Supplementary Material

The Allosteric Role of the Ca2+ Switch in Adhesion

and Elasticity of C-Cadherin.

Marcos Sotomayor and Klaus Schulten.

Movie I (mI.mpg)

Dynamics of C-cadherin extracellular domain in the absence of Ca2+ ions. The pro-tein is shown throughout a 5 ns equilibration, followed by 0.65 ns of stretching andsubsequent relaxation lasting 5 ns (simulations SimApo1, SimApo2, and SimApo3,respectively). The EC1 repeat has been aligned to itself along the trajectory so asto illustrate the motion of repeats EC2-EC5 with respect to EC1. The extracellulardomain is shown in cartoon representation and its surface is drawn in transparent or-ange. Terminal Cα atoms are shown as red spheres. The trajectory reveals significantmobility of repeat EC1.

Movie II (mII.mpg)

Dynamics of C-cadherin extracellular domain in the presence of Ca2+ ions. Theprotein is shown throughout a 5 ns equilibration, followed by 0.67 ns of stretchingand subsequent relaxation lasting 5 ns (simulations SimCa1, SimCa2, and SimCa3,respectively). The EC1 repeat has been aligned to itself along the trajectory so asto illustrate the motion of repeats EC2-EC5 with respect to EC1. The extracellulardomain is shown in cartoon representation and its surface is drawn in transparentorange. Crystallographic Ca2+ ions and terminal Cα atoms are shown as green andred spheres, respectively. The trajectory reveals limited motion of EC1.

Movie III (mIII.mpg)

Local deformations of C-cadherin in the presence of Ca2+ ions. The protein is shownthroughout a 5 ns equilibration, followed by 0.65 ns of stretching and subsequentrelaxation lasting 5 ns (simulations SimCa1, SimCa2, and SimCa3, respectively).Crystallographic Ca2+ ions and terminal Cα atoms are shown as green and ochrespheres, respectively. C-Cadherin is shown in cartoon representation and coloredaccording to average strain (ui(t), see Methods). Cα atoms of residues in whichstrain is above or below the thresholds indicated in the color bar are shown as red orblue spheres, respectively. The trajectory reveals that most of the protein strain islocalized at repeats EC3, EC4, and EC5 (mainly at linker regions).

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Movie IV (mIV.mpg)

Local deformations of C-cadherin in the absence of Ca2+ ions. The protein is shownthroughout a 5 ns equilibration, followed by 0.65 ns of stretching and subsequentrelaxation lasting 5 ns (simulations SimApo1, SimApo2, and SimApo3, respectively).Terminal Cα atoms are shown as ochre spheres. C-Cadherin is shown in cartoonrepresentation and colored according to strain (ui(t), see Methods). Cα atoms ofresidues in which strain is above or below the thresholds indicated in the color barare shown as red or blue spheres, respectively. The trajectory reveals that most ofthe protein strain in the absence of Ca2+ is localized throughout all linker regions.

Movie V (mV.mpg)

Unfolding of C-cadherin in the absence of Ca2+. The complete extracellular domain ofC-cadherin is shown during a stretching simulation (SimApo2–SimApo2E) in cartoonrepresentation with terminal Cα atoms shown as red spheres. The protein is firststraightened through extension of linker regions and then further extension is achievedthrough unfolding of repeat EC1.

Movie VI (mVI.mpg)

Unfolding of C-cadherin in the presence of Ca2+. The complete extracellular domainof C-cadherin is shown during a stretching simulation (SimCa2–SimCa2E) in cartoonrepresentation with calcium ions and terminal Cα atoms shown as green and redspheres, respectively. Ca2+ ions act as molecular bearings allowing straightening ofthe protein followed by unfolding of repeat EC1.

Movie VII (mVII.mpg)

Detail of C-cadherin unfolding in the presence of Ca2+. A close view of the EC1-EC2linker region during unfolding (SimCa2–SimCa2E) is shown as in movie VI. ResidueGlu11 is shown in licorice representation. Unfolding occurs after a bridge betweenresidue Glu11 and a Ca2+ ion is broken.

