Dynamics-Stability Relationships in Apo- and Holomyoglobin: A Combined Neutron Scattering and Molecular Dynamics Simulations Study

Abstract

The removal of the heme group from myoglobin (Mb) results in a destabilization of the protein structure. The dynamic basis of the destabilization was followed by comparative measurements on holo- (holo-Mb) and apomyoglobin (apo-Mb). Mean-squared displacements (MSD) and protein resilience on the picosecond-to-nanosecond timescale were measured by elastic incoherent neutron scattering. Differences in thermodynamic parameters, MSD, and resilience were observed for both proteins. The resilience of holo-Mb was significantly lower than that of apo-Mb, indicating entropic stabilization by a higher degree of conformational sampling in the heme-bound folded protein. Molecular dynamics simulations provided site-specific information. Averaged over the whole structure, the molecular dynamics simulations yielded similar MSD and resilience values for the two proteins. The mobility of residues around the heme group in holo-Mb showed a smaller MSD and higher resilience compared to the same residue group in apo-Mb. It is of interest that in holo-Mb, higher MSD values are observed for the residues outside the heme pocket, indicating an entropic contribution to protein stabilization by heme binding, which is in agreement with experimental results.

Introduction

The dynamics of myoglobin (Mb) has been studied in detail with various techniques, including Mössbauer spectroscopy, neutron scattering, and time-resolved x-ray crystallography, reviewed by Parak (1). Horse Mb has a molecular mass of ∼17.6 kDa and consists of 153 amino acids. Its three-dimensional structure is formed by eight α-helices with connecting loops (2). The protein contains a heme group that can carry an oxygen molecule or other small ligands. The protein with heme group is termed holo-Mb; without the heme group, it is called apo-Mb. In this context, we are using holo- and apo-Mb as model systems to study the role of molecular dynamics (MD) in protein stabilization by ligand binding. Binding of the heme group contributes significantly to thermal stability of Mb. Whereas holo-Mb denatures only at temperatures >80°C at neutral pH, apo-Mb unfolds at temperatures as low as 60°C (3). At temperatures >∼55°C and at basic solvent conditions of pH 9 apo-Mb is reported to form amyloid fibers (3, 4), which is not the case for the holoprotein. The high-temperature structure of apo-Mb is the cross-β, in which β-sheets are arranged perpendicular to the long axes of an amyloid fiber (4). In previous work (5), circular dichroism (CD) experiments in dilute solution emphasized that the α-to-β transition is present in both H₂O and D₂O solvent. By using neutron scattering, it has also been shown that the β-sheet structure in apo-Mb at temperatures >∼55°C is more resilient (stiffer) compared to the native α-helical structure below 55°C (5).

Insight into the mechanism of protein stability can be gained from thermodynamic analysis. The change in the free energy between the unfolded and folded states of a protein determines its thermodynamic stability (ΔG = G_unfolded − G_folded = ΔH − T × ΔS). However, the balance between enthalpic ΔH and entropic contributions T × ΔS is subtle and complex. Major components of the enthalpic stabilization are weak van der Waals forces, hydrogen bonding, and, to a smaller extent, screened electrostatic interactions. Not only protein conformational fluctuations but also disorder and dynamic mobility of water molecules in the hydration shell determine the entropic contributions. The unfolded state of a protein is typically less compact and more disordered than the folded state, which leads to a stabilization of the unfolded state by entropic disorder. However, during protein unfolding, nonpolar groups are exposed to the solvent, which modifies the structure of the surrounding water molecules, as they cannot form hydrogen bonds with the exposed nonpolar groups. The so-called hydrophobic effect induces ordering of the water molecules in the unfolded state, as compared to the folded state, and therefore stabilizes the folded state. Techniques measuring thermodynamic quantities always detect the total contributions from the protein as well as the hydration shell. Protein configurational fluctuations that contribute the entropic component are not limited to functional regions but can occur in principle at any location of the protein. The sum of all entropic components contributes to thermodynamic stability. Although this fact is of major biological relevance, relatively few studies have investigated how thermal fluctuations of the protein and intramolecular forces contribute to thermal stability. Tehei and co-workers (6) and Fitter et al. (7, 8) examined the connection between protein dynamics and melting temperatures of homologous extremophilic proteins using incoherent neutron scattering. Depending on the nature of the protein, either enthalpic (6) or entropic terms (7, 8) were found to be responsible for the increased stability of the thermophilic protein compared to the mesophilic homolog. MD simulations (9, 10) are also excellently suited to studying the correlation between protein dynamics and adaptation to high temperatures.

