 8), three unfolded states produced after 30 ns of simulation in DMSO + water mixture, and three compact states with disrupted native contacts produced after 130 ns of simulation in pure water. For each of these states, we conducted 10 ns-long simulations in 1:1 (x1 = 0.5) DMSO + water mixture with position-restrained heavy atoms of protein at 450 K recording the configurations each 2 ps. The mole fraction of DMSO within 0.5 nm thick solvation shell of HEWL averaged over all configurations was 0.387 for a native state, 0.462 for a partially unfolded state, 0.515, 0.508, 0.522 for three unfolded states from DMSO + water mixtures, and 0.391, 0.407, 0.400 for three compact states from simulations in water. (Schematic representations of the solvation shells are given in Supplementary section.) The fraction of water in solvation shell decreases during the process of unfolding in a row native > partially unfolded > unfolded state, while solvation with DMSO becomes more favorable upon exposure of the hydrophobic surface. This is in agreement with the experimental findings [37]. The intermediate compact state formed in water interacts with DMSO in a relatively unfavorable way and therefore does not form in DMSO + water mixtures during the process of unfolding.

4. Conclusions

In simulation studies, it is not simple to decide when the protein goes from the native to unfolded form. Our approach uses critical values of easy-to-compute structural parameters and can be applied to various proteins under various conditions. Another important thing for computational studies of unfolding kinetics is sufficient number of repetitive runs for each system. The confidence interval for the mean value decreases inverse proportionally to the square root of the number of repetitions, but the computational cost grows up proportionally to it. We have found that 10 repetitive runs in our case are enough to observe the concentration dependence of the times of unfolding. From the simulations, we have learned that even small amounts of DMSO greatly speed up and change the pathway of unfolding. In water, the compact globular state with disrupted tertiary and secondary structure is stable within hundreds of nanoseconds while DMSO favors rapid unfolding into random coil-like structures. An increase in preferential solvation of transition state with DMSO molecules in comparison with the initial native state is likely to cause its unfolding acceleration effect.

Acknowledgement

This work was supported by grant 14.Y26.31.0019 from the Ministry of Education and Science of Russian Federation.

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Fig. 1. Self-diffusion coefficients of DMSO (1) and water (2) in their binary mixtures from experiment [25] and our simulations at 298 K

3

DMSO (MD)

Dself (105cm2s 1 )

Water (MD) DMSO (exp)

2

Water (exp)

1

0 0

0.2

0.4

x1

0.6

0.8

1

Fig. 2. Native structure of HEWL and the residues forming contacts that have been used to determine the time of unfolding

Arg21

Ser100

Thr89

His15

Fig. 3. Example plots of D, radius of gyration Rg, hydrophobic SASA, and Cα-RMSD against time for a single simulation of HEWL in the mixture of 30 mole % of DMSO with water at 450 K 2.8

2.5

RMSD(nm) Rg(nm) D(nm) SASA(nm2)

2.0

12

70

10

60

8

50

6

40

1.0 4

30

2

20

0 30000

10

1.6 0.5

1.2

0.0 0

5000

10000

15000

t (ns)

20000

25000

SASA(nm2)

1.5

D(nm)

2.0

RMSD(nm)

Rg(nm)

2.4

Fig. 4. The dependences of on the mole fraction of DMSO x1 in simulations at 450 K determined using critical values of a) radius of gyration (Rg), b) hydrophobic SASA, c) CαRMSD, d) sum of the distances between particular pairs of residues (D), e) fraction of native contacts (FNC). Solid line connects the average of values from all the five approaches for each concentration. 60

60

Rg

40 30 20

30 20

10

0

0

0.2

0.4 x 0.6 1

0.8

0

1

0.2

0.4 x 0.6 1

0.8

1

b)

80 70 60 50 40 30 20 10 0

80

RMSD

D

60

 tu  (ns)

 tu  (ns)

a)

40

20 0

0

0.2

0.4

x1

0.6

0.8

1

c)

0 d)

70 60 50 40 30 20 10 0

 tu  (ns)

FNC

0 e)

40

10

0

SASA

50

 tu  (ns)

 tu  (ns)

50

0.2

0.4

x1 0.6

0.8

1

0.2

0.4

x1 0.6

0.8

1

Fig. 5. Time dependences of different structural parameters of lysozyme in pure water, 30 mole % of DMSO, and pure DMSO at 450 K from one representative trajectory: a) radius of gyration (Rg), b) hydrophobic SASA, c) Cα-RMSD, d) sum of the distances between particular pairs of residues (D), e) fraction of native contacts (FNC). Red line corresponds to the chosen critical values of parameters – the “border” between folded and unfolded states.

0% 30% 100%

b

50

30

2.5

c

0% 30% 100%

2

RMSD(nm)

SASA(nm2 )

70

1.5 1 0.5

10

0 0

10

20

30

40

50

60

t(ns) 12

0% 30% 100%

10

D(nm)

8

6 4 2 0 10

20

30

40

50

60

t(ns) 1.2

0% 30% 100%

e

1

FNC

0.8 0.6

0.4 0.2 0 0

10

20

30

t(ns)

10

20

30

t(ns)

d

0

0

40

50

60

40

50

60

Fig. 6. Dependence of the average “half-life time” of the secondary helical structure on the mole fraction of DMSO x1 in simulations at 450 K

Fig. 7. Average fraction of helical secondary structure that remains at the moment tu of the start of unfolding of the tertiary structure of HEWL in the mixtures of DMSO (1) with water (2) in simulations at 450 K

Fig. 8. Comparison of the native (red) and partially unfolded (green) lysozyme used as the starting structures in simulations at 450 and 400 K respectively

Fig. 9. Histogram of unfolding times of lysozyme from a partially unfolded structure at 400 K and different contents of DMSO. Numbers are the number of simulations in which HEWL unfolds within a certain time.

