Local Structure and Dynamics of Hydration Water in Intrinsically

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Local Structure and Dynamics of Hydration Water in Intrinsically Disordered Proteins Pooja Rani, and Parbati Biswas J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp511961c • Publication Date (Web): 14 Apr 2015 Downloaded from http://pubs.acs.org on April 18, 2015

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The Journal of Physical Chemistry

Local Structure and Dynamics of Hydration Water in Intrinsically Disordered Proteins Pooja Rani and Parbati Biswas∗ Department of Chemistry, University of Delhi, Delhi-110007 E-mail: [email protected]

∗

To whom correspondence should be addressed

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Abstract Hydration water around protein surface plays a key role in structure, folding and dynamics of proteins. Intrinsically disordered proteins lack secondary and/or tertiary structure in their native state. Thus characterizing the local structure and dynamics of hydration water around disordered proteins is challenging for both experimentalists and theoreticians. The local structure, orientation and dynamics of hydration water in the vicinity of intrinsically disordered proteins is investigated through molecular dynamics simulations. The analysis of the hydration capacity reveals that the disordered proteins have much larger binding capacity for hydration water than globular proteins. The surface and radial distribution of water molecules around the disordered proteins depict a similar trend. The local structure of the hydration water evaluated in terms of the tetrahedral order parameter, shows a higher order among the water molecules surrounding disordered proteins/regions. Residence time of water molecules clearly exhibit slow dynamics of hydration water around the surface of disordered proteins/regions as compared to globular proteins. The orientation of water molecules is found to be distinctly different for ordered and disordered proteins/regions. This analysis provides a better insight into the structure and dynamics of hydration water around disordered proteins.

Keywords Survival probability, Tetrahedral order parameter, Orientation, Residence time, Radial Distribution Function, Hydration Capacity

Introduction Water plays a versatile role in elucidating the structure, folding, function and dynamics of proteins. 1,2 Particularly, water in the protein interior bridges between the donors and acceptors of the hydrogen bond of a protein to stabilize its structure and also executes enzymatic 2


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functions by mediating proton transfer reactions. 3 Water-protein interactions delineate the free energy landscape of proteins that controls their structure, folding and stability respectively. 4 Water molecules are abundant at the interfaces of proteins and nucleic acids and the functions of these biomolecules are primarily regulated by the structure and dynamics of hydration water. 5 Hydration water occurs at the protein surface 6 and directly interacts with the protein in contrast to the bulk water molecules. Experimental techniques like NMR, 7 femtosecond fluorescence 8 and X-ray crystallography 9 have been extensively used to investigate the properties of hydration water in globular proteins. While most of these experimental techniques probe only the average properties of a protein across the hydration layer, computational algorithms like molecular dynamics simulations are able to provide a detailed residue-specific picture of the hydration dynamics. 10–12 Although hydration water around globular proteins are extensively studied, little is known about the hydration water around intrinsically disordered proteins (IDP). The lability of the hydration layer is a key factor governing the fast conformational fluctuations and the internal dynamics of the IDPs. Thus monitoring the hydration layer dynamics may provide the much needed insight into the oligomerization propensity, formation of protein aggregates and instantaneous non-cooperative structural transitions of IDPs promoting context-dependent functional specificity. 13–15 IDPs lack secondary and/or tertiary structure in their native state and exist as dynamic ensembles of flexible inter-convertible conformations under standard physiological conditions. IDPs are devoid of a regular hydrophobic core as found in globular proteins. The hydrophobic residues are distributed all over the protein with a preponderance of highly charged residues yielding a non-compact structure. The intrinsic disorder of a protein may be of two types: 16 (i) Intrinsically disordered protein regions (IDPRs) with well-defined secondary structures coexisting with highly flexible disordered regions (ii) Intrinsically disordered proteins (IDPs), which are characterized by the complete absence of well-defined tertiary structures, resembling a typical random coil. The functional importance of these proteins are illustrated by their indispensable role in cellular phenomena, regula-

