“…If the amount of free PEG increases considerably with an increase in the total PEG concentration, an attractive depletion interaction can occur between PEGadsorbed proteins, as discussed by Kuhl et al 29 This effect has been referred to as hairy depletion. [30][31][32][33][34] Taking the rapid nucleation at 9% PEG into account, the boundary between repulsive and attractive forces is around 8-9% PEG in zinccontaining solutions.…”
Section: Discussionmentioning
confidence: 99%
“…Although we assume the adsorption of PEG onto proteins, nonadsorbing free PEG might exist in the solution. If the amount of free PEG increases considerably with an increase in the total PEG concentration, an attractive depletion interaction can occur between PEG-adsorbed proteins, as discussed by Kuhl et al This effect has been referred to as hairy depletion. − Taking the rapid nucleation at 9% PEG into account, the boundary between repulsive and attractive forces is around 8−9% PEG in zinc-containing solutions. 9 Solubility curve of the bc 1 -complex crystal at 15 °C. 10 (a) Amorphous aggregates precipitated in zinc-free solution with 50 μM bc 1 -complex and 9% PEG.…”
The hydrodynamic radius of a membrane protein, bc 1 -complex, in aqueous solutions was investigated using a dynamic light scattering technique. The essential unit in the solutions was found to take the dimer form of bc 1 -complex molecules. The aggregates exceeding 100 nm appeared with an increase in the crystallizing reagent, PEG, and the precipitation of an amorphous phase was observed. This feature was characteristic of zinc-free solutions. When 2 mM zinc was in the solutions, large aggregates of proteins were not observed, and single crystals of bc 1 -complex directly nucleated when the PEG concentration reached a critical level. The mutual diffusion coefficient of the dimers in the zinc-free solutions decreased with an increase in the protein concentration when the concentration of PEG was constant, indicating an attractive force between molecules. When the solution contained zinc, the coefficient increased with an increase in the protein concentration, indicating a repulsive force between molecules.
“…If the amount of free PEG increases considerably with an increase in the total PEG concentration, an attractive depletion interaction can occur between PEGadsorbed proteins, as discussed by Kuhl et al 29 This effect has been referred to as hairy depletion. [30][31][32][33][34] Taking the rapid nucleation at 9% PEG into account, the boundary between repulsive and attractive forces is around 8-9% PEG in zinccontaining solutions.…”
Section: Discussionmentioning
confidence: 99%
“…Although we assume the adsorption of PEG onto proteins, nonadsorbing free PEG might exist in the solution. If the amount of free PEG increases considerably with an increase in the total PEG concentration, an attractive depletion interaction can occur between PEG-adsorbed proteins, as discussed by Kuhl et al This effect has been referred to as hairy depletion. − Taking the rapid nucleation at 9% PEG into account, the boundary between repulsive and attractive forces is around 8−9% PEG in zinc-containing solutions. 9 Solubility curve of the bc 1 -complex crystal at 15 °C. 10 (a) Amorphous aggregates precipitated in zinc-free solution with 50 μM bc 1 -complex and 9% PEG.…”
The hydrodynamic radius of a membrane protein, bc 1 -complex, in aqueous solutions was investigated using a dynamic light scattering technique. The essential unit in the solutions was found to take the dimer form of bc 1 -complex molecules. The aggregates exceeding 100 nm appeared with an increase in the crystallizing reagent, PEG, and the precipitation of an amorphous phase was observed. This feature was characteristic of zinc-free solutions. When 2 mM zinc was in the solutions, large aggregates of proteins were not observed, and single crystals of bc 1 -complex directly nucleated when the PEG concentration reached a critical level. The mutual diffusion coefficient of the dimers in the zinc-free solutions decreased with an increase in the protein concentration when the concentration of PEG was constant, indicating an attractive force between molecules. When the solution contained zinc, the coefficient increased with an increase in the protein concentration, indicating a repulsive force between molecules.
“…The former attraction can be shown 17,18 to be proportional to an effective Hamaker constant ͑A 1 1/2 − A 2 1/2 ͒ 2 where A 1 is the Hamaker constant for the colloidal particle and A 2 refers to the adsorbed layer consisting of grafted polymers and the dispersive medium solvent. Equation ͑9͒ permits a transposition from the R ͑p͒ -͑c͒ curve to ͑p͒ -͑c͒ , which is the phase diagram one commonly sees in colloidal experiments.…”
Treating the repulsive part of a pairwise potential by the hard-sphere form and its attractive part by the effective depletion potential form, we calculate using this model potential the colloidal domains of phase separation. Differing from the usual recipe of applying the thermodynamic conditions of equal pressure and equal chemical potential where the branches of coexisting phases are the ultimate target, we employ the free energy density minimization approach [G. F. Wang and S. K. Lai, Phys. Rev. E 70, 051402 (2004)] to crosshatch the domains of equilibrium phases, which consist of the gas, liquid, and solid homogeneous phases as well as the coexistence of these phases. This numerical procedure is attractive since it yields naturally the colloidal volume of space occupied by each of the coexisting phases. In this work, we first examine the change in structures of the fluid and solid free energy density landscapes with the effective polymer concentration. We show by explicit illustration the link between the free energy density landscapes and the development of both the metastable and stable coexisting phases. Then, attention is paid to the spatial volumes predicted at the triple point. It is found here that the volumes of spaces of the three coexisting phases at the triple point vary one dimensionally, whereas for the two coexisting phases, they are uniquely determined.
“…During recent years, the behavior of colloidal particles immersed in an electrolyte solution containing small particles has been extensively studied experimentally [1][2][3], theoretically [4][5][6][7][8], and by simulations [9][10][11]. In addition to van der Waals and double-layer interactions, a depletion interaction was present in such systems.…”
Section: Introductionmentioning
confidence: 98%
“…In their theory, a second-order perturbation approach was used to calculate the free energy. Rao and Ruckenstein [4,5] examined the phase behavior of systems involving steric, depletion, and van der Waals interactions.…”
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