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1.
Figure 7

Figure 7. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Spatial profile of sample diffusion gradients, with the rate of monomer diffusion decreasing close to the membrane (x = 0). Shown here are diffusion gradients that decrease the usual diffusion rate to 1/10 within 0.2 μm of the membrane (—) and 1/100 the usual rate within 5 μm of the membrane (···).

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
2.

Figure 6. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Steady state solution of with constant diffusion and homodimerization of cytoplasmic and bound α-catenin monomers, showing A) cytoplasmic monomer concentration and B) cytoplasmic homodimer concentration. A spatial gradient of α-catenin dimers are found in the cytoplasm when monomers bound to β- catenin are allowed to dimerize.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
3.
Figure 3

Figure 3. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

First possible mechanism for α-catenin homodimerization while bound to β-catenin. α-catenin, β-catenin/E-cadherin and the membrane are as described in . A. α-catenin monomers are bound to β-catenin/E-cadherin at an AJ. B. Homodimerization of E-cadherin brings α-catenin monomers into close proximity, and fluctuations in the position of α-catenin relative to β-catenin allows α-catenin to homodimerize while still bound to β-catenin. C. The α-catenin homodimer dissociates from β-catenin and diffuses into the cell.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
4.
Figure 4

Figure 4. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Second possible mechanism for α-catenin homodimerization while bound to β-catenin. α-catenin, β-catenin/E-cadherin and the membrane are as described in . A. The M fragment of α-catenin monomers bound to β-catenin/E-cadherin weakly homodimerize. B. The weak α-catenin homodimer dissociates from β-catenin, allowing binding of the strong homodimerization domain. C. The weak homodimerization domain unbinds, and the strongly bound homodimer diffuses into the cell.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
5.
Figure 2

Figure 2. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Sequence of events currently thought to lead to increased concentration of α-catenin homodimers near an AJ. A. α-catenin monomers (green) bind to β-catenin/E-cadherin (red) at an AJ. The plasma membrane is grey, and here the outside of the cell is below the membrane. B. α-catenin monomers are released from the AJ and diffuse into the cytoplasm. C. α-catenin monomers bind to form a homodimer that diffuses into the cell.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
6.

Figure 5. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

A) Analytic solution of at steady state and B) numeric solution of with constant diffusion and α-catenin homodimerization only in the cytoplasm, showing cytoplasmic monomer concentration (—), cytoplasmic dimer concentration (···), and membrane bound monomer concentration (●). When α-catenin bound to β-catenin can not homodimerize and there is no spatial diffusion gradient near the AJ, the cytoplasmic concentration of α-catenin monomers will never exceed the usual cytoplasmic concentration or increase the production of homodimers near an AJ.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
7.
Figure 9

Figure 9. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Wheel diagram of the amino acid sequence in the α-helical coiled-coil domains of α- catenin bound to β-catenin. Shown here are the α0 (amino acids 59–81), α1 (89–116) and α2 (124–144) helices of α-catenin, which include both the β-catenin binding (54–143) and homodimerization (82–279) domains (; ; ), along with the α-catenin binding domain of β-catenin (118–141). Hydrophobic residues are shown in red. Hydrophobic residues at the e and g positions of the α 2 helix of α-catenin suggest the α/β-catenin dimer is unstable.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
8.

Figure 8. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Numeric solution of in the presence of a diffusion gradient when both bound and cytoplasmic α-catenin monomers can homodimerize, showing A) cytoplasmic monomer concentration and B) cytoplasmic dimer concentration (membrane-bound monomer concentration not shown). When α-catenin can dimerize while bound to β-catenin, the spatial profile of cytoplasmic monomers and dimers depends on the size of the diffusion gradient and how much it slows diffusion. Shown here is a diffusion gradient that extends 1 μm into the cell and decreases monomer diffusion by a factor of 2 (—), 10 (···) and 100 (·-·-·).

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.
9.
Figure 1

Figure 1. From: A mathematical model of α-catenin dimerization at Adherens Junctions in polarized epithelial cells.

Schematic of polarized epithelial cell and molecular components that make up adherens junctions (AJs). β-catenin is localized to AJs by binding to the transmembrane protein E-cadherin. The E-cadherin/β-catenin complex (red rectangle) has both intracellular and extracellular domains and crosses the membrane (thick vertical line). There is a zone of decreased diffusion near the membrane (grey area), which may be the result of crowding or non-specific binding. α-catenin monomers (green) bind to β-catenin with high affinity while α-catenin homodimers bind to polymerized actin with high affinity. In the cytoplasm, α-catenin is predominantly monomeric, suggesting the need for a mechanism to accumulate homodimers near AJs.

Adriana T. Dawes. J Theor Biol. ;257(3):480-488.

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