Toward Understanding Allosteric Activation of Thrombin: A Conjecture

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Toward Understanding Allosteric Activation of Thrombin: A Conjecture for Important Roles of Unbound Na Molecules around Thrombin +

Ikuo Kurisaki, Masayoshi Takayanagi, and Masataka Nagaoka J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp510657n • Publication Date (Web): 05 Feb 2015 Downloaded from http://pubs.acs.org on February 18, 2015

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The Journal of Physical Chemistry

Toward Understanding Allosteric Activation of Thrombin: A Conjecture for Important Roles of Unbound Na+ Molecules around Thrombin

Ikuo Kurisaki†, Masayoshi Takayanagi†,‡, Masataka Nagaoka†,‡

†

Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan ‡

Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Honmachi, Kawaguchi 332-0012, Japan

*

Corresponding author: Masataka Nagaoka, Prof., Graduate School of Information

Science, Nagoya University, Furo-cho Chikusa-ku, Nagoya 464-8601, Japan. E-mail: [email protected], Tel & Fax: +81-52-789-5623

ACS Paragon Plus Environment


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Abstract We shed light on important roles of unbound Na+ molecules in enzymatic activation of thrombin. Molecular mechanism of Na+-activation of thrombin has been discussed in the context of allostery. However, the recent challenge to redesign K+-activated thrombin revealed that the allosteric interaction is insufficient to explain the mechanism. Under the circumstances, we have examined the roles of unbound Na+ molecule in maximization of thrombin-substrate association reaction rate. We performed all-atomic molecular dynamics (MD) simulations of thrombin in the presence of three different cations; Li+, Na+, and Cs+. Although these cations are commonly observed in the vicinity of the S1-pocket of thrombin, smaller cations are distributed more densely and extensively than larger ones. This suggests the two observation rules: i) thrombin surrounded by Na+ is at an advantage in the initial step of association reaction, namely, the formation of an encounter complex ensemble and ii) the presence of Na+ molecules does not necessarily have an advantage in the final step of association reaction, namely, the formation of the stereospecific complex. In conclusion, we propose a conjecture that unbound Na+ molecules also affect the maximization of rate constant of thrombin-substrate association reaction through optimally forming an encounter complex ensemble.


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Introduction Numerous enzymes demonstrate the maximum enzymatic activity in the presence of a specific monovalent cation.1 Among such enzymes, thrombin has long been studied as a paradigmatic protein to understand the mechanism of Na+-activated protein.2-8 This protein recognizes Arg or Lys at P1 site in a substrate by using Asp189 in the S1-pocket (Fig. 1A, 1B and 1C), and hydrolyzes the peptide bond vicinal to such positively charged residues by using the catalytic triad (His57, Asp102 and Ser195). The enzymatic activity of thrombin is maximized by the presence of Na+ with regard to every chemical step of the enzymatic reaction, namely, from association with a substrate to release of a product.2 The Na+-specific activation of thrmobin is quite reasonable for the functional expression because thrombin is distributed in the extracellular domain8, which contains relatively abundant Na+ molecules than the intracellular domain.



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Figure 1. Thrombin structure and the functional regions. (A) Overview of thrombin-substrate-Na+ complex structure. The substrate is Phe-Pro-Arg-p-nitroanilide (FPR). (B) Interaction between Asp189 and Arg P1 in FPR. (C) The S1-pocket. (D) Positional relation between the bound Na+ and the catalytic triad in the active site of thrombin. Thrombin, FPR and the catalytic triad (His57, Asp102 and Ser195) are distinguished by transparent grey, green and purple sticks, respectively. As for the S1-pocket (Asp189, Ala190, Cyt191, Val213, Trp215, Gly216, Gly219, Cyt220), Asp189 and the other residues forming the tunnel are indicated by stick and transparent orange surface, respectively. Na+ and Na+-binding region are distinguished by blue


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sphere and yellow tube, respectively. The thrombin-FPR-Na+ complex was modeled using thrombin-substrate complex structure (PDB entry 1PPB9). The amino acid residues in thrombin sequence are numbered according to chymotrypsin numbering.9

