Influence of modulated structural dynamics on the kinetics of a-chymotrypsin catalysis Insights through chemical glycosylation, molecular dynamics and domain motion analysis ´ Ricardo J Sola and Kai Griebenow ´ Laboratory for Applied Biochemistry and Biotechnology, Department of Chemistry, University of Puerto Rico, Rıo Piedras Campus, San Juan, PR, USA Keywords a-chymotrypsin; enzyme catalysis; glycosylation; molecular dynamics; serine protease Correspondence K Griebenow, Department of Chemistry, ´ University of Puerto Rico, Rıo Piedras Campus, Facundo Bueso Bldg Laboratory215, San Juan 23346, PR 00931-3346, USA Fax: +1 787 756 7717 Tel: +1 787 764 0000 ext.7815 E-mail: griebeno@adam.uprr.pr (Received July 2006, revised 26 September 2006, accepted October 2006) doi:10.1111/j.1742-4658.2006.05524.x Although the chemical nature of the catalytic mechanism of the serine protease a-chymotrypsin (a-CT) is largely understood, the influence of the enzyme’s structural dynamics on its catalysis remains uncertain Here we investigate whether a-CT’s structural dynamics directly influence the kinet´ ics of enzyme catalysis Chemical glycosylation [Sola RJ & Griebenow K (2006) FEBS Lett 580, 1685–1690] was used to generate a series of glycosylated a-CT conjugates with reduced structural dynamics, as determined from amide hydrogen ⁄ deuterium exchange kinetics (kHX) Determination of their catalytic behavior (KS, k2, and k3) for the hydrolysis of N-succinylAla-Ala-Pro-Phe p-nitroanilide (Suc-Ala-Ala-Pro-Phe-pNA) revealed decreased kinetics for the catalytic steps (k2 and k3) without affecting substrate binding (KS) at increasing glycosylation levels Statistical correlation analysis between the catalytic (DG „ki) and structurally dynamic (DGHX) parameters determined revealed that the enzyme acylation and deacylation steps are directly influenced by the changes in protein structural dynamics Molecular modelling of the a-CT glycoconjugates coupled with molecular dynamics simulations and domain motion analysis employing the Gaussian network model revealed structural insights into the relation between the protein’s surface glycosylation, the resulting structural dynamic changes, and the influence of these on the enzyme’s collective dynamics and catalytic residues The experimental and theoretical results presented here not only provide fundamental insights concerning the influence of glycosylation on the protein biophysical properties but also support the hypothesis that for a-CT the global structural dynamics directly influence the kinetics of enzyme catalysis via mechanochemical coupling between domain motions and active site chemical groups Unraveling the general mechanisms by which enzymes catalyze chemical reactions is fundamental to the understanding of biochemical processes While the chemical basis of enzyme catalysis is largely understood the same cannot be said about the influence of the intrinsic protein structural dynamics on enzyme catalysis [1–4] Although it has been known for decades that proteins are highly dynamic molecules which undergo a variety of structural motions [5,6] only recently has the relationship between protein structural Abbreviations a-CT, a-chymotrypsin; exchange, kinetics (kHX); GNM, Gaussian network model; H ⁄ D, hydrogen ⁄ deuterium; MD, molecular dynamics; pNA, p-nitroanilide; QM, quantum mechanics; Suc, N-succinyl; SBzl, thio-benzyl; SS-mLac, mono-(lactosylamido)-mono-(succinimidyl) suberate; SS-mDex, mono-(dextranamido)-mono-(succinimidyl) suberate; VDW, Van der Waals FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS 5303 ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis dynamics and enzyme catalysis become generally evident within multiple enzyme systems [7–11] Due to this it has been proposed that enzymes can accelerate chemical reactions by lowering the transition state free-energy of activation barrier (DGTS) through the influence of global thermally coupled structural motions (DGDyn) on the turnover step [12–15] One such enzyme for which this phenomenon has been proposed to occur but has not been fully experimentally shown is a-chymotrypsin (a-CT; EC 3.4.21.1) [16–19] Being a representative member of the chymotrypsinfold serine protease family, it catalyzes the selective hydrolysis of amide bonds adjacent to bulky hydrophobic side chains (Tyr, Trp, and Phe) from its peptide and protein substrates Its catalytic cycle (Fig 1) first involves the formation of a substrate–enzyme complex (ES), followed by formation and breakdown of the first tetrahedral intermediate (ES)TET1 leading to the liberation of the reaction’s first product and enzyme acylation The catalytic cycle ends with the hydrolysis of the acyl-enzyme intermediate, followed by formation and breakdown of a second tetrahedral intermediate (EP2)TET2, and liberation of the reaction’s second product with restoration of the original free enzyme From a structural perspective a-CT is composed of two six-stranded b-barrel domains with the nature of its collective structural dynamics being attributed to interdomain hinge-bending motions [16,20,21] Due to the location of the active site residues at the interface between these two structurally rigid b-sheet domains it has been suggested that global structural flexibility could directly influence their displacements, thus impacting the reaction kinetics [16,21–23] Theoretical free-energy calculations of the catalytic cycle for structurally related serine proteases (trypsin, elastase) have also suggested the necessity of structural displacements for the catalytic residues so that acylation and deacylation can take place [24–29] Thus, both local active site residues and global domain motions are thought to be implicated in the catalytically relevant structural dynamics of the enzyme The influence of structural dynamics on the enzyme’s kinetics has also been suggested in previous experimental works From 1H-NMR studies on the His57–Asp102 low barrier hydrogen bond, Frey and coworkers proposed the involvement of a conformational change during the formation of the tetrahedral intermediate [30] Kawai et al also studied the effect of medium viscosity on the hydrolysis of p-nitrophenyl ester and p-nitroanilide amide substrates [19,31] While for ester substrates the acylation and deacylation rates were found to decrease with increasing viscosity, for amide substrates they found the acylation step to be viscosity-independent From these results they proposed a catalytic mechanism in which induced-fit