Diffusion of Hydration Water around Intrinsically Disordered Proteins

Sep 29, 2015 - Pooja Rani and Parbati Biswas .... Shruti Arya , Avinash K. Singh , Karishma Bhasne , Priyanka Dogra , Anindya Datta , Payel Das , Samr...
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Diffusion of Hydration Water around Intrinsically Disordered Proteins Pooja Rani and Parbati Biswas* Department of Chemistry, University of Delhi, Delhi 110007, India S Supporting Information *

ABSTRACT: Hydration water dynamics around globular proteins have attracted considerable attention in the past decades. This work investigates the hydration water dynamics around partially/fully intrinsically disordered proteins and compares it to that of the globular proteins via molecular dynamics simulations. The translational diffusion of the hydration water is examined by evaluating the mean-square displacement and the velocity autocorrelation function, while the rotational diffusion is probed through the dipole− dipole time correlation function. The results reveal that the translational and rotational motions of water molecules at the surface of intrinsically disordered proteins/regions are less restricted as compared to those around globular proteins/ordered regions, which is reflected in their higher diffusion coefficient and lower orientational relaxation time. The restricted mobility of hydration water in the vicinity of the protein leads to a sublinear diffusion in a heterogeneous interface. A positive correlation between the mean number of hydrogen bonds and the diffusion coefficient of hydration water implies higher mobility of water molecules at the surface of disordered proteins, which is due to their higher number of hydrogen bonds. Enhanced hydration water mobility around disordered proteins/regions is also related to their higher hydration capacity, low hydrophobicity, and increased internal protein motions. Thus, we generalize that the intrinsically disordered proteins/regions are associated with higher hydration water mobility as compared to globular protein/ordered regions, which may help to elucidate their varied functional specificity.

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INTRODUCTION Hydration water at the surface of biomolecules like proteins, DNA, and RNA plays a pivotal role in determining their structure, function, and dynamics,1,2 which is considered relevant in protein−protein and protein−DNA recognition, electron and proton transfer, enzymatic reactions, protein folding, and allostery.3,4 The rotations of hydration water govern the internal motions of the protein, leading to hydration induced dynamical transitions,5 and also regulate its functional specificity. Compared to bulk water, many attributes of hydration water in the vicinity of the protein or nucleic acid are less understood. Several studies have attempted to investigate the structure and dynamics of hydration water in the vicinity of a protein surface, which includes X-ray crystallography,6 NMR,7,8 magnetic resonance dispersion,9 dielectric relaxation,10 neutron scattering,11 solvation dynamics,12 and molecular dynamics (MD) simulations.13,14 These studies suggest that the structural and the dynamic properties of the hydration water at the protein surface are distinctly different from those of the bulk;15,16 specifically, hydration water around a protein has a low mobility with an excess of low frequency vibrational modes, as compared to the bulk, and exhibits a heterogeneous dynamics with sublinear diffusion.13 The time scales of water dynamics typically range between the ultrafast 1−3 ps for bulk water and the slower limit of 30−60 ps for the hydration water, depending on the extent and specificity of the interactions of the hydration water with the protein. Similar © 2015 American Chemical Society

water dynamics is displayed near the surface of a globular protein or a micelle with hydrophilic functional groups.12,17 Thus, multiple experimental techniques are required to probe this wide range of relaxation time scales associated with the different dynamical phenomena, which may be practically difficult and cumbersome. While these experimental methods only explore the average effect of the biomolecule over its hydration layer, MD simulations provide the site-specific details of hydration dynamics. The translational and rotational dynamics of hydration water have been studied extensively for the globular proteins, while the hydration dynamics in the vicinity of the intrinsically disordered proteins (IDP) remains largely unexplored. To obtain a generalized perspective about the dynamics of hydration water molecules around the protein, different classes of proteins need to be studied along with an assessment of the influence of the protein surface on the spatial orientation and dynamics of hydration water. IDPs are proteins which fulfill their specific biological functions but are devoid of any welldefined secondary or tertiary structure under standard physiological conditions. The unfolded nature of these proteins is encoded in sequences of low complexity, characterized by a deficit of hydrophobic residues and a preponderance of charged Received: July 27, 2015 Revised: September 16, 2015 Published: September 29, 2015 13262