Thrombin specifically binds to Na+.6,10 This fact provided the perspective that Na+-binding activates thrombin.3 In the last two decades, Cera and his colleagues played a central role in establishing a molecular viewpoint of Na+-activation of thrombin.4,6,8 They resolved the thrombin-Na+ complex structure, and revealed that Na+ binds to thrombin at the site remote from the catalytic triad (Fig. 1D).11 Furthermore, the following X-ray crystallography study revealed “shift in the side chain of Ser-195 for

the optimal nucleophilic attack to the incoming substrate”.12 These structural observations provided such an insight that Na+-binding allosterically activates thrombin. Additionally, they identified amino acid residues critical for Na+-activation of thrombin using a panel of Ala mutants of thrombin12 and monumental X-ray structures of thrombin.10,12-20 After the vigorous research activities, they established the structural basis that the site-directed thrombin-Na+ interaction allosterically enhances the enzymatic activation of thrombin. According to the structural basis of Na+-activation of thrombin, Cera and his



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colleagues addressed redesign of K+-activated thrombin.21,22 It is true that they succeeded in constructing a mutant thrombin with higher K+-binding affinity than Na+-binding affinity.21 However, the mutant thrombin did not demonstrate the maximal enzymatic activity in the presence of K+, but still remained Na+-activated protein. They later succeeded in constructing a K+-activated thrombin with sufficient K+-binding affinity, but the alternative mutant thrombin show a reduced enzymatic activity even in the presence of K+, where the defect reaches 370 folds compared with wild-type thrombin.22 This apparent discrepancy between binding selectivity to a monovalent cation and maximization of the enzymatic activity of thrombin indicates that the site-directed thrombin-Na+ interaction is insufficient to explain how Na+ enhances the enzymatic activity of thrombin. Under such circumstances, we conjectured that unbound Na+ molecules also

contribute to maximization of the enzymatic activity of thrombin. To verify our conjecture, we first drew attention to the fact2 that thrombin-substrate association reaction rate constant is maximized by the presence of Na+. Moreover, the rate constant in the presence of Na+ is greater than those in the presence of Li+, Cs+ and K+ by a factor of 2.7, 2.7 and 1.2-fold, respectively.2 Then, we focused on the apparent difference between Na+ and Li+, or Cs+.


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Protein-substrate association reaction can be viewed as a two step chemical reaction, which consists of initial formation of an encounter complex ensemble and final well-defined stereoscopic complex formation23. Considering that thrombin specifically recognizes Arg or Lys in the P1 site of a substrate molecule, a cation’s density distribution around thrombin could potentially prevent formation of an encounter complex ensemble. Similarly, a local cation’s density distribution around the S1-pocket could potentially block interaction with such Arg and Lys in a substrate molecule in the formation of the sterospecific complex. In summary, it can be assumed that unbound cations surrounding thrombin also play roles in thrombin-substrate association reaction. In this study, we performed all-atom molecular dynamics (MD) simulations of three different thrombin-cation complex systems; Thrombin-Li+, Thrombin-Na+, and Thrombin-Cs+ (denoted by Thr-Li+, Thr-Na+, and Thr-Cs+, respectively). In each system, thrombin binds to a cation on the Na+-binding region and is solvated in 140-mM XCl aqueous solution (X is Li, Na or Cs.) We analyzed cation’s density distributions around thrombin, and discussed their effects on each step of thrombin-substrate association reaction. Finally, we shed light on important roles of unbound Na+ molecules in the maximization of thrombin-substrate association reaction rate constant.