conformational changes occur during the formation of the first tetrahedral intermediate and during the breakdown of the second tetrahedral intermediate Alternatively, thermodynamic kinetic work by Stein and coworkers revealed that the enzyme displays convex Eyring plots only for the acylation step (k2) during the hydrolysis of amide substrates of differing peptide chain length [17] From these results the researchers proposed that the convex Eyring plots could arise from the coupling of protein structural isomerizations to the active site chemistry [17,18] While all of these experimental works suggest the possible involvement of structural dynamics in the various kinetic steps of a-CT catalysis, no actual measurements of protein structural dynamics were performed to explain the observed kinetic catalytic behavior Thus, the question of whether the kinetics of a-CT catalysis are influenced by the enzyme’s intrinsic structural dynamics still remains experimentally unanswered Due to the well documented effect of natural glycans in modulating glycoprotein structural dynamics and function [32–35], chemical glycosylation represents a straightforward methodology to study the role of protein structural dynamics on enzyme catalysis [36] Herein we designed a series of differentially glycosylated a-CT variants with sequentially reduced structural dynamics through chemical glycosylation with monofunctionally activated glycans of differing molecular masses [36,37] These were employed in this work to address experimentally the questions of whether and how the enzyme’s structural dynamics influence the kinetics of a-CT catalysis This was done by determining the changes in the global structural dynamics (DGHX) [38] for the various chemically glycosylated a-CT conjugates through amide hydrogen ⁄ deuterium (H ⁄ D) exchange kinetic (kHX) experiments and then performing statistical correlation analysis with their kinetic parameters (KS, k2, and k3) for the hydrolysis of N-succinyl-Ala-Ala-Pro-Phe p-nitroanilide (Suc-Ala- Fig General mechanism of serine protease catalysis 5304 FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS ´ R J Sola and K Griebenow Ala-Pro-Phe-pNA) Molecular modelling of the a-CT glycoconjugates coupled with molecular dynamics (MD) simulations and domain motion analysis employing the Gaussian network model (GNM) was additionally employed to provide structural insights into the relation between the protein’s surface glycosylation, the resulting structural dynamic changes, and the influence of these on the enzyme’s collective dynamics and catalytic residues Results and Discussion Chemical glycosylation of a-CT Chemical glycosylation was recently introduced by us as a useful methodology for the sequential modulation of protein structural dynamics without altering the protein’s internal amino acid composition, thus allowing the study of its impact on the protein fundamental biophysical properties [36] It was employed in this work to study the influence of structural dynamics on the kinetics of a-CT catalysis Two glycans of contrasting molecular mass [mono-(lactosylamido)mono-(succinimidyl) suberate (SS-mLac; 500 Da) and mono-(dextranamido)-mono-(succinimidyl) suberate (SS-mDex; 10 kDa)] were employed to highlight any steric effects induced by the chemical glycosylation that could potentially alter the substrate binding affinities of the conjugates and thus impact their catalytic behavior The chemistry used for chemical glycosylation is based on the succinimidyl functionality (Fig 2) which allows coupling of the glycans to the protein surface via the lysine e-amino groups at pH and above (Table 1) The resulting conjugates are heterogeneous mixtures of noncrosslinked single protein species characterized by a variable distribution of glycans attached to the protein’s surface Average glycan molar contents for these a-CT glycoconjugates were sequentially increased to levels of around 7–8 mol of glycan per mol of protein This is approximately 50– 60% of the total glycan content that can theoretically be attached to a-CT by the chemistry employed because the protein has 14 surface accessible lysine Structural dynamics and serine protease catalysis residues Previous structural characterizations revealed that protein structural integrity was not adversely impacted during the chemical glycosylation and that the thermodynamic stability of the conjugates was increased with increasing glycosylation [36,37] Changes in a-CT’s structural dynamics upon chemical glycosylation Determination of H ⁄ D exchange kinetics represents one of the principal techniques for the experimental measurement of changes in protein structural dynamics [9,34,36,38–46] Due to the heterogeneous nature of the glycoconjugates we chose to determine the global amide H ⁄ D exchange rates by FTIR spectroscopy [7,36,44,45] These measurements thus represent the average dynamic nature of the enzyme Figure shows the spectroscopic results from a typical FTIR H ⁄ D exchange experiment for a-CT including both the spectra of the undeuterated and completely deuterated protein H ⁄ D exchange kinetics were determined by following the decrease in the absorbance of the amide II band (N-H, 1500–1600 cm)1) relative to the nonexchanging amide I band (C ¼ O, 1600–1700 cm)1) From thermodynamic analysis (EX2 exchange mechanism; pH 7.1) of the H ⁄ D exchange kinetic plots (Fig S1), the global Gibbs free-energy of microscopic unfolding (DGHX,1) for the various glycoconjugates prepared was calculated This parameter is representative of the global structural dynamic free-energy of the protein (DGDyn % DGHX,1) [13,38,47,48] The results (Table 2) show the reduced global structural dynamic free-energy of a-CT as a function of the glycosylation levels independent of the glycan size as had been previously described by us [36] Additionally, molecular models of the Lac-a-CT glycoconjugates (Fig 4) were constructed based on the lysine reactivity index presented in Table (see below) to provide a detailed picture of the possible changes in structural dynamics upon chemical glycosylation These glycoconjugate structures were then subjected to conformational energetic equilibration by molecular dynamics (MD) simulation methods (Fig S2) Models Fig Succinimidyl activated lactose molecule (SS-mLac) employed for the chemical glycosylation of a-CT and for the molecular modelling and molecular dynamics simulations The succinimidyl functionality serves as leaving group during the glycosylation reaction FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS 5305 ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis Table Reactivity order based on the calculated electrostatic potentials (EP) for the Ne of the lysine residues of a-CT at pH EP, EwaldEi EP is the Ewald energy of placing a charge of +1 at the location of the ith ionizable atom [89] Reactivity order Lysine no EP (kcalỈmol)1) 10 11 12 13 14 177 170 175 93 169 202 84 87 90 36 107 203 82 79 146.44 123.85 122.91 122.08 89.31 84.68 66.50 64.70 53.07 43.81 36.10 31.94 13.51 )24.94 Fig Measurement of global amide H ⁄ D exchange rates by FTIR spectroscopy Results from a typical H ⁄ D exchange experiment for a-chymotrypsin (pD 7.1 at 25 °C) Arrows highlight both the decreasing amide II band (N-H; 1550 cm)1) and the increasing amide II¢ band (N-D; 1450 cm)1) for the dextran modified protein could not be constructed due to the technical limitations involved in modelling linear polymeric molecules of such large size ˚ (> 300 A) While molecular modelling and MD simulations have previously been employed with great success to provide a deeper mechanistic understanding towards the roles of glycans on glycoprotein and glycoconjugates structure, stability, dynamics, and function [13,49–55], the influence of the degree of glycosylation on the protein biophysical properties has remained unexplored To obtain a general thermodynamic and entropic picture from the MD simulations we calculated the global energetic parameters and Debye–Waller 5306 temperature B-factors for the protein portion of the thermodynamically optimized a-CT glycoconjugate structures (Table 3) Comparison with the parameters for the full conjugates (protein-glycan) revealed that these changes are not due to the presence of the glycans because many of the energy parameters remained unchanged when calculated with and without the glycans (Table S1) The results from the MD simulations show how the total energy of the protein decreases at increasing glycosylation levels This is in accord with the increased thermodynamic stability exhibited by natural glycoproteins [34,56–59] and also with data obtained by differential scanning calorimetry for our glycoconjugates [36,37] Examination of the individual energy parameters contributing to the decrease in total energy of the glycoconjugates revealed that the bond, angle, and Van der Waals (VDW) energy parameters increased due to glycosylation with a decrease in the dihedral and the coulombic electrostatic energy parameters Because the protein portion of the conjugates remains constant for these models, the changes in bond, angle, and dihedral energy must arise from a rearrangement of their noncovalent interactions While the contributions of the VDW and coulombic energy parameters to these changes are evident from the results, other noncovalent interactions such as internal hydrogen bonds could also contribute to the increase in these parameters Analysis of the changes in internal hydrogen bond composition for the protein-glycan conjugates indicates that for all of the conjugates there was also an increase in these internal hydrogen bonds formed due to glycosylation (Table S2) However, they are too small to sustain the observed changes in the bond and angle parameters These are most probably increased due to the increased VDW interactions The changes in some of these parameters (e.g reduced dihedral and increased VDW energies) also suggest a more rigid and compact protein structure for the glycoconjugates This increase in rigidity due to glycosylation can be also be appreciated from the decrease in the calculated Debye–Waller temperature B-factors (Table 3, [60]) This reduction in dynamics due to chemical glycosylation does not appear to be caused by the modified lysine residue charges as it has been well established that natural glycosylation also reduces substantially the dynamics of natural glycoproteins where the modification occurs in noncharged residues [32–34] However, future experiments will be performed to investigate this The observed changes in the coulombic energy parameter also highlight the large contribution that the internal electrostatics have towards decreasing the total energy of the conjugates, which agrees with the hypothesis of global electrostatics being relevant to FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis Table Kinetic and thermodynamic parameters derived from amide H ⁄ D exchange rates for a-CT and for the various lactose-a-CT and dextran-a-CT conjugates at pH 7.1, 25 °C Glycoconjugate Lac-a-CTa 0.0 ± 0.0 1.8 ± 0.7 2.5 ± 0.4 3.8 ± 0.4 5.2 ± 0.3 7.4 ± 0.3 Dex-a-CTa 0.0 ± 0.0 1.4 ± 0.1 2.5 ± 0.3 4.2 ± 0.1 6.7 ± 0.4 7.6 ± 0.1 kHX,1 (min)1) A1 b A2 b kHX,2 (min)1) A3b ỈDGHX,1ỉc (kcalỈmol)1) 0.56 0.53 0.51 0.48 0.46 0.43 ± ± ± ± ± ± 0.04 0.03 0.02 0.01 0.01 0.01 0.757 0.715 0.708 0.628 0.573 0.434 ± ± ± ± ± ± 0.139 0.109 0.102 0.049 0.029 0.019 0.22 0.19 0.16 0.11 0.10 0.08 ± ± ± ± ± ± 0.03 0.03 0.02 0.01 0.01 0.01 0.064 0.064 0.041 0.023 0.017 0.017 ± ± ± ± ± ± 0.016 0.017 0.010 0.003 0.002 0.003 0.22 0.28 0.33 0.41 0.44 0.49 ± ± ± ± ± ± 0.01 0.01 0.01 0.01 0.01 0.01 5.442 5.477 5.482 5.553 5.608 5.772 0.56 0.55 0.49 0.44 0.43 0.40 ± ± ± ± ± ± 0.04 0.01 0.02 0.03 0.01 0.02 0.757 0.741 0.677 0.650 0.539 0.394 ± ± ± ± ± ± 0.139 0.060 0.074 0.096 0.043 0.050 0.22 0.14 0.15 0.17 0.15 0.14 ± ± ± ± ± ± 0.03 0.01 0.02 0.02 0.01 0.01 0.064 0.029 0.058 0.063 0.023 0.021 ± ± ± ± ± ± 0.016 0.005 0.013 0.015 0.003 0.006 0.22 0.31 0.36 0.39 0.42 0.46 ± ± ± ± ± ± 0.01 0.01 0.01 0.01 0.01 0.01 5.442 5.455 5.509 5.533 5.643 5.830 a Average moles of lactose and dextran per mole of a-CT b Ai are the fractions of amide protons in the ith population that exchange with a rate constant kHX,i c Gibbs free-energy of microscopic unfolding per mol of peptide hydrogen for the fast exchanging amide protons [48] Fig Representative a-CT and Lac-a-CT glycoconjugates structures after equilibration of conformational energetics by MD simulations with YASARADynamics Coloring scheme: domain (blue), domain (red), catalytic triad (yellow), and mLac glycans (grey) Structures were rendered with PYMOL [92] protein stability [61] The decrease in structural dynamics due to glycosylation could also be attributed to the decrease in the coulombic energy parameter because electrostatics are also known to influence protein dynamics [62] This decrease in the internal electrostatic energy of the protein as a result of glycosylation and its consequences on protein dynamics and stability seems to