Hydration Water Distribution around Intrinsically Disordered Proteins

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Hydration Water Distribution Around Intrinsically Disordered Proteins Leena Aggarwal, and Parbati Biswas J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b11091 • Publication Date (Web): 19 Mar 2018 Downloaded from http://pubs.acs.org on March 20, 2018

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The Journal of Physical Chemistry

Hydration Water Distribution around Intrinsically Disordered Proteins Leena Aggarwal and Parbati Biswas∗ Department of Chemistry, University of Delhi, Delhi-110007 E-mail: [email protected]

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Abstract The distribution and local structural order of hydration water in the proximity of intrinsically disordered proteins/regions are investigated within the frame work of 3DRISM theory. The hydration water distribution around the protein surface is quantified in terms of the 3D distribution function and the water-protein radial distribution function, while the local ordering of water molecules around the protein surface is measured in terms of the tetrahedral order parameter. To the best of our knowledge, this is the first theoretical study of the 3D hydration water distribution profiles of disordered proteins. The analysis of the 3D hydration profiles reveal a non-uniform distribution and higher hydration water density around disordered proteins as compared to the globular ones due to their noncompact structures with more solvent accessible surface area and the abundance of charged residues. This difference is also evident in the residue-specific radial distribution functions of water around different polar and non-polar atoms of charged and hydrophobic residues of the globular and disordered proteins. The average tetrahedral order parameter evaluated as a function of the water-water distance shows that water molecules are more ordered around disordered regions/proteins due to their higher mean net charge facilitating stronger water-protein interactions.

Introduction As an ubiquitous solvent for biomolecules, water has been known to play a central role in regulating the structure, function and biological activity of proteins. 1,2 While the water molecules in the protein interior stabilize the structure of a protein via hydrogen bonding, hydration water around the protein directly interacts with different solvent-exposed amino acid residues and the complex surface topology of the protein. 3,4 A minimal hydration is a prerequisite for imparting the functional resilience to the protein as demonstrated in protein folding and dynamics, 5–7 substrate/ligand binding, 8,9 molecular recognition 6,10,11 and enzyme catalysis, 12–14 which often involve specific interactions with particular water molecules. 2


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Understanding protein hydration thus requires the knowledge of protein-water interactions, which include local changes in structure and dynamics of the water in the vicinity of the protein, that typically span a couple of hydration layers. Numerous experimental and computational studies have established that the structural and dynamic properties of hydration water are significantly different from that of the bulk. X-ray crystallography, 15,16 NMR, 17–19 magnetic resonance dispersion, 20 dielectric relaxation, 21–23 neutron scattering, 24,25 time resolved fluorescence 26,27 provide information about the structural order and characteristic sluggish dynamics of water in the vicinity of the surface of a protein. 28,29 The results reveal that the structure, diffusion and the intramolecular vibration modes of hydration water are distinctly different as compared to that of bulk water. 28,30–33 However, these experimental techniques only probe/measure the averaged behavior/properties of hydration water around the protein surface. Molecular dynamics (MD) simulations successfully capture the key features of hydration water near the surface of a protein. 3 Despite providing a residue-specific picture, MD simulations of proteins are often computationally expensive and are limited by restricted sampling of the large conformational ensemble of the protein with explicit solvent. The reference interaction site model (RISM) 34–36 is an alternative computational method for calculating the equilibrium distribution of water molecules around the surface of a protein. RISM is an integral equation theory based on the Ornstein-Zernike equation, 37 where the total correlation between any two particles is evaluated as a sum of a direct and indirect correlation. This theory was originally developed for simple liquids. 34,37 A three-dimensional version of the RISM integral equation, known as 3D-RISM 38 is adapted to depict the three-dimensional equilibrium spatial profile of the solvent around proteins. 39–43 The analysis of 3D-RISM theory provides an atomistic picture of the distribution of water molecules around the protein, which matches with high-resolution experimental results. For the first time, this work portrays the three-dimensional hydration profiles of intrinsically disordered proteins relative to that of a globular protein using 3D-RISM theory with

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Kovalenko-Hirata (KH) closure. 44,45 Intrinsically disordered proteins (IDP) lack well-defined secondary and/or tertiary structure and exist as a heterogeneous ensemble of interconverting conformations in solution. 46 IDPs are typically flexible molecules with extended noncompact structures due to the lack of a well-defined hydrophobic core and an abundance of polar and charged residues. Thus, it is difficult to experimentally characterize the conformational ensemble of these proteins with the same resolution as that of the globular proteins, where the structures may be determined by X-ray crystallography or NMR spectroscopy with atomiclevel accuracy. These proteins may be fully disordered marked by an overall absence of any secondary or tertiary structure throughout the entire protein (IDP) or partly disordered with regions of well-defined secondary structure linked by flexible random coil like motifs (IDPR). Despite lacking a stable three dimensional structure, these proteins are functionally diverse and play a significant role in different cellular processes. 47,48 Thus, it is important to analyze the hydration behavior of such proteins where the lability of the hydration layer may facilitate non-cooperative conformational transitions that modifies their context-dependent functional selectivity. The three-dimensional spatial profiles of hydration water around disordered proteins are investigated in terms of the 3D distribution function, and water-protein radial distribution function (RDF) while the local structural ordering of water molecules is quantified in terms of tetrahedral order parameter for two IDPRs (1F0R and 1CD3) and two IDPs (α-synuclein and amyloid-β) as compared to a globular protein (1A4V). 49–51