Movie VIII (mVIII.mpg)

Dynamics of conserved residue Trp2 in the absence of Ca2+ ions. The EC1 repeatand Trp2 residue are shown throughout a 10 ns equilibration (SimApo1). The EC1repeat is shown in surface representation and colored according to hydrophobicity(white, hydrophobic residues; green, polar residues; red or blue, charged residues).Trp2 is shown in licorice representation. The Trp2 side-chain switches from exposedto partially buried during the simulation.

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Movie IX (mIX.mpg)

Dynamics of conserved residue Trp2 in the presence of Ca2+ ions. The EC1 repeatand Trp2 residue are shown throughout a 10 ns equilibration (SimCa1). The EC1repeat is shown in surface representation and colored according to hydrophobicity(white, hydrophobic residues; green, polar residues; red or blue, charged residues).Trp2 is shown in licorice representation. The Trp2 side-chain is exposed to solventthroughout the entire trajectory.

Movie X (mX.mpg)

Dynamics of conserved residue Trp2 in the presence of K+ ions. The EC1 repeatand Trp2 residue are shown throughout a 10 ns equilibration (SimK1). The EC1repeat is shown in surface representation and colored according to hydrophobicity(white, hydrophobic residues; green, polar residues; red or blue, charged residues).Trp2 is shown in licorice representation. The Trp2 side-chain switches from exposedto partially buried during the simulation.

Movie XI (mXI.mpg)

Dynamics of conserved residue Trp2 in the presence of Na+ ions. The EC1 repeatand Trp2 residue are shown throughout a 10 ns equilibration (SimNa1). The EC1repeat is shown in surface representation and colored according to hydrophobicity(white, hydrophobic residues; green, polar residues; red or blue, charged residues).Trp2 is shown in licorice representation. The Trp2 side-chain switches from exposedto partially buried during the simulation.

CHARMM22/CMAP protein force field in NAMD

The outcome of the molecular dynamics simulations presented here relies on theforce-field employed. An accurate description of backbone dynamics and structuralfluctuations is particularly relevant when evaluating the flexibility of C-cadherin andprotein fluctuations that determine the availability of key residues involved in C-cadherin mediated cell adhesion. We have therefore used the CHARMM22/TIP3Pforce field with the CMAP correction (48–50) implemented in NAMD. The CMAPcorrection has been shown to result in improved backbone dynamics and a betterdescription of structural properties of proteins over multinanosecond time scales (52).

The NAMD implementation of the CMAP correction was validated by reproducingpart of the results presented in (52). Two systems containing hen lysozyme (1.9 Aresolution; pdb code 6LYT (51)) solvated in water (0.61 × 0.57 × 0.63 nm3) werebuilt using the psfgen and solvate plugins of VMD. The only difference between thetwo systems (simulations labeled SimLX and SimLCX) was the presence or absenceof the CMAP correction term. Residues Glu35, Asp101 were assumed neutral and

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residue His15 was assumed charged to mimic conditions in which experimental datawere obtained (pH 3.8). Disulfide bonds for cysteines 6-127, 30-115, 64-80, and 94-76were explicitly modeled. Chloride ions (11) were included to neutralize the systemswhich each encompassed 19,932 atoms. Simulations of the lysozyme systems wereperformed using NAMD2.6 at T = 310 K and conditions otherwise identical to thoseused for the C-cadherin systems (time step, cutoffs, PME). A summary of the henlysozyme simulations performed using different thermodynamic ensembles is shownin Table 2.

Label tsim (ns) Ensemble γ (ps−1) Start CMAPSimL1 24.66 NpTa 5.0 – noSimL2 24.22 NVE – SimL1 (1.1 ns) noSimL3 23.84 NpT 0.1 SimL1 (1.1 ns) noSimLC1 25.00 NpTa 5.0 – yesSimLC2 25.00 NVE – SimLC1 (1.4 ns) yesSimLC3 23.33 NpT 0.1 SimLC1 (1.4 ns) yes

aThese simulations consisted of 1000 steps of minimization, 100 ps of dynamics with the backboneof the protein restrained (k = 1 Kcal/mol/A2), followed by free dynamics in the NpT ensemble.