Incoherent neutron scattering is a method well suited to the study of the conformational fluctuations of complex biological macromolecules. Thermal and cold neutrons have wavelengths on the order of some Å and energies of some meV and are therefore sensitive probes to measure thermal molecular motions on an atomic lengthscale and picosecond-to-nanosecond timescale. In biological systems, the incoherent scattering is dominated by the signal of hydrogen atoms, as their incoherent scattering cross section is much larger than that of the other elements in the sample. Furthermore, the incoherent scattering cross section of hydrogen is one order of magnitude larger than that of deuterium. In the timescale of neutron experiments, the H atoms reflect the motion of the chemical groups to which they are bound. As hydrogen atoms are uniformly distributed in proteins, neutron scattering detects average internal macromolecular motions. Two parameters can be obtained from elastic incoherent neutron scattering (EINS) (11): mean-squared displacements (MSDs), recorded as a function of temperature, and effective force constants <k′>. The MSD describes the flexibility of the protein structure in absolute units of Ų, and the <k′> provides information about the resilience—or stiffness—of the macromolecules in units of N/m.

In this article, we report a study on the relation between protein stability and molecular dynamics. The dynamic basis of the destabilization of Mb by the removal of the heme group was followed by comparative measurements on holo- and apo-Mb. The melting temperatures and enthalpy and entropy changes between the unfolded and folded states of the proteins were determined with CD and are compared to corresponding thermodynamic parameters obtained with differential scanning calorimetry (DSC). MSD and protein resilience in the picosecond-to-nanosecond timescale were measured by elastic incoherent neutron scattering. MD simulations of the two proteins were validated by experimental data and allowed a site-specific understanding of the experimental results. We show how the combination of the neutron-scattering experiments and MD simulations can contribute to a detailed understanding of the experimental results.

Material and Methods

Sample preparation

Apo-Mb was obtained by removing the heme group from holo-Mb. We used a modified version of the method of Rothgeb (12) to obtain the apoprotein: Horse-heart holo-Mb (purchased from Sigma-Aldrich, St. Louis, MO) was dissolved in water. The pH of the holo-Mb solution was then lowered to 1.5 with concentrated HCl on ice. The solution was mixed with four volumes of 2-butanone. The upper organic layer was decanted, and the extraction was repeated twice. The obtained apo-Mb solution was extensively dialyzed against buffer (20 mM KH₂PO₄, pH 7) followed by distilled water. The apo-Mb solution was then lyophilized. The holoprotein was dialyzed against pure water, to remove traces of contamination, and afterward freeze-dried. For the experiments using D₂O solvent, the apo- and holoproteins were dissolved in heavy water to remove the exchangeable protons, incubated for ∼1 day, and lyophilized afterward. Before the neutron experiments, the dry powder samples were rehydrated by pipetting uniformly H₂O or D₂O potassium phosphate buffer (20 mM KH₂PO_4, pH/pD 9) to the protein powder in the aluminum sample holder to a level of 0.73 g H₂O/1 g protein or 0.8 g D₂O/1 g protein. The pD was calculated by adding 0.4 to the value measured on a normally calibrated pH meter (13). The samples were then sealed and allowed to equilibrate for one night in the refrigerator. The chosen hydration level corresponds to approximately two hydration layers/protein and was intended to allow for pH effects. The weight of the sample and the added buffer was monitored using a balance with a precision of 0.1 mg, which results in an uncertainty of the hydration level of <1% in the produced samples. For the CD and DLS experiments, the Mb powder was dissolved in the buffer solution and centrifuged at 20,000 relative centrifugal force to remove aggregated particles. The concentration was then adjusted to ∼0.2 mg/ml for CD and ∼1 mg/ml for DLS measurements.

Dynamic light scattering

DLS was measured with a DynaPro instrument from Protein Solutions (Wyatt Technology, Santa Barbara, CA) at a constant temperature of 20°C. The software package from the manufacturer was used for data acquisition and calculation of the diffusion coefficients and hydrodynamic radii.

Circular dichroism and thermodynamic analysis

CD spectroscopy was used to determine the temperature-dependent loss of protein secondary structure. A J-810 spectropolarimeter (JASCO, Tokyo, Japan) equipped with a temperature-controlled cuvette holder was used for the experiments. The samples were measured in 1-mm-thick quartz cuvettes under constant nitrogen flow. Thermal unfolding transitions were recorded at 222 nm at a constant heating rate of 1°C/min. The raw data were corrected for pre- and posttransition slopes.

A van' t Hoff analysis was used to determine the values of ΔH(T_m) and ΔS(T_m). The model assumes a simple two-state equilibrium between the unfolded and the folded state, without stable intermediates. In the unfolding transition region, the difference in free energy was calculated using $\Delta G\left(T\right)=-RT\text{ln}\left(f_U/f_F\right)$, with f_U and f_F the unfolded and folded fractions. The enthalpy and entropy differences at the melting temperature, T_m, were determined according to $\Delta G\left(T\right)=\Delta H-T\times \Delta S$ in the linear regime.

