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Transforming binding affinities from three dimensions to two with application to cadherin clustering


Membrane-bound receptors often form large assemblies resulting from binding to soluble ligands, cell-surface molecules on other cells and extracellular matrix proteins1. For example, the association of membrane proteins with proteins on different cells (trans-interactions) can drive the oligomerization of proteins on the same cell2 (cis-interactions). A central problem in understanding the molecular basis of such phenomena is that equilibrium constants are generally measured in three-dimensional solution and are thus difficult to relate to the two-dimensional environment of a membrane surface. Here we present a theoretical treatment that converts three-dimensional affinities to two dimensions, accounting directly for the structure and dynamics of the membrane-bound molecules. Using a multiscale simulation approach, we apply the theory to explain the formation of ordered, junction-like clusters by classical cadherin adhesion proteins. The approach features atomic-scale molecular dynamics simulations to determine interdomain flexibility, Monte Carlo simulations of multidomain motion and lattice simulations of junction formation3. A finding of general relevance is that changes in interdomain motion on trans-binding have a crucial role in driving the lateral, cis-, clustering of adhesion receptors.

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Figure 1: Structures of cis -dimers formed from cadherin monomers and from trans -dimers.
Figure 2: Essential coordinates that characterize the dimerization processes of classical cadherins in a 2D membrane environment.
Figure 3: Monte Carlo simulations of the flexibility of the cadherin ectodomain.
Figure 4: Simulation of junction formation.


  1. 1

    Aplin, A. E., Howe, A. K. & Juliano, R. L. Cell adhesion molecules, signal transduction and cell growth. Curr. Opin. Cell Biol. 11, 737–744 (1999)

    CAS  Article  Google Scholar 

  2. 2

    Aricescu, A. R. & Jones, E. Y. Immunoglobulin superfamily cell adhesion molecules: zippers and signals. Curr. Opin. Cell Biol. 19, 543–550 (2007)

    CAS  Article  Google Scholar 

  3. 3

    Wu, Y. et al. Cooperativity between trans and cis interactions in cadherin-mediated junction formation. Proc. Natl Acad. Sci. USA 107, 17592–17597 (2010)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Dustin, M. L., Ferguson, L. M., Chan, P. Y., Springer, T. A. & Golan, D. E. Visualization of CD2 interaction with LFA-3 and determination of the two-dimensional dissociation constant for adhesion receptors in a contact area. J. Cell Biol. 132, 465–474 (1996)

    CAS  Article  Google Scholar 

  5. 5

    Dustin, M. L., Bromley, S. K., Davis, M. M. & Zhu, C. Identification of self through two-dimensional chemistry and synapses. Annu. Rev. Cell Dev. Biol. 17, 133–157 (2001)

    CAS  Article  Google Scholar 

  6. 6

    Bell, G. I. Models for the specific adhesion of cells to cells. Science 200, 618–627 (1978)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Bell, G. I., Dembo, M. & Bongrand, P. Cell adhesion. Competition between nonspecific repulsion and specific bonding. Biophys. J. 45, 1051–1064 (1984)

    CAS  Article  Google Scholar 

  8. 8

    Chen, C. P., Posy, S., Ben-Shaul, A., Shapiro, L. & Honig, B. H. Specificity of cell-cell adhesion by classical cadherins: critical role for low-affinity dimerization through beta-strand swapping. Proc. Natl Acad. Sci. USA 102, 8531–8536 (2005)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Patel, S. D. et al. Type II cadherin ectodomain structures: implications for classical cadherin specificity. Cell 124, 1255–1268 (2006)

    CAS  Article  Google Scholar 

  10. 10

    Harrison, O. J. et al. The extracellular architecture of adherens junctions revealed by crystal structures of type I cadherins. Structure 19, 244–256 (2011)

    CAS  Article  Google Scholar 

  11. 11

    Katsamba, P. et al. Linking molecular affinity and cellular specificity in cadherin-mediated adhesion. Proc. Natl Acad. Sci. USA 106, 11594–11599 (2009)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Gov, N. S. & Safran, S. A. Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. Biophys. J. 88, 1859–1874 (2005)