Materials and Methods The 3D-RISM theory is a statistical-mechanical theory of molecular liquids based on the Ornstein Zernike equation that is used to portray the distribution of the solvation water around proteins in terms of 3D distribution functions. The 3D-RISM integral equation may be derived from the six dimensional molecular Ornstein-Zernike equation by averaging over the molecular orientations of the solvent, while retaining the orientational coordinates

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of the solute molecule. 37 The solvent distribution functions, gγ (r) for each solvent site γ, is related to the total correlation function, hγ (r) between two molecules by the relation hγ (r) = gγ (r) − 1. The total correlation function is related to the direct correlation function, cα (r), through the solute(U)-solvent(V) 3D-RISM integral equation given by 52

hUγ V (r) =

X

VV cUα V (r) ∗ (ωαγ (r) + ρhVαγV (r))

(1)

α

VV where ωαγ (r) represents the intramolecular pair correlation function of the solvent molecules

located at the respective sites α and γ, ρ is the number density of solvent molecules and ∗ represents the operation of convolution in the direct space. The site-site susceptibility of the pure solvent, χVαγV (r) is an input to the theory and depends only on the site-site distance r, given by

VV χVαγV (r) = ωαγ (r) + ρhVαγV (r)

(2)

which is obtained from 1D-RISM theory. 34,35,53,54 Eq.(1) may be solved by transforming the equation using 3D Fast Fourier transform (3D-FFT) technique. 55,56 The resultant equation in Fourier space is expressed as 54

VV ˜ U V (k) = c˜U V (k).(˜ ˜ V V (k)) h ωαγ (k) + ρh γ α αγ

(3)

˜ γ (k), c˜α (k), ω ˜ αγ (k) represent the symmetric matrices and ω where h ˜ αγ (k) and h ˜ αγ (k) = sin(klαγ )/(klαγ ) with lαγ as the distance between the site pairs of the solvent α and γ. For a given conformation of the protein, the 3D-RISM integral equation, Eq.(3) may be solved by complementing it with an appropriate closure relation between the total correlation VV (r) function and the direct correlation function. The intramolecular correlation function, ωαγ

is determined by the topology of the water model chosen. The 3D-RISM integral equation is solved via the Kovalenko-Hirata closure approximation, 44,45 which is a combination of the hypernetted chain closure (HNC) 37 and the mean spherical approximation (MSA) 37 yielding 5



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a closed set of equations given by

gγU V (r) =

   exp(ηγU V (r)), for ηγU V (r) ≤ 0   1 + ηγU V (r),

for ηγU V (r) > 0

(4)

ηγU V (r) = −βuUγ V (r) + hUγ V (r) − cUγ V (r) where the 3D solute-solvent site interaction potential uUγ V (r) is an input for a specific force field and β = 1/kB T with the Boltzmann constant kB and temperature T . The 3D-RISM theory with Kovalenko-Hirata closure approximation accurately accounts for both electrostatic and steric effects of biomolecules in solution. Eq.(4) ensures that the long ranged contributions of the electrostatic interactions are separated from the shortranged ones and are calculated analytically. 54,57 The 3D-RISM equation defined by Eq.(3) coupled with KH closure equation given by Eq.(4) is solved numerically to obtain the 3D distribution functions of SPC/E 58 and TIP3P 59 water centered around the oxygen atom, in the vicinity of partially and completely disordered proteins and a globular protein using the modified direct inversion in iterative subspace (MDIIS) method. 60 1D-RISM or dielectrically consistent RISM (DRISM) was first employed to calculate the bulk solvent susceptibility. 53 This approach accounts for the dielectric properties of ions in polar solvents. The combination of 3D-RISM theory with KH closure and DRISM accurately describes solvation induced short-ranged interactions like the steric interactions, hydrogen bonding and the hydrophobic effect. The DRISM-HNC equations were solved on a grid of 16384 points with grid spacing of 0.025 Å for SPC/E 58 and TIP3P 59 water models which comprises three sites, one oxygen and two hydrogen atoms. All calculations were carried out at the room temperature of 298 K with a number density of ρ = 0.03334 Å−3 and a dielectric constant of ǫ = 78.49. The 3D-RISM-KH equations were solved on a grid of 512 × 512 × 512 points in a cubic box of size 128 × 128 × 128 Å3 . These calculations were performed with AMBER 12 package 61 with the ff99SB-ILDN force field 62,63 and a solute solvent interaction

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cutoff distance of 32 Å. The continuous solvent distribution obtained from 3D-RISM calculations was translated to explicit solvent atom distribution using the Placevent algorithm. 64 In Placevent, the 3D distribution function g(r) is converted to a population function P (r) which is given as

