In the computational study, we carried out atomistic MD simulations of wtRop and RM6 model proteins at three different temperatures: 300 K, 350 K, and 368 K. Long trajectories have been produced which contain all dynamical information that is needed for our analysis. The model systems that have been simulated in this work are presented in
Table 1. Systems involve one wtRop or RM6 protein (Np), and different numbers of solvent (water) molecules (Ns), total number of atoms in the system (N), and ions of Na
+ (Nions) added to neutralize our systems. All the above, as well as the temperature of the simulation and the sides of the (cubic) simulation box, are shown in
Table 1. wtRop protein in systems NSR1, NSR2, and NSR3, and RM6 proteins MRM1, MRM2, and MRM3 are at their native states.
In the upcoming discussion of the simulation results, different names for each subunit of each protein are used. For wtRop protein, the two subunits (monomers) are referred to as ChainA and ChainB. The complete RM6 molecule is a tetramer comprised of four individual subunits (chains A–D). The antiparallel α-helical pair ChainA and ChainB constitutes the asymmetric unit in the RM6 crystals, being symmetrically related to the second α-helical pair (ChainC and ChainD) via a crystallographic (i.e., exact) twofold axis.
2.2.1. Root Mean Square Deviation (rmsd)
We start the analysis of the atomistic simulations by examining the stability of both model proteins at their native state. A widely used measure for the calculation of the conformational stability of proteins is the root mean square deviation (
rmsd) [
39,
40]. The conformation of the protein is a set of 3D coordinates. We denote the coordinates of the reference structure as
(
t = 0), obtained from the protein data bank, and the coordinates of the protein at any instant time t as
, where
,
, and
the number of atoms of a protein. In the current analysis, the calculation of
rmsd was based on the alpha carbon, Ca, atoms, so
N refers to the number of Ca in the protein. The
rmsd is calculated as a function of time according to Equation (1), by comparing the equivalent pairs of Ca atoms between the reference and the instant structure:
with
being the Euclidean distance between the instant and the reference structure of the
ith Ca atom.
According to the literature [
41,
42],
rmsd values in the range of (0.15–0.25) nm suggest a high degree of similarity to the reference structure. However, the resolution of the experimental structure determination is an important factor for the
rmsd values; in particular when the initial structure is provided by X-ray crystallography [
42], the
rmsd values tend to increase and their interpretation is harder if the two proteins being compared have been refined crystallographically at different resolutions [
42]. In terms of the
rmsd analysis presented here, the Ca atoms of the seven tail residues of each subunit have been excluded for both proteins, because of the well-known high flexibility of tail parts [
43]. Furthermore, in the case of the RM6 protein, the initial four Ca atoms of each chain were also excluded since they were not given in the initial structure.
Figure 2a illustrates the
rmsd values of wtRop as a function of time during the MD simulation at 300 K (blue line), 350 K (green line), and 368 K (red line). All averages and error bars were calculated through average blocking over the last 100 ns of the produced trajectory. At 300 K, it is clear that the
rmsd is almost stable around ~0.11 nm throughout the whole simulation. This value ensures a rather good simulation model of wtRop [
41]. At 350 K, the
rmsd values seem to be almost stable around the value ~0.14 nm up to ~150 ns whereas, later on an abrupt increase is observed and an almost stable value of ~0.32 nm is attained beyond ~175 ns. So,
rmsd at 350 K shows a late departure from the structure of the native state, as a result of temperature increasing, attaining a different conformational state. However, with a further increase of temperature to 368 K, conformational change of wtRop is observed immediately and after ~100 ns, the
rmsd values tend to be stabilized around ~0.30 nm. The bigger values indicate a greater deviation from the initial structure.
The corresponding
rmsd curves as a function of time of the RM6 protein, at all three different temperatures, are presented in
Figure 2b. At both 300 K (blue curve) and 350 K (green curve), the
rmsd attains similar values, slightly higher at 350 K, (i.e., ~0.15 nm and ~0.19 nm, respectively), remaining almost stable throughout the simulation. At 368 K (red curve), the
rmsd gradually increases, reaching a value ~0.28 nm, after ~100 ns. Comparing the results for the two proteins, RM6 is found to be less sensitive to temperature increase and hence more thermostable than wtRop in this temperature range.