Table 2: Summary of hen lysozyme simulations (totaling > 125 nanoseconds). Labels indicatethe presence (SimLX) or absence (SimLCX) of the CMAP correction term. Initial coordinates andvelocities were obtained from the last frame of the simulations mentioned in the Start column.

Root mean square deviations (RMSD) computed during the entire trajectories(Supplementary Material’s Fig. 23) show that the protein simulated with the CMAPcorrection deviates less from its crystal conformation than the protein simulated withthe CHARMM22 force field alone. Root mean square fluctuations (RMSF) were com-puted over the last 20 ns of the corresponding trajectories. The computed values werecompared to experimental temperature factors (B) using < δx >2= 3B/8π2. RMSFvalues from simulation were systematically closer to those obtained from temperaturefactors when using the CMAP correction (Supplementary Material’s Fig. 23). Theseresults are in line with those presented in (52) and validate the current implementa-tion of CMAP in NAMD 2.6 along with the simulation protocols used here.

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Supplementary Figures

Figure 8: Influence of ions and temperature control protocols on C-cadherin equilibrium dynam-ics.(A-B) Initial (top) and final (bottom) conformations of the complete C-cadherin extracellulardomain with and without Ca2+ ions for simulations performed using Langevin dynamics and a damp-ing coefficient of 5 ps−1 (SimCa4 and SimApo4). The large damping coefficient utilized prevents(in the short time scale of the simulation) deformation of the overall curved shape of C-Cadherin asobserved in simulations performed in the NVE ensemble in the absence of Ca2+. (C) Initial (top)and final (bottom) conformation of the complete C-cadherin extracellular domain without Ca2+

ions for a simulation performed using Langevin dynamics and a damping coefficient of 0.1 ps−1

(SimApo5). The extracellular domain quickly loses its shape and at the end of the simulationexhibits a disordered conformation.

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Figure 9: C-Cadherin equilibrium dynamics and influence of ions and temperature control protocolson inter-repeat motion. Conformations of the extracellular domain of C-cadherin during simulationsSimCa4 (left), SimApo4 (center), and SimApo5 (right) were aligned so as to illustrate the rela-tive motion of individual repeats with respect to their neighbors. The simulations were performedusing Langevin dynamics and a damping coefficient of 5 ps−1 (SimCa4, SimApo4) and 0.1 ps−1

(SimApo5). Individual repeats (EC1 to EC5 as indicated by arrows) were aligned throughout thetrajectories using the crystal conformation as a reference. The rest of the protein was moved usingthe same matrix transformation required to align the corresponding repeat. The resulting alignedmolecules are shown superimposed every 40 ps. Color indicates time, with red being early stagesof the simulations and blue indicating the latest stages of the simulations. Inter-repeat motion insimulations using a large damping coefficient with and without calcium is limited when comparedwith simulations performed in the NVE ensemble (see Fig. 3). However, inter-repeat motion isstill more evident in simulations without Ca2+. Use of small damping coefficients clearly enhancedinter-repeat motion.

Figure 10: Root mean-square deviations for cadherin repeats. (A-D) RMSD was computed forrepeats EC1 (black curve, residues 1–100), EC2 (red curve, residues 103–213), EC3 (green curve,residues 216–325), EC4 (blue curve, residues 327–432), and EC5 (yellow curve, residues 433–531)throughout simulations SimCa1, SimApo1, SimK1, and SimNa1, respectively. The RMSD of allrepeats (except EC5) reached stable values below 0.3 nm after 10 ns of simulation in the presenceand absence of Ca2+. Repeats EC1 and EC2 consistently exhibited smaller RMSD values than otherrepeats throughout simulations SimCa1, SimK1, and SimNa1.