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tory processes of eukaryotic cell, transcriptional and translational processes. 17–19 IDPs are also associated with a variety of deposition diseases like Alzheimer’s disease, prion disease, Parkinson’s disease and Huntington’s disease 20,21 and pathological conditions like amyloidosis, some forms of cancer, diabetes and cardiovascular diseases. 18,22 Solid state NMR relaxation measurements suggested significant differences between the hydration pattern of globular proteins and IDPs. 23 This work investigates the structure and dynamics of hydration water in the vicinity of partially disordered (IDPRs) and completely disordered (IDPs) proteins relative to that of the globular proteins. In this regard, the properties of hydration water such as the radial distribution functions, tetrahedral order parameter, orientation and survival probability, are evaluated for one globular (1A4V ), three partially disordered (1CD3, 1M V F and 1F 0R) and one completely disordered (α-synuclein) protein. The results obtained from the molecular dynamics (MD) simulations depict that the IDP/IDPRs have a higher capacity to bind hydration water as compared to the globular proteins. The radial distribution function also supports this observation by exhibiting a higher density of hydration water around the disordered proteins. Local structure of the water molecules around the protein surface is evaluated in terms of the tetrahedral order parameter, which portrays a tetrahedral arrangement of water molecules around disordered protein/regions as compared to those around globular proteins. This finding is irrespective of whether the nearest neighbors of the target water molecules includes or excludes the protein heavy atoms. The orientation of hydration water molecules around disordered proteins are markedly different from that of the globular proteins. The survival probability of each of the selected proteins is calculated to find the residence time of hydration water molecules. These results confirm the sluggish dynamics of water molecules around disordered proteins as compared to those of globular proteins.

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Materials and Methods Protein Selection for Molecular Dynamics Simulation The structure and dynamics of hydration water around globular and disordered proteins is evaluated through molecular dynamics simulations of selected globular and disordered proteins. The disordered proteins are chosen based on the following criteria: (i) all four proteins have varying percentage of structural disorder. While 1CD3 has the minimum percentage of disorder content, α-synuclein is a completely disordered protein with maximum structural disorder (ii) the location of the disordered regions are different for the four disordered proteins i.e., C-terminus for 1M V F , N-terminus for 1F 0R, middle regions for 1CD3 and complete disorder in α-synuclein (iii) the selected proteins collectively represent all 20 amino acids in their disordered regions respectively. The crystal structure of α-lactalbumin is obtained from the RCSB PDB (ID: 1A4V ) and is used as an initial template to perform MD simulations. The scaffolding protein GPB (PDB ID: 1CD3) with 120 residues is present in complexed form with single stranded DNA, scaffolding protein GPD and capsid proteins. Scaffolding protein GPB plays a significant role in the conformational changes coupled with capsid maturation. 24 Human factor Xa (PDB ID: 1F 0R) with 134 residues is complexed with the potent inhibitor and is involved in the cascade-like activation of the coagulation system. This protein may be used as a target for the development of anticoagulant/antithrombotic drugs, which may be used for the treatment of thromboembolic disorders. 25 PemI-like protein (PDB ID: 1M V F ) comprising of 82 residues occurs as a complex with the antibody fragment (cAbmaz1). This protein is a part of the unique bacterial genetic system known as the addiction module and is involved in bacterial programmed cell death. 26 The three-dimensional structures of the ordered regions of 1CD3, 1M V F and 1F 0R are obtained from the RCSB PDB, while the disordered regions of these proteins have missing electron density in their respective PDB files. MODELLER 27 is used to model the missing residues of the disordered regions based on the fact that disordered regions are primarily non-compact with minimal

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secondary structures. MODELLER is provided with the dual input i.e. the sequence in the FASTA format and the X-ray crystal structure of the ordered region for the given protein. The modeling of disordered regions is done in such a way that the structure of the ordered part of the protein is exactly conserved, i.e., the RMSD (root-mean-square deviation) of the ordered part of the modeled protein relative to its native state is zero. α-synuclein with 140 residue is completely disordered in its unbound monomeric state but may self-assemble into ordered oligomeric and fibrillar aggregates. α-synuclein plays an important role in proper functioning of brain 28 and its aggregation is directly related to Parkinson’s disease. 29 For α-synuclein, sequence is used as the only input to model its structure.