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and the ordered regions of 1CD3, 1MVF, and 1F0R were obtained from RCSB PDB24 while the disordered regions for the partially and fully disordered proteins were modeled using MODELLER.25 Molecular Dynamics Simulation. The local order and dynamics of hydration water of five proteins (one globular, three partially disordered, and one fully disordered) were evaluated using explicit-water MD simulations in a related study.22 These simulations were performed with AMBER 1226 for 100 ns in NPT ensemble at T = 300 K using ff99SB force field27,28 and TIP3P29 water model. The calculation of the diffusion coefficient depends on the simulation time and particle ensemble size.30,31 Thus, 25 conformations of each of the five proteins were selected from their respective 100 ns simulation trajectory, and the water molecules were stripped off. For each protein, these conformations were chosen in a specified range of RG, which varied as 15.7 ± 0.2 for 1A4V, 33.0 ± 2.0 for α-synuclein, 19.98 ± 2.0 for the disordered region of 1CD3, 16.25 ± 2.0 for the disordered region of 1MVF, and 25.34 ± 2.0 for the disordered region of 1F0R. Additional 25 explicit-water MD simulations of 500 ps were executed using ff99SB force field, by solvating each protein in a cubic box of SPC/E water molecules32 with the box edge at a distance of 10 Å from the protein surface. The choice of SPC/E water model is justified since it reproduces the experimental values of the diffusion coefficient of bulk water accurately.33,34 After solvating the protein, Na+ or Cl− ions were added to neutralize the charge on the protein, and motions of hydrogen atoms were constrained to their equilibrium bond lengths with the SHAKE algorithm.35 Long-range electrostatic interactions were treated using particle mesh Ewald (PME) algorithm36 with a real space cutoff of 8.0 Å, while minimum image convention was applied with a cutoff distance of 8.0 Å for the nonbonded interactions. Each protein was energy minimized twice; initial energy minimization of the solvent molecules was followed by the energy minimization of the solvated protein using the conjugate gradient method to remove unfavorable interactions. The energy minimized solvated protein was then equilibrated in an NVT ensemble for 100 ps with a gradual increase of the temperature from 100 to 300 K. This was followed by the equilibration in NVE ensemble for 300 ps. A 500 ps MD simulation run was performed for each of the selected 25 conformations for all five proteins in NVE ensemble with a time step of 1 fs. Coordinates were saved at each 10 fs to ensure the better resolution for the analysis of diffusion coefficient.15 The average temperature of the system obtained from the equilibrated NVE trajectory was 300 K. An additional 25 independent MD simulations of 500 ps each were also performed for bulk water using the SPC/E water model.

residues. These proteins may be classified in two groups: (i) intrinsically disordered proteins, IDPs, with completely disordered sequences that lack tertiary structures, and (ii) intrinsically disordered regions, IDPRs, which are the polypeptide segments lacking secondary/tertiary structure linked with regions having well-defined secondary structures. It may be conjectured that IDPs due to their larger solvent accessible surface area possess distinctly different interactions with hydration water molecules as compared to the globular proteins. Hydration water around IDPs has a specific biological function of ensuring protein activity in desiccated cells.18 The translational diffusion of water at the surface of biomolecules is a direct measure of the hydrogen bond network that controls the protein dynamical transitions.19 Since the mobility of hydration water is crucial for the functional specificity of proteins,20,21 a detailed analysis of the diffusion of water therefore may help to understand the protein−solvent coupling and transitions between different conformations in disordered proteins. This work analyzes the effect of the extent of structural disorder on the transport properties of the hydration water in the vicinity of disordered proteins through MD simulations. Hydration water dynamics around a protein surface may be characterized by analyzing the translational and rotational mobility of water molecules in the hydration layer. In this context, the diffusion coefficient is evaluated from the meansquare displacement and the velocity autocorrelation function, respectively, and the corresponding relaxation times for the reorientational motion of hydration water are calculated for three different regions of the hydration shell around the globular protein, IDPs, and the ordered and disordered regions of IDPRs. Mobility of water molecules in the hydration layer of IDPs and disordered regions of IDPRs, i.e., the region within a distance of 4 Å from the protein surface, are found to be higher as compared to those around the globular protein and the ordered regions of IDPRs, respectively. Further analysis confirms that high values of translational and rotational diffusion coefficient of water around disordered proteins/ regions may be correlated to the higher number of mean water−water hydrogen bonds. Compared to the globular proteins/ordered regions, disordered proteins/regions are associated with low hydrophobicity, larger internal protein motions, and higher hydration capacity, which may be attributed to higher mobility of hydration water. Thus, intrinsically disordered proteins/regions impose lesser restrictions on the mobility of hydration water, as compared to the globular proteins/ordered regions.