    CAS  Article  Google Scholar 

  13. 13

    Zilker, A., Engelhardt, H. & Sackmann, E. Dynamic reflection interference contrast (RIC-) microscopy: a new method to study surface excitations of cells and to measure membrane bending elastic moduli. J. Phys. 48, 2139–2151 (1987)

    Article  Google Scholar 

  14. 14

    Hill, T. L. An Introduction to Statistical Thermodynamics 147–176 (Dover, 1987)

    Google Scholar 

  15. 15

    Boggon, T. J. et al. C-cadherin ectodomain structure and implications for cell adhesion mechanisms. Science 296, 1308–1313 (2002)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Dustin, M. L. et al. Low affinity interaction of human or rat T cell adhesion molecule CD2 with its ligand aligns adhering membranes to achieve high physiological affinity. J. Biol. Chem. 272, 30889–30898 (1997)

    CAS  Article  Google Scholar 

  17. 17

    Hong, S., Troyanovsky, R. B. & Troyanovsky, S. M. Spontaneous assembly and active disassembly balance adherens junction homeostasis. Proc. Natl Acad. Sci. USA 107, 3528–3533 (2010)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Huppa, J. B. et al. TCR-peptide-MHC interactions in situ show accelerated kinetics and increased affinity. Nature 463, 963–967 (2010)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Milstein, O. et al. Nanoscale increases in CD2–CD48-mediated intermembrane spacing decrease adhesion and reorganize the immunological synapse. J. Biol. Chem. 283, 34414–34422 (2008)

    CAS  Article  Google Scholar 

  20. 20

    Atilgan, A. R. et al. Anisotropy of fluctuation dynamics of proteins with an elastic network model. Biophys. J. 80, 505–515 (2001)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Li, G. H. & Cui, Q. A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca2+-ATPase. Biophys. J. 83, 2457–2474 (2002)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Tama, F., Gadea, F. X., Marques, O. & Sanejouand, Y. H. Building-block approach for determining low-frequency normal modes of macromolecules. Proteins 41, 1–7 (2000)

    CAS  Article  Google Scholar 

  23. 23

    Van Der Spoel, D. et al. GROMACS: fast, flexible, and free. J. Comput. Chem. 26, 1701–1718 (2005)

    CAS  Article  Google Scholar 

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This work was supported by National Science Foundation grant MCB-0918535 (to B.H.) and National Institutes of Health grant R01 GM062270-07 (to L.S.). The financial support of the US-Israel Binational Science Foundation (grant no. 2006-401, to A.B.-S., B.H. and L.S.) and the Israel Science Foundation (ISF 1448/10 and 695/06) (to A.B.-S.) is acknowledged. We thank E. Sackmann for an email exchange concerning membrane fluctuations.

Author information




Y.W., J.V., L.S., B.H. and A.B.-S. designed the research; Y.W. performed the multiscale simulations; J.V. carried out the all-atom molecular dynamics simulations; Y.W., B.H. and A.B.-S. analysed the data; Y.W., A.B.-S. and B.H. contributed analytic tools; and Y.W., L.S., B.H. and A.B.-S. wrote the paper.

Corresponding authors

Correspondence to Avinoam Ben-Shaul or Barry Honig.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods and Data, Supplementary Figures 1-5 with legends, Supplementary Table 1 and additional references. (PDF 451 kb)

Supplementary Movie 1

This movie shows domain fluctuations in monomer generated by coarse-grained Monte-Carlo simulations. (MOV 4233 kb)

Supplementary Movie 2

This movie shows domain fluctuations in trans-dimer generated by coarse-grained Monte-Carlo simulations. (MOV 10229 kb)

Supplementary Movie 3

This movie shows lattice simulation of junction formation. (MOV 5828 kb)

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Wu, Y., Vendome, J., Shapiro, L. et al. Transforming binding affinities from three dimensions to two with application to cadherin clustering. Nature 475, 510–513 (2011).

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