be in agreement with the notion that glycosylation perturbs the protein’s surrounding solvation-shell [36] This could lead to solvent dielectric FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS 5307 ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis Table Global energetic parameters and Debye–Waller temperature factors calculated for the protein portion of a-CT and the various lactose-a-CT conjugate structures modeled and submitted MD simulations at pH 7.1, 25 °C Energy values in McalỈmol)1 Energy Glycoconjugate Bond Angle Dihedral Planar VdW Coulomb Total Global B-Factor a-CT Lac1-a-CT Lac3-a-CT Lac5-a-CT Lac7-a-CT Lac14-a-CT 11.8 11.1 15.1 16.5 20.2 23.5 5.6 5.7 7.0 7.4 8.9 10.1 13.5 13.1 13.0 12.9 12.9 12.7 0.084 0.083 0.079 0.077 0.082 0.086 15.4 15.6 21.1 23.4 30.1 35.9 ) ) ) ) ) ) ) 90.1 ) 87.7 ) 111.9 ) 122.2 ) 151.9 ) 177.1 14.1 13.8 13.3 12.8 12.4 11.0 shielding [63] thereby transforming the protein biophysical properties from being solvent slaved to nonslaved [64,65] We have analyzed the effect that glycosylation has on the protein-solvent hydrogen bonds and the solvent accessible surface areas for the protein portion of the conjugates to provide evidence for this concept within our system While the total number of hydrogen bonds and solvent accessible area increases for the conjugates with increased glycosylation levels, the actual number of protein-solvent hydrogen bonds and solvent accessible area decreases for the protein portion of the conjugates (Tables S2 and S3) providing support to this notion While it is traditionally believed that increased glycan-protein hydrogen bonds are responsible for the changes in protein dynamics and stability, our results clearly show that this is not necessarily the case These results thus highlight an alternative fundamental mechanism by which glycans can modulate the protein’s biophysical properties (dielectric shielding due to decreased contact of the protein’s surface with the bulk solvent) This could have profound implications for the design of novel protein stabilization strategies as these effects in principle could be achieved by other types of chemical modifications Next we performed a statistical analysis of variance (anova) to determine if the changes in the theoretical conformational dynamics and energetics parameters for the modeled structures accurately reflect the changes in the experimental parameters of the glycoconjugates (Fig 5) This was confirmed by the significant statistical correlation (P < 0.05) found These results also provide theoretical and experimental support to the hypothesis that glycosylation leads to the thermodynamic stabilization of proteins through a decrease in their structural dynamics [7,34,36,58,66,67] These experimental and theoretical results thus provide evidence that chemical glycosylation does indeed decrease the global conformational dynamics of the protein This allowed us to then examine the effects of chemical 5308 136.5 133.3 168.2 182.5 224.1 259.4 Fig Statistical correlation analysis (ANOVA) between the theoretical (*) and experimental global conformational (A) dynamics and (B) energetics parameters determined for the Lac-a-CT conjugates TM values used from [36] glycosylation on the kinetics of enzymatic catalysis from both an experimental and theoretical perspective Changes in the kinetics of a-CT catalysis upon chemical glycosylation The catalytic behavior of a-CT after chemical glycosylation was determined from the hydrolysis of FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis Table Kinetic parameters for the a-CT-, lactose-a-CT-, and dextran-a-CT catalyzed hydrolysis of Suc-Ala-Ala-Pro-Phe-pNA at pH 7.1, 25 °C KS ¼ KM[(k2 + k3) ⁄ k3] k2 ¼ k3kcat ⁄ (k3 – kcat) k3 is equal to kcat for the hydrolysis of Suc-AAPF-SBzl Glycoconjugate Lac-a-CT 0.0 ± 0.0 1.8 ± 0.7 2.5 ± 0.4 3.8 ± 0.4 5.2 ± 0.3 7.4 ± 0.3 Dex-a-CT 0.0 ± 0.0 1.4 ± 0.1 2.5 ± 0.3 4.2 ± 0.1 6.7 ± 0.4 7.6 ± 0.1 kcat (s)1) KM (mM) KS (mM) 9.9 7.9 7.3 6.7 6.6 5.4 ± ± ± ± ± ± 0.1 0.1 0.1 0.1 0.3 0.3 0.046 0.049 0.053 0.047 0.051 0.047 ± ± ± ± ± ± 0.001 0.002 0.001 0.001 0.005 0.006 0.096 0.098 0.108 0.101 0.109 0.099 ± ± ± ± ± ± 0.001 0.008 0.003 0.003 0.012 0.011 20.5 15.8 15.0 14.5 14.3 11.3 ± ± ± ± ± ± 0.2 0.9 0.8 0.4 0.8 0.5 19.1 15.7 14.4 12.5 12.8 10.2 ± ± ± ± ± ± 0.1 0.3 0.3 0.1 0.4 0.7 9.9 9.4 8.6 8.1 5.5 4.3 ± ± ± ± ± ± 0.1 0.1 0.1 0.2 0.4 0.1 0.046 0.052 0.048 0.046 0.044 0.046 ± ± ± ± ± ± 0.001 0.004 0.001 0.004 0.004 0.003 0.096 0.107 0.098 0.094 0.092 0.094 ± ± ± ± ± ± 0.001 0.006 0.003 0.007 0.007 0.006 20.5 19.5 17.7 16.5 11.5 8.8 ± ± ± ± ± ± 0.2 0.1 0.4 0.4 0.8 0.3 19.1 18.3 16.8 15.8 10.6 8.3 ± ± ± ± ± ± 0.1 0.5 0.5 0.4 0.9 0.1 Suc-Ala-Ala-Pro-Phe-pNA (Table 4) These experiments revealed that for the a-CT glycoconjugates only the turnover rate (kcat) was reduced as a function of the glycan molar content independent of the glycan’s molecular mass; similarly to the behavior observed for the global protein dynamics, while the substrate binding affinity (KM) remained unchanged This reduction in kcat with constant KM values upon chemical glycosylation agrees with the results found previously during the study of the catalytic behavior of natural glycoproteins [34,68] Interestingly, this reduction in catalysis was not caused due to inactivation during the chemical glycosylation of the enzyme because it was previously demonstrated that native-like activity and dynamics could be restored at increased temperature regimes for these glycoconjugates [36] Evaluation of the glycoconjugates surface potential reveals that the decreased kinetics are also not due to a perturbation of the enzyme’s active site groove electrostatics due to lysine charge modification (Fig S3) Because for the substrate used the kcat and KM parameters are a combination of the reaction’s individual rate constants (KS, k2, and k3) we determined these by kinetic chemical dissection with a thio-benzyl (SBzl) functionalized substrate as previously described by Stein and coworkers [17] This experiments revealed that both the kinetics of enzyme acylation (k2) and deacylation (k3) are reduced by chemical glycosylation, also as a function of the glycan molar content of the conjugates (Table 4) In contrast, the substrate binding step (KS) was unaffected by the chemical glycosylation; even for the high molecular mass dextran modified a-CT conjugates, revealing that this type of modification did not lead to any active-site steric effects that could affect the catalytic steps Here we