Quantification of the stiffness and strength of cadherin ectodomain binding with different ions

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1 THEORETICAL & APPLIED MECHANICS LETTERS 4, (2014) Quantification of the stiffness and strength of cadherin ectodomain binding with different ions Zhiyang Xu, Dechang Li, a) Baohua Ji Biomechanics and Biomaterials Laboratory, Department of Applied Mechanics, Beijing Institute of Technology, Beijing , China (Received 4 December 2013; revised 6 January 2014; accepted 20 January 2014) Abstract The stiffness and strength of extracellular (EC) region of cadherin are proposed to be two important mechanical properties both for cadherin as a mechanotransductor and for the formation of cell-cell adhesion. In this study, we quantitatively characterized the stiffness and strength of EC structure when it binds with different types of ions by molecular dynamics simulations. Results show that EC structure exhibits a rod-like shape with high stiffness and strength when it binds with the bivalent ions of calcium or magnesium. However, it switches to a soft and collapsed conformation when it binds with the monovalent ions of sodium or potassium. This study sheds light on the important role of the bivalent ions of calcium in the physiological function of EC. c 2014 The Chinese Society of Theoretical and Applied Mechanics. [doi: / ] Keywords cell-cell adhesion, cadherin, stiffness, strength, molecular dynamic simulations Cell adhesion plays an important role in regulating many physiological and pathological processes. Living cells can sense their environment and respond in terms of morphology, proliferation, differentiation, migration, and survival through cell adhesion. 1,2 Cadherins form one of the most important families of molecules involved in cell-cell adhesion. 3,4 They participate in cell-cell interactions in a lot of multi-cellular organisms through forming homophilic interactions, which serves as mechanotransductor in cell-cell adhesion, 5 as shown in Fig. 1(a). In this study, we focus our attention on the extracellular (EC) region of cadherin (ectodomain), which mediates cell-cell adhesion through trans interactions (Fig. 1(a)). Calcium ions are proposed to regulate the function of EC in the way of stabilizing and rigidifying the EC structure. 3,4 Electron microscopy researches on the whole EC molecule and the first two successive repeated domains ( EC2) showed that the physiological concentration of leads to a rod-like shape conformation (elongated and slightly curved) of EC, as shown in Fig. 1(b). However, in the absence of, the structure collapses to be a compact one. 6,7 The crystal structure (Protein Data Bank (PDB) code: 1L3W) showed that three ions bind with EC at the gap between successive repeated domains. The binding site of EC is mostly constituted by polar residues, such as Asp and Glu, which can perform the so called chelate interactions with ions (Fig. 1(c)). The chelate interactions mediated by can stabilize the conformation of the EC structure. The experiments by Chitaev and Troyanovsky 8 showed that the trans interaction between ECs strictly depends on extracellular concentration, suggesting that plays a major role in EC s function. a) Corresponding author. dcli@bit.edu.cn.

2 Z. Y. Xu, D. C. Li, B. H. Ji Theor. Appl. Mech. Lett. 4, (2014) (a) (b) Cell I Cell II Trp2 (c) EC2 EC2 EC3 EC4 Asp101 EC5 Gln102 Asp104 Glu70 Fig. 1. (a) Illustration of cell-cell adhesion mediated by EC. (b) Crystal structure of EC structure: EC2 EC3 EC4 EC5, PDB code: 1L3W. The ions of are represented by red spheres. (c) Detailed illustration of the crystal structure of EC2 domain and the chelate interactions with ions. Molecular dynamics (MD) simulations were penformed by Cailliez and Lavery 9 to study the dynamics of EC2 in the presence and absence of. Their results confirmed that apocadherin shows much higher flexibility on a nano-second timescale than the bound form. Similarly, Sotomayor and Schulten 10 studied a complete EC by MD simulations and showed that EC maintains its crystal conformation when are present, while it assumes a disordered conformation in the absence of. The above studies qualitatively indicate that stabilizes the conformation of EC structure with high stiffness and strength which are proposed to be important for cadherin to be a mechanotransductor, such as for cell-cell adhesion forming. Sotomayor et al. 11 studied the elastic properties of one cadherin repeats () through MD simulations. More recently, Oroz et al. 12 examined the nanomechanics of EC using the single molecule force spectroscopy experiments and MD simulations with implicit solvent, and they found it strongly dependent on the concentration. Although a variety of thought-provoking views of the dynamics of EC have been provided by previous studies, the mechanism of the dependence of cadherin on is still unclear. In this study, we perform MD simulations to study how ions regulates the stiffness and strength of EC, by switching the mechanical properties and conformation of the EC s between the soft and compact regime and the one that is stiff and rod-like. To quantitatively compare the effect of different types of ions, we chose two bivalent cation ions of magnesium and and two monovalent cation ions of sodium and potassium in our study. To characterize the stability of EC structure binding with different ions, we calculated the root mean standard deviation (RMSD) of EC with respect to its crystallographic conformation with different ions using a 50 ns MD simulation. All of the MD simulations in this study were performed using the Gromacs package 13,14 with the AMBER force field ffamber Appropriate ions same as the binding ions were added to neutralize the system. The particle mesh Ewald (PME) method 16 was applied to calculate the electrostatic interactions. The systems were first minimized by a steepest descent algorithm with steps, then it was heated gradually to 300 K in 200 ps when positional restraints were applied and the restraint force constants decreased gradually from 2.39 to 0 kcal mol 1 Å 2 (1 cal = 4.2 J, 1 Å = 0.1 nm) in a few stages. Production simulations were fully unrestrained at 300 K with a pressure of 1 bar (1 bar = 10 5 Pa) with