In
Section 2.1, experimental evidence for thermal stability of both proteins in provided. In agreement with the CD results,
rmsd analysis of our model confirms the instability of wtRop in rising temperatures in contrast to the more stable structure of RM6. However, at the highest temperature value, clear departure from the native state is observed in simulation, whereas a milder change is shown in CD results.
The overlap among the final conformations at the three temperatures (i.e., 300 K (blue), 350 K (green), and 368 K (red)) for wtRop and RM6 is schematically illustrated in
Figure 3a,b, respectively, with the use of the VMD tool [
44]. A good identification in the conformations for both proteins is observed, in terms of α-helical region. Deviations are obvious in the loop region for wtRop and tail regions for both wtRop and RM6. Concerning the α-helical parts, the overlap at high temperatures is better for RM6.
A further quantification of the thermostability of both proteins is provided by the calculation of the percentage of increase of the
rmsd values (%
D), from 300 (which is used as the reference point, since it attains the value of the native state almost constantly) to 350 K and from 300 to 368 K, for both proteins, as a function of time:
In Equation (2),
refers to instant time, with
and
is the total number of configurations and
is the
rmsd value at 300 K, and T stands for 350 K and 368 K. The percentage of increase of
rmsd as a function of time is shown in
Figure 4. The effect of temperature is obviously smaller in RM6, which is rather unaffected up to 350 K, indicating a much higher thermostability in the range of the studied temperatures. Averages over time provide the following values for %
D: from 300 to 350 K ~224% and ~30% for wtRop and RM6, respectively, and from 300 to 368 K and ~211% and ~89% for wtRop and RM6, correspondingly.
The above findings are in good agreement with experimental data for the melting temperature T
m which indicates that T
m ≥ 331 K for wtRop, while for RM6, T
m ≥ 363 K [
37].
2.2.2. Root Mean Square Fluctuation (rmsf)
In order to gain deeper insight into the most sensitive parts (residues) of proteins to temperature stimuli, we computed the
rmsd for each individual residue of a protein, which is typically called the root mean square fluctuation (
rmsf) [
22]. The
rmsf is a numerical calculation for how much a particular residue moves/fluctuates during the simulation. It is plotted versus the residue number and points to the amino acids that contribute the most to the molecular motion.
rmsf is given by:
where
TR is the total time of the simulation,
are the coordinates of atom
of each residue at time
, and
is the reference position of atom
. The computation of
rmsf was done based on the Ca atom of residue. High
rmsf values reveal high flexibility whereas low
rmsf shows limited motion. The time averages of
rmsf per residue for wtRop and RM6 are shown in
Figure 5a,b, respectively. Averaging of
rmsf values for every residue were also performed on the two chains of wtRop and the four chains of RM6, correspondingly.
Figure 5a illustrates the average
rmsf values of wtRop protein at three temperatures, versus the residue index. Fluctuations are enhanced at higher temperatures (i.e., 350 K and 368 K) whereas at 300 K motion is limited. Each chain of wtRop protein consists of 63 residues. Special attention has to be paid to the residues which belong to the loop region and their nearest neighbors (residues 25–33), which seem to be more flexible at any temperature. There is an obvious deformation (i.e., jump in
rmsf) in this region at both 350 K and 368 K which is much less pronounced at 300 K. Different regions of the protein (i.e., N-, C-terminus, α-helices, loop) appear to have different sensitivities at the various temperatures. The higher
rmsf values correspond to the more flexible parts. Therefore, the most flexible are the residues which belong to N-terminal region (residues 1–3) and to the tail region (residues 57–63), followed by the loop region, whereas the residues of α-helices (3–24 and 34–52) are more stable at any temperature. Moreover,
Figure S2 shows the
rmsf values for each individual subunit of wtRop. Differences in the values of the corresponding residues between the two different chains provide an estimation of the confidential interval for these calculations, which ranges between 0.0–0.10, 0.0–0.12, and 0.0–0.18, for 300 K, 350 K, and 368 K, respectively. The corresponding analysis for RM6 is presented in
Figure 5b, where the average
rmsf values of RM6 protein against the index of the residue are shown. RM6 has 58 residues per chain. The
rmsf analysis of RM6 mutant reveals higher flexibility of the N-terminal residues as well as the tail residues compared to the α-helices region, similarly to the wtRop, at all three temperatures. Moreover, flexible end regions are more extended in RM6 (i.e., 1–13 and 35–58, respectively), where temperature effect is mostly apparent, whereas the rest part of the chains seems unaffected by the increase of temperature. In agreement with
rmsd results, this analysis highlights the higher thermostability of RM6 mutant also pointing to the more thermo-sensitive parts of both proteins.