want to point k2 (s)1) k3 (s)1) out that while the values for the acylation and deacylation rates appear similar under the experimental conditions employed in this work (25 °C, pH 7.1, Ca+2 free), acylation does become slightly larger than deacylation when the experimental conditions become more traditional (30 °C, pH 8.0, 10 mm Ca+2) [17] Although the similarity in k2 and k3 values for this substrate might appear strange due to the notion that acylation is rate limiting for amide substrates (k2 > k3) and deacylation is rate limiting for ester substrate (k2 ? k3) this generalized assumption is not always accurate for all substrates as previously pointed out by Hedstrom [16] This can be appreciated experimentally in the already mentioned work by Stein [17], where they measured the changes in kS, k2, and k3 as a function of pH and temperature for three different sized amide substrates (Suc-F-pNA, Suc-AF-pNA, and Suc-AAPF-pNA) While for the two smaller substrates k2 is generally smaller than k3, for the larger substrate that we use in our study k2 is equivalent to k3 Correlation between the changes in a-CT’s global structural dynamics and enzyme kinetics Next we performed a statistical correlation analysis (Fig 6) between the structural dynamic (DGHX,1) and catalytic (DG „k2, DG „k3) thermodynamic parameters (Tables and 5) for the glycoconjugates to determine the dependence of the individual rate constants on the changes in the enzyme’s structural dynamics The parameters for both the lactose and dextran conjugates were combined within the analysis of variance to provide a larger and thus statistically more significant sample group This combination was possible because both the dynamic and catalytic parameters derived FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS 5309 ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis Table Thermodynamic activation parameters derived from the k2 and k3 steps for the hydrolysis of Suc-Ala-Ala-Pro-Phe-pNA by a-CT and the various lactose-a-CT, and dextran-a-CT conjugates DG „ ki ¼ –RTln(kih ⁄ kBT) Glycoconjugate Lac-a-CT 0.0 ± 0.0 1.8 ± 0.7 2.5 ± 0.4 3.8 ± 0.4 5.2 ± 0.3 7.4 ± 0.3 Dex-a-CT 0.0 ± 0.0 1.4 ± 0.1 2.5 ± 0.3 4.2 ± 0.1 6.7 ± 0.4 7.6 ± 0.1 Fig Statistical correlation analysis (ANOVA) between the Gibbs free-energy of microscopic unfolding per mol of peptide hydrogen for the fast exchanging amide protons (DGHX,1) and the Gibbs freeenergy of activation for reactions (A) acylation (DG „k2) and (B) deacylation steps (DG „k3) for the Lac-a-CT (s) and Dex-a-CT (n) conjugates were independent of the size of the glycan (Tables and 5, [36]) The analysis revealed that the changes in these parameters statistically correlate for both the acylation and deacylation steps (DGHX,1 ⁄ DG „k2: R ¼ 0.9245, P < 0.0001; DGHX,1 ⁄ DG „k3: R ¼ 0.9370, P < 0.0001) Interestingly, the reaction’s activation energy for both steps increases linearly with a decrease in the structural dynamics of the enzyme (DG „k2 ¼ DG „k3 ¼ 1.12DGHX,1 + 9.65) 1.06DGHX,1 + 9.94; This linear relation can be rationalized if one considers that the enzyme’s dynamical free-energy can be transferred to the reaction’s activation energy by influencing the transition-state activation energy (DG „ ¼ DGTS ± DGDyn) [13–15,42,69,70] Here we want to point out that although DGHX,1 is an experimental parameter representative of DGDyn, these two free-energy functions are most probably not on the same energetic 5310 DG „ k2 (kcalỈmol)1) DG „ k3 (kcalỈmol)1) 15.65 15.81 15.84 15.86 15.87 16.00 ± ± ± ± ± ± 0.01 0.03 0.03 0.02 0.03 0.03 15.69 15.81 15.86 15.94 15.93 16.07 ± ± ± ± ± ± 0.01 0.01 0.01 0.01 0.02 0.04 15.65 15.68 15.74 15.78 16.00 16.15 ± ± ± ± ± ± 0.01 0.01 0.01 0.02 0.04 0.02 15.69 15.72 15.77 15.81 16.04 16.19 ± ± ± ± ± ± 0.01 0.02 0.02 0.03 0.05 0.01 scale, because the timescales of H ⁄ D exchange measured in this work (kHX,1) are 103 times slower that those observed during catalysis (k2 and k3) This discrepancy in timescales between the observed catalytic rates and the rates of the H ⁄ D exchange process was previously noted by Klinman and coworkers in their correlation studies on a thermophilic alcohol dehydrogenase [71] This was attributed to the fact that during the employment of a composite global exchange constant, the rates of the catalytically relevant residues will probably be masked by the rates of slower residues and that the protein conformational fluctuations responsible for H ⁄ D exchange are not necessarily in the same timescales as the protein motions of catalysis Nevertheless, the slope values for the linear correlations obtained here [which are close to unity (m % 1)] clearly support the notion that the dynamical energy of the enzyme is transferred directly into catalysis The correlations thus provide direct experimental evidence indicating that both acylation and deacylation rates are influenced by the changes in an enzyme’s structural dynamics This observed similar response for k2 and k3 to the changes in the enzyme’s structural dynamics could be attributed to the fact that the enzyme employs similar structural and chemical mechanisms for proton transfer during the acylation and deacylation steps but just in a reverse order [16] These results provide support to the kinetic mechanism previously presented by Kawai et al [19,31] in which a substrateinduced conformational change occurs during the formation of the first tetrahedral intermediate and during the breakdown of the second tetrahedral intermediate Nonetheless, an observation that becomes clearly evident from our results is that to some degree the FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS ´ R J Sola and K Griebenow catalytically relevant dynamics of a-CT appear to be an intrinsic structural feature of the protein This notion is indirectly supported by more detailed NMR N15-relaxation experiments in another enzyme system (cyclophilin A; prolyl cis-trans isomerase) with the Suc-AAPF-pNA substrate employed in this work [11], as this enzyme has similar substrate binding specificity as a-CT From these experiments it was deduced that the presence of this type of substrate in the enzyme’s active site during catalysis does not lead to new catalytically relevant motions that were not already present within the enzyme Because we previously showed that for a-CT these catalytically relevant motions are thermally activated [36] we suggest a minor correction to the mechanism proposed by Kawai et al in which the substrate triggered induced-fit conformational