Regular Paper Molecular Dynamics Study of Forced Dissociation Process of Wheat Germ Agglutinin Dimer

Molecular dynamics simulations are performed to study the mechanical dissociation pathways of a wheat germ agglutinin (WGA) dimer under the tensile force exerted by the atomic force microscopy (AFM). We found a dissociation pathway in which both monomer units are elongated and their tertial structures are destroyed before the rupture. The force extension (F-E) curves are found to show successive saw-tooth peaks indicating the stepwise destruction of interactions inside monomer structures. In addition, the interactions at their interfaces are found to be destroyed at the largest force peak. At the rupture where the dimer dissociates completely, a small jump is observed in the F-E curve, which amounts to 70 pN. [DOI: 10.1380/ejssnt.2009.825]


I. INTRODUCTION
Atomic force microscopy (AFM) has been widely used as a tool for obtaining insights of physical interactions inside a single protein molecule or its complex with some other molecules.In particular, for single protein molecules, by measuring force extension (F-E) curves showing saw-tooth patterns, typical strengths of their internal interactions such as hydrogen bonds have been clarified step by step [1][2][3][4][5].In addition, the atomic details of their mechanical unfolding process have been studied well by theoretical simulations including the steered molecular dynamics (SMD) simulations [6][7][8][9][10][11][12][13][14][15].Owing to these works, the relationships between the saw-tooth patterns in the F-E curves and the structural changes such as hydrogen bond breaking have been clarified for single protein molecules.
In contrast, for complexes of protein and ligands (including co-enzyme, sugar, and protein), the F-E curves have been measured focusing on unbinding (rupture) forces [16][17][18][19][20][21][22][23].As long as the ligands are small molecules, it has been straightforward to analyze the rupture events through the SMD simulations [24][25][26].However, as the ligand size becomes larger, not only the protein-ligand interactions but also the interactions inside the monomer units become complicated.Due to this, the underlying mechanism of dissociation process of complexes under the tensile force by AFM has not been well understood yet at the atomic level.For example, it is not obvious whether the protein-ligand complexes always dissociate with no structural deformations inside each component.At this stage, therefore, it is significant to accumulate knowledge of dissociation processes for various protein complexes.
In the SMD simulation for the CD2-CD58 complex, Bayas et al. [27] have indicated that each monomer structure is maintained unless the pulling velocity exceeds * Corresponding author: k.tagami@advancesoft.jp v = 10 nm/ns.On the other hand, for the insulin dimer, Kim et al. [28] have shown that significant conformational changes can occur in the monomer units even at v = 2.5 nm/ns.In addition, for the selectin and SGP-3 complex, Lü et al. [29] have shown that the monomer units are completely destroyed before dissociation at v = 5 nm/ns.These indicate that the dissociation pathway depends on the characteristics not only of the interactions at the interfaces but also of the interactions along the monomer chains.
In this work, we focus on the dissociation process of a wheat germ agglutinin (WGA) dimer molecule.Each of the monomer units is composed of two domains, and each domain structure can be further divided into two subdomains [30].Our concern is to reveal by theoretical simulations how the existence of these repeated subdomain structures shows up on the F-E curve and how the dimer ruptures.For this purpose, MD simulations are performed in which the C-terminus of one monomer unit is pulled with a constant velocity.The whole calculations are performed using the code NAMD [31] version 2.6 with the all-atom CHARMM force field version 22.
We found that there is a dissociation pathway in which both monomer units are elongated and their tertial structures are destroyed before the rupture.Even in this case part of the α-helix structures are kept unchanged due to reinforcement by the disulfide bonds.The structural deformations of the monomer units show up in the obtained F-E curves which assume successive saw-tooth peaks, indicating that the structural destructions proceed in a stepwise manner.It is found that these saw-tooth peaks would be observed more easily using stiff cantilevers.At the largest force peak the interactions at their interfaces are found to decrease abruptly.At the moment of rupture the remaining interactions between the vicinities of N-termini of the two chains are broken, which shows up as a small jump (70 pN) in the F-E curve.
The rest of the paper is organized as follows.In Section II the computational model and simulation method will be described.In Section III the results of our calculations ISSN 1348-0391 c 2009 The Surface Science Society of Japan (http://www.sssj.org/ejssnt)will be presented, and the possibility of measuring sawtooth peaks in actual experiments will be discussed.In section IV the paper will be concluded.