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Materials and Methods Preparation of thrombin structure Although several thrombin-Na+ complex structures are registered in Protein Data Bank (PDB)24,25, their atomic coordinates of thrombin are not completely resolved. Then we obtained atomic coordinates of wild-type human thrombin from thrombin-ligands complex structure (PDB entry 1FPH26) by removing all ligands and crystal water molecules. Nδ and Nε protonation states were employed for His57 in the catalytic triad and the other histidine residues, respectively. The four disulfide bonds in thrombin were formed according to the earlier X-ray crystallography study.9 We refer to this thrombin structure as Thr1FPH. To determine the atomic coordination of Na+ bound to Thr1FPH, Thr1FPH was superposed on a thrombin-Na+ complex structure (PDB entry 1SG812) using RMS-fit with UCSF Chimera.27 Next, the atomic coordinates of the thrombin-bound Na+ and 6 crystal water molecules in the Na+-binding region were added to Thr1FPH. Finally, we obtained the thrombin-Na+ complex structure, referred to as Thr1FPH-Na+. Thr1FPH-Li+ and Thr1FPH-Cs+ were prepared by replacing Na+ in Thr1FPH-Na+ with Li+ and Cs+, respectively.

System setup


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Each thrombin-cation complex structure, i.e., Thr1FPH-Li+, Thr1FPH-Na+ and Thr1FPH-Cs+, was solvated in the rectangular box, which was set so that the minimum distance from the box’s face to the thrombin surface was 10 Å and 11595 water molecules were finally included in the box. Furthermore, 32 cations, i.e., Li+, Na+ or Cs+, and 36 chloride anions were added to each solvated system to electrically neutralize the system at 140-mM salt concentration. We refer to the systems, thrombin-X+ complex in 140-mM XCl aqueous solution, as Thr-X+. To calculate the forces acting among atoms, AMBER force field 99SB28, SPC/E water model29,30, and JC ion parameters adjusted for the SPC/E water model31,32 were applied for amino acid residues, water molecules, and ions, respectively. All simulations were performed under the periodic boundary condition. Electrostatic interaction was treated by the Particle Mesh Ewald method, where the real space cutoff was set to 9 [Å]. The vibrational motions associated with hydrogen atoms were frozen by the SHAKE algorithm. The translational center-of-mass motion of the whole system was removed by every 500 steps to keep the whole system around the origin, avoiding the overflow of coordinate information from the MD trajectory format. Each of the thrombin-cation complex systems was energetically minimized by the following three-step molecular mechanics (MM) simulations. The first MM simulation



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was for hydrogen atoms for thrombin, the second one was for all atoms for thrombin and, the third one was for X+ bound to thrombin and the atoms making contact with the Na+ (i.e. oxygen atoms for Arg221a and Lys224 in thrombin). Each MM simulation consists of 1000 steps of steepest descent method followed by 4000 steps of conjugate gradient method. Subsequently, we randomized atomic coordinates of the ions except for the cation bound to thrombin through the four-step procedure (see SI-1 for details). This ion-randomization procedure was repeated for 100 times, leading to independent 100 initial atomic coordinates for each system.

Production run Using the initial atomic coordinates obtained above, the following 6-step MD simulations are performed for each system: NVT (1 to 300 [K], 30 [ps], 10 [kcal/mol/Å]) → NVT (300 [K], 10 [ps], 10 [kcal/mol/Å]) → NVT (300 [K], 40 [ps], 5 [kcal/mol/Å]) → NVT (300 [K], 40 [ps], 1 [kcal/mol/Å]) → NVT (300 [K], 40 [ps]) → NPT (300 [K], 1 [bar], 20 [ns]). The last 20-ns NPT simulation was used for the following analyses. Each simulation used the time step of 2 [fs] for the integration. In the first NVT simulation, the reference temperature was linearly increased along the time course. In the first 4 steps, thrombin and the bound cation were restrained by


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harmonic potential around the initial atomic coordinates. In each NVT simulation, temperature was regulated using Langevin thermostat with 1-ps-1 collision coefficient. In the last 20-ns NPT simulation, temperature and pressure were regulated by Berendsen thermostat33 with a 5-ps coupling constant and Berendsen barostat33 with a 0.1-ps coupling constant, respectively. The initial atomic velocities were randomly assigned from a Maxwellian distribution at 1 [K]. MD trajectories were recorded every 10-ps interval for the following analyses. Molecular modeling, randomization of ion’s atomic coordinates and both MD and MM simulations were performed using the LEaP module in AmberTools 1.5 package34, ptraj module in AmberTools 1.5 package34 and CPU-version PMEMD module in AMBER 12 package35, respectively. The 6th-step MD simulation procedure, i.e., the last 20-ns NPT simulation, was performed using the GPU-version PMEMD module based on SPFP algorism36 with NVIDIA GeForce GTX680.