2.2.3. Hydrogen Bonds
At the atomic level, a more detailed investigation can be performed through the computation of the hydrogen bonds (HB) between the various components in all systems, which play an important role in the stability of proteins [
45].
In the following analysis, all average values and error bars were calculated through block averaging over the last 100 ns of the trajectory beyond which
rmsd values remain almost constant.
Table 2 contains the average number of HBs between the various components, i.e., protein-protein (P-P), protein-water (P-W), and water-water per water molecule (W-W/W), for all systems studied here. The results reveal a decrease in the number of HBs within the protein molecule by raising the temperature for both proteins (wtRop and RM6). In wtRop there is a reduction of HBs of about 9.7% at 350 K with no further change with temperature rising to 368 K. In RM6 a gradual reduction is observed with temperature increasing which reaches ~8.7% at 368 K. Moreover, the average number of HBs between P and W also decreases when temperature increases. At 368 K this reduction is ~6.43% for wtRop and ~6.8% for RM6. The increased kinetic energy induces conformational changes, as is discussed in detail in a following
Section 2.2.5, which are responsible for the reduced hydrogen bonding. The average value of HBs between water molecules per water is comparable to pure water systems, i.e., 3.57 at 300 K [
46], 3.361 at 350 K, and 3.277 at 368 K, respectively, according to the specific model. Note here that these numbers attribute hydrogen bonds between waters to both molecules. Very small error bars (less than ~10
−3) are calculated for the last column data of
Table 2 (not included).
A more comprehensive analysis of HB has been performed based on their classification to interchain and intrachain components. Results are presented in
Tables S1 and S2, respectively, in the Supporting Material. A decrease of intrachain HBs is observed at higher temperatures, which is attributed to the deformation of α-helices. However, an interesting comparison concerns the hydrogen bonding per amino acid within the chain of each protein (intrachain contribution). More hydrogen bonds are formed in wtRop compared to RM6, which can possibly excuse its smaller helix radius as it will be discussed later. Values of ~0.94 and ~0.83 for wtRop and RM6, respectively, correspond to their native states (i.e., 300 K). Similar differences remain at higher temperatures (i.e., ~0.83 and ~0.77 for wtRop and RM6, respectively, at 350 K; ~0.84 and ~0.72 for wtRop and RM6, respectively, at 368 K).
Using a classification of protein residues analogous to the one used in a recent paper of Kefala et al. [
47] (p. 3 Figure 1A), we examined the effect of temperature on the hydrophobic contacts. This calculation provides a manifestation of the way that temperature increasing affects the hydrophobic core, through a possible loss of hydrophobic contacts, or a general rearrangement of all protein residues, which can induce attenuation of the hydrophobicity of the core. The pair radial distribution functions (rdf) between the interchain hydrophobic residues (i.e., ChainA-ChainB for wtRop) and between the interpair hydrophobic residues (i.e., chains A,B-chains C,D for RM6), provide a measure of the proximity between the hydrophobic contacts. rdfs have been calculated between the C
β carbon atoms of the hydrophobic residues at various T-values, for both proteins and are presented in
Figure 6. A gradual decrease of the first peak with rising temperature is observed, which indicates a reduced probability for their approach, thus a loss of hydrophobic contacts. Moreover, temperature effect is observed from 350 K and beyond for wtRop, whereas for RM6 it appears gradually and becomes more pronounced at 368 K. A similar conclusion is drawn from the calculation of the distance between the centers of mass (CM) of all C
β carbon atoms which belong to the hydrophobic residues of each chain/pair for wtRop and RM6, respectively. Hydrophobic residues are mostly oriented towards the interior of the hydrophobic core and their CMs interchain/interpair distance roughly indicates the extension of the core region.
Figure S3 in the
Supporting Material shows the increases of this distance at higher temperatures, which is more evident for RM6.