II. THEORETICAL
The initial atomic coordinates of a WGA dimer are prepared from the two chains A and B which are listed in the PDB code 2cwg.The structures of these chains are illustrated in the left panel of Fig. 1.Both chains are composed of 171 amino acid residues and have repeated domain structures I and II.Each of these two domains can be further divided into two subdomain structures [30], i.e., Ia (PCA1-CYS41), Ib (GLY42-LYS88), IIa (CYS89-THR128), and IIb (ASP129-GLY171).They are illustrated in the NewCartoon representation, being colored red, green, blue, and pink, respectively.The C-terminal GLY171 and N-terminal PCA1 (pyroglutamic acid) are colored yellow and cyan/orange in the van der Waals (vdW) representation.In the right panel of Fig. 1, the dimer structure is shown where the PCA1 of both chains are in contact with each other.For clarity, only the subdomains of the chain A are colored here.The number of atoms in this dimer structure amounts to 4,332, and its spatial dimensions are about 5.2×4.7×7.1 nm 3 .
The molecular dynamics simulations in the followings are performed in the supercell whose dimensions are 7.0×7.0×42.0nm 3 .In the simulation box, not only the protein molecule denoted above but also 64,003 water molecules, 29 Na + ions, and 31 Cl − ions are added in order to realize the 5% salt concentration.The number of atoms is 196,401 in total.The whole MD trajectory calculations are performed using the package NAMD [31] version 2.6 with the all-atom CHARMM force field version 22.As for the water molecules, the TIP3P model is used.On the other hand, as for the PCA which is not found in the original CHARMM22, the parameters developed by Poker are used [32].The time step is set to 2.0 fs with the constraint on the bond length of hydrogen atoms.The periodic boundary condition is applied along each direction of the supercell, and the Particle Mesh Ewald (PME) grid is assumed to be 64×64×384.
Before stretching the dimer molecule, its equilibrated structure is obtained by two successive MD simulations.In the first simulation, the protein molecule and 1,167 water molecules in the vicinity of the protein are fixed at their initial positions.The other atoms are allowed to move for 0.2 ns.In the second simulation all the atoms are allowed to move for 1.0 ns.Here the system temperatures are maintained at 310 K using the Langevin damping parameter γ = 5.0 ps −1 .
The stretching simulation is performed by pulling down the 'C' atom of the C-terminal residue GLY171 of the chain B, while the corresponding 'C' atom of the chain A is fixed at its position.Here, the locations of two Ctermini are drawn with yellow spheres in Fig. 1.The Langevin damping is set off and the pulling velocity is kept to v = 1.5 nm/ns.Note here that our method is similar to the SMD in which virtual springs are attached to the atoms to be pulled.However, in our method, no virtual springs are used, and the target atoms are forced to move directly.At every MD step during this stretching simulation, the atomic force on the fixed 'C' atom of the chain A is monitored.The F-E curve is plotted after performing moving averages of the time-fluctuating force values over 0.4 ns.

A. structural deformations of monomer units
The upper panel of Fig. 2 shows the snapshots of the WGA dimer as a function of the pulled length ∆L.Here only the subdomains in the chain A are colored for clarity.The snapshot at the leftmost correspond to the configuration just before pulling, i.e., ∆L = 0.At ∆L = 12 nm, the subdomain IIb of the chain A (colored pink), abbreviated as A-IIb, is found to be pulled apart from the remaining part of the dimer.Then, at ∆L = 18 nm, A-IIb is stretched and A-IIa (colored blue) is pulled apart.The subdomains of the chain B seem to follow similar unfolding pathways.At ∆L = 24 nm, A-Ib (colored green) is stretched and pulled off from the contact area between the two monomer units.At this stage, all the inter-subunit interactions are lost except between A-Ia and B-Ia.At ∆L = 30 nm, finally, the dimer structure is observed to be ruptured completely.As a general trend, part of secondary structures such as α-helices survive while the other regions are stretched well.This reflects a specific feature of the WGA, i.e., the disulfide bonds which lie in the middle region of the subdomains reinforce the α-helix structures.http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology At a first sight, it might be surprising that the monomer units are unraveled before dissociation.However, the possibilities of structural deformation of monomer units during the dissociation process have been reported in the other SMD simulations.For example, in the forced dissociation of insulin dimmers, Kim et al. [28] have claimed that the monomer units can be fully stretched before dissociation, which explains their experimentally measured force spectroscopy data.For the selectin-ligand complexes Lü et al. have reported that the complex can dissociate with the protein monomer structure destroyed [29].In these works the lowest pulling velocities are 2.5 and 5.0 nm/ns, respectively, which are close to the velocity adopted in this work, 1.5 nm/ns.Therefore, at least in this range of loading rate, it seems plausible that monomer structures can change their configurations before the dissociation.