Assuming a reversible two-state transition between the unfolded and the folded state, the entropy change can be calculated with $\Delta S=\Delta H/T_m+\Delta C_p\times \text{ln}\left(T/T_m\right)$ from the calorimetrically determined heat-capacity change, ΔC_p, the enthalpy difference ΔH, and the melting temperature, T_m. The free-energy change, ΔG, was determined from the calorimetric parameters over the whole temperature range by using the Gibbs-Helmholtz equation, $\Delta G\left(T\right)=\Delta H\times \left(1-T/T_m\right)+\Delta C_p\left[T-T_m-T\times \text{ln}\left(T/T_m\right)\right]$.

Elastic incoherent neutron scattering

Elastic incoherent neutron scattering was measured on the neutron backscattering spectrometer IN13 at the Institut Laue-Langevin (Grenoble, France). The instrument is characterized by an energy resolution of 8 μeV (full width at half-maximum (FHWH)) and a large scattering vector range between 0.2 and 4.9 Å⁻¹ (14), corresponding to observable motions in the timescale of ∼0.1 ns and in the lengthscale of some Å. The relation between the scattering angle 2θ and the modulus of the scattering vector is $q=4\pi /\lambda \text{sin}\left(\theta \right)$ for elastically scattered neutrons. The characteristics of the instruments allow the determination of macromolecular dynamics in solutions using D₂O and H₂O solvent. Free and hydration water motions are outside the time-space window for roughly q ≥ 1 Å⁻¹ and contribute to the measured signal as a background. Measured data were analyzed in the q² range from 0.6 to 3.5 Å⁻² and from 1.6 to 4.3 Å⁻². Between 120 mg (H₂O hydrated) and 190 mg (D₂O hydrated) protein powder was inserted in a flat aluminum cell with internal spacing of 0.2 and 0.3 mm, respectively. All samples were oriented with an angle of 135° with respect to the incident beam. The experiments were performed between 6.9 and 46.9°C. Multiple scattering was neglected, as the transmissions of all samples were ≥0.9. The measured data were corrected for empty cell scattering and the neutron detectors were calibrated with a vanadium reference. The measured intensities are proportional to the amount of sample in the neutron beam, and we did not normalize the measured data by the amount of sample. The weight of the samples was measured before and after the measurements to ensure that no loss of material occurred.

Mean-squared displacements, <u²>, were calculated within the Gaussian approximation according to

$$\langle u^2\rangle =\frac{-6\times \Delta \left(\text{ln}I\left(q\right)\right)}{\Delta q^2},$$ (1)

where I(q) represents the measured elastic intensity and q the modulus of the scattering vector. We use in this work the definition of <u²> introduced by Smith (15), which accounts for the full amplitude of motions. The validity of the Gaussian approximation is mathematically similar to that of the Guinier region of small-angle scattering and depends on the geometry of the motion or the shape (<u²> = 2 × R_G², where R_G is the Guinier radius). The Gaussian approximation is strictly valid for localized motions at $q^2\to 0$ but holds up to $\sqrt{\langle u^2\rangle \times q^2}=\sqrt{2R_G^2\times q^2}\sim \sqrt{2}$ for localized motions within any shape. For the most compact shape—the sphere—there is reasonable agreement between the Guinier approximation and the form factor of a sphere up to values of $\sqrt{R_G^2\times q^2}\sim 2$. This corresponds to a maximal value of $\sqrt{\langle u^2\rangle \times q^2}\sim 2.8$ for localized motions in a sphere. Kidera and Go used normal-mode refinement of x-ray crystallography data and showed that protein dynamics are intrinsically anisotropic, with ellipsoidal shape and axes of 1:1:1.7 (16). For thermal motions with ellipsoidal axes of 1:1:∼2, the Gaussian approximation holds to significantly larger values of roughly $\sqrt{\langle u^2\rangle \times q^2}\sim 3$, as reported by Tehei et al. (6). In our article, the maximal values are <u²> ∼ 2.5 Å² for H₂O-hydrated samples and <u²> ∼ 3 Å² for D₂O-hydrated samples at the highest temperatures. We obtain maximal values of $\sqrt{\langle u^2\rangle \times q^2}$ ∼ 3 and 3.2 for H₂O- and D₂O-hydrated samples, respectively. Although the measured <u²> values are large, the Gaussian approximation holds up to the highest temperatures. Performing the analysis at the slightly larger q² values, we obtain a maximal value of $\sqrt{\langle u^2\rangle \times q^2}$ ∼ 2.9, which also satisfies the Guinier criterion.