P (r) = ρVgrid g(r)

(5)

where ρ denotes the bulk density and Vgrid is the volume of the grid in a cubic box. The first explicit atom will be placed at the location with highest population rmax , while the next atom would be placed iteratively in the new highest population point, rmax,i . The particle conservation law is used to maintain the total population at iteration, i, which is given as Z

P0 (r) = Ni + V

Z

Pi (r)

(6)

V

In order to ensure that no two explicit atoms will be placed very close to each other, Pi (r) is reduced by one in the vicinity of the explicit atom at ri . This is done practically by calculating an arbitrary distance δi such that the volume within the sphere of radius δi , centered at ri contains the population of one unit which is then set to zero. 64 This process may be then repeated till there are enough number of explicit atoms. Z

ri +δi ′

′

Pi (r )dr = 1, ri

Z

ri +δi

Pi+1 (r′ )dr′ = 0

(7)

ri

The resulting discrete distribution of explicit solvent atoms represent the most probable solvent sites especially the atoms that are placed earliest, while the later atoms are closer to the bulk solvent atoms. The explicit water distribution around the proteins was then used to characterize the local structure of water molecules in terms of tetrahedral order parameter of water molecules. Tetrahedral Order Parameter. Tetrahedral order parameter quantifies the local

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structural order in terms of a tetrahedral arrangement of water molecules. The orientational order parameter or tetrahedral order parameter is defined as 65,66

qtet

3 4 3X X =1− 8 j=1 k=j+1

1 cos(ψj,k ) + 3

!2

(8)

where ψj,k is the angle formed between the oxygen atom of the i-th water molecule and the bond vectors rij and rik of its four nearest neighbor atoms, j and k. The average value of qtet varies between 0 and 1. For a perfect tetrahedral arrangement around the central water molecule, qtet = 1, while for a non-tetrahedral random arrangement, qtet = 0. Several studies have reported the distribution of tetrahedral order parameter of water molecules in the hydration shell of proteins. 49,67–69 It may be noted that the water molecules present close to the surface of the protein may use the non-hydrogen atoms of the protein in order to complete their tetrahedral geometry. Thus, the tetrahedral order parameter of the tagged water molecule is calculated either (i) by considering only water molecules as the four nearest neighbors, or (ii) by considering non-hydrogen atoms (C,N,O etc) of the protein along with water molecules. Mean Net Charge and Mean Hydrophobicity. The net charge Q of the protein at any pH is given as 70 Q=

X

Q− +

X

(9)

Q+

where Q− (for -COOH, -SH, -PhOH) and Q+ (for -NH3 + , =NH2 + , ≡ NH+ ) are the fraction of negative and positive charges respectively, calculated as

Q− =

(−1) 1 + 10−(pH−pKa )

and

Q+ =

(+1) 1 + 10+(pH−pKa )

(10)

The commonly reported pKa values for the side chain groups of the respective amino acids are as follows, Asp -COOH (pKa = 3.9), Glu -COOH (pKa = 4.35), His ≡ NH+ (pKa = 6.5), Tyr -OH (pKa = 9.9), Lys -NH3 + (pKa = 10.35), and Arg =NH2 + (pKa = 12.5). 70 The pKa 8


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values for the N- and C-termini groups of the protein are approximated by their respective average values, i.e., 3.3 for the C-terminus and 8.5 for N-terminus. The mean net charge per residue is defined as the net charge of protein at pH 7.0 divided by total number of residues in the protein. The mean hydrophobicity of protein is quantified using Kyte and Doolittle approximation. 71 The hydrophobicity of each amino acid residue is first normalized on a 0 to 1 scale. The mean hydrophobicity is calculated by dividing the sum of normalized hydrophobicities of all residues by the total number of residues in the protein. The ratio of the mean net charge to hydrophobicity is calculated for the respective protein. Protein Selection. The X-ray crystal structure of a globular protein, α-lactalbumin with resolution 1.8 Å and R-factor= 0.210 is extracted from RCSB PDB (ID 1A4V) which is used as an initial template for 3D-RISM calculations of the three-dimensional spatial profile of hydration water. Two IDPRs with PDB ID 1CD3 (120 residues) and 1F0R (134 residues) are selected along with two IDPs, α-synuclein (140 residues) and amyloid-β (42 residues). The ordered regions of the IDPRs are obtained from RCSB PDB, while the disordered regions are modeled via MODELLER. 72 The X-ray crystal structure of the ordered regions of 1CD3 and 1F0R obtained from RCSB PDB and the sequence of the protein are used as input parameters in the MODELLER to model the missing residues of the disordered regions. The disordered regions are modeled in such a way that the structure of the ordered region of the protein is exactly conserved. For amyloid-β and α-synuclein, the FASTA sequences are the only input to the MODELLER to model their structures. The scaffolding protein GPB (PDB ID 1CD3) with 120 residues plays an important role in the conformational changes accompanying capsid maturation. 73,74 Human factor Xa (PDB ID 1F0R) with 134 residues is involved in the coagulation cascade and may act as potential target for the development of new antithrombotic drugs which may be advantageous for the treatment of thromboembolic disorders. 75 α-synuclein is a neuronal protein that is localized at the tip of neurons in specialized structures called presynaptic terminals and its aggregation