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MATERIALS AND METHODS Protein Selection. A globular protein, α-lactalbumin (PDB ID 1A4V), three partially disordered proteins (a scaffolding protein GPB, PDB ID 1CD3; PemI-like protein, PDB ID 1MVF; Human factor Xa, PDB ID 1F0R) with different degrees of structural disorder content in their native states, and one fully disordered (α-synuclein) protein were selected for comparing their hydration water dynamics. The disordered proteins differ in (i) their content of structural disorder, i.e., 43.3% for 1CD3, 46.3% for 1MVF, 61.2% for 1F0R, and 100% for α-synuclein, and (ii) the location of their disordered regions, i.e., C-terminus for 1MVF, N-terminus for 1F0R, middle regions for 1CD3, and complete disorder for αsynuclein. The details of the selection criteria of these proteins are provided in refs 22 and 23. The initial structures for 1A4V

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RESULTS AND DISCUSSION The hydration water dynamics is expected to be distinctly different for the globular and intrinsically disordered proteins. The translational and rotational diffusion of water molecules around globular IDPs and IDPRs is explored in this context. The translational and rotational diffusion coefficient is calculated by considering three different water layers around the protein surface. These three layers are the following: (i) hydration layer, which comprises water molecules within a distance of 4 Å from the protein surface, (ii) layer I, which consists of water molecules within a distance of 4 and 8 Å from the protein surface, and (iii) layer II, with water molecules lying between a distance 8−12 Å from the protein surface. Ordered 13263

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The Journal of Physical Chemistry B and disordered regions of IDPRs are denoted as IDPRs-O and IDPRs-D, respectively, and used throughout the paper. All calculations are valid for water molecules that remain in the respective layers (i.e., hydration layer, layer I, and layer II) around the protein surface for a given time period. Since water molecules continuously enter and leave the respective layers around the protein surface during the simulation, checking their positions at each MD step is required. This dynamic checking of water positions facilitates the calculation of the diffusion coeffficient in these three layers for those water molecules that continuously reside in the respective layers. Translational Diffusion. A self-diffusion coefficient may be used as a measure of the mobility of hydration water molecules surrounding a protein surface. Self-diffusion coefficient may be determined from (i) the Green−Kubo equation37−39 that relates the self-diffusion coefficient to the integral of the velocity autocorrelation function and (ii) the Einstein equation,40 which relates the mean-square displacement of the water molecules to the time at which this displacement occurs. Velocity Autocorrelation Function, VACF. Water dynamics in the hydration layer of the protein may be analyzed through the evaluation of the normalized velocity autocorrelation function, Cvv(t). A zero value of the normalized Cvv(t) represents the onset of the diffusive regime, which may be obtained from the plot of normalized Cvv(t) versus time. Cvv(t) may be calculated as

Figure 1. Normalized velocity autocorrelation function of water molecules in the hydration layer at the surface of ordered proteins/ regions (black solid line) and disordered proteins/regions (red dashed line). The blue solid line is the normalized VACF for SPC/E bulk water. The inset figure magnifies the VACF from 0.07 to 0.2 ps.

where C vv (t) in eq 2 is the unnormalized velocity autocorrelation function and the spatial dimensionality is d = 3. The values of DVACF obtained from eq 2 are provided in Table 1. The value of DVACF for bulk water is found to be 2.635 × 10−5 cm2/s which matches with the earlier reported values of the diffusion coefficient for SPC/E water model.34,42 The values of DVACF in Table 1 reveal that the water molecules in the disordered proteins/regions have greater mobility as compared to the globular protein/ordered regions, as indicated by a higher value of DVACF of water around IDPs and IDPRs-D. This difference in the values of DVACF between the globular and disordered proteins/ordered and disordered regions is more pronounced in the hydration layer, while the water molecules in layer I and layer II for all proteins show a similar behavior as that of the bulk water. Mean-Square Displacement, MSD. Alternatively, the mobility of water molecules may be also calculated from Einstein’s equation which relates DMSD with the slope of the mean-square displacement (MSD) as