The temperature variation of the MSD was interpreted in terms of an empirical effective force constant, <k′>, called resilience by Zaccai (11):

$$\langle k^{\prime }\rangle =\frac{0.00276}{\left(d\langle u^2\rangle /dT\right)}.$$ (2)

The units are chosen such that <k′> is in N/m when <u²> is in Ų and T is in K (11). The force constants describe the rigidity, or resilience, of the protein. Bicout and Zaccai proposed a quasiharmonic approximation of the complex macromolecular force field (17). However, independent of the quasiharmonic model interpretation, the MSD and resilience parameters have proven to be very useful for comparison between neutron-scattering experimental and MD simulation data (18).

Molecular dynamics simulations

We performed MD simulations at different temperatures on both apo-Mb and holo-Mb using NAMD version 2.6 (19) coupled to the CHARMM 27 all-atom force field (20). In both cases, the original structure was the same, namely, a structure of the ferrous deoxy-Mb obtained at pH 6.8 with a resolution of 1.25 Å (PDB code 2V1K) (21). The holo-Mb structure was obtained by cleaning out the 2V1K structure from the glycerol molecules, the sulfate ions, and the structural waters, whereas the apo-Mb structure was obtained by also removing the heme molecule. From these intermediate structures, the starting structure and topology files were generated by hydrogenating the system with standard pH 8.4 acid protonation states. Then, the apo-Mb and holo-Mb were solvated using a 10-Å surrounding TIP3P (22) water box. The holo-Mb had to be further electrostatically neutralized by adding two sodium counterions. This led to starting systems that consisted for each protein of a box of ∼62 × 59 × 69 Å³. In the case of apo-Mb, the box contained 6916 water molecules and one protein molecule. For holo-Mb, the box contained one protein molecule including the heme group, 6901 water molecules, and two sodium ions. The protonation, solvation, and counterionization steps were performed using the VMD program. The initial aim of the MD simulation was also to investigate the α-to-β transition in apo-Mb at ∼55°C and pH 9. The α-to-β transition could not be observed in the simulations, but there were large fluctuations of the MSD at temperatures >55°C.

MD simulations were performed on both systems at a target temperature ranging from 280 to 330 K by steps of 10 K (i.e., 12 different simulations). For each simulation, the simulation cycle started with a first equilibration cycle made of a 1000-step conjugated-gradient minimization followed by a short 100-ps NPT equilibration where the protein atom coordinates were kept fixed using harmonic restraints (force constant of 5 kcal mol⁻¹ Å⁻²). Then, the system underwent another equilibration cycle made of a 1000-step conjugated-gradient minimization followed by a 1-ns NPT equilibration, where this time all constraints were released.

Once equilibrated, the system underwent the so-called production cycle made up of a 10-ns NVE MD simulation in which the coordinates were saved every 10 ps. The backbone RMSD of one typical 10-ns NVE production run is shown in Fig. S1 in the Supporting Material. The RMSD indicates equilibrated structures during the simulation. The dimensions of the water box in the NVE ensemble are given in Fig. S2. As expected, the box dimensions increase slightly in the simulated temperature range.

The time step in the simulations was 1 fs. The NPT simulations were performed using Langevin molecular dynamics, with a damping coefficient of 2/ps for constant temperature control, coupled with a Nosé-Hoover Langevin piston set at 1 bar, with an oscillation time of 100 fs and a damping time of 50 fs, for constant pressure. Switching functions were used for the calculation of nonbonded interactions, with a switch distance of 10 Å, a cutoff of 12 Å, and a pair-list distance of 13.5 Å. Long-range electrostatic interactions were calculated using particle mesh Ewald summation. Nonbonded interactions were calculated every 2 fs, full electrostatic interactions were calculated every 4 fs, and pair lists were updated every 20 fs.

MD simulations were analyzed using nMOLDYN (23). The trajectories were first filtered to remove the translational and rotational global motions. The MSDs at a time resolution of τ were calculated using the relation $MSD\left(\tau \right)=\frac{1}{N-\tau }{\sum }_{t=0}^{N-\tau -1}{\left[\overrightarrow{r}\left(t+\tau \right)-\overrightarrow{r}\left(t\right)\right]}^2,$ where t runs over all saved time steps and $\overrightarrow{r}\left(t\right)$ is the particle trajectory. For a detailed description of the algorithms, we refer to the user guide of nMOLDYN (24). The MSDs at 0.1 ns were calculated over the whole 10-ns simulation. The MSDs were then analyzed for 1-ns time slices and the average values were further used. This enabled us to observe the effect of fluctuations within the 10-ns production run and we estimated an error of ±10% on the calculated MSD. Analyzing time slices in this way demonstrates that equilibrium is reached during the production runs. MSDs were calculated for all residues, as well as for only those residues within 5 Å of the heme group, referred to as active-site residues. The MSD of the H-atoms were calculated for a direct comparison with the measured <u²>. The residue-specific MSDs were calculated for the heavy atoms, and because they showed large fluctuations at 330 K, the residue-specific MSDs at that temperature were not included in the analysis. The simulations for apo-Mb were performed in two ways. First, after removing the heme, the resulting pocket was filled with water before running the above protocol. In the second approach, the pocket was not hydrated. Minimization did not lead to the collapse of the pocket; instead, during the MD run, water entered the pocket before any annealing could take place. The results reported below are independent of the approaches.