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Figure 11: End-to-end distance and RMSD of C-cadherin. (A) The end-to-end distance of C-cadherin during short stretching simulations (SimCa2 and SimApo2) and subsequent relaxation(SimCa3 and SimApo3) are shown for systems with (black) or without (red) Ca2+. Partial recovery ofthe original end-to-end distance is observed during relaxation simulations in both cases. (B) RMSDfor the complete C-cadherin extracellular domain computed during short stretching simulations(SimCa2 and SimApo2) and subsequent relaxation (SimCa3 and SimApo3) are shown for systemswith (black) or without (red) Ca2+. Partial recovery of RMSD values was observed only for therelaxation performed in the presence of Ca2+. The superimposed red and black curves at the 0.3 nmlevel correspond to RMSD values for each individual repeat throughout simulations SimCa2-SimCa3and SimApo2-SimApo3.

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Figure 12: C-Cadherin tertiary structure elasticity and inter-repeat motion. Conformations ofthe extracellular domain of C-cadherin during 5 ns of equilibration (SimCa1/SimApo1), followed by0.67/0.65 ns of a constant velocity stretching (SimCa2/SimApo2), and a subsequent relaxation of5 ns (SimCa3/SimApo3) were aligned so as to illustrate the relative motion of individual repeatswith respect to their neighbors. Individual repeats (EC1 to EC5 as indicated by arrows) were alignedthroughout the trajectories using the crystal conformation as a reference. The rest of the proteinwas moved using the same matrix transformation required to align the corresponding repeat. Theresulting aligned molecules are shown superimposed every 40 ps. Color indicates time, with red beingearly stages of the simulations and blue indicating the latest stages of the simulations. Inter-repeatmotions are larger for the system without Ca2+.

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Figure 13: C-Cadherin viscoelasticity. (A) The end-to-end distance is shown for ‘length-clamp’SMD simulations of C-cadherin in the presence of calcium (SimCa12, black; SimCa13, red; SimCa14,green). The simulation consisted of two phases. First, the protein is stretched at a constant ve-locity from the C-terminus. Once a predetermined extension has been achieved (see Methods andTable 1), a second phase starts in which the steering atom is held in place and the protein is permit-ted to relax while the force required to keep the corresponding extension is monitored. (B) Forcesmonitored during ‘length-clamp’ SMD simulations are plotted against time. Simulations SimCa12and SimCa14 resulted in unfolding and negligible forces during the second phase of the stretchingprotocol. However, C-cadherin did not unfold in SimCa13, and the monitored force decreased asshown in the inset (see arrows). The elastic force is defined as the force at equilibrium (bottomarrow), while the viscous component is defined as the peak force (top arrow) minus the elasticforce (67). (C) End-to-end distance for ‘length-clamp’ SMD simulations in which the N-terminusof C-cadherin is stretched (SimCa15, black; SimCa16, red; SimCa17, green). (D) Forces moni-tored during ‘length-clamp’ SMD simulations are plotted against time. (E) End-to-end distance for‘length-clamp’ SMD simulations in which the C-terminus of C-cadherin is stretched in the absenceof Ca2+ ions (SimApo9) (F) Forces monitored during ‘length-clamp’ SMD simulations are plottedagainst time. The force relaxed to a an equilibrium value that is considerably smaller than whenstretching cadherin to the same extension when Ca2+ is present.

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Figure 14: Force profile during C-cadherin unfolding. Forces applied to the N- and C- terminusof C-cadherin during stretching simulation SimCa2-SimCa2E are plotted against time in blue andindigo, respectively. Distances between atoms forming hydrogen bonds of the first β-strand unraveled(I7HN–T95O; I7O–N97HN; V9HN–N97O; V9O–I99HN) are shown in light gray. Distances betweenatoms forming hydrogen bonds of the second β-strand unraveled (K19HN–V62O; K19O–V62HN;L21HN–M60O; V22O–M60HN) are shown in light brown. Distances between atom Cδ of Glu11 andtwo Ca2+ ions located at the linker region between EC1 and EC2 are shown in red and black. Thevertical dashed line marks the point of peak force which coincides with rupture of a bond betweenGlu11 and one of the Ca2+ ions. Force peaks at N- and C- terminus are not synchronous.