Analyses of MD trajectories Interatomic distance and root mean square deviation (RMSD) were calculated by the ptraj module in AmberTools 1.5 package.34 Numbers of each ion within thrombin’s hydration shell was calculated by in-house program (see Results and Discussion section



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for the definition of hydration shell). We calculated RMSD to Thr1FPH using the backbone atoms (i.e., Cα, N, C and O) of all 295 residues. Solvent Accessible Surface Area (SASA) was calculated by the NACCESS package.37 Residual accessibility (RA) is defined as the ratio of residual SASA value calculated from a MD-derived snapshot to the standard residual SASA value prepared by NACCESS package.37 Thrombin-cation interaction energy was calculated under the free boundary condition with non-bonded interaction cutoff of 999 [Å]. The interaction energy is defined as E(thrombin and the 32 unbound cations) − {E(thrombin) + E(the 32 unbound cations)}, where E(X) denotes the potential energy of molecule(s) X. Energy values were calculated by using the SANDER module in AMBER 12. RMSD was averaged at each time point, and then we determined the period where RMSD is converged. MD trajectories within this period were used to calculate the other quantities. Each of the other quantities was time-averaged over each MD trajectory, and then these time-averaged values were ensemble-averaged over 100 MD trajectories. As for these quantities, the significant difference between the systems was tested at 95% confidence interval. Molecular structures were illustrated using Visual Molecular Dynamics (VMD).38 Similarly, a density distribution of each ion species (i.e., Li+, Na+, Cs+ or Cl-) was


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calculated and visualized using Volmap plugin of VMD.38 To calculate ion’s density distribution around thrombin, each snapshot structure was superposed on Thr1FPH using RMSD-fit for Cα, N and C in Asp189, and then atomic coordinates of an ion species were picked up. Values of an ion’s distribution density at each grid point were scaled using the bulk concentration of the ion (see SI-2 for details). For each system, all snapshot structures derived from MD trajectories were integrated into one trajectory to calculate the ion’s density distribution.

Results and Discussion

Dependence of cation’s distribution around thrombin on ionic radius We performed 100 MD simulations for each of the three systems. In each of the 300 MD simulations, cation-binding was preserved. We assumed that each system was in equilibrium after 15 [ns] because of the convergence of RMSD and the number of ions surrounding thrombin (See Fig. S1 and S2). Thus, for the following analyses, we employed a set of 100 partial MD trajectories consisting of each last 5-ns period. First, we examined ion’s density distribution around thrombin remembering the initial step of thrombin-substrate association reaction, namely, formation of a non-specific



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encounter complex ensemble. To obtain atomic insights into cations surrounding thrombin, we visualized cation’s density distributions (Fig. 2A-C). In the vicinity of the S1-pocket, each type of cations is commonly observed. However, the density distribution of Li+ molecules is relatively dense and extensive compared with those of the other two cations (Fig. 2A): the density distribution is observed on the thrombin’s surface remote from the S1-pocket and the Na+-binding region. On the other hand, the density distribution of Cs+ is relatively sparse and localized: the density is observed only in the vicinity of the S1-pocket and the Na+-binding region (Fig. 2C). Among them, the density distribution of Na+ shows intermediate characteristics between those of Li+ and Cs+ (Fig. 2B).


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Figure 2. Ion’s density distribution. (A-C) cation’s density distribution; (A) Li+ in Thr-Li+; (B) Na+ in Thr-Na+; (C) Cs+ in Thr-Cs+. (D-F) chloride’s density distribution; (D) Cl− in Thr-Li+; (E) Cl− in Thr-Na+; (F) Cl− in Thr-Cs+. Density distributions for Thr-Li+, Thr-Na+ and Thr-Cs+ are colored by green, blue and pink, respectively. Locations of cation with density > 5 Å-3 and > 50 Å-3 are drawn with wire frame and solid surface, respectively. Locations of chloride ion with density > 2.5 Å-3 are drawn with wire frame. The vicinity of the Na+-binding region and the S1-pocket is highlighted in the red frame. Thrombin and the Na+-binding region are distinguished by grey and yellow, respectively.