process is modified by the enzyme’s intrinsic thermally activated structural mobility (Fig 7) While the results presented here experimentally highlight the importance of structural dynamics to rate acceleration by the enzyme this is clearly not the only contributor to catalysis as it is well known that other phenomena, such as electrostatic stabilization of the transition state, formation of covalent intermediates, steric strain, near attack conformations, substrate desolvation, low barrier hydrogen bonds, and entropic effects are present in the mechanism of serine protease catalysis [16,72] Interestingly, the observed relation between the changes in the enzyme’s internal electrostatics and its structural dynamics suggests that some of these phenomena may be interconnected within the catalytic mechanism of the enzyme Structural insights into the mechanochemical nature of a-CT catalysis A more detailed analysis of the influence of chemical glycosylation on the dynamics of a-CT from the theoretical simulations was additionally performed to gain a deeper perspective into the mechanism of coupling between the structural dynamic and functional properties of the enzyme Although decreases in the dynamics of catalytically important regions (e.g catalytic triad, S1 binding site, and L1 specificity site) can certainly be Structural dynamics and serine protease catalysis observed from the analysis of the MD trajectories (Fig S4 and Table S4), these changes are not necessarily relevant to the changes in catalysis as the timescales that are accessible to MD simulation techniques are computationally limited so that catalytically important phenomena which occur on larger time scales (e.g collective domain motions) are not accurately sampled The Gaussian network model (GNM) was developed to provide a simple and computationally inexpensive yet accurate description of residue mobilities within the collective vibrational modes of proteins and supramolecular structures [73,74] Results from this type of calculation have been found to be in excellent agreement with X-ray crystallographic B-factors, H ⁄ D exchange free energies of amide protons, and NMRrelaxation order parameters [75,76] Due to this GNM has been extensively used to describe the influence of collective structural motions on the functional properties of proteins Because these calculations are traditionally performed on crystal structures their only drawback is that they not take into consideration environmental variables relevant to protein dynamics (i.e pH, pressure, temperature, and ions) [77] We overcame this problem in our analysis because we performed our GNM calculations with structures for which the protein-solvent system was previously equilibrated with these variables during the MD simulations Figure displays the average relative residue mobilities ([(DRi)2]1)2) for the two slowest collective vibrational modes of a-CT and the interresidue mobility crosscorrelations within the structure These two slowest modes correspond to the most collective ones which have been found to be the most significant to enzyme function [78,79] The relative mobility plot (Fig 8A) displays that a-CT’s structure is composed of two rigid domains [domain (residues 1–119) and domain (residues 151–245)] linked by an interdomain hinge (residues 120–150) Interestingly, the connection between the two domains and the hinge appears to be via two highly mobile loops (85–105, 160–175) located at the structural edges of the two domains Positive cross-correlations within the two domains (Fig 8B) reveal how the motions of the residues comprising both domains are correlated and thus move in the Fig Catalytic steps influenced by the enzyme’s intrinsic structural dynamics FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS 5311 ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis A B 0.5 20 0.4 40 60 0.3 Residue j 80 0.2 100 120 0.1 140 160 180 –0.1 200 220 –0.2 50 100 150 Residue i 200 same direction (squared patterns in the upper left and in the lower right areas of plot) within the collective vibrational modes Additionally, significant crosscorrelations are observed between catalytically relevant residues (Cys42–Ser195, His57–Asp102, His57–Ser195, Gly140–Ser195, Cys182–Ser214) present in similar and in separate domains The motion of these collective vibrational modes can be better appreciated from a movie generated with the normal mode analysis morph server at Yale University (http://molmovdb.org) (Video S1) [80] When the GNM analysis was applied to the a-CT glycoconjugates (Fig 9), the relative mobilities of both interdomain connecting loops (85–105, 160–175) were 5312 Fig Relative mobility ([(DRi)2]1)2) in the slowest two collective vibrational modes versus residue index (A) and interresidue cross-correlation map (B) for a-CT calculated by GNM Coloring scheme on scale: positive correlations (red), negative correlations (blue) largely reduced with an increase in the relative mobility of the interdomain hinge residues (120–150) and the C-terminal a-helix (230–245) (Fig 10) While most of the glycosylation sites occur in these interdomain connecting loop regions (Fig 9) we can also see a reduction in the dynamics of regions far away from the glycosylation sites This is most probably due to the very well known fact that the network of hydrogen bonds within the protein’s interior can relay information to other distant regions of the protein Also the large increase in the mobility of some regions can be expected to occur due to a redistribution of the protein’s configurational dynamics as to minimize the potential entropy loss due to glycosylation [81] FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS ´ R J Sola and K Griebenow Fig Changes in relative mobility (D[(DRi)2]1)2) in the slowest two collective vibrational modes versus residue index for the various Lac-a-CT glycoconjugates structures with respect to a-CT Circles denote glycosylation sites Fig 10 Structural regions in a-CT subject to changes in mobility due to chemical glycosylation Coloring scheme: decreased mobility (blue), increased mobility (red), nonaltered mobility (yellow) Structure rendered with PYMOL [92] Because the cross-correlation maps for the glycosylated conjugates were not significantly different from those of the nonglycosylated protein (results not shown), this result implies that glycosylation can reduce the kinetics of the protein’s collective domain motions without altering the shape of the collective vibrational