B. force curve with saw-tooth peaks
The F-E curve is illustrated in the lower panel of Fig. 2. Apart from the successive saw-tooth peaks, the attractive force increases in a monotonic manner until the pulled length ∆L reaches 21.0 nm.Then the strongly attractive force drops abruptly from −447 pN to about −100 pN, and gradually approaches zero.In this subsection, we will discuss the origin of the saw-tooth peaks observed in the former region.
For this purpose, as illustrated examples, the three sawtooth peaks found at 10 < ∆L < 20 nm are chosen and In the lower panel of Fig. 3 the values of N ac are plotted for the three subunits, B-IIb (black), A-IIb(green), and A-Ib (red).Here N ac is an abbreviation of the numbers of atoms being in contact.Any two atoms whose distance is less than 0.5nm are judged to be in contact with each other.The spatial positions of these three subdomains are illustrated in the right panel.At the pulled length where the N ac of a certain subdomain changes abruptly, its spatial structure is considered to deform dramatically.At the shaded regions, the N ac of B-IIb, A-IIb, or A-Ib decrease abruptly, by which the strain accumulated under the tensile force is released.
In a similar manner, the peaks at around 3.5 < ∆L < 4.7 nm and 5.9 < ∆L < 7.0 nm (see Fig. 2) are also identified to the structural changes inside the subunits A-Ia and B-Ib, respectively (not shown).These indicate that the monomer structures are destroyed before dissociation, which can show up as saw-tooth peaks in the F-E curves.

C. rupture event
As mentioned in the previous subsection, the F-E curve shows an abrupt drop at around ∆L = 21.0 nm, which has the largest amplitude.At a first sight this peak seems to correspond to a rupture event, but the two monomer units still interact with each other.In order to look at this point closely, the F-E curve in the range of 15 < ∆L < 25 nm is closed up in the upper panel of Fig. 4. The shaded region colored green indicate the force dropping The hydrogen bonds between the two chains also decrease during this rupture process.Figures 6(a) and 6(b) illustrate the snapshots taken at ∆L = 28.6 and 28.8 nm, respectively.It is found that the last surviving hydrogen bond between A-CYS24 and B-ASN9 is broken at ∆L = 28.8nm.
Then, finally at ∆L = 29.4nm, the contact between A-Ia and B-Ia is completely lost, and the two isolated monomer units are obtained.Judging from the force peak in the gray-colored shaded region of Fig. 5, the dissocia- tion force is estimated to be about 70 pN.