Simulation details Molecular Dynamics Simulation Explicit-water molecular dynamics simulations for the selected proteins (1A4V , 1CD3, 1F 0R, 1M V F and α-synuclein) were performed using AMBER 12 simulation package. 30 LEAP subroutine was used to add the missing hydrogen atoms in each protein structure. The water model TIP3P 31 was used for water molecules, while the protein atoms were treated with ff99SB force field 32,33 with the periodic boundary conditions. Each protein was solvated in a cubic box of TIP3P water molecules with the box edge at a distance of 10 ˚ A from the protein surface, with a closeness parameter of 1 ˚ A. The dimensions of the simulation box for the solvated proteins 1A4V , 1CD3, 1F 0R, 1M V F and α-synuclein were A×98.363 A×118.869 ˚ A, 91.309 ˚ A×80.771 ˚ A×128.131 ˚ A, 70.402 ˚ A×67.045 ˚ A×69.842 ˚ 63.118 ˚ ˚ A respectively. The A×87.569 ˚ A×69.842 ˚ A and 131.270 ˚ A×59.244 ˚ A×62.546 ˚ A, 112.477 ˚ charge on the solvated proteins were neutralized by adding either Na+ or Cl- ions. Particle mesh Ewald (PME) algorithm 34 with a real space cutoff of 8.0 ˚ A was employed for treating the long-range electrostatic interactions with a grid spacing of 1.0 ˚ A. Non-bonded interactions were treated using the minimum image convention with a cutoff distance of 8.0 ˚ A. The SHAKE algorithm 35 was used to constrain the motions of hydrogen atoms to their equilib6


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rium bond lengths. Energy minimization of each protein system was performed to remove any unfavorable steric repulsions resulting from the system preparation. Each solvated protein was energy minimized twice by the conjugate gradient method; initially, the solvent was energy minimized by keeping the protein constrained followed by the energy minimization of the solvated protein. The energy minimized system was equilibrated in a NVT ensemble for 100 ps at an initial temperature of 100 K and the temperature was gradually raised to 300 K at constant volume. This was followed by equilibration in NPT ensemble for 5 ns at constant temperature of 300 K and a pressure of 1 bar. Constant temperature and pressure were maintained through Berendsen’s temperature bath with a coupling constant of 2 ps and barostat with a coupling constant of 1 ps, respectively. 36 The equilibrated system was subjected to a NPT production run of 100 ns with a time step of 2 fs for each protein. Snapshots of the trajectory are saved at an interval of 2 ps. Root-mean-square deviation (RMSD) is plotted as a function of simulation time for each protein in Figure S1 of the Supplementary material. The simulation trajectory of the final production run was used to calculate the water distribution functions, tetrahedral order parameter, orientation and survival probability to analyze the behavior of hydration water around partially and completely disordered proteins.

Radial distribution The extent of organization of hydration water around the protein surface may be evaluated in terms of the surface (water-protein) and the radial (water-water) distribution functions. The surface distribution function (SDF) gives the average density of water molecules around protein as a function of distance from the protein surface. 37 The average number density of water molecules is calculated as the ratio of the number of water molecules present per unit volume of the ellipsoidal shells located at different distances from the protein surface. 38

ρwp (l) =

4 π 3

n (a + l) (b + l) (c + l) − 43 πabc 7


(1)


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where, l represents the distance between water molecules and protein surface; a, b and c are three principal semi-axis lengths of the inertial ellipsoid, which characterize the shape of a given protein. The inertial tensor, T, which may be used to define this inertial ellipsoid is expressed as 39,40

T(β,γ) =

N N 1 XX (riβ − rjβ ) (riγ − rjγ ) 2N 2 i=1 j=1

(2)

where, N is the total number of atoms of a protein, riβ denotes the β th component of position coordinates of the ith atom in three-dimensional space and β/γ = x, y, z. The eigenvalues, λi , are defined as the values of the three semi axis lengths of the inertial ellipsoid 1

and are related as αi = (3λi ) 2 , where αi = a, b, c. 41 The radial distribution function (RDF) gives the density of water molecules as a function of the distance from a tagged water molecule. The raw RDF gives the actual number of water molecules around a tagged water and is related to the water-water interactions. The raw distribution of water is calculated as the average number density of water molecules around a tagged water molecule and is given by 37

ρww raw (rw ) =

4 π 3

nww (rw + drw )3 − 43 πrw3

(3)

where nww is the number of water molecules in shell of thickness drw around a tagged water molecule; rw denotes the distance between the oxygen atom of the tagged water molecule and any other water molecule. The distribution of water molecules at protein surface is different from that of bulk water, where only water-water interactions are considered, due to interactions between water molecule and protein atoms. The presence of the protein molecule alters the normalized density of water molecules as compared to that of the bulk water. The raw RDF of water is modified due to water-protein interactions, and is represented by the density normalization factor. The details for the calculation of the density normalization factor is given in Ref. 38 (see Supplementary material for brief explanation). The normalized

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radial distribution function (normalized RDF) may be represented in terms of the relative density of water, calculated as

ρnormalized =

hρraw (rw )i hρnor (rw )i

(4)

The calculation of raw RDF, hρraw (rw )i, and the density normalization factor, hρnor (rw )i, is provided in the Supplementary material.