Results and Discussion

Thermal stability of proteins and MD are inherently connected. Thermal motions in the time range of picoseconds to nanoseconds, with amplitudes on the order of some Å, allow fluctuations of the atoms around the equilibrium structures and are considered to act as a lubricant for slower conformational motions in the time range up to several milliseconds (25). In Mb, the interplay of fast localized fluctuations is necessary to open transient channels to allow the diffusion of an oxygen molecule from the surface of the protein to the heme group (26). A certain degree of flexibility is therefore needed so that proteins can fulfill their biological function. Molecular forces, on the other hand, play an equally important role. The folding of proteins into their specific three-dimensional structures is determined by molecular forces to a large extent. Relevant forces in biological macromolecules arise from hydrogen bonds, van der Waals interactions, screened electrostatic interactions, the hydrophobic effect, and others. These forces are rather weak, and proteins are therefore soft objects, as the corresponding energies are similar to thermal energy at room temperature. Proteins are nevertheless compact objects and need to maintain their more or less defined structures for function.

Protein stability in thermodynamic terms can be described by the difference in Gibbs free energy between the unfolded and the folded state, ΔG = ΔH − T × ΔS. Measured melting transitions of apo- and holo-Mb at the specific solvent condition of pH 9 are shown in Fig. 1 A. The unfolding transitions of the proteins at that pH value were reported previously by Fändrich et al. (3, 4) and are shown here for completeness. The difference in free energy, ΔG, is shown in Fig. 1 B. The values obtained for the enthalpy and entropy differences at the melting temperature, T_m, are given in Table 1. Griko and co-workers (27) and Privalov and Khechinashvili (28) investigated the thermodynamic stability of sperm whale apo- and holo-Mb at pH 5 and pH 10, respectively, using DSC in the native states. The thermodynamic quantities from DSC are given for comparison in Table 1. The thermodynamic parameters obtained from CD and DSC data are rather similar. The reason for the small discrepancy could be that in our study, we used horse Mb, whereas in the DSC experiment, sperm whale Mb was investigated. The pH values in the CD and DSC experiments are also slightly different, which could also contribute to the deviations.

Figure 1.

(A) Unfolding transitions of holo- and apo-myoglobin in H₂O at pH 9, measured with CD spectroscopy. (B) Difference in free energy, ΔG, between the unfolded and folded states of the proteins. Symbols correspond to data extracted from the CD measurements. The dashed and dotted lines were calculated using the Gibbs-Helmholtz equation and thermodynamic parameters determined by DSC of sperm whale Mb (27, 28). The dashed line corresponds to holo-Mb and the dotted line to apo-Mb.

Table 1.

Comparison between thermodynamic parameters of apo- and holo-Mb obtained with CD and literature values determined with DSC

	Apo-Mb	Holo-Mb
CD
Tm (°C)	65	79
ΔH (kJ/mol) at Tm	262	435
ΔS (J/mol/K) at Tm	775	1236
DSC
Tm (°C)	61	81
ΔCp (kJ/K/mol)	6.5	11.9
ΔH (kJ/mol) at Tm	222	615
ΔS (J/mol/K) at Tm	665	1737

Thermodynamic parameters obtained with CD were determined at pH 9, and the values taken from the literature (27, 28) at pH 5 for apo-Mb and pH 10 for holo-Mb. Sperm whale Mb was used in the DSC study, whereas horse heart Mb was used in the CD experiment. The errors of T^m are ∼1%. The errors of ΔH and ΔS determined with CD from the fitting routine are ∼2%. The intrinsic errors are certainly larger, especially for ΔH.

It is clear from a comparison of the data that ΔH(T_m) is smaller in apo-Mb than in holo-Mb. The entropy difference ΔS(T_m) is significantly smaller in apo-Mb than in holo-Mb. Assuming that the unfolded states of apo- and holo-Mb are similar in their thermodynamic properties, this would indicate that the folded state of apo-Mb has a larger entropy than the folded state of holo-Mb. However, thermodynamic quantities always contain the contributions from both the protein and the water molecules in the hydration shell. Therefore, the smaller entropy difference, ΔS, of apo-Mb compared to holo-Mb could be related to the native state of apo-Mb having more disordered and dynamically mobile water molecules in the hydration shell, larger conformational fluctuations of the protein, or a combination of the two.