⟨vi(t + t ) ·vi(t )⟩ ° ° ⟨vi(t ) ·vi(t )⟩ (1) ° ° where vi(to) and vi(to + t) are the initial velocity (i.e., at t = to) and velocity at time t of the ith water molecule. The angular brackets indicate that the Cvv(t) is calculated by averaging over the total number of water molecules and 10 different time origins for each of the 25 runs for each protein. The final value of Cvv(t) is averaged over 25 independent simulation runs for each protein. Normalized VACF is calculated for the SPC/E bulk water and water molecules in three different layers (hydration layer, layer I, and layer II) around globular protein surface and plotted versus time in Figure S1 of the Supporting Information. The figure depicts that the diffusive regime is established within a fraction of 1 ps, which is depicted by value of the normalized Cvv(t), which sharply decays to 0 within a very short time. The relaxation of normalized Cvv(t) for bulk water matches well with the earlier reported results.41 While water molecules in layer I and layer II follow a similar trend for relaxation as that of the bulk water, those in the hydration layer show a maximum deviation from the bulk water behavior. Similar to globular proteins, Cvv(t) is also calculated for water molecules in three layers around IDPs, IDPRs-O, and IDPRs-D. Globular proteins/ordered regions are compared with the disordered proteins/regions on the basis of the normalized Cvv(t) in the hydration layer (see Figure 1), layer I (see Figure S2 of the Supporting Information), and layer II (see Figure S3 of the Supporting Information). Figure 1 and Figures S2, S3 of the Supporting Information depict different relaxation behavior of Cvv(t) around the ordered and disordered protein/ regions; this difference is especially discernible in the hydration layer. The self-diffusion coefficient of water, DVACF, may be calculated from Cvv(t), which may be given by Cvv(t ) =

D VACF = lim

t →∞

1 d

∫0

⟨|ri(t + t ) − ri(t )|2 ⟩ 1 ° ° lim Δt 2d Δt →∞ ⟨|Δri(t )|2 ⟩ 1 = lim 2d Δt →∞ Δt

DMSD =

where ri(to + t) and ri(to) are the position vectors of the ith water molecule at time t and time origin t = to, respectively, and the spatial dimension, d = 3. The MSD for each MD simulation run is evaluated by averaging over the total number of water molecules and 10 different time origins. The final value of MSD is averaged over 25 independent simulation runs for each protein. MSD is evaluated as a function of time for water molecules in the hydration layer, layer I, and layer II around globular protein, IDPs, IDPRs-O, and IDPRs-D. The results are displayed in Figure 2 along with the MSD of SPC/E bulk water. The figure depicts that MSD for bulk water shows a linear dependence on time, while MSD of water molecules in three different layers around proteins (globular and intrinsically

t

Cvv(t ) dt

(3)

(2) 13264

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Table 1. Mean Hydrophobicity (Hmean) Evaluated Using Kyte and Doolittle Scale, Diffusion Coefficient Calculated Using MSD (DMSD) and VACF (DVACF), α Values Obtained Using MSD for Water Molecules in Hydration Layer, Layer I, and Layer II around Globular Protein (1A4V), IDPs (α-synuclein), IDPRs-O (1CD3-O, 1MVF-O, and 1F0R-O), and IDPRs-D (1CD3-D, 1MVF-D, and 1F0R-D) DMSD/DVACF (×10−5 cm2/s)

a

α

protein

Hmean

hydration layer

layer I

layer II

hydration layer

layer I

layer II

1A4V α-synuclein 1CD3-Oa 1CD3-Db 1MVF-Oa 1MVF-Db 1F0R-Oa 1F0R-Db

0.475 0.455 0.382 0.369 0.508 0.413 0.439 0.359

1.67/1.60 1.87/1.90 1.72/1.72 1.90/1.92 1.75/1.78 1.82/1.85 1.81/1.82 1.90/1.85

2.65/2.51 2.57/2.49 2.82/2.78 2.80/2.82 2.86/2.64 2.57/2.62 2.74/2.76 2.58/2.52

2.38/2.29 2.47/2.45 2.59/2.58 2.56/2.49 2.51/2.60 2.56/2.55 2.50/2.48 2.49/2.62

0.775 0.793 0.788 0.794 0.783 0.808 0.785 0.819

0.877 0.899 0.864 0.876 0.858 0.889 0.879 0.902

0.949 0.950 0.930 0.941 0.936 0.937 0.946 0.954

Ordered regions of IDPRs. bDisordered regions of IDPRs.