Tetrahedral Order Parameter Tetrahedral order parameter or orientational order parameter characterizes the local structure of water molecules by measuring the extent to which a given water molecule and its four nearest neighbors adopt a tetrahedral arrangement. Several studies have reported the tetrahedral order parameter of hydration water molecule around small proteins and DNA. 42–46 The orientational order parameter may be calculated as 47,48

qtet

µ ¶2 3 4 1 3X X cos (ψj,k ) + =1− 8 j=1 k=j+1 3

(5)

where ψj,k is the angle formed between the oxygen atom of a given water molecule and the bond vectors rij and rjk of its four nearest neighbor atoms j and k. The value of qtet is 1 for a perfect tetrahedral arrangement and 0 for a random arrangement. The calculation of tetrahedral order parameter is performed in two ways depending upon the selection of four nearest neighbors of a particular water molecule as: (i) considering only water molecules as nearest neighbors and (ii) including protein heavy atoms (C, N, O etc.) along with water molecules. The distribution of the tetrahedral order parameter is calculated as a function of both water-protein and water-water distances. 48

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Survival Probability Survival probability quantitatively characterizes the relaxation dynamics of water molecules surrounding the protein by measuring the mobility of water molecules in terms of the local residence time. Survival probability represents the probability that a water molecule is continuously present within a specified region for a time t and may be expressed as 5,49

S (t) =

N X i=1

trun −to X 1 Pi (r, to , to + t) trun − t + 1 t

(6)

o

where N represents the total number of water molecules, trun is the total time duration of the simulation run and r is the region defined by volume element within the cutoff radius of 4 ˚ A around protein surface. The value of Pi (r, to , to + t) is taken as 1 if water molecule resides continuously in volume element r between times to and to + t and as 0 otherwise. It is assumed that the time interval (i.e. 2 ps) between snapshots is sufficiently small for a significant displacement of the water molecules.

Figure 1: The distribution of the ratio of total number of water molecules and total residues in proteins.

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Results and discussion The structure and dynamics of the hydration water around intrinsically disordered proteins is expected to be significantly different from those of the globular ones. The hydration pattern of the intrinsically disordered proteins (IDPs and IDPRs) are investigated with respect to the distribution, structure, orientation and survival probability of water molecules in the vicinity of the protein. Globular and intrinsically disordered (IDPs and IDPRs) proteins may be differentiated by evaluating their hydration capacity. The hydration capacity may be denoted as the ratio of the number of water molecules within a distance cutoff of 4 ˚ A from the protein surface to the total number of amino acid residues present in the protein. Hydration capacity is calculated for the globular (1A4V ), ordered and disordered regions of partially disordered, 1CD3, 1M V F and 1F 0R and completely disordered protein, α-synuclein and plotted in Figure 1. The distribution of the hydration capacity reveals that the number of hydration water molecules for IDPs is much higher than that of the globular protein. The higher hydration capacity of IDPs may be attributed to the largely exposed surface of disordered protein/regions. Extended surface of IDPs facilitates the binding of larger number of water molecules as compared to globular proteins. This implies that intrinsically disordered proteins have much larger binding capacity for hydration water which is in accordance with the earlier results. 23 It is also observed that among the IDPRs, the disordered regions show much larger hydration capacity as compared to their corresponding ordered regions. The organization of hydration water molecules around protein surface may be characterized by the SDF and RDF respectively. The average density of water molecules as a function of water-protein distance is plotted in Figure S2 of the Supplementary material for globular proteins, IDPRs and IDPs respectively. The average density of water molecules is found to be higher for the disordered regions of the IDPRs, while the ordered regions depict a slightly decreased density corresponding to the first and second peak of SDF. 1F 0R with maximum percentage of disordered regions, records a maximum difference in the density of water at the ordered and disordered regions. The density of the hydration water around the completely 11