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is strongly linked to Parkinson’s disease. 76 Amyloid-β is a primary peptide that aggregates to form oligomers, protofibrils and fibrils which eventually leads to the deposition of amyloid plaques associated with Alzheimer’s disease. 77,78 The disordered proteins are chosen on the basis of varied disorder content i.e, 43.3% for 1CD3 (9-60 residues), 61.2% for 1F0R (1-82 residues), and 100% for each of α-synuclein and amyloid-β and location of the disordered regions i.e, N-terminus for 1F0R, middle regions for 1CD3 and complete disorder for each of α-synuclein and amyloid-β. Simulation Details. Two conformations of each of the four proteins were randomly chosen from their 100 ns explicit water molecular dynamics (MD) simulation trajectories. 49 These simulations were performed with AMBER 12 using ff99SB force field 79,80 by solvating each protein in a cubic box of TIP3P 59 water molecules with the box edge at a distance of 10 Å from the protein surface. Na+ or Cl− ions were added to neutralize the overall charge on the solvated proteins depending upon the charge of the proteins. The motions of hydrogen atoms were constrained to their equilibrium bond lengths using the SHAKE algorithm. 81 Longrange electrostatic interactions were treated with particle mesh Ewald (PME) method. 82 The cutoff for non-bonded interactions including van der Waals and coulombic interactions was set to 8 Å. The energy of each solvated protein was minimized twice, the solvent was energy minimized first by keeping the protein constrained followed by energy minimization of the whole system using the conjugate gradient method to remove the unfavorable interactions. The energy-minimized solvated protein was then equilibrated by simulating the solvated protein in NVT ensemble for 100 ps at 100 K with a gradual increase of temperature from 100 K to 300 K. This was followed by equilibration in NPT ensemble for 5 ns at a constant temperature of 300 K using Berendsen’s temperature bath 83 with a coupling constant of 2 ps and a pressure of 1 bar using barostat with a coupling constant of 1 ps. The production run of 100 ns was then performed in NPT ensemble for each of the equilibrated system with a time step of 2 fs. Coordinates of the trajectory were saved at an interval of 2 ps. The selected conformation of each of the four proteins was used to compare the results

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obtained from MD simulation and 3D-RISM-KH theory. Explicit water molecular dynamics simulations for the selected conformations of each of the four proteins were performed using ff99SB-ILDN force field and SPC/E water model. Only water molecules and ions in the system were allowed to move and the coordinates of all protein residues were frozen for the entire simulation. The system was energy minimized and equilibriated in the NVT ensemble for 10 ps followed by volume equilibriation in NPT ensemble for 5 ns. The energy minimized systems were subjected to a production run of 10 ns in NVT ensemble such that the simulation conditions are identical to that of the 3D-RISM calculations. All other simulation conditions are similar to the 100 ns simulations.

Results and Discussion This study investigates the spatial profiles of hydration water in different conformations of partially and completely intrinsically disordered proteins (IDPRs and IDPs) using 3DRISM theory. The hydration water distribution and local ordering of water molecules around intrinsically disordered proteins are distinctly different from that around globular proteins. 49 The hydration water distribution around the protein surface is characterized in terms of the 3D distribution function g(r) (g(x, y, z)) and the water-protein radial distribution function (RDF) that describes the density of water molecules as a function of the distance from a particular protein atom. In addition, the local structural order of water molecules around the protein surface is also measured in terms of the tetrahedral order parameter. Figures 1, 2, 3, 4 and 5 depict the 3D distribution profiles of SPC/E water oxygen atom around the globular protein (1A4V), IDPRs (1CD3 and 1F0R) and IDPs (α-synuclein and amyloid-β) in the XOY plane (a plane passing through the solute protein molecule) as calculated from 3D-RISM-KH approach. gO represents the maximum value of g(x,y,z) for a particular value of z when only z is varying in (x,y,z). The 3D distribution profile of SPC/E water oxygen atom around the central SPC/E water molecule in the XOY plane (a

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Figure 1: (a) The X-ray crystal structure of globular protein, 1A4V, (b) 3D hydration water distribution profile of the globular protein, 1A4V

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Figure 2: (a) Modeled structure of 1CD3, (b) 3D hydration water distribution profile of 1CD3. Blue color represents the ordered region and red color represents the disordered region in the modeled structure of 1CD3. The green(acidic) and yellow(basic) beads represent the positions of the charged residues.

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Figure 3: (a) Modeled structure of 1F0R, (b) 3D hydration water distribution profile of 1F0R. Blue color represents the ordered region and red color represents the disordered region in the modeled structure of 1F0R. The green(acidic) and yellow(basic) beads represent the positions of the charged residues.

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Figure 4: (a) Modeled structure of α-synuclein, (b) 3D hydration water distribution profile of α-synuclein. The green(acidic) and yellow(basic) beads represent the positions of the charged residues.