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To describe quantitative characterization of these cations’ distributions, we counted the number of ions surrounding thrombin. We assumed that thrombin’s surface consist of the 137 residues, which show > 25% of relative residual accessibility (RA) (see Fig. S3 and S4). Under the assumption, we defined a hydration shell as a spatial region within a certain distance from thrombin’s surface. In particular, the vicinity of thrombin’s surface is defined as the hydration shell with 4 Å distance from thrombin’s surface. Then, the numbers of ions within such hydration shells were calculated (the bound cation was excluded from the calculations.) Figure 3A shows the number of cations distributing around thrombin. Similar to the above observation for the cation’s density distributions, in a smaller hydration shell, e.g., the vicinity of thrombin’s surface, small-size cations more frequently gain access to thrombin than large-size ones. The differences in the number of cations among the three systems are remarkable as the hydration shell is relatively small. For example, in the vicinity of the thrombin’s surface, 13.99 ± 0.39 Li+, 5.48 ± 0.23 Na+ and 1.70 ± 0.08 Cs+ are found for Thr-Li+, Thr-Na+ and Thr-Cs+, respectively. These observations indicate that the number of cations in the vicinity of thrombin’s surface changes in inverse proportion of the ionic radius. Such a characteristic of cation’s coordination almost holds for the number of cations around an amino acid residue (see Fig. S5, Fig.


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S6 and related discussion in SI-3).

Figure 3. Number of ions within the hydration shell of thrombin. (A) Cations. (B) Chloride ions. The values for Thr-Li+, Thr-Na+ and Thr-Cs+ are distinguished by green, blue and red lines, respectively. Error bars means 95 % confidence interval. In the panel (A), the cation bound to thrombin is excluded from the calculations.

The relatively sparse and localized density distribution of Cs+ can be explained by the larger ionic radius of Cs+, and relatively unstable thrombin-Cs+ interaction (Table 1). A Cs+ in aqueous solution makes contact with 8 oxygen atoms derived from water molecules. However, due to the larger ionic radius, a Cs+ could not maintain stable contacts with atoms in hollows on the thrombin’s surface, so that it could not keep making contact with 8 oxygen atoms in the vicinity of thrombin’s surface. In fact,



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considering 26 negatively charged residues, which are extensively distributed on thrombin’s surface (see Fig. S7 and related discussion in SI-3), each of frequencies of Cs+ access is smaller than those of Li+ and Na+ access. We can remember that interactions between cations and negatively charged residues should, generally, provide greater gain in enthalpy than those between cations and water molecules. These observations suggest that Cs+ coordination around thrombin does not contribute to gain in enthalpy of the system. This insight into gain in enthalpy is supported by the analysis of thrombin-cation interaction energies, where that of Thr-Cs+ is relatively unstable (i.e. 523.1 ± 17.2 [kcal/mol]), in contrast to those of other two systems (−1268.0 ± 64.1 [kcal/mol] for Thr-Li+; 52.6 ± 39.2 [kcal/mol] for Thr-Na+). Thus, it is possible to say that an insufficient gain in enthalpy leads to sparse and localized density distribution of Cs+ around thrombin.

Table 1. Thrombin-cation interaction energy thrombin-cation interaction energy [kcal/mol] +

Thr-Li

-1268.0 ± 64.1

+

52.6 ± 39.2

+

523.1 ± 17.2

Thr-Na Thr-Cs *

A value indicates mean ± (2.0 x standard error).