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Figure 2: Average tetrahedral order parameter calculated by (a) excluding and (b) including the protein heavy atoms, as a function of water-proteins distance. disordered protein, α-synuclein, is found to be higher as compared to that around the globular protein. The increased density of hydration water molecules around disordered region and/or proteins may be attributed to their net charge. Earlier study also shows that the residues with net charges are associated with an increased density of water around them. 50 Since the sequences of IDPs/IDPRs are characterized by high mean net charge, they depict an increased water density in their respective hydration shells. The radial distribution function of these proteins are plotted in Figures S3 and S4 of the Supplementary material. The density normalization factor, which accounts for the water-protein interactions is evaluated from the SDF (density of water molecules as a function of water-protein distance) and is observed to be different for globular and disordered proteins. Thus the density normalization function and the RDF of water molecules around disordered proteins is different compared to those of globular proteins (refer to Figures S3 and S4 of the Supplementary material). A closer look at the SDF reveals a higher density of water molecules around the surface of disordered proteins as compared to globular ones. Thus, the distribution of hydration water around disordered proteins is found to be markedly different from that of the globular proteins.

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Figures 2(a) and (b) depict the average tetrahedral order parameter, qtet , of water molecules as a function of the water-protein distance. Figure 2(a) depicts the average value of qtet calculated by considering only water molecules as four nearest neighbors, while the average qtet value calculated by including protein heavy atoms along with water molecules as four nearest neighbors is plotted in Figure 2(b). The order parameter, qtet , increases with an increase in the distance of the water molecules from the protein surface when only water molecules are considered as four nearest neighbors. But when protein heavy atoms are considered as nearest neighbors, the value of qtet for water molecules records an initial decrease, followed by a steady increase beyond a distance of 3.5 ˚ A from the protein surface. The minimum value of qtet is recorded at 3.5 ˚ A. The maximum value of qtet is 0.559 (excluding protein heavy atom) and 0.565 (including protein heavy atom) for 1A4V . For α-synuclein, this value is 0.565 (excluding protein heavy atom) and 0.568 (including protein heavy atom) depicting that the hydration water molecules are more ordered around disordered proteins. A similar trend is observed for the qtet values of the ordered and disordered regions of partially disordered proteins. The qtet values for the ordered regions of 1CD3, 1M V F and 1F 0R display maxima at 0.542, 0.545 and 0.547, respectively, when the protein heavy atoms are excluded, while this value changes to 0.543, 0.547 and 0.550, respectively, with the inclusion of protein heavy atoms as four nearest neighbors. The maximum values of qtet for the disordered regions of 1CD3, 1M V F and 1F 0R are 0.553, 0.553 and 0.558, respectively, when the protein heavy atoms are excluded, while it changes to 0.551, 0.549 and 0.559, respectively, with the inclusion of the protein heavy atoms. An additional MD simulation is also performed for bulk water. The simulation box with a dimension of 83.105 ˚ A comprised of 16062 TIP3P water molecules. The production run was A×82.905 ˚ A×83.053 ˚ performed for 100 ns at 300 K in the NPT ensemble. The value of qtet ranges between 0.525 and 0.572, which is in good agreement with the previous results for the tetrahedral order parameter of TIP3P water. 43 The maximum value of qtet is found to be higher when the protein heavy atoms are included in the calculation of order parameter. Figures 2(a) and (b) depict

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that qtet value of hydration water calculated by including and excluding the protein heavy atoms lie in a similar range as that of the bulk water (i.e. 0.525-0.572) at higher distances. The value of qtet , calculated by including and excluding the protein heavy atoms lead to similar conclusions that water molecules exhibit higher order around the disordered regions of IDPRs than their corresponding ordered regions. The extent of order in the arrangement of water molecules is directly proportional to the increase in the percentage of structural disorder of IDPRs. The water molecules surrounding completely disordered proteins are found to be more ordered compared to water molecules around globular proteins with a similar size. The disordered proteins/regions have large exposed surfaces due to extended structures and are characterized by high mean net charge (see Table 1). Thus the interaction between the residues of disordered proteins and water molecules are relatively higher compared to those of the globular proteins. The increased tetrahedral order of water molecules for the disordered proteins/regions may be attributed to the increased interaction between the charged residues on the protein surface with the surrounding water molecules. A recent study 42 in lysozyme accounts for a relatively higher tetrahedral order of water molecules due to similar type of interactions. Another work 51 proposed that water molecules are more tetrahedrally structured around unfolded conformations rather than folded conformations of peptides. The result is more pronounced for 1F 0R, which has maximum structural disorder among the chosen IDPRs. Apart from average value of qtet , the distribution of qtet is also calculated at various distances of water molecules from the protein surface. The distribution of tetrahedral order parameter at water-protein distance 4 ˚ A depicted in Figure S5 and Figure S6 of the Supplementary material also support the higher value of qtet for water molecules surrounding the disordered regions. The average tetrahedral order parameter of hydration water molecules is also evaluated as a function of the water-water distance. Figures 3(a) and (b) depict average qtet of water molecules calculated as a function of the water-water distance by excluding and including the protein heavy atoms as four nearest neighbors respectively. Both figures show that water