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Figure 5: (a) Modeled structure of amyloid-β, (b) 3D hydration water distribution profile of amyloid-β. The green(acidic) and yellow(basic) beads represent the positions of the charged residues. plane passing through the central water molecule) is given in Figure S1 of the Supporting Information. In Figure S1, the narrow high peaks correspond to the hydrogen bonding between water molecules and hydrogen bonds are strongly localized in front of the hydrogen atoms of the central water molecule. Figure 1(a),(b) reveals that the globular protein, 1A4V

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has a compact folded structure as is evident from the 3D spatial profile of the hydration water molecules surrounding the protein. The lack of structural compactness of 1CD3, 1F0R and αsynuclein is reflected in Figure 2(a),(b), Figure 3(a),(b) and Figure 4(a),(b), respectively from the non-uniform hydration profiles around these proteins. These proteins are devoid of a wellpacked hydrophobic core, with the hydrophobic and polar residues interspersed throughout the entire protein. However, Figure 5(a),(b) for amyloid-β indicates a compact hydration profile, similar to that of the globular protein. Despite being completely disordered, amyloidβ is a small protein with a relatively higher content of hydrophobic residues and an abundance of charged residues, which promotes hydrogen bonding between the polar atoms of charged residues and water molecules. The peaks in the 3D spatial profile correspond to a higher local density of water at the specified locations. Disordered regions/proteins show a higher density of these peaks in the 3D hydration profile as compared to the globular proteins due to the abundance of charged residues scattered throughout the protein, which are highlighted by green (acidic residues) and yellow (basic residues) beads. To rationalize this observation, the residues adjacent to the hydration water molecules with higher local density are counted and shown in the histogram. Figure 6 shows the side-chain propensity of 20 different amino acid residues to interact with water for 1A4V, 1CD3, 1F0R, α-synuclein and amyloid-β. A residue is counted only if the water molecule is located within the distance of 3 Å from its side chain atoms. The side chain propensity of residues is considered with respect to the side chain nitrogen and oxygen atoms of the charged residues, which have a more favorable hydrogen bonding interaction with water than that of any main chain atoms. 84 From the histogram, it may be observed that the number of charged residues (GLU, ASP, LYS, ARG) are higher adjacent to the hydration water molecules, which indicates that the charged residues interact more favorably with hydration water. The number of charged residues are less in the globular protein, 1A4V and the weakly disordered protein, 1CD3, however, polar residues (ASN and GLN) have similar interactions with the hydration water molecules. The hydration propensities of the charged residues is

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Figure 6: Histogram to show the side chain propensities of 20 different amino acids for the hydration water molecules. higher as they interact with water molecules to create a low dielectric environment and shield the electrostatic interactions between charged residues (salt-bridges). 84 The overall 3D distribution profiles of water around disordered regions/proteins are compared with that of globular protein instead of comparing a particular high density peak at a particular position, r(x, y, z). Water molecules that remain at the same position at all times may exhibit very high peaks in the 3D density distribution profiles for very fine grid spacing which may lead to a bias for the grid-based approach while comparing the relevant hydration water densities. 39,40 The water density peaks around particular atoms of proteins are compared in terms of the water-protein radial distribution function. The total number of peaks are compared at positions where 1 < g(r) < 10 thus, excluding very low and very high density peaks from the analysis of 3D distribution profiles.

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Maximum number of peaks with 1 < g(r) < 10 is recorded for α-synuclein (Figure 4(b)) and 1F0R (Figure 3(b)). 1F0R with a significantly higher disorder content shows higher hydration water density as compared to the globular protein, 1A4V. A similar trend is also revealed for α-synuclein, which is a completely disordered protein. Higher hydration water density of IDPs/IDPRs may be attributed to the larger binding capacity of hydration water due to an increased exposed surface area and high mean net charge of IDPRs (1CD3: −0.025, 1F0R: −0.0895) and IDPs (α-synuclein: −0.071, amyloid-β: −0.0714) as compared to that of a globular protein (1A4V: −0.0569). 60 The number of peaks with 1 < g(r) < 10 for 1CD3 is more as compared to 1A4V as shown in Figure 2(b) and Figure 1(b) respectively. However, 1CD3 is a partially disordered protein with less mean net charge as compared to 1A4V. The increase in the number of peaks is largely due to increased solvent exposed surface area which facilitates the confinement of more hydration water in 1CD3 than 1A4V. The number of peaks with 1 < g(r) < 10 for amyloid-β in Figure 5(b) is less than that of 1A4V in Figure 1(b). Since amyloid-β is a 42 residue protein, the total number of charged residues are less as compared to 1A4V, which comprises of 123 residues. Further, a comparison of the radial distribution function of water around a particular atom of protein, clearly shows that amyloid-β binds more hydration water molecules as compared to the globular protein, 1A4V due to its high mean net charge and higher exposed surface area as compared to the globular protein. Since, IDPs lack a hydrophobic core, their noncompact conformations are more solvent accessible as compared to the well-packed conformations of a globular protein, which contributes to higher hydration water density of IDPs as compared to that of a globular protein. This may be explained on the basis of protein confinement effect 85 due to protein-water interactions. The structure of IDPs confine more water molecules in the interspaces of protein side chains and domains in contrast to the well-packed structure of the globular proteins, as the side chains of IDPs interact more with hydration water molecules than with each other. 86 Representative extended and compact conformations of each IDP are chosen from

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Figure 7: 3D hydration water distribution profiles of 1CD3 (a) Extended conformation, (b) Compact conformation.