Alpha Helices
Alpha-helices are defined by a pattern of hydrogen-bonds (HB
α-helix) between the carbonyl oxygen (C=O) of the
ith residue and the amide nitrogen (N-H) of the (
i + 4)th residue (e.g., the C=O of the 3rd residue is hydrogen bonded to the N-H of the 7th residue) (
Figure S4) [
48]. These HBs are analyzed for all four α-helices of both proteins (each chain of wtRop has two helices connected by a loop). The results are presented in
Table 3 where the notation is as follows: Ca and Cb denote the ChainA and the ChainB, respectively, whereas, indices 1 and 2, in the case of wtRop, indicate the two helices of each chain. For RM6, Ca, Cb, Cc, and Cd indicate ChainA, ChainB, ChainC, and ChainD, respectively. A general trend of decrease of the number of HB with the increase of temperature is found, which can be attributed to the extension of the α-helices, however the trend is not systematic with temperature.
Hydrogen Bonds of Loop Region
We now turn our attention to the four residues (29Leu (blue), 30Asp (orange), 31Ala (green), and 32Asp (purple) of the loop region, as shown in Figure 10c. According to the references [
13,
43], among the loop residues, 31Ala is the only one which creates HBs with both α-helices of a chain simultaneously, acting as a bridge between them. Moreover,
rmsf analysis in
Section 2.2.2, shows that residues of the loop are highly flexible at high temperatures. Therefore, the study of the HBs of these loop residues was performed at the various temperature values, in order to examine destruction of hydrogen bond bridges or possible formation of new ones. Results, which are contained in
Table 4 for all three temperatures, show that the bridge of 31Ala at 300 K is destroyed at 368 K, whereas a new bridge is formed by 30Asp at 350 K which is destroyed again at 368 K.
2.2.4. Ramachandran Plot
A better insight into the conformational state of proteins is achieved through the Ramachandran plot [
49,
50,
51]. A Ramachandran plot is a phase diagram of two sequential torsion angles,
, ψ (
and ψ
).
Ramachandran plots of RM6 protein for the combinations of (
φ − ψ) angles, at the various temperatures, are presented in
Figure 7. These are produced using the PROCHECK tool [
52,
53]. All the residues of wtRop and RM6 are identified by squares with the exception of Gly residue, which is represented by triangles. Each black square represents the conformation of the backbone of every residue of the protein. The different regions of the Ramachandran plots are presented by shading that is obtained from data of high-resolution crystal structures. The darker they are, the more favorable the combination (
φ − ψ). The most preferred regions are illustrated with red and are marked with A, B, and L, which correspond to the α-helix, the β-strand, and the left-handed α-helix conformations, respectively. The gradient of yellow from darker to lighter regions indicates the passage from more to less favorable conformations. Further details about the different regions of the Ramachandran plot are given in the Supporting Material. We observe that the majority of points are clustered in the area which is represented with red (marked with A) since both proteins attain α-helices secondary structures. Fewer points are present in the red (B) region which corresponds to β-sheets conformations. The corresponding plots for wtRop are shown in
Figure S5 in the Supporting Material, with almost identical features. The effect of temperature is captured through this measure as well, by the counting of the percentage of the (
φ/ψ) angles that exist in the α-helix and in the β-sheet regions, respectively, in all the studied systems. For wtRop, decrease of this percentage from ~86% at 300 K to ~77% at 350 K and ~76% at 368 K in the α-helix region is observed, with a corresponding increase for the β-sheet region from ~6% at 300 K to ~8.0% at higher temperatures. In the case of RM6, a similar decrease from ~85% at 300 K to ~82% at 350 K and ~75% at 368 K in the α-helix region is found, followed by an increase from ~6% to ~9.0% in the β-sheet region.
Map of Dihedral Angles of the Loop Residues
Herein, once again the focus is concentrated on the loop residues of the wtRop protein. The time evolution of all the combinations of (
φ,ψ) dihedral angles during the trajectory for each residue of the loop is recorded and mapped in isosurface plots. The corresponding results for residues, 30Asp and 31Ala, are presented in
Figure 8 at all three different temperatures, whereas for the residues, 29Leu and 32Asp, are shown in
Figure S6. The color scale bar to the right side of each plot indicates the simulation time in ns. Each symbol in the plot shows a combination of (
φ/ψ) angles and the color indicates the time instant that the current combination is obtained. More broader distributions in time of (
φ/ψ) combinations are found at higher temperatures for all four residues. This result is consistent with the creation or destruction of new hydrogen bonds from loop residues (30Asp and 31Ala) as well as with the total conformational changes. In addition to loop residues, a corresponding isosurface plot has been made for a residue that belongs to α-helix region (43Asp) at all three temperatures. Results in
Figure S7 indicate completely located distributions, unaffected by temperature.
