Interaction between Finite-Sized Particles and End Grafted Polymers

Subramanian, G.; Williams, D. R. M.; Pincus, P.

doi:10.1021/ma946439r

Cited by 76 publications

(90 citation statements)

References 29 publications

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“…This agreed with the predicted chain extension of 45 Å (24,25,47). These findings were exactly as expected for the compression of grafted, unstructured chains by inert, colloidal particles in isotropic solvents (17,18,48). While this was indeed the case for weak protein-polymer contact, the behavior differed significantly, if the protein was pushed into or incubated in contact with the PEG layers.…”

Section: Resultssupporting

confidence: 86%

Measurements of attractive forces between proteins and end-grafted poly(ethylene glycol) chains

Sheth

Leckband

1997

Proc. Natl. Acad. Sci. U.S.A.

255

259

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The surface force apparatus was used to measure directly the molecular forces between streptavidin and lipid bilayers displaying grafted M r 2,000 poly(ethylene glycol) (PEG). These measurements provide direct evidence for the formation of relatively strong attractive forces between PEG and protein. At low compressive loads, the forces were repulsive, but they became attractive when the proteins were pressed into the polymer layer at higher loads. The adhesion was sufficiently robust that separation of the streptavidin and PEG uprooted anchored polymer from the supporting membrane. These interactions altered the properties of the grafted chains. After the onset of the attraction, the polymer continued to bind protein for several hours. The changes were not due to protein denaturation. These data demonstrate directly that the biological activity of PEG is not due solely to properties of simple polymers such as the excluded volume. It is also coupled to the competitive interactions between solvent and other materials such as proteins for the chain segments and to the ability of this material to adopt higher order intrachain structures.Poly(ethylene glycol) (PEG) is used extensively to improve the biocompatibility of foreign materials for both in vivo and ex vivo applications (1-3). Its prevalent use is due largely to its low toxicity and low immunogenicity (1). In addition, due to its protein resistance, it is widely used as a stabilizing surface coating in biological environments (3-7). For example, PEG-functionalization of liposomes increased their blood circulation times by nearly an order of magnitude (4). In the clinic, ethylene oxide surface grafts are used to reduce protein adsorption onto the surfaces of biomedical polymers (1-3, 5-7). This is important for controlling the biological responses to the latter, in part, because protein adsorption is a well established first step in the humoral response against foreign materials (2,8,9). Thus, by preventing the unwanted adsorption of bioactive agents onto the surfaces of medical polymers, the surface grafting of hydrophilic polymers is one of the more effective, general strategies used to manipulate the biological activity of medical materials (3,(9)(10)(11)(12)(13)(14).The unusual efficacy of PEG as an apparently biologically passivating surface coating is linked to both the presumed biological inertness of the polymer backbone and to its solvated configuration (1, 3, 5, 7). In most cases, the proposed mechanisms for the protein resistance of PEG borrow from current theories for structureless polymers in isotropic liquids (5,(15)(16)(17)(18)(19). For example, PEG's ability to repel proteins is attributed to its large excluded volume (3,5,(15)(16)(17)(18)(19), its configurational entropy (20, 21), surface coverage by grafted chains (3,15,18), and the thickness of grafted layers (1,3,9,17,18). These latter attributes are all well described theoretically for both terminally anchored and soluble simple chains in simple solvents (22)(23)(24)(25). Based on ...

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Section: Resultssupporting

confidence: 86%

Measurements of attractive forces between proteins and end-grafted poly(ethylene glycol) chains

Sheth

Leckband

1997

Proc. Natl. Acad. Sci. U.S.A.