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Figure 8: 3D hydration water distribution profiles of amyloid-β (a) Extended conformation, (b) Compact conformation. their respective simulation trajectories and the water density distribution is characterized in terms of 3D water density distribution function. The 3D water density distribution profiles 21



for the extended and compact conformations of 1CD3 and amyloid-β are shown in Figures 7 and 8 respectively, while the density distribution profiles for other proteins are given in Figures S2 and S3 of the Supporting Information. Figures 7 and 8 exhibit that the extended conformations of 1CD3 and amyloid-β show more peaks with 1 < g(r) < 10 as compared to their respective compact conformations which indicates higher water density in the extended conformations as compared to their compact counterparts.

Figure 9: Average local water densities in a 4 Å solvation shell around different residue types in extended and compact conformations of 1CD3. Figures 9 and 10 depict the average local water densities around different protein residue types in 4 Å solvation shell for the compact and stretched conformations of 1CD3 and amyloid-β respectively. The average values of the local water densities are lower than expected as the averaging includes grid points that includes the excluded volume of the protein. 39 It is observed that the average local water densities in the noncompact conformations of 1CD3 and amyloid-β is more around any residues as compared to those around their compact counterparts. However, the overall average water densities around different residue types of IDPs/IDPRs is more as compared to those of the globular protein irrespective of the 22


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Figure 10: Average local water densities in a 4 Å solvation shell around different residue types in extended and compact conformations of amyloid-β. compactness of the conformations. The noncompact structures of IDPs confine more water molecules that strongly interacts with the protein side chains in contrast to the compact folded structures of the globular protein. Thus, the density of water molecules is higher for IDPs/IDPRs as compared to that of the globular protein due to their higher mean net charge. The expanded structures of IDPs/IDPRs encompass more confined hydration water molecules due to stronger water protein interactions. Hence, the 3D distribution profile of hydration water around IDPs/IDPRs is found to be remarkably different from that of a globular protein. This difference in the hydration pattern is reflected in the RDF of water molecule centered around the oxygen atom in the vicinity of different polar and apolar atoms of the charged and hydrophobic residues, respectively. The water-water and water-protein RDFs are obtained by orientational averaging of their respective 3D distribution profiles. The RDF of SPC/E water oxygen atom around the central water molecule is given in Figure S6 of Supporting Information. Figure S6 shows a comparison between RDF of bulk SPC/E water resulting from 1D-RISM and HNC equations 23



Figure 11: RDF of water oxygen around LYS-NZ of the selected proteins. and that obtained by orientational averaging of its respective 3D distribution function. It is clear from Figure S6 that the 1D-RISM-HNC and 3D-RISM-KH results closely resemble each other. Figures 11, 12, 13, 14 and 15 portray a comparison between the radial distribution functions of SPC/E water oxygen atom around a particular residue of the globular protein, ordered and disordered regions of IDPRs and IDPs obtained by orientational averaging of their respective 3D distribution function gγU V (r). The two-fold characterization of the hydration environment involves i) the polar atoms of the charged residues, i.e., LYS-NZ, ASP-OD1, GLU-OE1 and ARG-NH1 as depicted in Figure 11, Figure 12, Figure 13 and Figure 14, respectively and ii) the non-polar atoms of hydrophobic residues like ILE-CD1 and VAL-CG2 as shown in Figure 15. The radial distribution function centered around the water oxygen atom is depicted for these two types of hydration environment. Two peaks are mainly observed in the radial distribution functions of the water oxygen atom. The first peak corresponds to the first or inner hydration shell, while the second peak corresponds to 24


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Figure 12: RDF of water oxygen around ASP-OD1 of the selected proteins. the second or outer hydration shell. 87 The hydration environment around these two types of residues is characterized on the basis of the relative accessible surface area or the relative solvent accessibility (RSA), which denotes the ratio of the solvent accessible surface area to the maximum solvent accessible surface area for any residue X, obtained from Gly-XGly tripeptides, where X is the residue of interest. The solvent accessible surface area is obtained from DSSP, 88 while the values of the maximum solvent accessible surface area are procured from Tien et al. 89 The residues with at least 40% surface accessibility are selected. For a comparison among IDPs, globular protein and the ordered and disordered regions of IDPRs, residues with similar RSA values are chosen. When residues with similar values of RSA are not available, residues with maximum values of RSA are selected from the ordered regions of intrinsically disordered proteins and globular protein as compared to the disordered regions/proteins. The peaks are sharper for the charged residues as compared to the hydrophobic residues 25