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Figure 15: Energy conservation. The energy of the complete simulated system was monitoredthroughout stretching and relaxation simulations. Blue and red curves show the energy changeduring stretching simulations with (SimCa2-SimCa2E) and without (SimApo2-SimApo2E) Ca2+

ions, respectively. The increase in energy (1591 kcal/mol and 1004 kcal/mol) matches well, althoughis slightly larger than, the estimated work (W ) done by the steering forces (F ) during extension(d) computed using W = F × d (1574 kcal/mol and 984 kcal/mol). A negligible increase in thetemperature of the system was observed (0.518 K and 0.364 K). Indigo and orange curves show (ascontrol) energy conservation during relaxation simulations SimCa3 and SimApo3, respectively.

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Figure 16: Influence of ions on C-cadherin secondary structure elasticity. (A) Force versus end-to-end distance profile for constant-velocity stretching simulations with crystallographic Ca2+ ions(blue and indigo, SimCa2-SimCa2E), with Na+ replacing Ca2+ (green and light blue, SimNa2), andwithout Ca2+ (red and orange, SimApo2-SimApo2E). (B-D) Snapshots of the unfolding pathwayduring simulation SimNa2. Views show the complete C-cadherin extracellular domains in cartoonrepresentation with the corresponding surface drawn in transparent orange. The Cα atoms of thetermini are shown as red spheres and Na+ ions as yellow spheres. Residues at linker regions areshown in licorice representation. Disruption of secondary structure elements (secondary structureelasticity) proceeds upon dissociation of Na+ ions starting at linker EC3-EC4 and EC4-EC5. Forcesrequired to unfold C-cadherin in the presence of Na+ ions (replacing Ca2+) are similar to thosemeasured in the absence of ions at linker regions.

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Figure 17: Force profile during unfolding at different stretching speeds. (A-B) Forces applied to theN-terminus of C-cadherin are plotted against the end-to-end distance during simulations performedat different stretching speeds with and without Ca2+, respectively. The force profiles correspond tosimulations performed at effective speeds of 100 nm/ns (black, SimCa7); 50 nm/ns (red, SimCa8);10 nm/ns (blue, SimCa2-SimCa2E/SimApo2-SimApo2E); and 1 nm/ns (green, SimCa9/SimApo8).(C-D) Forces applied to the C-terminus of C-cadherin are plotted against the end-to-end distanceduring the same simulations mentioned above. A reduction in unfolding force peaks can be observedas stretching speeds are reduced. Comparison of unfolding peak forces for simulations SimApo2-SimApo2E/SimApo8 and SimCa7/SimCa8, however, may be misleading due to different unfoldingpathways observed in each case.

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Figure 18: Force profile during unfolding using different temperature control protocols. Forcesapplied to the N-terminus (red) and C-terminus (black) of C-cadherin are plotted against timeduring simulations performed using different Langevin damping coefficients (γ) with (A-C; SimCa5,SimCa6, SimCa2-SimCa2E) and without (D-F; SimApo6, SimApo7, SimApo2-SimApo2E) Ca2+.Unfolding forces are artificially increased when using temperature control (γ 6= 0). Protein endsbecome decoupled from each other when a large Langevin damping coefficient is used (A, D).

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Figure 19: Mechanical hierarchy and mechanical intermediates of C-cadherin repeats. (A) Forceversus end-to-end distance profile for constant-velocity stretching simulations of repeat EC2 (blueand indigo, SimCa10) and EC4 (dark and light red, SimCa11). In these simulations the centerof mass of repeats EC3/EC1 and repeats EC5/EC3 were pulled in opposite directions effectivelystretching repeats EC2 and EC4 as indicated in the insets. (B) The magnitude of the unfoldingforce for repeat EC2 within the complete C-cadherin extracellular domain (black) is comparable tothat required to unfold an isolated EC2 domain (red curve adapted from (39)). (C-E) Snapshots ofthe unfolding pathway during simulation SimCa10. An intermediate conformation in which part ofthe linker region between repeats EC2 and EC1 is disrupted are shown.