experimental and simulation studies.14,43−45 The value of α reflects the extent of restriction imposed by the protein surface on the diffusion of water molecules.15 Water molecules in the hydration layer exhibit a lowest value of α, which implies that water molecules interacting directly with the protein surface are highly restricted and move slowly. Comparison of the values of DMSD and α for the bulk water and water molecules in three layers around the surface of the globular protein reveal a maximum retardation of the water movement in the hydration layer around the protein surface. Similar to globular proteins, αsynuclein exhibits an anomalous diffusion of water molecules in the hydration layer indicating comparatively less restriction of the motion of water molecules at the surface of IDPs. An analysis of DMSD and α values of the hydration water molecules around IDPRs-O and IDPRs-D reveals that the motion of water molecules around the disordered regions is less restricted as compared to those around their ordered counterparts. This trend is followed in layer I and layer II as is evident from the α values. At larger water−protein distances (i.e., in layers I and II), where the water molecules are not in direct contact with the protein surface, DMSD approaches the value of that of the bulk water. The analysis of IDPRs-D reveals that the water molecules in the hydration layer of disordered regions of 1F0R with maximum structural disorder record the maximum value of α, while the disordered regions of 1CD3 with minimum structural disorder content are associated with a lowest value of α. Thus, among the partially disordered proteins, the extent of restrictions imposed by protein surface on hydration water is inversely proportional to the percentaged structural disorder of IDPRs (see Table 1). The values of DVACF and DMSD do not differ appreciably. Thus, disordered proteins/ regions are associated with a reduced anomaly in the diffusive behavior of hydration water as compared to ordered protein/ regions. Rotational Diffusion. Higher translational mobility of the hydration water molecules is also associated with a corresponding higher rotational mobility.15,46 The rotational diffusion of water molecules in all three layers around globular protein, IDPs, IDPRs-O, and IDPRs-D is evaluated to explore the rotational mobility. The reorientational dynamics of the dipole moment vector, μ⃗, of water molecules may be characterized in terms of the dipole−dipole time correlation function (TCF) defined as15,46,47

Figure 2. Mean-square displacement of water molecules as a function of time in hydration layer (black), layer I (red), and layer II (green) at the surface of ordered protein/regions (solid lines) and disordered protein/regions (dashed lines). Blue solid line is the MSD for SPC/E bulk water.

disordered proteins) displays a subdiffusive behavior with a power law as given by ⟨|r(t )|2 ⟩ ≃ t α

(4)

where the exponent α is 1 for a linear relationship between MSD and time, while deviation of α from 1 denotes anomalous diffusion. At very short times (i.e., < 1 ps), the MSD follows a ballistic regime where Δr2 ∝ t2, but at the long time limit, after establishment of the diffusive regime, MSD shows a linear dependence on time.13 From Figure 1, it is evident that VACF approaches a value of 0 within a fraction of 1 ps, which indicates the establishment of diffusive regime within 1 ps. Thus, the values of DMSD are calculated from the MSD values after 1 ps. The values of DMSD and α for the bulk water and water molecules in each layer surrounding globular, IDPs, IDPRs-O, and IDPRs-D are calculated and reported in Table 1. The value of DMSD for bulk water is found to be 2.66 × 10−5 cm2/s which matches well with the earlier results.43 Table 1 and Figure 2 depict that the MSD of water molecules in the hydration layer exhibit a subdiffusive behavior (indicated by α < 1) with time, which may be attributed to the roughness and geometrical disorder of the protein surface as reported in earlier 13265

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Table 2. τ and β Values Calculated by Fitting the Dipole− Dipole Time Correlation Function, Cμ(t), for Water Molecules in the Hydration Layer, Layer I, and Layer II, around Globular Protein (1A4V), IDPs (α-Synuclein), IDPRs-O (1CD3-O, 1MVF-O, and 1F0R-O), and IDPRs-D (1CD3-D, 1MVF-D, and 1F0R-D)

⟨μî (t + t ) ·μî (t )⟩ ° ° ⟨μî (t ) ·μî (t )⟩ (5) ° ° where μ̂ i(to + t) and μ̂ i(to) represents the unit dipole moment vector of the ith water molecule at time t and time t = to. The ensemble averaged behavior of the dipole−dipole time correlation function ⟨Cμ(t)⟩ is evaluated by averaging over the trajectories of 10 different time origins and 25 independent simulation runs for each protein. Cμ(t) is evaluated as a function of time for water molecules in the hydration layer (see Figure 3), layers I and II (see Figures S4 and S5, respectively, of Cμ(t ) =

τ protein 1A4V α-synuclein 1CD3-Oa 1CD3-Db 1MVF-Oa 1MVF-Db 1F0R-Oa 1F0R-Db bulk water a

18.18 15.72 17.95 15.16 14.48 14.12 15.27 13.64

β

layer I layer II 4.11 4.03 3.95 3.92 4.16 3.93 4.08 4.04 3.49

3.71 3.65 3.68 3.63 3.86 3.69 3.72 3.66

hydration layer 0.569 0.583 0.547 0.591 0.604 0.647 0.577 0.623

layer I

layer II

0.714 0.728 0.691 0.739 0.692 0.713 0.743 0.729 0.770

0.755 0.782 0.745 0.763 0.754 0.787 0.747 0.774

Ordered regions of IDPRs. bDisordered regions of IDPRs.