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On the other hand, the relatively dense and extensive density distribution of Li+ can be explained by the smaller ionic radius of Li+, and relatively stable thrombin-Li+ interaction (Table 1). A Li+ in aqueous solution makes contact with 4 oxygen atoms derived from water molecules. Due to the smaller ionic radius, Li+ could more easily gain access to atoms in hollows on thrombin’s surface, and then maintain more stable contact with them than Na+ and Cs+. Furthermore, interactions between Li+ and negatively charged residues should provide greater gain in enthalpy than those between Li+ and water molecules. In fact, thrombin-cation interaction energy of Thr-Li+ (−1268.0 ± 64.1 [kcal/mol]) show additional stabilization compared with those of Thr-Na+ and Thr-Cs+ (52.6 ± 39.2 and 523.1 ± 17.2 [kcal/mol], respectively). These observations suggest that Li+ coordination around thrombin contributes to gain in enthalpy of the system, thus leading to dense and extensive density distribution of Li+ around thrombin. Compared with Li+ and Cs+, Na+ has the intermediate ionic size, and makes contact with 6 oxygen atoms derived from water molecules in aqueous solution. Then, Na+ coordination around thrombin’s surface possibly contributes to intermediate gain in enthalpy, and then leads to the density distributions of Na+ showing intermediate



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characteristics between those of Li+ and Cs+. Similar to these cations, we examined chloride ion’s density distribution and the number of chloride ion surrounding thrombin. However, these characteristics seem to be similar among the three systems and the number of chloride ion around thrombin is smaller than those of cations (see Fig. 2D-F, Fig. 3B and the related discussion in SI-4). This result suggests that, in the formation of an encounter complex ensemble, thrombin-Cl− interaction is similar among the three systems and less important for the kinetic rate constant than thrombin-cation interaction. Finally, we deduce from these observations that the difference of cation’s distributions should more greatly affect the formation of an encounter complex ensemble than a chloride’s ones, and also the cation bound to thrombin.

Dependence of cation’s distribution in the vicinity of the S1-pocket on ionic radius We examined the effect of cations on the structure of the S1-pocket and cation’s distribution in the vicinity of the S1-pocket, remembering the final step of the thrombin-substrate association reaction, namely, the formation of the stereospecific thrombin-substrate complex.


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First, we analyzed the structural difference of the S1-pocket between Thr-Na+ and the other two systems using values of RA, especially, focusing on the residues important for thrombin’s function (i.e., the residues forming in the S1-pocket, and those consisting of the catalytic triad). We found statistically-meaningful RA changes between Thr-Na+ and Thr-Li+ in 8 residues (Table 2) and 5 of them are the functionally important residues. In addition, in 4 of the 5 residues, Asp189, Ala190, Ser195 and Gly216, the RA value of Thr-Na+ is greater than that of Thr-Li+.

This indicates that these functional residues

are more accessible to substrate molecules in the presence of Na+ than in the presence of Li+. Of note, this observation is supported by the earlier structural study7,12, which reported that the S1-pocket in the presence of Na+ assumes the structure more suitable for substrate’s access than that in the presence of Li+. Accordingly, it is possible to say that thrombin in the presence of Na+ has advantage over that in the presence of Li+ molecule with respect to the suitable formation of the S1-pocket.

Table 2. Residual accessibilities (%) of Thr-Na+ and Thr-Li+ systems.



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+

+

res. num.

Thr-Na

Thr-Li

L144

29.5 ± 1.1

32.0 ± 1.2

A183

0.6 ± 0.1

0.9 ± 0.1

D189

11.1 ± 0.4

9.8 ± 0.4

A190

12.1 ± 0.4

10.7 ± 0.3

S195

14.1 ± 0.8

12.4 ± 0.8

S214

6.7 ± 0.4

7.6 ± 0.4

G216

49.7 ± 1.6

44.8 ± 1.7

D221

25.9 ± 0.6

24.1 ± 1.1

*

A value indicates mean ± (2.0 x standard error). The difference between values is

tested with 95% confidence interval. The functionally important residues are shown in boldface.

Similarly, we found statistically-meaningful RA changes between Thr-Na+ and Thr-Cs+ in 9 residues (Table 3). However, none of them are the functionally important residues.

Then, thrombin in the presence of Na+ should be similar to that in the

presence of Cs+ in the structure of the S1-pocket. Accordingly, it is possible to say that thrombin in the presence of Na+ is not at an advantage over that in the presence of Cs+ molecule with respect to the suitable formation of the S1-pocket.