Moreover, it is expected that the values for
φ,ψ angles of an ideal α-helix are
φ = −60° and ψ = −50° [
54].
Figure S8 contains the average values of the (
φ,ψ) dihedral angles for each α-helix of wtRop and RM6 proteins, respectively. Average values were calculated by initially averaging all (
φ,ψ) pairs along the α-helix at each time frame and then with block time averaging over the last 100 ns of the trajectories. Error bars are the standard deviation among the values of the blocks. For RM6, (
φ,ψ) values are in the range of −63.4 to −61.3° and −44.51° to −39.64°, respectively, at both 300 K and 350 K, whereas, at the highest temperature of 368 K, big changes in torsional angles (i.e., decrease of
φ and increase of ψ) indicates deformation of α-helices. Quantification of various measures concerning helix dimensions is presented in the next subsection. (
φ,ψ) values at 300 K, are in a similar range for wtRop (i.e., −63.05 to −57.32° and −44.4 to −41.94°, respectively) as in RM6. T-rising affects wtRop earlier (i.e., at lower temperatures) compared to the RM6 protein. Thus, a decrease of
φ and an increase of ψ is observed from 350 K and remains at 368 K in the same intervals. This constitutes an additional evidence for the higher thermostability of the RM6 protein at the examined temperature range. Note that the differences among the corresponding values of (
φ,ψ) between the two/four chains for wtRop/RM6, respectively, provide an estimation for the statistical uncertainty of these values. Differences are of the order of 3.7–4.9%, 5.6–21.4%, and 3.6–9.1%, for wtRop and 0.9–3.8%, 2.0–2.6%, and 2.4–15.17%, for RM6, at 300 K, 350 K, and 368 K, respectively.
2.2.5. Local Conformation Analysis of Alpha-Helices: Helix Properties
Next, we investigate in detail the α-helical structures that both wtRop and RM6 attain at their native states, as well as their dependence on temperature. The conformation of an α-helix can be characterized via specific metrics, which are schematically presented in
Figure 9 and are the following [
54,
55]: (i) Rise per residue, (d), is the distance in nm between sequential residues along the helix axis, which is calculated based on the positions of Ca atoms of the residues. (ii) Total helix length, (L), is the total length of α-helix in nm and it is defined as the product of the average rise (d) and the number of residues of the helix (n), as depicted in
Figure 9. (iii) Helix radius, (r), which is defined as follows:
, where
N is the number of Ca atoms of the helix backbone. The helix radius is the radius of a circle centered on the axis of the helix with the Ca atoms on its periphery (
Figure 9). (iv) Twist angle, (θ), is the average helical angle that is formed between two successive Ca atoms with the helix axis.
Averaging each property has been calculated along the α-helix at each time frame, and then block averaging was performed over the last 100 ns of the trajectories. The error bars were computed as standard deviation between the values of the blocks. Further averaging over the two/four α-helices of wtRop/RM6 was performed.
Average values of all the properties of α-helix for both proteins are shown in
Table 5, where the second, third, fourth, and fifth columns depict the rise per residue, the total helix length, the helix radius, and the twist angle, respectively. Results indicate that temperature increasing affects some conformational characteristics of α-helices. More specifically: (a) T-increasing slightly affects the rise per residue (d) in both proteins at the highest temperature. (b) A small elongation of both proteins with T-rising is observed through L, which is also found in the end-to-end distance (Ree) calculations, as presented in
Table S3 in the Supporting Material. Ree is defined as the distance between the first atom of the first residue and the last atom of the last residue that participates in the helical part for each subunit. This slight extension of α-helix is in agreement with the decrease in the number of the formed HBs within the α-helix region, discussed above. (c) A slight increase is observed in the helix radius with T-rising for wtRop, while there is no T-effect in RM6. (d) Finally, a decrease in the values of twist angle is observed by increasing the temperature for wtRop, whereas twist angle increases with temperature in RM6, which means correspondingly tighter and looser helices. The structural changes that temperature induces become clearer by monitoring the time evolution of the average value of the helix properties: d, L, r, and θ which are presented in
Figures S9–S12, respectively, in Supporting Materials for both proteins. The deformation of wtRop is obvious through all measures with r and θ the most affected by temperature rising. At the same time the effect of temperature is considerably smaller on these two properties in RM6 which highlights its higher thermostability.