protein surface. A value of β < 1 denotes complex dynamics (characterized by multiple exponentials) of hydration water molecules around a protein caused by its surface roughness and topology. Thus, the rotational motion of the water molecules around the protein surface is also restricted in a similar way as the translational motion. The values of τ and β imply the slow reorientation of water molecules around the globular protein/ ordered regions as compared to that around the disordered proteins/regions. The behavior of water molecules around the disordered proteins/regions does not differ appreciably from that of the bulk as indicated from the trend of variation of Cμ(t). The difference in the orientational relaxation dynamics of water molecules around the ordered and disordered proteins/ regions is more pronounced in the hydration layer where IDPs and IDPRs have a high value of β and a low value of τ as compared to globular protein and IDPRs-O, respectively. The values of τ (see Table 2) of IDPRs-D depict that the orientational motion of water molecules in the hydration layer is fastest around the disordered regions of 1F0R with maximum structural disorder, and slowest around 1CD3, with minimum structural disorder. Thus, the orientational motion of water molecules in the hydration layer is directly proportional to the structural disorder content in IDPRs. Thus, the trend of variation of Cμ(t) reveals that the reorientational diffusion of water molecules around the disordered proteins/regions is less restricted with respect to the bulk water, while the water molecules in the vicinity of globular proteins/ordered regions display highly restricted orientational motions. To test whether results are dependent on the chosen water model (SPC/E), simulations of all five proteins are also performed using the TIP3P water model. For this purpose, 3 out of 25 conformations are selected randomly for all five proteins, and 500 ps MD simulation runs are performed for each of them in NVE ensemble with a time step of 1 fs. Three independent MD simulations of 500 ps each are also performed for TIP3P bulk water. MSD and dipole−dipole time correlation function are evaluated in the same manner as explained above and the results are presented for bulk water and water molecules in three different layers around 1A4V, IDPRs-O, IDPRs-D, and α-synuclein in Figures S6 and S7 and Table S1 of the Supporting Information. Translational and rotational diffusion of water molecules reveals the SPC/E and TIP3P

Figure 3. Rotational reorientation of the SPC/E bulk water (blue solid line) and water molecules in the hydration layer at the surface of ordered protein/regions (black solid line) and disordered proteins/ regions (black dashed line).

the Supporting Information) around the globular protein, IDPs, IDPRs-O, and IDPRs-D, respectively. The value of Cμ(t) for bulk water (SPC/E) is also plotted in all three figures for comparison. The reorientational time for water molecules is estimated from the decay of Cμ(t) curves fitted to a single stretched-exponential function as Cμ(t ) = A exp −(t /τ )β

hydration layer

(6)

where τ is the orientational relaxation time required for the rotation of tagged water molecule, and β denotes the exponent of the stretched-exponential. For a simple exponential decay β = 1, while the value β < 1 indicates the deviation from a first order decay.41 The values of τ and β obtained by fitting to a stretched-exponential function are reported in Table 2. For each protein, water molecules in the hydration layer, and in layers I and II, have longer orientational relaxation times as compared to that of bulk water. Water molecules in the hydration layer depict the maximum deviation from the simple exponential behavior as suggested by β values. The reciprocal of the exponent of the stretched-exponential, β, is related to the heterogeneity, h,48 in the water dynamics. For h = 1 (i.e., β = 1), the dipole−dipole correlation decay curve is characterized by a single exponential, while for h > 1 (i.e., β < 1), the decay curve comprises multiple exponentials. Hydration water around the protein surface exhibits heterogeneous dynamics at different time and length scales; even water molecules very near to the protein surface display different dynamics depending upon their interactions with polar/nonpolar or charged sites on the 13266

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anomalous behavior of water around IDPs/IDPRs to some extent as compared to the globular proteins, which is also supported by the results of earlier studies.45,50 Since intrinsically disordered proteins/regions exist as an ensemble of interconverting conformations, their internal fluctuations and rapid conformational changes lead to a relatively higher mobility of hydration water molecules as compared to those around globular proteins/ordered regions. Mean Number of H-Bonds. The enhanced mobility of the hydration water molecules around IDPs/IDPRs-D as compared to those around the globular protein/IDPRs-O may be rationalized by analyzing the water−water interactions at the surface of the selected proteins. Water−water hydrogen bonds which characterize the water−water interactions, around the protein surface, are calculated from the geometrical criteria according to which two water molecules are considered to be hydrogen-bonded if the following are true: (i) Oxygen−oxygen distance between these two water molecules is less than 3.5 Å. (ii) Their oxygen−hydrogen−oxygen angle is more than 150°. The mean number of hydrogen bonds, ηHB, is evaluated by averaging over a set of 25 independent runs for water molecules in the hydration layer of 1A4V, α-synuclein, 1CD3, 1MVF, and 1F0R, respectively, and plotted against DMSD in Figure 5. A