mode, the protein structure, or even the interresidue connections More specifically the decrease in mobility of the Asp102 loop (85–105) seems to be largely dependent on the degree of glycosylation Interestingly, the mobility of the His57 loop (55–65) and the calcium binding loop (70–80) which are adjacent to the Asp102 loop Structural dynamics and serine protease catalysis were also reduced (but to a lesser extent) as a function of the glycosylation degree The decrease in mobility of the His57 and Asp102 loops could explain the decreased acylation and deacylation rates observed for the glycosylated a-CT conjugates as these residues are directly involved in the hydrogen transfer steps of catalysis A decrease in the dynamics of these two loops could reinforce the H-bond strength between the His57 and Asp102 residues leading to a possible anticatalytic situation [29] which could indirectly affect the deprotonation and protonation rates of Ser195 thus reducing the kinetics of catalysis The results also suggest that the dynamics of the calcium binding site in this structural class of proteins (chymotrypsin-fold proteases) is directly interlinked with the dynamics of the regions containing the His57 and Asp102 catalytic residues While the importance of this calcium binding site has been primarily assigned as a contributor to increased protease stability less emphasis has been put on the increased rates of catalysis observed upon calcium binding which might be linked to its allosteric regulation in vivo [82] Because the biophysical mechanism of allosteric activation by calcium for chymotrypsin-fold proteases has not yet been resolved we hypothesize (based on the theoretical results presented herein and on preliminary unpublished experimental results) that the calcium induced activation is due to an increase in the structural dynamics of these catalytically relevant regions upon calcium binding The results from GNM analysis together with those from MD simulations thus provide support to the proposal of mechanochemical coupling between the enzyme’s conformational dynamics and active-site chemistry through domain motions [17,18,21,78] Conclusions In this article, we further demonstrate the value of chemical glycosylation as a tool for studying the effects of modulated structural dynamics on the protein biophysical properties We have also been able to provide some novel insights concerning the mechanism by which glycans modulate the fundamental biophysical protein properties By applying this methodology to the study of the kinetics of catalysis by the serine protease a-CT we were able to statistically correlate the structurally dynamic behavior of the enzyme with its kinetics of catalysis From a mechanistic perspective we have provided evidence that supports a catalytic mechanism for a-CT in which both the enzyme acylation (k2) and deacylation (k3) steps are influenced by the enzyme’s intrinsic thermally activated structural dynamics Additionally, through the use molecular FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS 5313 ´ R J Sola and K Griebenow Structural dynamics and serine protease catalysis modelling and structural dynamics simulation techniques (MD and GNM) we have provided structurally dynamic insights supporting the proposal of mechanochemical coupling in a-CT catalysis Experimental procedures Chemical glycosylation of a-CT Mono-(dextranamido)-mono-(succinimidyl) suberate (SSmDex; 10 kDa) was synthesized by monofunctional succinnylation as described previously [37] a-CT glycoconjugates were prepared by chemical protein glycosylation with SS-mLac and SS-mDex (10 kDa) as described previously [36] Glycosylation levels (average glycan molar content) and protein integrity were determined from trinitrobenzene sulfonic acid assay, capillary zone electrophoresis, and circular dichroism spectroscopy as described previously [36,37] FTIR H ⁄ D exchange measurements Amide H ⁄ D exchange FTIR spectra were recorded on a Nicolet NEXUS 470 infrared spectrophotometer equipped with a thermally controlled sample cell (Spectra-Tech Inc., Shelton, CT) using CaF2 windows and 25 lm Teflon spacers (Buck Scientific, East Norwalk, CT) Kinetic experiments were designed and performed similarly to those reported previously [7,36,42–46,69] Processing of H ⁄ D exchange data H ⁄ D exchange spectra were processed for quantitative analysis in the form of hydrogen exchange (HX) decay plots (X versus time) [36,42,44,45] In these plots the fraction of unexchanged peptide hydrogen atoms (X) was determined as: Xẳ wtị w1ị w0ị w1ị where w(t) is the ratio of the amide II (1550 cm)1) and amide I (1637.5 cm)1) absorbencies corrected with the baseline absorbance (1789 cm)1) at time t, w(0) is the amide II ⁄ amide I ratio of the undeuterated proteins and w [8] is the amide II ⁄ amide I ratio for the fully deuterated proteins Wtị ẳ AamideII tị Abase tị AamideI ðtÞ À Abase ðtÞ w(0) was obtained from IR spectra for the undeuterated proteins measured as KBr pellets The value of w(¥) was determined from samples incubated for 15 days in D2O at 65 °C These samples were prepared at pH were a-CT’s activity is negligible and the protein unfolding reversible [36] Kinetic quantitative analysis of the HX decay data was done by a two-exponential model: 5314 X ẳ A1 expkHX;1 ịt ỵ A2 expkHX;2 ịt ỵ A3 where A1, A2, and A3 are the fractions of the fast, slow and stable amide protons and kHX,1 and kHX,2 are the apparent exchange rate constants for the fast and slow amide protons Results were interpreted thermodynamically under the EX2 exchange mechanism (pH 7.1) [41,43] where the Gibbs free-energy of microscopic unfolding per mol of peptide hydrogens for the fast exchanging amide protons is based on the chemical exchange rate constant (k0) and the measured rate constant (kHX,1) [42,44,45]: DGHX;1 ¼ ÀRTlnðkHX;1 =k0 Þ: Enzyme activity and kinetic measurements Initial velocities were measured by spectroscopically following the product formation of p-nitroanilide at 410 nm (e410 ẳ 8.8 mm)1ặcm)1) on a Shimadzu (Columbia, MD, USA) UV 160U spectrophotometer with a 0.1 cm path length cuvette Reactions were carried out in 10 mm KPi (pH 7.1) employing Suc-Ala-Ala-Pro-Phe-pNA as substrate [17] Calcium was excluded from the experiments to simplify the analysis of the results because preliminary experiments revealed that the binding of calcium to the protein surface was perturbed by the chemical glycosylation [36] The reaction was started by addition of 60 lL of enzyme ([E]o ¼ 0.8 lm) to a 