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Figure 3: Average tetrahedral order parameter calculated by (a) excluding and (b) including the protein heavy atoms as a function of water-water distance. molecules are more ordered at a distance of 2.5 ˚ A , while the lowest value of qtet is recorded at a distance of 3.5 ˚ A. The variation of average qtet with water-water distance show a similar trend for IDPRs, IDPs and globular proteins. The values of qtet are higher for disordered regions in case of IDPRs and completely disordered proteins as compared to the ordered regions of disordered proteins and globular proteins. This observation is also supported by Figures 3(a) and (b) which depict average qtet and Figures S7 and S8 of the Supplementary material showing the distribution of qtet as a function of water-water distance. Table 1: Mean net charge and mean hydrophobicity values for proteins. Protein 1A4V α-synuclein 1CD3 (Ordered Regions) 1CD3 (Disordered Regions) 1M V F (Ordered Regions) 1M V F (Disordered Regions) 1F 0R (Ordered Regions) 1F 0R (Disordered Regions)

Mean net charge −0.057 −0.071 0.029 −0.096 −0.023 −0.132 −0.058 −0.109

Mean hydrophobicity 0.475 0.455 0.382 0.369 0.508 0.413 0.439 0.359

Thus, it may be expected that α-synuclein being a completely disordered protein should have higher tetrahedral order than all other selected proteins. However, the difference in the

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values of qtet of water molecules around α-synuclein and the globular protein is not markedly pronounced. This behavior may be related to the to the ratio of charge and hydrophobicity of the disordered proteins. The mean net charge 52 and mean net hydrophobicity 53 of globular proteins, ordered and disordered regions of IDPRs and IDPs 38 are provided in the Table 1. A closer inspection of these values reveal that α-synuclein has high charge to hydrophobicity ratio compared to the globular protein 1A4V , but lower than those of the disordered regions of the IDPRs. Thus the values of qtet of the water molecules lie in the intermediate region between those of the globular and partially disordered proteins.

Figure 4: Schematic representation of the vectors used to evaluate the orientation (i.e. cosθ and sinφ) of the water molecule. d is the dipole moment vector of the water molecule, rOP is the vector joining the oxygen atom of that water molecule to the nearest oxygen/nitrogen atom of the protein and rHH is the vector joining both hydrogens of the water molecule. The spatial arrangement of the water molecules in the vicinity of the protein may be assessed by measuring the orientation angles between water molecules’s oxygen atom and the oxygen/nitrogen atom of the protein. 54 To analyze the orientation of the hydration water relative to the surface of globular/disordered proteins, two orientational angles i.e. θ and φ are chosen as cosθ and sinφ, for a given water molecule. The angle between the dipole moment vector, d, of the water molecule and the vector, rOP , joining oxygen atom of water molecule to the nearest oxygen/nitrogen atom of the protein is denoted by θ. The angle φ is 16