Table 3. Residual accessibilities (%) of Thr-Na+ and Thr-Cs+ systems.


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+

+

res. num

Thr-Na

Thr-Cs

R15

98.2 ± 2.7

92.9 ± 2.5

V138

0.2 ± 0.0

0.1 ± 0.0

T139

0.9 ± 0.1

0.7 ± 0.1

V158

6.8 ± 0.4

7.9 ± 0.4

P186

80.0 ± 2.4

71.1 ± 2.1

G186C

86.5 ± 1.4

82.8 ± 1.3

D221

25.9 ± 0.6

23.1 ± 0.7

G223

57.6 ± 2.6

50.2 ± 2.7

Y225

14.6 ± 0.7

12.7 ± 0.8

*

A value indicates mean ± (2.0 x standard error). The difference between values is

tested with 95% confidence interval.

To obtain insights into the direct effect of cations on substrate’s access to the S1-pocket, we analyzed the cation’s density distribution in the vicinity of the portal of the S1-pocket (Fig. 1C). As shown in Figure 4, smaller cations are distributed more abundantly in the vicinity of the portal than larger ones. Furthermore, we calculated the number of cations within 4 Å from the S1-pocket residues (of note, among the 8 residues, Asp189 was excluded from the calculation because we are just interested in the portal of the S1-pocket, not the direct binding site, i.e., Asp189). Then, we found that the number of cations around the S1-pocket is inverse proportional to the size of ionic radius (Li+: 0.79±0.12; Na+: 0.40±0.09; Cs+: 0.16±0.05).



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Li+ molecules are more abundantly distributed in the vicinity of the portal than the other two cations (see Fig. 4A, 4B and 4C). Then, they should more frequently gain access to the portal of the S1-pocket ahead to substrate’s access than Na+ molecules so that substrate‘s access to the S1-pocket could be blocked by repulsive interaction acting between such Li+ molecules with Arg or Lys in the substrate. Accordingly, based on the differences in both the structure of the S1-pocket and the relatively sparse Na+ density distribution, we deduced that thrombin in the presence of Na+ has an advantage over that in the presence of Li+ in formation of the stereospecific complex.

Figure 4. Cation’s density distribution around the S1-pocket. (A) Li+ in Thr-Li+. (B) Na+ in Thr-Na+. (C) Cs+ in Thr-Cs+. The distributions for Thr-Li+, Thr-Na+ and Thr-Cs+ are distinguished by green, blue and pink, respectively. Locations of cation with density > 5 Å-3 and > 50 Å-3 are drawn with wire frame and solid surface, respectively. The thrombin structure is derived from PDB entry 1FPH26.


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On the other hand, Cs+ molecules are more sparsely distributed in the vicinity of the portal than Na+ molecules (See Fig. 4B and 4C). Then, Cs+ molecules should less frequently gain access to the portal than Na+ molecules so that the S1-pockets could be more accessible to substrate molecules in the presence of Cs+ molecules than in the presence of Na+ molecules. Remembering that the structure of the S1-pocket is similar between Thr-Na+ and Thr-Cs+ (see Table 3 and the related discussion), it is possible that thrombin in the presence of Cs+ has an advantage in the formation of the stereospecific complex over that in the presence of Na+ due to the sparser Cs+ density distribution. This suggests an observation rule that thrombin in the presence of Na+ does not necessarily have an advantage over other cations in the formation of the stereospecific complex.

Important roles of unbound Na+ in the maximization of the rate constant According to the insights obtained above, we discuss how density distributions of Li+ and Cs+ disadvantage the formation of an encounter complex ensemble. Under the relatively sparse and localized density distribution of Cs+, amino acid residues on