D. effects of cantilever stiffness
Then, in a realistic experiment, is it possible to observe such saw-tooth peaks in the dissociation of a WGA dimer?In many of the dissociation experiments using the other protein complexes, the averaged values of the rupture forces have attracted attentions while the shapes of individual F-E curves have not been discussed well.
In order to disucss this possibility, two significant factors should be considered, i.e., the pulling velocity and the cantilever stiffness.First, the pulling velocities adopted in experiments (v = 10 −7 nm/ns) are much slower than those accessible in the simulations.(As mentioned in Section II, the pulling velocity adopted in this work is 1.5 nm/ns.)As the pulling velocity is lowered, wider area http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology on the energy landscape is surveyed, and the possibility of finding paths to escape abrupt energy changes is increased.This indicates that the numbers and heights of saw-tooth peaks might be decreased in experimentally measured F-E curves.
Second, in experimental measurements of force spectroscopy, the normal forces (F z ) are estimated from the deflection (∆Z) of cantilever, assuming a simple relation F z = k∆Z.Here the coefficient k is the spring constant of cantilever.Note that the AFM tip which interacts with target protein molecules is fabricated at the end of cantilever beam.In our simulation, in contrast, we calculated the normal forces from the atomic force on the C-terminus of chain A. Thus, the cantilever motion was not considered, or equivalently, the simulation was performed in the hard limit of the spring constant.
In order to investigate effects of the latter factor, we performed another MD simulation in which a virtual spring is connected to the C-terminus of chain A. The other end of this spring was fixed at a certain spatial position.The spring constant is assumed to be k = 0.06 N/m whose strength was adopted in the SMD simulations for dissociation of avidin-biotin complex [25].Note that such a soft cantilever can be actually realized in the commercial AFM tip.The other parameters used in simulations were assumed to be common to those mentioned previously.
Figure 7(a) illustrates the obtained F-E curve, which indicates that the number of saw-tooth peaks is significantly reduced from the lower panel of Fig. 2, but a few peaks survive.Here we will comment briefly on the origin of these peaks.At the peak positions the attractive forces changes from −117.3 pN (∆L = 6.14 nm) to −45.2 pN (∆L = 9.24 nm), from −306.7 pN (∆L = 19.4nm) to −180.7 pN (∆L = 20.7 nm).The analysis of Nac revealed that the contact inside the A-Ia is reduced at the first peak (not shown).At the second peak the interactions inside the two subunits, i.e., A-IIa and A-IIb, are found to decrease significantly.
On the other hand, at the peak with the largest amplitude, the attractive forces drops from −454.5 pN (∆L = 26.9nm) to −103.5 pN (∆L = 29.3nm).At this peak the interactions at the interfaces are found to change dramatically.Namely, the interaction between A-Ia and A-Ib, and that between B-Ia and B-Ib are reduced.In addition, the interaction between A-Ia and B-Ib disappears.These features agree with the results obtained in the previous section.
Note here that although the peak position of the last peak (∆L = 26.9nm) is apart from that found in Fig. 2 (∆L = 21.0 nm), this does not indicate an overstretching of a monomer.The quantity ∆L is defined by the pulled length of the C-terminus of chain B. Thus it contains not only the height difference between the C-termini of the two chains, but also the deflection of cantilever.The red curve in Fig. 7(b) shows the F-E curve plotted after eliminating the latter contribution.Now the corresponding peak positions are found at 4.3, 14.2, and 19.3 nm, respectively.For comparison, the F-E curve shown in Fig. 2 is plotted again by the blue curve.It is found that the positions and heights take similar values to those obtained in Fig. 2.This might indicate that the nature of structural deformations is not changed significantly even if soft cantilevers are used.
The dissociation is found to proceed in a similar manner to the previous subsection.Namely, the rupture of the WGA dimer does not occur at the peak which has the largest amplitude (∆L = 29.3nm), but occurs at around ∆L = 31.8nm (see Fig. 7(a)).
Finally, we will mention the experimentally measured F-E curves in the authors' group.Some of the F-E curves are found to assume saw-tooth patterns as presented in this article.The details of the experiments and measured spectroscopy data will be presented elsewhere [33].

IV. CONCLUSIONS
Based on the MD simulations of WGA dimer under the tensile force exerted by the atomic force microscopy (AFM), we found a dissociation pathway in which both monomer units are elongated and their tertial structures are destroyed before the rupture.Even in this case part of the α-helix structures are kept unchanged due to reinforcement by the disulfide bonds.As a consequence of repeated subdomain structures in the monomer units, the F-E curves assume successive saw-tooth peaks, indicating the stepwise destruction of interactions inside monomer structures.It is found that these saw-tooth peaks would be observed more easily using stiff cantilevers.At the largest force peak the interactions at their interfaces are found to decrease abruptly.At the moment of rupture the remaining interactions between the vicinities of N-termini of the two chains are lost, which shows up as a small jump (70 pN) in the F-E curve.
However, the dissociation pathway might depend on the loading rate, pulling direction, and so on.In addition, the loading rates adopted in experiments are much slower than those accessible in the simulations.In order to fully understand the dissociation mechanism at the atomic levels, further simulations would be required.

FIG. 1 :
FIG. 1: (Left) Initial structures of WGA monomer chains A and B. (Right) Dimer structure.The yellow and cyan/orange colored spheres correspond to the C-and N-terminal residues.The labels Ia, Ib, IIa, and IIb indicate the subdomains in each chain.

Volume 7 (
FIG. 4: (Upper) Close-up of F-E curve at 15 < ∆L < 25 nm.(Lower) The numbers of atoms in contact between two subdomains are plotted with red, green and black colored curves for the three sets, (A-Ia, B-IIa), (A-Ib, B-IIa), and (A-Ib, B-Ib).

FIG. 5 :
FIG. 5: (Upper) Close-up of F-E curve at 20 < ∆L < 30 nm. (Lower) The numbers of atoms in contact between two subdomains are plotted with red, green and black colored curves for the three sets, (A-Ia, B-Ia), (A-Ia, B-Ib), and (A-Ib,B-Ia).

FIG. 7 :
FIG. 7: (a) F-E curve calculated using the soft cantilever.(b)The F-E curve plotted with the contribution of the cantilever deflection deleted (red).The F-E curve in Fig.2is plotted again for comparison (blue).