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the dihedral angle between the plane spanned by the dipole moment vector, d, of the water molecule and the vector, rOP , joining the oxygen atom of that water molecule to the nearest oxygen/nitrogen atom of the protein and the plane spanned by the dipole moment vector, d, of the water molecule and the vector, rHH , joining two hydrogen atoms of water molecules (refer to Figure 4). For a given water molecule around the protein surface, cosθ = ed .eOP and sinφ = (ed × eOP ).(ed × eHH ), 49,54 where e is an unit vector in a given direction. The distribution of the fraction (i.e. fraction×100) of water molecules as a function of cosθ and sinφ are plotted in Figure 5 for the globular (1A4V ), ordered and disordered regions of partially disordered (1CD3, 1M V F and 1F 0R) and completely disordered (α-synuclein) proteins. The spatial distribution of the orientation (cosθ and sinφ) of hydration water molecules is found to be different for ordered and disordered proteins/regions. This difference is best exemplified for the ordered and disordered regions of 1F 0R. The results show that the orientation of water molecules around the ordered and disordered parts mainly differ in (i) the region R1 where the orientations of water molecules are defined by 101.537 < θ < 180.0 and −36.869 < φ < 36.869, (ii) the region R2 where the orientations of water molecules are denoted by 0.0 < θ < 66.422 and −36.869 < φ < 36.869. Water molecules around disordered protein/regions are preferred in the regions R1 and R2, while ordered protein/regions depict a less preference of water molecules in these regions (except 1M V F ). This implies that water molecules prefer specific orientations in R1 and R2 spanning the angular range −36.869 < φ < 36.869, with a significant population around disordered proteins/regions, while these orientations in R1 and R2 are abhorred by water molecules surrounding globular protein/regions. Thus, orientation of water molecules around ordered and disordered proteins differ significantly. The survival probability calculated for the globular (1A4V), partially disordered (1CD3, 1MVF and 1F0R) and completely disordered (α-synuclein) proteins are plotted in Figure 6. The survival probability may be fitted to a exponential function to extract the residence times as 5

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Figure 5: The percentage fraction of water molecules as a function of cosθ and sinφ for globular, partially disordered and completely disordered proteins.

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Figure 6: Survival probability of the hydration water molecules as a function of time. Solid line represents the data obtained using eq 6 while dotted lines show the fit function calculated using eq 7.

S (t) = a exp (− (t/τs )γ ) + b exp (− (t/τ2 )) + c exp (− (t/τ3 )) + np

(7)

where np is the number of water molecules present at the protein surface throughout the entire simulation, τs denotes the residence time for the decay of the stretched exponential. τ2 and τ3 represents the first and second component, respectively, of the residence time for slow biexponential decay. γ is a quantitative measure of the deviation of the relaxation curve from a classical exponential function. γ = 1 for a classical exponential function and a large deviation of γ from 1.0 depicts the presence of temporal disorder in the system. 55 The residence time of the hydration water around a protein surface is defined as the time duration for which a specific water molecule is continuously present within volume element r (4 ˚ A in present work) around protein surface. 56 The best fit parameters obtained for all proteins in Figure 6 are reported in Table 2. The average residence time for the stretched exponential is calculated using the expression 57 τs hτs i = Γ γ

µ ¶ 1 γ

19


(8)


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where Γ is the gamma function. Table 2: Residence times calculated by fitting the Survival probability for proteins. Protein 1A4V α-synuclein 1CD3 (Ordered Regions) 1CD3 (Disordered Regions) 1M V F (Ordered Regions) 1M V F (Disordered Regions) 1F 0R (Ordered Regions) 1F 0R (Disordered Regions) Bulk Water

a 421.9 901.6 512.5 386.3 306.6 384.6 298.5 537.5 579.9

hτs i 10.675 11.225 8.290 7.287 4.793 4.870 7.123 7.217 0.097

γ 0.476 0.341 0.329 0.380 0.317 0.324 0.560 0.549 0.901

b 131.30 160.70 65.87 11.40 45.98 58.85 12.54 25.65 1.44

τ2 5.973 6.892 7.987 12.372 7.348 7.257 111.136 124.797 0.498

c 7.98 7.669 4.605 3.263 2.274 2.553 1.875 5.439 0.799

τ3 666.670 805.802 856.164 1003.512 945.251 950.570 742.390 916.590 0.517

np 3.118 0.985 0.237 0.804 0.126 0.098 0.354 0.555 2.3 × 10−14

Figure 6 and Table 2 depict that most of the water molecules (indicated by a in Table 2) present in the hydration layer experience a fast decay which is characterized by a stretched exponential. The residence time of the hydration water around ordered regions of proteins is observed to be less compared to those of the water molecules around disordered regions. α-synuclein shows slow dynamics (indicated by higher value of residence times) of water molecules around its surface as compared to the water dynamics around a globular protein (1A4V ). Similarly, for partially disordered proteins i.e. 1CD3, 1F 0R and 1M V F , disordered regions exhibit longer residence times (i.e. slow dynamics) as compared to their ordered counterparts. The difference in the residence times between the ordered and disordered regions ranges between 1.0% (τ2 ) for 1M V F and 35.44% (τ2 ) for 1CD3. The three components of residence time for the bulk water consisting of 16062 TIP3P water molecules is found to be 0.097, 0.498 and 0.517 ps, which agrees well with the earlier reported results. 8,58 The values of residence time in Table 2 depict that the fast decay of water molecules near globular/disordered protein surface is 48-114 fold slower than that of the bulk water. 6 The slow component of residence time for hydration water molecules around globular and disordered proteins ranges between 666.67 ps and 1003.51 ps, while it is 0.517 ps for bulk water. This implies that the slow component of residence time for hydration water molecules around globular/disordered protein surface is 3-4 orders of magnitude larger as 20