water model differ quantitatively while depicting a qualitatively similar trend, which is reflected in higher mobility of water molecules (both for SPC/E and TIP3P) around disordered regions/proteins as compared to those around ordered regions/proteins. Thus, the conclusions presented in this work are consistent, irrespective of the water models used to simulate the proteins. Mean-Square Fluctuations. The dynamics of lysozyme, a globular protein, strongly influences the dynamics of water molecules around it with maximum dynamical coupling in the hydration layer.49 The mean-square fluctuations of the amino acid residues, MSF, which characterize the time-averaged internal motions of a protein are analyzed to examine a possible connection between the diffusion of the hydration water molecules and the flexibility of that protein. Only Cα atoms of the amino acid residues are considered in this analysis. Mean-square fluctuation, MSF, for each amino acid residue is calculated as 1 MSF = T

T

∑ (ri(t ) − ri)̃ 2 t=1

(7)

where T is the total simulation time, ri(t) represents the position of the ith residue at time t, and r̃i is the time averaged position of the ith residue. Figure 4 depicts the MSF of the Cα

Figure 4. Average mean-square fluctuations (MSF) of Cα atoms of 1A4V (black solid line), α-synuclein (red circled line), IDPRs-O (red solid line), and IDPRs-D (red circled line).

Figure 5. Mean number of water−water hydrogen bond at the protein surface plotted against their hydration water diffusion coefficient calculated from (a) MSD and (b) VACF.

atoms of the amino acid residues of 1A4V, α-synuclein, 1CD3, 1MVF, and 1F0R. The plot depicts that the amino acid residues of both IDPs and IDPRs-D experience more fluctuations with time as compared to the globular protein. Even IDPRs-O show more fluctuations of their residues with respect to the completely ordered protein, 1A4V. The residues of the disordered regions (IDPRs-D) of the partially disordered proteins show more fluctuations compared to those in the ordered regions (IDPRs-O). Increased residue fluctuations in IDPs and IDPRs-D as compared to those around the globular protein and IDPRs-O may lead to higher values of α and DMSD for the water molecules around the disordered proteins/ regions, respectively. Figure 4 and Tables 1 and 2 reveal that increased internal motions in proteins are also associated with higher translational and rotational mobility of water molecules in their vicinity. Thus, protein motion reduces the restriction on the movement of hydration water molecules and reduces the

linear correlation is observed with a correlation coefficient of 95.9, between ηHB and the diffusion coefficient of water molecules in the hydration layer. This result is consistent with that of Kuffel et al.,50 where they reported a direct correlation of the mean number of water−water hydrogen bonds with the diffusion coefficient and a structural order parameter. A higher value of this order parameter depicts a tetrahedral arrangement of a tagged water molecule with its four nearest neighbors. This order parameter is correlated to a higher mean number of water−water hydrogen bonds, which in turn is correlated to a higher value of the diffusion coefficient. Our recent work22 establishes that the water molecules around intrinsically disordered proteins/regions have a higher value of the tetrahedral order parameter (representing a more symmetric tetrahedral arrangement) as compared to water molecules around ordered proteins/regions. This implies that since water molecules around intrinsically disordered proteins possess a 13267

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analyzed the water motion relative to the protein surface. While the present work analyzes the motion of water molecules that reside in the hydration layer for a given time relative to their respective initial position coordinates. Since disordered proteins exhibit increased conformational fluctuations (refer to the Mean-Square Fluctuations section as discussed above), therefore, the hydration water molecules electrostatically associated with the charged residues also fluctuate along with the disordered regions of the protein. These water molecules may also switch between the different charged sites of the disordered proteins/regions thereby showing higher water movements. Since this switching of water molecules among different charged sites on disordered proteins/regions surface does not allow water molecules to leave the hydration layer, water molecules around disordered proteins/regions show higher residence times. Thus, our earlier results confirm the findings of this study and conclude that increased fluctuations in disordered proteins/regions facilitate higher mobility of the surrounding water molecules, while confining them within the hydration layer.