Figure 13: RDF of water oxygen around GLU-OE1 of the selected proteins. indicating favorable interactions of hydration water with the polar atoms of the charged residues as compared to the non-polar atoms of the hydrophobic residues. The peaks are sharper for the disordered regions/proteins as compared to the ordered regions/proteins. The largely exposed surface of the disordered regions/proteins with charged residues bind a larger number of water molecules than the ordered regions. NMR relaxation studies on the hydration layer of intrinsically disordered proteins indicate that IDPs bind more hydration water than globular proteins. 90 Since, there is no ARG in α-synuclein and no ILE in disordered region of 1F0R, therefore Figures 14 and 15 do not show ARG for α-synuclein and ILE for 1F0R. Valine (VAL) is not shown for 1F0R as there is only one VAL in the disordered region of 1F0R with surface accessiblility less than 40%. For IDPRs, the difference in the hydration water density between the ordered and disordered regions is maximum for 1F0R. This difference is more pronounced for hydrophobic residues as compared to the charged residues. The hydration water density around IDPs, α-synuclein and amyloid-β is observed 26


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Figure 14: RDF of water oxygen around ARG-NH1 of the selected proteins.

Figure 15: RDF of water oxygen around ILE-CD1 and VAL-CG2 of the selected proteins. to be higher than that around the globular protein, 1A4V. The disordered regions of IDPRs have a higher hydration water density as compared to the ordered regions. This may be explained on the basis of high mean net charge and low hydrophobicity (see Table 1) of the disordered regions as compared to the ordered ones. The mean net charge

27



Table 1: Mean Net Charge and Mean Hydrophobicity of Proteins protein mean net charge 1A4V −0.057 α-synuclein −0.071 Amyloid-β −0.071 1CD3 (ordered region) 0.029 1CD3 (disordered region) −0.096 1F0R (ordered region) −0.058 1F0R (disordered region) −0.109

mean hydrophobicity 0.475 0.455 0.514 0.382 0.369 0.439 0.359

to hydrophobicity ratio of the IDPs, α-synuclein and amyloid-β, is higher compared to the globular protein, 1A4V but lower than the disordered regions of IDPRs. The disordered regions/proteins have a large content of polar and charged residues as compared to the hydrophobic residues, that prevents hydrophobic collapse to a compact folded structure. Thus, the disordered regions/proteins possess extended structures with larger solvent accessible surface area as compared to the compact globular proteins. The mean net charge 70,91,92 and mean hydrophobicity 71 of the globular protein, ordered and disordered regions of IDPRs and IDPs are given in Table 1. Different atoms of different residues in a protein distinctly influence the hydration pattern in their vicinity. However, the position of the first peak remains almost similar for the globular protein, IDPs and IDPRs, while the amplitude of this peak is greater for the disordered regions/proteins as compared to their ordered counterpartss and globular proteins. The first peak of the water-protein radial distribution function is close to the protein surface for polar atoms (LYS NZ, ASP OD1, GLU OE1, ARG NH1), as compared to the non-polar atoms (ILE CD1, VAL CG2) of the protein. The local structural ordering of water molecules around the protein surface is characterized in terms of the average tetrahedral order parameter which is evaluated as a function of water-water distance. Figure S11 depicts the average tetrahedral order parameter of bulk SPC/E water which shows that the values for bulk water ranges between 0.517 and 0.598 which is in agreement with the earlier results. 93 Figures 16 and 17 show the average

28


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tetrahedral order parameter, of the tagged water molecules around the protein surface as a function of the water-water distance. In Figure 16, the qtet values are calculated by considering only water molecules as four nearest neighbors, while in Figure 17 the protein heavy atoms are also considered as four nearest neighbors of a given water molecule. The

Figure 16: Average tetrahedral order parameter calculated by excluding protein heavy atoms as a function of the water-water distance. The error bars represent the standard errors accumulated while averaging the tetrahedral order parameter. maximum value of average tetrahedral order parameter, is recorded at an approximate distance of 2.5 Å which implies that the water molecules have maximum order at 2.5 Å and this represents the first solvation layer around the tagged water molecules. The order parameter decreases with an increase in the distance of the water molecules and the minimum value of is recorded at a distance of 3.5 Å. The value of increases beyond 3.5 Å and a small hump is observed at a distance of the second solvation shell of the tagged water molecules. The average tetrahedral order parameter is found to be higher for the disordered regions/proteins as compared to the ordered regions of IDPRs and the glob29



Figure 17: Average tetrahedral order parameter calculated by including protein heavy atoms as a function of the water-water distance. The error bars represent the standard errors accumulated while averaging the tetrahedral order parameter. ular protein. A similar trend of is observed by including and excluding the protein heavy atoms for IDPRs, IDPs and globular protein. Among IDPRs (1CD3 and 1F0R), the maximum value of is observed for the disordered region of 1F0R which implies that the structural order of water molecules increases with the increase in the percentage disorder in proteins. The completely disordered proteins α-synuclein and amyloid-β should have higher average tetrahedral order parameter as compared to IDPRs and the globular protein. However, values are found to be higher for the disordered region of 1F0R as compared to α-synuclein and amyloid-β. A closer inspection of the mean net charge and mean hydrophobicity (refer to Table 1) of these proteins indicates that the ratio of the mean net charge to hydrophobicity is higher for α-synuclein and amyloid-β as compared to the globular protein, 1A4V but less than that of the disordered regions of 1F0R. Thus, the tetrahedral order 30