We further consider the secondary structure content and the compactness of apo- and holo-Mb in the folded states. The α-helical content of apo-Mb and holo-Mb at pH 6.0 in the native states was reported to be 55% and 65% (29), respectively. We determined an α-helical content of apo- and holo-Mb at pH 9 of 53% and 67% (5), respectively. The structural content of the native states at the two solution conditions is nearly identical. Using small-angle x-ray scattering, radii of gyration of apo-Mb and holo-Mb at pH 6.0 were found to be R_g = 19.7 and 17.5 Å, respectively (30). Using DLS, we obtained hydrodynamic radii of R_h = 26 Å for apo-Mb and 22 Å for holo-Mb at pH 9. Assuming a spherical shape of the proteins, this corresponds to radii of gyration of R_g = 20 Å for apo-Mb and 17 Å for holo-Mb using the equation R_g = (3/5)^0.5 × R_h (31). The results are similar at the two solvent conditions, demonstrating that apo- and holo-Mb at pH 9 are in the native folded states. A direct comparison between our work and studies that investigated the native states of the proteins is therefore justified. At this point, we can shortly summarize the following facts: The folded state of apo-Mb has a lower degree of secondary structure, is less compact, and is characterized by a smaller entropy change upon unfolding compared to holo-Mb. According to these observations, one would expect intuitively that thermal fluctuations of apo-Mb should be larger than those of holo-Mb, and that apo-Mb has a softer structure than the holoprotein. In the following, we demonstrate using neutron scattering and MD that this is not the case.

Thermal motions of folded states below the melting temperatures were studied with neutron scattering. Measured data for apo-Mb and holo-Mb hydrated with H₂O and D₂O solvent are shown in Fig. 2. MSDs (<u²>) were determined from the recorded intensities, as given in Fig. 3. Finally, effective force constants, <k′>, were calculated from the slope of <u²> versus temperature and are summarized in Table 2. The upturn in the recorded intensities at q² < 0.6 Å⁻² in the H₂O-hydrated samples is related to H₂O molecules that enter the time-space window of the instrument. The neutron experiments were performed with powder samples prepared with pH-adjusted H₂O and D₂O buffer solutions to control pH and suppress global protein diffusion. However, the precise pH value of the hydrated power is not known. We assume that the thermal stabilities of the proteins (with and without bound heme) in hydrated powders and in dilute solutions are similar, even if the denaturation transitions might not be fully reversible in powder samples. Previous experiments using the IN13 spectrometer allowed the determination of protein dynamics in concentrated solution with natural-abundance solvent with a negligible contribution of hydration water (5, 32, 33). Thermal motions of water molecules in the first hydration shell are strongly slowed down compared to bulk solvent (34) and still might contribute to the measured signal in hydrated powder samples, especially at small q² values. Using D₂O, the incoherent scattering contribution of the solvent is reduced by a factor of 40 compared to H₂O, but heavy water is also reported to influence protein thermal stability (35). Therefore, as a control, the experiments were performed in both H₂O and D₂O solvent. The <u²> of apo-Mb are clearly smaller than those of holo-Mb, and the force constants of apo-Mb are significantly larger than those of holo-Mb under both isotopic solvent conditions (see also Table 2). The larger force constants indicate that apo-Mb is more resilient than holo-Mb. The <u²> values for the proteins are slightly shifted to lower values in H₂O compared to D₂O solvent. The small differences in <u²> between apo-Mb in H₂O and apo-Mb in D₂O are safely within the statistical error. The smaller <u²> of holo-Mb in D₂O might indicate that heavy water promotes conformational fluctuations of the protein. However, it could also be related to intrinsic errors of the neutron detectors at the very small q² values. The observed differences in <u²> and <k′> between apo-Mb and holo-Mb become stronger and more visible by analyzing the measured data at slightly larger q² values from 1.6 to 4.3 Å⁻². The measured intensities, <u²>, and <k′> obtained from that analysis are presented in Fig. S3, Fig. S4, and Fig. S5. There is no significant difference in the absolute values of <u²> obtained from the detectors at larger q² when changing from D₂O to H₂O solvent. In that sense, the <k′> values appear to be stronger parameters than comparing the absolute values of <u²> alone.

Figure 2.