more symmetric tetrahedral arrangement, they should have a higher order parameter, which may lead to a higher mean number of water−water hydrogen bonds around intrinsically disordered proteins. Thus, higher mobility of the hydration water molecules around disordered proteins/regions may be correlated with an increased number of water−water hydrogen bonds and a symmetric tetrahedral arrangement of hydration water molecules. Hydration Capacity and Hydrophobicity. The greater mobility of hydration water around disordered proteins may be also related to their respective hydration capacities. The decrease in the hydration level may cause more restricted motion of water molecules in the hydration layer which is confirmed by both experiment and simulation studies.14,51,52 Intrinsically disordered proteins are associated with more hydration capacity,22 as compared to globular proteins, which is given by the ratio of the total number of water molecules to the total number of residues in a protein. Since disordered proteins/regions are typically extended, they provide more interaction sites to the surrounding water molecules. Hence, disordered proteins/regions bind relatively more hydration water molecules as compared to the globular protein/regions. Several studies have confirmed that, at low hydration level, less hydrogen-bonded water clusters are present, while with an increase in the hydration level, the protein surface is covered with a greater number of hydrogen-bonded water clusters,49,53 which leads to an increase in the mean number of water−water hydrogen bonds. A higher value of the mean number of water− water hydrogen bonds is correlated with a higher diffusion coefficient. Thus, higher hydration capacity of IDPs/IDPRs leads to a higher mean number of water−water hydrogen bonds which implies higher mobility of hydration water around them. Also, it would be interesting to examine the relation between the hydration water mobility and the mean hydrophobicity of the protein surface. In this regard, we have calculated mean hydrophobicity, Hmean, using the Kyte and Doolittle scale54,55 for each protein. The values of Hmean for globular protein, IDPs, IDPRs-O, and IDPRs-D, are provided in Table 1 along with their diffusion coefficient values. These values indicate that low mean hydrophobicity, Hmean, of a fully disordered protein is accompanied by a high value of diffusion coefficient of the hydration water molecules as compared to that of a globular protein. Similarly, there is a decrease in the value of hydrophobicity from IDPRs-O to IDRPs-D with a corresponding increase in their hydration water mobility as is evident from the diffusion coefficient. This implies that higher mobility of the hydration water molecules around the protein surface may be due to its low mean hydrophobicity. Our recent work22 suggested slow dynamics of hydration water around the surface of disordered proteins/regions as compared to those around globular proteins. Since disordered proteins/regions are associated with more charged residues, these proteins are stabilized by the attractive electrostatic interactions with the surrounding water molecules. These interactions restrict water molecules to reside within the hydration layer for a longer time and prevent them to leave the hydration layer as depicted by their higher residence times. In the present work, we found higher mobility of water molecules around disordered proteins/regions as compared to those around ordered proteins/regions which may seem counterintuitive. However, these two works do not contradict each other since our earlier work described the residence time of water molecules within the hydration layer, and therefore

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CONCLUSIONS

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ASSOCIATED CONTENT

This work explores the hydration water dynamics at the surface of partially/fully intrinsically disordered proteins. In this context, 25 independent simulations of five proteins (one globular, three partially disordered, and one fully disordered) are performed using the SPC/E water model. The mean-square displacement, velocity autocorrelation function, and dipole− dipole time correlation function are evaluated to probe the translational and the rotational diffusion of water molecules in the hydration layer, layer I, and layer II at the surface of the globular and disordered proteins and ordered/disordered regions. Results from the MSD and VACF reveal that the diffusion of water molecules at the surface of IDPs/IDPRs-D is less restricted as compared to the globular protein/IDPRs-O. Restriction imposed by the protein surface is inversely proportional to the distance of water molecules from the protein surface. Likewise, water molecules at surface of ordered protein/regions reorient slowly as compared to the water molecules around disordered proteins/regions. Higher mobility of the hydration water at the surface of IDPs/IDPRs-D is correlated to the higher number of mean water−water hydrogen bonds with respect to the globular proteins/ IDPRs-O. Higher hydration capacity, low mean hydrophobicity, and increased inner protein motions of the disordered proteins/regions also support higher mobility of the hydration water. Thus, hydration water exhibits a heterogeneous dynamics at different length scales in the vicinity of the globular and intrinsically disordered proteins/regions, reflecting the different type and extent of interactions due to the varied topology of the protein surface.

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b07248. Velocity autocorrelation function and reorientational relaxation for bulk water and water molecules around the protein surface (PDF) 13268

DOI: 10.1021/acs.jpcb.5b07248 J. Phys. Chem. B 2015, 119, 13262−13270

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the University of Delhi and DST, India (Project No. SB/S1/PC-023/2013), for financial support. P.R. acknowledges University Grant Commission, India, for providing financial support in the form of a Senior Research Fellowship. The authors also gratefully acknowledge Bioinformatics Resources and Applications Facility (BRAF) of the Center for Development of Advanced Computing (CDAC), India, for providing the adequate computational facility in the Biogene cluster.

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