3 Quantification of the stiffness and strength of cadherin ectodomain binding with different ions Parrinello Rahman algorithm. 17 Bonds with H-atoms were constrained with LINCS algorithm. 18 The time step of the simulations was 2.0 fs. The cutoff of the nonbonded interactions was set to 10 Å. The nonbonded pairs were modified in every 10 steps. According to the RMSD plots (Fig. 2), the EC structure without ions deviated from the crystallographic conformation as much as 30 Å at the end of the 50 ns simulation. Similarly, the EC structure binding with both ions and also showed large RMSD values, which are comparable with the results without ions, indicating that the dynamics of EC structure binding with and is similar to that without ions. In contrast, the EC structure binding with ions and showed considerable stability, with RMSD fluctuation about 10 Å. Figure 3 shows one of the snapshots of EC structures during 50 ns simulations for different ions. We can see that the EC structure binding with and shows similar rod-like shape conformation as the crystal structure (Fig. 1(b)), which is consistent with the RMSD calculations. However, the EC structure binding with and showed significantly deviations, and could not maintain the rod-like shape conformation (Figs. 3(c) and 3(d)). Interestingly, some of the ions and would diffuse away from the binding site. The release of ions and led to a large increase of RMSD in the simulation and then the collapse of EC structure to a compact conformation. This may be the reason why the dynamics of EC structure binding with and is similar to that without ions. Figure 3(e) shows that the structure collapses to a compact form in the absence of calcium, which is consistent with experiments. 6,7 The above results indicate that the ions and can stabilize the EC structure to a rod-like shape conformation, while the other two ions and led to disordered ones. RMSD/m Τ10 10 Without ion Time/ns Fig. 2. RMSD of EC binding with different ions in 50 ns MD simulations. (a) (b) (c) Fig. 3. ions. (d) (e) Without ion Snapshots of EC binding with different Different stabilities of EC structure imply that there should be different binding strengths between EC and different ions. Therefore, we further probed EC structure stability by using the steered molecular dynamics (SMD) simulations. SMD simulation is widely used in detecting interaction strength of ligand-receptor systems and mechanics of protein unfolding Because the ions bind with EC structure between successive domains, we chose EC2 as the simulation system so as to reduce the computation. A constant pulling speed is used to apply force to the system. One steered dummy atom was bonded to centers of mass (COM) of and EC2 via a spring, and they were moved at a constant velocity in the opposite direction, as illustrated by the inset in Fig. 4. In the simulation, the applied force is given by f = (vt + L 0 L(t))K spring, where K spring = pn/nm is spring constant to mimic the stiffness of pulling device, v is the

