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.


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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.

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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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