# Interplay Between Long-Range And Short-Range Interactions In Polymer Self-Assembly And Cell Adhesion

Abstract: Interplay between long-range and short-range interactions is a common theme in soft and biological matter, which results in complicated self-assembly behaviors. We study two examples of this interplay: reversible gelation of associating polymers and ligand-receptor interactions in membrane adhesion. In associating polymer solutions, the competition between the conformation flexibility of polymer chains and the enthalpic monomer interactions results in phase-separated micro-structures at the mesoscopic scale; both gelation and the microphase order-disorder transition are manifestations of this self-assembly. We further establish that reversible gelation is similar to the glass transition: both are characterized by ergodicity breaking, aperiodic micro-structures, and non-equilibrium relaxations over a finite temperature range. In the study of ligand-receptor interactions between surfaces, we emphasize the interplay between specific ligand-receptor binding, and generic physical interactions. We find that both the finite spatial extension of receptors and their mobilities affect their binding affinity. As a special case of the interplay between receptor binding and generic interactions, we study the dynamics of membrane adhesion that is mediated by receptor binding but fulfilled through membrane deformations. We calculate the energy barrier of the adhesion as a result of membrane bending deformations and the double-well adhesion potential, and analyze the different scenarios according to the shape of the adhesion potential by scaling arguments.

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### "Interplay Between Long-Range And Sh..." refers background in this paper

..., 2006; Moore and Kuhl, 2006; Moreira and Marques, 2004; Sain and Wortis, 2004), and suggests a new route to controlling the interactions between surfaces typically achieved by generic physical interactions (Israelachvili, 1992; Hiddessen et al., 2000; Carignano and Szleifer, 2003; Nap and Szleifer, 2005)....

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...The interplay between specific and other generic physical interactions, such as electrostatic, hydrophobic and steric interactions (Israelachvili, 1992), is crucial to the adhesion and signalling between cells and the extracellular matrix, and has been extensively studied by researchers in physiology, biochemistry, biophysics, and bioengineering (Alberts et al....

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16,813 citations

### "Interplay Between Long-Range And Sh..." refers background or methods in this paper

...Near the mean-field spinodal γ2(q,−q) can be approximated as γ2(q,−q) = c2 4 ( q2Nb2 − q2mNb2 )2 + 2 (χN)S − 2χN, where χN is the Flory-Huggins interaction parameter between A and B blocks, (χN)S is its value at the spinodal, and c is a parameter independent of N ....

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...It was Flory (1953) who first calculated the amount of crosslinkers that are necessary to generate a macroscopic network (Flory-Stockmayer model) and studied the elasticity of this network (“rubber elasticity” theory)....

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...In the classical model by Flory and Stockmayer (see Flory, 1953), the crosslinked network (e.g., vulcanized rubber) is assumed to be an infinitely large branched tree (without cycles), which is the mean-field limit of the percolation model (i.e., percolation on a Cayley tree)....

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...The polymer solution is treated following the mean-field theory of Flory and Huggins (Flory, 1953) and the reversible gelation is treated as a micellation....

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10,758 citations

### "Interplay Between Long-Range And Sh..." refers background in this paper

...Such polyfunctional units are interconnected 1An exception is the network generated by topological entanglements, such as in melts of very long polymer chains, or a series of interconnected rings (de Gennes, 1979)....

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...Furthermore, as each crosslinker (multi-functional unit) is surrounded by many monomers, cycle structures are rare, therefore the Flory-Stockmayer model is accurate even near the critical threshold (de Gennes, 1979)....

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10,219 citations

### "Interplay Between Long-Range And Sh..." refers background in this paper

...Second, we construct the mean-field phase diagram through a quadratic expansion of the free energy (effective potential) from the Edwards Hamiltonian....

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...A continuum Gaussian chain with length N in an external field V (r) is described by the Edwards Hamiltonian (Doi and Edwards, 1986) h0[R(t)] = 3kBT 2Nb2 ∫ 1 0 [( ∂R(t) ∂t )2 + V (R(t)) ] dt (2.1) where R(t) maps the configuration of the polymer (0 ≤ t ≤ 1 is a parametrization of the polymer chain), and Nb2 is mean square end-to-end distance....

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...A continuum Gaussian chain with length N in an external field V (r) is described by the Edwards Hamiltonian (Doi and Edwards, 1986) h0[R(t)] = 3kBT 2Nb2 ∫ 1 0 [( ∂R(t) ∂t )2 + V (R(t)) ] dt (2.1) where R(t) maps the configuration of the polymer (0 ≤ t ≤ 1 is a parametrization of the polymer chain),…...

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...Using the Green’s function for Gaussian chains (Doi and Edwards, 1986) we can express the partition function qp as qp = ∫ G(r, r′;N), where G(r, r′;N) satisfies [ ∂ ∂N − b 2 6 ∇2r +W (r) ] G(r, r′;N) = δ(r− r′)....

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7,047 citations