Experimental EINS data of (A) holo-Mb hydrated with H₂O, (B) holo-Mb hydrated with D₂O, (C) apo-Mb hydrated with H₂O, and (D) apo-Mb hydrated with D₂O. Straight lines are linear fits to the data and were used to determine the MSDs, <u²>. The deviation from linear behavior at q² < 0.6 Å⁻² in the H₂O-hydrated samples is most probably caused by H₂O diffusion, and the data points were not used for the linear fits.

Figure 3.

MSDs, <u²>, as a function of temperature for holo- and apo-Mb hydrated with H₂O buffer (A) and D₂O buffer (B). The straight lines are linear fits to the data.

Table 2.

Effective force constants, <k′>, determined from measured experimental MSDs and MD simulations

	Holo-Mb experiment	Apo-Mb experiment	Holo-Mb simulation	Apo-Mb simulation	Holo-Mb AS simulation	Apo-Mb AS simulation
<k′> (N/m) H2O solvent	0.13	0.19	0.14	0.09	0.21	0.11
<k′> (N/m) D2O solvent	0.10	0.18	—	—	—	—

MSDs from the simulations were calculated for the H atoms to allow a direct comparison with experimental values. The <k′> values from the simulations were determined for the whole protein and for the active-site (AS) residues. The errors of <k′> are typically ∼10%.

As explained previously, the entropy difference ΔS between the unfolded and folded states contributes to thermodynamic stability. It is important to note that the entropic component is not limited to fluctuations of specific amino acids but contains the contribution of the whole protein, including the hydration water. Incoherent neutron scattering detects average protein dynamics and is therefore useful for measuring the conformational entropy component of the protein. It is evident from the <u²> that the removal of the heme group does not lead to larger fluctuations in apo-Mb as compared to holo-Mb. It is a surprising result that holo-Mb with a bound heme group is less resilient and has larger <u²> values than apo-Mb, although holo-Mb in dilute solution is more thermostable and more compact and has a larger α-helical content. The experimental neutron scattering results indicate that the larger entropy content of apo-Mb compared to holo-Mb has to be related to more disordered and mobile water molecules in the hydration shell of apo-Mb.

The contribution of global diffusion to the amplitudes of motion will be estimated shortly. Apo-Mb was found to form dimers at high concentrations of ∼200 mg/ml of the crowder protein ribonuclease A (36). It might well be that apo-Mb also forms dimers in the hydrated powder samples, but we cannot determine the association state from our neutron scattering results. Further small-angle scattering experiments might help to elucidate this issue. Obviously, dimeric apo-Mb has a lower diffusion coefficient than monomeric holo-Mb in solution. The volume fraction of structural arrest in a colloidal hard-sphere suspension was reported to be ϕ = 0.58 (37), and the volume fraction in our study is ϕ ∼ 0.5. Global macromolecular diffusion is highly suppressed at that volume fraction, with only two hydration layers around the protein. The contribution of global diffusion to the measured <u²> should be quasinegligible in the 0.1-ns timescale and Å lengthscale.

Supporting MD simulations were performed to gain an atomistic understanding of the experimental neutron scattering results. The MSDs were calculated from the simulations, as described in Materials and Methods. The MSDs of the H-atoms were extracted at 0.1 ns—a timescale comparable to the resolution of the IN13 spectrometer—and correspond directly to the <u²> measured with neutron scattering. Fig. 4 A shows these results as a function of temperature for apo-Mb and holo-Mb. Experimental results of holo- and apo-Mb in D₂O are given in Fig. 4 A to show the validity of the starting assumptions of the simulations by experiment. Indeed, the measured and simulated MSD of holo-Mb are in excellent agreement. However, the simulations overestimate the motions of apo-Mb. The simulated MSDs of apo-Mb are up to 50% larger than the measured MSDs. The simulations show no particular difference in MSD or slope between apo- and holo-Mb, whereas the experiments clearly show differences. Effective force constants determined from the MSDs are given in Table 2. Taking the errors into consideration, they indicate that the two simulated proteins have very similar resilience and flexibility.

Figure 4.

(A) MSD at 0.1 ns averaged over all 153 residues of Mb. The MSDs were calculated for the H-atoms. MSDs from the simulations correspond directly to the <u²> from neutron experiments. The thick dashed and dotted lines are linear fits to the simulated MSDs for apo- and holo-Mb, respectively. The thin dashed and dotted lines represent the measured <u²> of apo- and holo-Mb, respectively. (B) MSDs of the H-atoms at 0.1 ns averaged over all 29 active-site residues of Mb. The dashed and dotted lines are linear fits in the indicated temperature range.