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Figure 20: Influence of ions on Trp2 availability. Snapshots show Trp2 in licorice representation attimes t = 0, 2.5, 5, 7.5, and 10 ns during simulations SimCa1 (A), SimK1 (B), and SimNa1 (C). Therest of the EC1 domain is shown in surface representation and colored according to hydrophobicity(white, hydrophobic residues; green, polar residues; red or blue, charged residues). The Trp2 sidechain is mostly exposed to solvent only when Ca2+ ions are present in the simulations.

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Figure 21: Structural fluctuations of cadherin repeats. (A-E) The root mean-square fluctuation ofCα atom positions are shown for repeats EC1, EC2, EC3, EC4, and EC5, respectively. The top rowshows fluctuations computed over 4 ns of dynamics during simulations SimCa1 and SimApo1 (blackand red, respectively; 1 to 5 ns denoted with *). The bottom row shows fluctuations computedover the last 5 ns (**) of dynamics during simulations SimCa1 and SimApo1. Overall fluctuationsduring simulations performed in the absence of Ca2+ are generally larger than those observed forsimulations performed in the presence of Ca2+ ions. EC1 residues (Ile24, Lys25, Ser26, and Glu90, seearrows) forming a hydrophobic cavity where Trp2 docks, exhibited larger fluctuations in the absenceof Ca2+. A similar trend was observed for Asp134 and neighboring residues.

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Figure 22: Accessibility of residue Trp2. (A) Solvent accessible surface area (SASA) of Trp2

computed during simulations in the NVE ensemble SimCa1 (black; 2.25±0.13 nm2), SimApo1 (red;1.52±0.61 nm2), SimK1 (green; 1.50±0.54 nm2), and SimNa1 (blue; 1.86±0.29 nm2). Trp2 is mostexposed when C-cadherin is simulated in the presence of crystallographically resolved Ca2+ ions(SimCa1). (B) SASA of Trp2 computed during simulations in the NpT ensemble SimCa4 (black;2.27 ± 0.18 nm2), SimApo4 (red; 2.01 ± 0.37 nm2), and SimApo5 (green; 2.16 ± 0.37 nm2). Theuse of a temperature control protocol and different Langevin damping coefficients favors exposureof Trp2. Nevertheless, Trp2 is most exposed only when C-cadherin is simulated in the presence ofCa2+ (SimCa4).

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Figure 23: Hen lysozyme dynamics using the CHARMM/CMAP protein force-field. (A) Rootmean square deviation (RMSD) during two simulations of lysozyme performed with (red, SimLC1)and without (black, SimL1) the CMAP correction while using Langevin dynamics to control tem-perature (γ = 5 ps−1). (B) Root mean square fluctuations (RMSF) computed for trajectories shownin A (red and black) and from temperature factors (blue). (C) RMSD during two simulations oflysozyme performed with (red, SimLC2) and without (black, SimL2) the CMAP correction in theNVE ensemble (γ = 0 ps−1). (D) RMSF computed for trajectories shown in C (red and black) andfrom temperature factors (blue). (E) RMSD during two simulations of lysozyme performed with(red, SimLC2) and without (black, SimL2) the CMAP correction while using Langevin dynamics tocontrol temperature (γ = 0.1 ps−1). (F) RMSF computed for trajectories shown in E (red and black)and from temperature factors (blue). RMSD during trajectories in which the CMAP correction wasused reached lower values than those observed for systems simulated with the CHARMM22 force-field alone in all cases. RMSF values computed from simulations in which CMAP was utilized arecloser to those computed from experimentally determined temperature factors when no temperaturecontrol is used or when a small damping coefficient is used.

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