1

2

2

1 1

1

8-10 ns

7 3

2 19

4

3

>10 ns

5

6-8 ns 4-6 ns

3

2-4 ns

1

0-2 ns 5

11 8

9

4 1

1

0

5

2

2

2

10

15

20

x1

Fig. 10. 2D property space histograms for the process of unfolding of HEWL at 450 K and different concentrations of DMSO. The most populated areas are colored with red, zero population is indicated with blue.

5

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

FNC

FNC

Water

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3 20 30 40 50 60 70 80 SASA

20 30 40 50 60 70 80 SASA

DMSO

15

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

FNC

FNC

10

0.6

DMSO

0.6

0.5

0.5

0.4

0.4

0.3

0.3 20 30 40 50 60 70 80 SASA

DMSO

20 30 40 50 60 70 80 SASA

DMSO

25

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

FNC

FNC

20

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3 20 30 40 50 60 70 80 SASA

20 30 40 50 60 70 80 SASA

DMSO

40

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

FNC

FNC

30

0.6

DMSO

0.6

0.5

0.5

0.4

0.4

0.3

0.3 20 30 40 50 60 70 80 SASA

DMSO

20 30 40 50 60 70 80 SASA

DMSO

60

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

FNC

FNC

50

0.6

0.5

0.4

0.4

0.3

0.3

80

20 30 40 50 60 70 80 SASA

DMSO

100

1.0

1.0

0.9

0.9

0.8

0.8

0.7

0.7

FNC

FNC

0.6

0.5

20 30 40 50 60 70 80 SASA

0.6

DMSO

0.6

0.5

0.5

0.4

0.4

0.3

0.3 20 30 40 50 60 70 80 SASA

DMSO

20 30 40 50 60 70 80 SASA

Table 1. Experimental and simulated densities of DMSO (1) + water (2) binary mixtures at 298 and 338 K and 1 bar pressure

ρ298 x1

(MD), ρ298

(exp)

[22], ρ338

(MD), ρ338

g·ml–1

g·ml–1

g·ml–1

g·ml–1

0.0

0.997

0.998

0.973

0.981

0.1

1.038

1.042

1.005

1.018

0.2

1.061

1.072

1.025

1.041

0.3

1.076

1.088

1.037

1.054

0.4

1.086

1.095

1.047

1.060

0.5

1.091

1.097

1.051

1.061

0.6

1.093

1.096

1.054

1.061

0.7

1.095

1.095

1.056

1.060

0.8

1.096

1.096

1.058

1.058

0.9

1.097

1.096

1.060

1.057

1.0

1.099

1.096

1.061

1.056

(exp)

[23],

Table 2. Experimental and simulated molar enthalpies of mixing of DMSO (1) with water (2) at 298 K and 1 bar ΔmixH

ΔmixH (exp)

(MD),

[24],

kJ·mol–1

kJ·mol–1

0

0.00

0.00

0.1

–0.65

–1.47

0.2

–1.15

–2.33

0.3

–1.53

–2.72

0.4

–1.73

–2.74

0.5

–1.66

–2.51

0.6

–1.35

–2.11

0.7

–0.87

–1.61

0.8

–0.42

–1.07

0.9

–0.11

–0.52

1

0.00

0.00

x1

Table 3. Average times (ns) of unfolding of the tertiary structure of HEWL in mixtures of DMSO (1) with water (2) determined using different approaches from simulations at 450 K*

x1

SASA

D

Cα-RMSD

Rg

FNC

Visual

0.05

20.1±5.5

16.2±5.3

16.0±5.7

19.0±5.5

15.9±4.6

17.8

0.1

11.3±3.7

10.5±2.7

10.8±2.8

10.6±3.6

10.4±2.6

10.9

0.15

9.5±2.8

8.6±2.3

9.7±2.4

8.8±2.1

10.3±3.1

10.6

0.2

7.9±1.8

7.0±2.2

8.5±2.2

7.5±2

8.3±1.9

8.1

0.25

7.8±1.4

9.0±2.6

8.0±1.7

7.4±1.6

7.9±1.3

8.5

0.3

7.8±1.8

6.7±1.3

7.7±1.3

6.8±1.2

8.2±1.9

7.6

0.4

7.0±1.4

7.5±2.9

7.6±2.1

6.6±1.7

8.2±1.9

7.5

0.5

8.0±1.3

8.2±3.2

9.3±2.1

8.0±1.7

8.7±1.6

7.5

0.6

7.0±2.2

6.5±2

8.6±2.6

7.0±2.3

8.3±2.3

7.3

0.8

7.7±0.9

6.9±1.6

10.5±2.4

8.2±1.8

10.4±2.2

8.7

1

7.4±3

9.1±2.9

8.8±3.3

7.0±2.9

8.8±3.2

8.4

* Individual values of times of unfolding for each run and criterion are given in Supplementary material.