4 Z. Y. Xu, D. C. Li, B. H. Ji Theor. Appl. Mech. Lett. 4, (2014) constant pulling velocity of the dummy atom, t is the simulation time, L 0 is the initial length of EC2, and L(t) is the transient length of EC2, respectively. Because the increase of L(t) due to deformation is much smaller than that of vt, the force rate can be well approximated as ḟ = K spring v. To study the binding strength, a series of computational simulations are performed through a wide range of force rate over three orders of magnitude from to pn/ns by systematically varying the pulling velocity from 0.1 to 100 nm/ns. Every force rate was simulated three times to obtain the average rupture forces and deviations. The rupture force is the peak force for disrupting the chelate interactions between the binding site of EC2 and the ions. As shown in Fig. 4, the rupture forces depend on the force rate ḟ = K spring v, which are well consistent with Bell s model. 23 The results show that ion binds with EC2 with the largest strength, with intermediate strength, while ions and with the smallest strength. The SMD simulation results are in good agreement with the above stability analysis. Based on the SMD simulations, we applied umbrella sampling (US) simulation to calculate the potential of mean force (PMF) U( L/L 0 ) of stretching EC2 domain binding with different ions, as shown in Fig. 5. The PMF can be well fitted by a harmonic function U( L/L 0 ) = KL 2 0 ( L/L 0) 2 /2, where L 0 is the initial length of EC2 structure, L is the deformation, and K is defined as the stiffness of EC2 structure. The binding strength is defined as the work needed for disrupting the chelate interactions between successive domains and ions, as shown in the inset of Fig. 5. The arrow line illustrates the increasing of rupture strain and strength of EC structure while binding with different ions. The US results show significant differences in stiffness and strength of the EC2 structure when binding with different ions, as shown in Table 1, which shows large strength differences of EC2 binding with different valence ions, e.g., U = k BT = kcal/mol. The significantly high binding strength difference suggests that binding with would be much stronger than binding with, which would lead to more stable and larger rupture forces of EC EC2 while binding with, compared with the forces when binding with, as shown in Figs. 3 and 4. Consequently, our results show that EC2 binding with bivalent ions and results in high stiffness and high binding strength, while binding with the other monovalent ions of and leads to low stiffness and low strength. Rupture force/pn Τ10 3 v K spring v/(pn.ns -1 ) Fig. 4. Rupture forces of EC2 domain binding with different ions under different force rates. The inset illustrates the simulation system in SMD. v U(DL/L0)/(kcal.mol -1 ) Without ion Rupture strain DL/L 0 Fig. 5. PMF of stretching EC2 domain binding with different ions. The insets represent the conformation evolutions at respective states.

5 Quantification of the stiffness and strength of cadherin ectodomain binding with different ions Table 1. Stiffness and strength of EC2 binding with different ions from US simulation. Ions Stiffness K/(pN nm 1 ) Critical strain ( L L0 1 Strength U/(kcal mol 1 ) Without ion Our simulation results show that binding with ions or can cause the switch of the EC structure to a rod-like shape conformation with high stiffness and high strength. In addition, we show that the binding of with EC is much stronger than that of. However, experiments 24 showed that is insufficient to promote the conformational changes seen in EC2 domains at the equivalent concentration. This insufficient binding is attributed to the higher free energy cost of dehydrating during the binding process in comparison with that of, 25,26 which is not considered in this study. On the other hand, the monovalent ions and binding with EC structure results in a soft, collapse conformation because of the weak binding strength. Many previous studies showed that cells prefer to spread and form stable adhesion at stiff substrate. 2,27 30 Our previous study 31 also showed that high molecular stiffness can enhance the molecular interaction because of more frequency of rebinding in a stiff molecule system. For the cell-cell adhesion, the high stiffness of EC stabilizes the trans interactions. This may be the reason why EC needs to bind with to switch to a stiff, rod-like conformation, and then to form stable trans interactions between adjacent cells. In summary, we have studied the stability, stiffness and binding strength of EC structure when it binds with different ions using MD simulations. In this study, we quantitatively characterized the changing of stiffness and strength of EC structure when binding with different ions. The results show that the EC structure can maintain rod-like shape with high stiffness and strength when binding with bivalent ions and. However, EC switches to be soft, collapse conformation when binding with monovalent ions and because of the weak binding strength of monovalent ions with EC. This may be the reason why the function of EC highly depends on bivalent ions but not on other monovalent ions. The work was supported by the National Natural Science Foundation of China ( , , , and ) and the Excellent Young Scholars Research Fund of Beijing Institute of Technology. The authors want to thank Dr. Guangkui Xu from Xi an Jiaotong University for helpful discussion. 1. B. Ji, G. Bao. Cell and molecular biomechanics: Perspectives and challenges. Acta Mechanica Solida Sinica 24, (2011). 2. D. E. Discher, P. Janmey, Y. L. Wang. Tissue cells feel and respond to the stiffness of their substrate. Science 310, (2005). 3. S. Pokutta, W. I. Weis. Structure and mechanism of cadherins and catenins in cell-cell contacts. Annu. Rev. Cell Dev. Biol. 23, (2007). 4. S. D. Patel, C. P. Chen, F. Bahna, et al. Cadherin-mediated cell-cell adhesion: Sticking together as a family. Current Opinion in Structural Biology 13, (2003). 5. D. E. Leckband, Q. le Duc, N. Wang, et al. Mechanotransduction at cadherin-mediated adhesions. Current Opinion in Cell Biology 23, (2011).

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