240 lL substrate solution ([S]o ¼ 0.4 mm) in a final volume of mL For determination of steady state kinetic parameters, initial velocities were determined for seven initial substrate concentrations in the range between 0.01 and 0.5 mm kcat and KM parameters were determined from Eadie–Hofstee plot analysis Determination of the individual rate constants (KS, k2, and k3) was performed by chemical kinetic dissection experiments employing as substrate Suc-Ala-Ala-Pro-Phe-SBzl as described previously by Stein and coworkers [17] For these reactions the thiol product derived from thioester hydrolysis was detected by a coupled assay with 5,5¢-dithiobis(2-nitrobenzic acid) (DTNB) (100 lL; [DTNB]o ¼ mm) at 412 nm (e412 ¼ 13 mm)1Ỉcm)1) [17] The rest of the kinetic method was the same as that used for the p-nitroanilide (pNA) substrate Glycoconjugate modelling and molecular dynamics simulations For all molecular modelling and molecular dynamics (MD) simulation experiments the yasara suite of programs (YASARA Biosciences, Neue-Welt-Hoehe, Graz, Austria) was used [83] The starting a-CT coordinates originated ˚ from the 1.68 A atomic resolution crystal structure of bovine a-CT [84] These were acquired from the protein data bank [85]; accession code 4CHA All of the crystallization waters and one of the crystallization dimers (B) were removed Hydrogen atoms were added and fractional bond FEBS Journal 273 (2006) 5303–5319 ª 2006 The Authors Journal compilation ª 2006 FEBS ´ R J Sola and K Griebenow orders adjusted to the corresponding pH of the system (pH 7.1) This ensemble was subjected to yasara’s energy minimization protocol (steepest descent, simulated annealing minimizations) and yasara’s MD protocol (see parameters below) using the AMBER99 force field [86] To generate the various Lac-a-CT conjugates, the SS-mLac molecule (Fig 1) was modeled and parametrized quantum mechanically (QM) with yasara’s AutoSMILES protocol [83] This methodology allows semiempirical quantum chemical geometry optimization of newly modeled structures and generation of their general AMBER force field using the AM1-BCC QM method [87] and COSMO solvation model [88] Lysine reactivity order (nucleophilicity) for the in silico creation of the various glycoconjugates was determined by calculating the electrostatic potentials (EP) for the Ne of the lysine residues of a-CT at pH were the chemical glycosylation reaction takes places using yasara’s cell neutralization and pKa prediction module (Table 1) [89] The parametrized SS-mLac molecule was then coupled in silico to the various lysine residues of the MD optimized protein structure using this reactivity order, yielding the glycoconjugates: Lac1-a-CT, Lac3-a-CT, Lac5-a-CT, Lac7a-CT, Lac14-a-CT The novel amide bonds of the resulting glycoconjugates were also QM parametrized with yasara’s AutoSMILES protocol The protein models were subjected to yasara’s MD protocol using the AMBER99 force field with the GLYCAM force field parameters for carbohydrates [54,86] Simulation temperature was 25 °C, density 0.997, and pH 7.1 Van der ˚ Waals pairs cutoff distance was 7.86 A and particle mesh Ewald (PME) long range electrostatics were employed [90] Multiple timesteps of 1.5 fs for intramolecular and fs for intermolecular forces and periodic cell boundaries with a ˚ simulation cell 20 A larger than the protein along each axis were used Filling of the simulation cell with water, prediction of charged residues pKa’s, placement of counter ions, and cell neutralization were done automatically by yasara’s MD protocol [83] Simulations were started by a short steepest descent minimization (atom speed < 2200 mỈs)1) followed by 500 steps of simulated annealing (equilibration phase) and finally a 660 ps MD production run Simulation snapshots were saved every 2500 steps (7.5 ps) yielding 88 snapshots for trajectory analysis for which rmsd’s were calculated for the heavy atoms Global energetic parameters [86], Debye–Waller temperature B-factors [60], surface electrostatics, hydrogen bonds, and solvent accessible surface areas were calculated with YASARA’s analysis module Structural dynamics and serine protease catalysis and conformationally optimized protein structures submitted to 660 ps of solvated MD simulations by uploading the generated PDB files to the iGNM online web-server calculation engine (http://ignm.ccbb.pitt.edu) [73] Here, the modeled glycoprotein structures were treated as threedimensional elastic networks where the amino acid a-carbons are defined as nodes interconnected by Hookean springs with a uniform spring constant [c ¼ kcal ⁄ (mol ˚ ˚ A2)] within a cutoff distance (rc ¼ 6.0 A) The dynamics of the resulting network are then defined by the Ni · Nj Kirchhoff connectivity matrix of interresidue contacts (G) where the off diagonal elements of G are defined as: Gij ¼ )1 if the distance between residues i and j (Rij) is shorter than rc, meaning that they interact and Gij ¼ if Rij is larger than rc and the residues not interact The statistical thermodynamics of the network are then described by its potential V ¼ (c ⁄ 2)(DR)G(DR)T; where DR is a vector, with DRi representing the displacement of the ith residue from its equilibrium position Cross-correlations between the fluctuations (DRi and DRj) of residues i and j are then scaled with the ijth off-diagonal elements of G)1: hDRi Á DRj i ẳ 3KB Tc1 ịẵC1 ij where kB is the Boltzmann constant and T is the absolute temperature Correlations in GNM are normalized [)1 to 1]: Cij ¼ hDRi Á DRj i=ẵhDR2 i hDR2 i1=2 ẳ ẵC1 ij =ẵC1 ii ½CÀ1 Šij Þ1=2 i j so that positive values describe residue movement in the same direction while negative values describe movement in opposite directions From this analysis the dynamics of the protein are described by a set of N)1 normal modes, the kth eigenvector (uk) of G gives the residue displacements along mode k, and the kth eigenvalue, kk, scales with its frequency So that the contribution of mode k to the residue mobility is described by the mean-squared fluctuations of residue i which is scaled with the ith diagonal element of [uk]ii: ẵDRi ị2 k ẳ 3kB Tc1 ịkk ½uk Šii Statistical analysis All statistical analyses were performed by one-way analysis of variance (anova) with a P-value of < 0.05 considered significant using sigmaplot 8.0 (SPSS UKD Ltd, Woking, UK) statistical analysis module Gaussian network model analysis Acknowledgements GNM analysis represents a simplified version of normal mode analysis 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