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compared to that of the bulk water. The slow dynamics of the water molecules in the vicinity of disordered proteins/regions may be attributed to the lack of a well-defined hydrophobic core in disordered proteins. Such behavior is also observed and reported by Bagchi 59 near hydrophilic surfaces due to the possibility of hydrogen bonding between water molecules and protein surface. Water molecules surrounding a disordered protein/region experience increased attractive electrostatic interactions with the charged hydrophilic residues on the protein surface giving rise to the slow dynamics. This is also confirmed by a study of Zhang et al., 60 which reported the slow dynamics of water molecules around the protein surface comprising of predominantly charged residues. The slow dynamics of water molecules around disordered proteins/regions may be thus rationalized due to the characteristic preponderance of charged residues and deficiency of hydrophobic residues (see Table 1) in disordered proteins. A recent experimental study by Gallat et. al. 61 showed that the completely disordered tau protein exhibits low hydration water mobility compared to globular proteins. This is due to the geometrical constraints imposed by side-chains of disordered proteins on the water molecules. Our observations are in accordance with these experimental results. Thus, water molecules around disordered proteins/regions exhibit slow dynamics and are characterized by long residence times. Two additional 100 ns long MD simulations are also performed for α-synuclein to check the robustness of the results with respect to the variation in the water model and the protein forcefield. In the first simulation, TIP4P water model 62 is used for water molecules alongwith ff99SB forcefield for protein atoms, while second simulation is performed by using ff03* forcefield 33 alongwith the TIP3P water model. The organization and local structure of hydration water is analyzed for these two simulations and results are plotted as Figures S9, S10, S11 and S12 in the Supplementary material. Results depict that the hydration pattern is less sensitive on the choice of the forcefield as SDF, RDF and the tetrahedral order parameter show marginal difference irrespective of the forcefield. SDF and RDF of TIP3P and TIP4P water model depict a quantitative, rather than qualitative, difference in the distribution

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of the hydration water molecules. TIP4P water model shows second peak in RDF while TIP3P lacks this peak and this behavior is reported in an earlier study. 63,64 The analysis of the local structure of water molecules reveal that the tetrahedral order parameter shows a similar trend for the TIP3P and TIP4P water model, even though TIP4P water exhibits a higher tetrahedral order as compared to the TIP3P water model. The results portray similar hydration pattern with respect to the protein forcefield and the water models.

Conclusions This work aims at exploring the the local order and mobility of hydration water around intrinsically disordered proteins. Results of MD simulations on globular and partially/completely disordered proteins reveal that disordered proteins/regions bind larger number of water molecules as compared to the globular proteins due to the exposure and abundance of charged residues. The quantitative characterization of structural order of water molecules is achieved by the evaluation of the tetrahedral order parameter, which is calculated by including or excluding the protein heavy atoms as four nearest neighbors for a target water molecule. Water molecules around disordered protein/regions are found to be more tetrahedrally ordered as compared to those around globular proteins. The analysis of the spatial arrangement of hydration water molecules, calculated in terms of orientational angles of water molecules relative to the nearest protein atoms, depicts a distinctly different distribution of orientational angles of water molecules around the globular and disordered proteins. The mobility and dynamics of hydration water molecules is analyzed by evaluating the residence time of water molecules around protein surface. Water molecules around intrinsically disordered proteins/regions depict slow dynamics with longer residence times as compared to those around globular protein/regions. Thus, the organization, structure and dynamics of hydration water molecules is distinctly different for globular and disordered proteins/regions.

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Acknowledgement The authors gratefully acknowledge the University of Delhi and DST, India (Project No. SB/S1/PC-023/2013) for financial support. P. Rani acknowledges University Grant Commission, India for providing financial support in form of 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 adequate computational facility in the Biogene cluster.

Supporting Information Available The calculation of the density normalization factor and raw density of water molecules, plots for the distribution functions (SDF and RDF), distribution of qtet for hydration water molecules. This material is available free of charge via the Internet at http://pubs.acs. org/.

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