255

259

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“…The resistance force decreases abruptly, indicating a first-order transition. The escape transition was studied rather extensively both by analytical [22][23][24][25][26] and numerical [27][28][29][30][31][32][33][34][35][36] methods.…”

Section: Introductionmentioning

confidence: 99%

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Skvortsov

Klushin

Leermakers

2007

The Journal of Chemical Physics

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An end-tethered polymer chain compressed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flowerlike conformation partially escaped from the gap. This phase transition is first order in the thermodynamic limit of infinitely long chains. A rigorous analytical theory is presented for a Gaussian chain in two ensembles: ͑a͒ the H-ensemble, in which the distance H between the pistons plays the role of the independent control parameter, and ͑b͒ the conjugate f-ensemble, in which the external compression force f is the independent parameter. Details about the metastable chain configurations are analyzed by introducing the Landau free energy as a function of the chain stretching order parameter. The binodal and spinodal lines, as well as the barrier heights between the stable and metastable states in the free energy landscape, are presented in both ensembles. In the loop region for the average force with dependence on the distance H ͑i.e., in the H-ensemble͒ a negative compressibility exists, whereas in the f-ensemble the average distance as a function of the force is strictly monotonic. The average fraction of imprisoned segments and the lateral force, taken as functions of the distance H or the average H, respectively, have different behaviors in the two ensembles. These results demonstrate a clear counterexample of a main principle of statistical mechanics, stating that all ensembles are equivalent in the thermodynamic limit. The authors show that the negative compressibility in the escape transition is a purely equilibrium result and analyze in detail the origin of the nonequivalence of the ensembles. It is argued that it should be possible to employ the escape transition and its anomalous behavior in macroscopically homogeneous, but microscopically inhomogeneous, materials.

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“…The goal of this paper is to present a rigorous analytical theory for a phase transition in a single macromolecule that has received much attention recently, namely the escape transition observed for an end-tethered chain compressed between two pistons [8][9][10][11][12][13][14][15][16][17][18]. At weak compressions, the chain is deformed uniformly to make a relatively thick pancake; the resistance force due to the compressed chain increases monotonously as the distance between two pistons, H, decreases.…”

Section: Introductionmentioning

confidence: 99%

“…The equilibrium properties of the escape transition were investigated thoroughly by scaling theory [8,9], numerical calculations [10,15], and computer modeling [13,14,18]. The main result relates the critical compression distance H * to the piston radius, L, and the chain length, Na.…”

Section: Introductionmentioning

confidence: 99%

“…For ideal chains, it is given by H * ϳ Na / L. Excluded-volume interactions change the relationship between H * and the N / L ratio, H * ϳ͑Na / L͒ /͑1− ͒ , where Ϸ 3 / 5, but the nature of the transition remains the same [8,9]. In their pioneering paper based on the blob picture of the compressed and escaped phases, Subramanian et al [8,9] predicted the possibility of metastable states and indicated the broad range of parameters within which these states exist. They also indicated that the free energy barrier to be overcome by a compressed chain in order to escape is due to the elastic free energy invested in the stretching.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Partition function, metastability, and kinetics of the escape transition for an ideal chain

2004

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An end-tethered polymer chain squeezed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flower-like conformation partially escaped from the gap. We present a rigorous analytical theory for the equilibrium and kinetic aspects of this phenomenon for a Gaussian chain. Applying the analogy with the problem of the adsorption of an ideal chain constrained by one of its ends, we obtain a closed analytical expression for the exact partition function. Various equilibrium thermodynamic characteristics (the fraction of imprisoned segments, the average compression, and lateral forces) are calculated as a function of the piston separation. The force versus separation curve is studied in two complementary statistical ensembles, the constant force and the constant confinement width ones. The differences in these force curves are significant in the transition region for large systems, but disappear for small systems. The effects of metastability are analyzed by introducing the Landau free energy as a function of the chain stretching, which serves as the order parameter. The phase diagram showing the binodal and two spinodal lines is presented. We obtain the barrier heights between the stable and metastable states in the free energy landscape. The mean first passage time, i.e., the lifetime of the metastable coil and flower states, is estimated on the basis of the Fokker-Planck formalism. Equilibrium analytical theory for a Gaussian chain is complemented by numerical calculations for a lattice freely jointed chain model.

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Interaction between Finite-Sized Particles and End Grafted Polymers

Cited by 76 publications

References 29 publications

Measurements of attractive forces between proteins and end-grafted poly(ethylene glycol) chains

Measurements of attractive forces between proteins and end-grafted poly(ethylene glycol) chains

Negative compressibility and nonequivalence of two statistical ensembles in the escape transition of a polymer chain

Partition function, metastability, and kinetics of the escape transition for an ideal chain

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