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thrombin’s surface, which include the 26 negatively charged residues (see SI-3 for details), are more highly exposed to solvent molecules, and also substrates. Such negatively charged residues are irrelevant to thrombin’s recognition of Lys or Arg at the P1 site in a substrate but they possibly attract these positively charged residues to thrombin’s surface remote from the S1-pocket non-specifically. This could increase repertoire of encounter complexes. Of note, every encounter complexes do not necessarily convert into the stereospecific complex.39 Increased repertoire of encounter complexes would result in decrease in the number of encounter complexes which are formed around the S1-pocket and thus active in the formation of the stereospecific complex. Accordingly, decreasing the number of “active” encounter complexes could involve reduction of thrombin-substrate association reaction rate constant. On the other hand, under the relatively dense and extensive density distribution of Li+, thrombin’s surface is relatively abundantly covered with the positive charges of Li+, thus covering the negatively charged residues on the thrombin’s surface. Then, under the circumstances, a positively charged residue in a substrate would be prevented from accessing thrombin’s surface by repulsive interaction with Li+ molecules surrounding thrombin. Considering that Li+ molecules covers the vicinity of the S1-pocket, such a repulsive interaction could block the formation of an encounter complex around the


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S1-pocket, finally decreasing the number of “active” encounter complexes. This would involve reduction of thrombin-substrate association reaction rate constant. According to the observations obtained above, we discuss an advantage of Na+ in the formation of an encounter complex ensemble. Compared with the density distributions of Li+ and Cs+, that of Na+ intermediately covers thrombin’s surface. Then, the presence of Na+ molecules could permit an easier substrate access to thrombin’s surface than that of Li+ molecule. Meanwhile, the presence of Na+ molecules could result in the decreased number of encounter complexes which are formed at a site remote from the S1-pocket than that of Cs+ molecules. These insights suggest another observation rule that thrombin surrounded by Na+ molecules is at an advantage in the formation of an encounter complex ensemble which includes the maximum number of ”active” encounter complexes. The earlier thrombin studies had discussed the advantage of Na+ in formation of the stereospecific complex, where they focused on the site-directed thrombin-Na+ interaction.7,12 Furthermore, the insights we obtained suggest the two observation rules with respect to the effect of unbound Na+ on thrombin-substrate association reaction: i) unbound Na+ molecules have an advantage in the formation of an encounter complex ensemble and ii) thrombin in the presence of Na+ does not necessarily have an



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advantage in the formation of the stereospecific complex. According to these observation rules, we propose a conjecture that unbound Na+ molecules are also involved in maximization of thrombin-substrate association reaction rate constant by optimizing the formation of an encounter complex ensemble.

Concluding Remarks Understanding of the molecular basis of Na+-activation of thrombin has been a long-standing problem in the field of monovalent cation-activated proteins.2-4,8,12 To address this problem, we performed MD simulations and examined the atomic characteristics of cation’s distribution around thrombin. The results we obtained suggest the two observation rules with respect to the effect of unbound Na+ on the thrombin-substrate association reaction. According to the observation rules, we propose the conjecture, which sheds light on important roles of unbound Na+ molecules in thrombin enzymatic activation. This conjecture will be elucidated in our future study. Considering that thrombin is distributed in the extracellular domain, which contains relatively abundant Na+ molecules compared with the intracellular domain, thrombin could be well designed to be activated not only by the site-directed interaction, but also by the presence of unbound Na+ molecules. Meanwhile, we have already reported that


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conformational change of hemoglobin is enhanced by the presence of oxygen molecules although the site-directed interaction with an effector molecule (i.e., oxygen binding to the heme) is absent.40 Remembering the results of the earlier study and the present one, we deduce that unbound effector molecules also play important roles in the functional expression of allosteric proteins.

Acknowledgements This work was partially supported by the Core Research for Evolutional Science and Technology (CREST), “Establishment of Molecular Technology towards the Creation of New Functions” of the Japan Science Technology Agency and by a Grant-in-Aid for Science Research from the Ministry of Education, Culture, Sport, Science and Technology in Japan. The calculations were partially performed using several computing systems at the Information Technology Center in Nagoya University. I.K. also thanks for the support from Japan Society for the Promotion of Science (JSPS) by the Research Fellowship for Young Scientist.

Supporting information Available: Supporting figures (S1-S7) and supporting discussion are available free of charge via the Internet at http://pubs.acs.org.



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Toward Understanding Allosteric Activation of Thrombin: A Conjecture

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