Inspecting the calculated values more closely reveals a possible stabilizing effect of the heme at 310 K (36.9°C), 320 K (46.9°C), and 330 K (56.9°C). Exploiting the site-specific information from the simulations (see Fig. 4 B), the MSDs of the H-atoms of the active-site residues within 5 Å of the heme group show the stabilizing effect of the heme group across the whole temperature range. According to the definition of the active site, given above, 29 of 153 residues are considered. Fig. 4 A shows comparable MSDs for the whole molecules, especially at lower temperatures, from 280 to 300 K (6.9 to 26.9°C), demonstrating that residues that are not located in the vicinity of the heme group in holo-Mb have larger MSDs than the corresponding residues in apo-Mb. Effective force constants, <k′>, were determined from the MSDs of the active-site residues and are given in Table 2. The active-site residues in apo-Mb were found to be clearly more flexible and less resilient than those in holo-Mb (see Fig. 4 B).

Furthermore, the simulations allowed site-specific calculation of MSDs. These values are compared for all residues at 320 K in Fig. 5, and for the active site residues at 280 K and 320 K in Fig. 6, A and B. In Fig. 6 C, the MSD differences between apo- and holo-Mb, ΔMSD = MSD_apo-Mb − MSD_holo-Mb, are given. As discussed above, the average MSDs of the whole proteins are very similar. However, the active-site residues show clear differences between apo- and holo-Mb. Active-site residues with significantly larger fluctuations in apo-Mb are visible in the MSDs and in the ΔMSD values: Lys⁴², Phe⁴³, Asp⁴⁴, and Lys⁴⁵ are located between helices C and D; Lys⁹⁶ and His⁹⁷ are at the end of helix F. These residues form the entrance of the heme pocket. Leu⁷² is in the middle of helix E and is at the opposite side of the heme cavity.

Figure 5.

Residue-specific MSDs of the heavy atoms at 0.1 ns at 320 K for (A) apo-Mb and (B) holo-Mb. The positions of the α-helices are indicated by rectangles at the top of the panels.

Figure 6.

(A and B) Site-specific MSDs of the heavy atoms at 0.1 ns for the 29 active-site residues of apo- and holo-Mb at 280 K (A) and 320 K (B). (C) Residue-specific differences, ΔMSD = MSD_apo-Mb – MSD_holo-Mb, compared at different temperatures.

The similar MSD and <k′> values for apo- and holo-Mb given by MD simulations (Fig. 4 A), in contrast to the experiment, could also be related to the two methods employed to generate the structure of apo-Mb used in our MD calculations (an x-ray structure of apo-Mb is not available). Since the crystallographic structure of apo-Mb is not known, we cannot rule out the existence of another apo-Mb structure, which may explain the data and could possibly be generated by annealing simulation schemes.

Conclusions

We investigated in a comparative study the dynamics-stability relation of holo- and apo-Mb using CD, incoherent neutron scattering, and MD simulations. The combination of the experimental neutron scattering and the MD data was rich in information, and the strong complementarity of the two methods was fruitful. Apo-Mb is less compact and has a smaller amount of α-helical structure than holo-Mb. However, both the simulations and the experimental data show that apo-Mb is not more flexible than holo-Mb. Incoherent neutron scattering data show holo-Mb to be more flexible, whereas MD simulations show comparable flexibility for the two proteins. The simulations, giving site-specific information, reveal the expected reduced MSDs around the heme group, for which the other residues compensate with higher MSDs. Assuming a similar type of protein structure for apo- and holo-Mb, it seems that removing a rigidifying part of the molecule can result in a redistribution of flexibility without increasing the overall flexibility. Thus, we demonstrate in our study that having a less compact structure and lower thermal stability do not necessarily imply that a protein is also more flexible. Our study shows that protein thermal stability and flexibility are not always inversely correlated.

Thermodynamic stability is determined both by enthalpic and entropic contributions. In general, it is not known on an atomistic level which protein conformational fluctuations dominate the entropic stabilization. The aim of future studies would be to investigate the role of protein conformational fluctuations on different timescales. The ultimate goal would be to identify on an atomistic and quantitative level which conformational fluctuations determine protein stability.

To investigate in more detail the contribution of protein fluctuations to thermodynamic stability, it would be useful to measure quasielastic incoherent neutron scattering of proteins in the unfolded and folded states in solution, as demonstrated by Fitter (38). In the case of Mb, thermal unfolding transitions are fully reversible in solution (27, 28), and global protein diffusion and internal dynamics can be separated from the quasielastic measurements (39, 40). It is important to note that protein conformational fluctuations extend over a large time range from picoseconds to milliseconds (25). Neutron spectrometers with different time resolutions could be used to investigate the contribution of conformational entropy to thermodynamic stability in different time windows from picoseconds to several nanoseconds.

Furthermore, we hope that our results might be useful for the evaluation and optimization of force fields used in biomolecular simulations.

Editor: Gerhard Hummer.