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parameter exhibits a higher order among the water molecules surrounding the disordered regions/proteins. The robustness of the results is verified by sampling different conformations of IDPs and IDPRs from the simulation trajectory, which is provided in the Supporting Information (Figures S7, S8, S9, S10, S12, S13). The hydration water spatial profile is also investigated with respect to the variation in water model. The 3D distribution function, water-water RDF and water-protein RDF are plotted using TIP3P water model in Figures S14, S15, S17, S18, S19 of the Supporting Information. The TIP3P water model shows a second peak in the RDF although it was reported in an earlier study that TIP3P lacks this peak. 94 However, the second peak in the RDF of TIP3P water model is in agreement with the experimental results. 95 Figure S16 of Supporting Information shows a comparison between the radial distribution function of SPC/E and TIP3P water models obtained from 1D-RISMHNC approach. The qualitative pattern of the results obtained using SPC/E and TIP3P water models is similar, which confirms the high correlation between the results obtained from SPC/E and TIP3P water models. 39 This analysis reveals that the qualitative pattern of the hydration profiles around IDPs/IDPRs and globular protein remains unaffected by the choice of the water model. Figures 18 and 19 represent a comparison of the density profiles of SPC/E water oxygen evaluated in terms of the water-protein RDF around the non-polar and polar atoms of the hydrophobic and charged residues of the disordered poteins obtained from MD simulation and 3D-RISM-KH approach. It is observed that the position of the first and second peaks is quite similar in the density profiles however, the height is lower in the density profiles obtained from 3D-RISM-KH theory as compared to those obtained from MD simulations. This underestimation of water densities by 3D-RISM-KH theory in the solvation shells, especially the strong associative peak for the first solvation shell, is due to the MSA linearization applied to KH closure in the spatial regions of solvent density enhancement (relative density or g(r) > 1). 54 However, the qualitative distribution of water in the solvation shells around

31



Figure 18: Density profiles of water oxygen around ILE-CD1 and VAL-CG2 of selected proteins calculated with MD simulation and 3D-RISM-KH theory.

Figure 19: Density profiles of water oxygen around ARG-NH1 of selected proteins calculated with MD simulation and 3D-RISM-KH theory. the proteins is similar for the density profiles evaluated from MD simulation trajectories and 3D-RISM-KH approach. The density profiles obtained from 3D-RISM-KH approach are relatively smoother as compared to MD simulations, since RISM directly calculates the equi32


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librium distribution of water molecules around the protein surface, while in MD simulations, the statistical fluctuations of the solvated protein about its equilibrium state lead to noisy density profiles.

Conclusions The present work explores the 3D hydration water distribution profiles and the local structural order of water molecules around intrinsically disordered proteins/regions using 3DRISM theory. The hydration water distribution is characterized in terms of the 3D distribution function and the water-protein radial distribution function. This work for the first time describes the 3D hydration profiles of IDPs/IDPRs. The 3D hydration water distribution profiles reveal non-uniform hydration water distribution around disordered proteins as compared to a compact distribution around globular proteins. The higher hydration water density of disordered regions/proteins is clearly observed in the 3D hydration water distribution and in the water-protein radial distribution function around the polar and non-polar atoms of the charged and hydrophobic residues, respectively. The local ordering of water molecules around the protein surface is quantified in terms of the tetrahedral order parameter evaluated as a function of the water-water distance by excluding and including the protein heavy atoms as the four nearest neighbors of the tagged water molecules. The water molecules are found to be more tetrahedrally ordered around disordered regions/proteins as compared to ordered regions/globular protein due to higher mean net charge promoting stronger water-protein interactions in disordered regions/proteins. The hydration profile of the IDPs/IDPRs hardly depend on the choice of the water model. Thus, the 3D hydration water distribution profile and the local structure of hydration water around the intrinsically disordered proteins is distinctly different from that around globular proteins. In addition, the water densities around disordered proteins calculated in terms of the water-protein radial distribution function with 3D-RISM and those with MD simulation are found to be qualitatively similar to each other. 33



Supporting Information Available 3D hydration water distribution profiles, water-water RDF, water-protein RDF and average tetrahedral order parameter.

This material is available free of charge via the Internet at

http://pubs.acs.org/.

Acknowledgement The authors gratefully acknowledge DST-SERB, India (Project No. EMR/2016/006619) for the financial assistance. L.A. acknowledges CSIR, India for providing financial support in the form of Senior Research Fellowship. Authors thank Dr. Pooja Rani for useful discussions. The authors 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.

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Hydration Water Distribution around Intrinsically Disordered Proteins

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