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A simple patchy colloid model for the phase behavior of lysozyme dispersions
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Image of FIG. 1.
FIG. 1.

Schematic drawing of a configuration of two model proteins, each carrying two attractive patches (gray areas). For the given configuration, the two particles repel each other according to the screened electrostatic potential in Eq. (3), with the surface charge assumed to be smeared out homogeneously over the sphere surface. There is no attractive interaction part since the center-to-center vector does not intersect simultaneously the shaded attractive patches on particles 1 and 2. See the main text for the definitions of the remaining symbols.

Image of FIG. 2.
FIG. 2.

Repulsive electrostatic pair potential part (thick dashed curve), angular-averaged attractive interaction part (thick dashed-dotted curve), and total perturbational pair potential (thick solid curve) for parameters at the critical point, where , using , . The parameters used in the perturbational interactions for the attractive and repulsive Yukawa-type potential parts are listed in Table I. At larger , is dominated by the attractive interaction part.

Image of FIG. 3.
FIG. 3.

Angular-averaged total perturbation potential, [see Eq. (1)] for various salt concentrations as indicated. With decreasing , the contact value of decreases due to the enlarged range of the electrostatic repulsion part.

Image of FIG. 4.
FIG. 4.

The phase diagram of aqueous lysozyme solutions for HEPES buffer, and , NaCl. The circles describe the experimentally found metastable gas-liquid coexistence curve (Ref. 38), the squares indicate the spinodal (Ref. 38), and the black triangles depict the experimental fluid-crystal coexistence curve. The two dashed curves show the calculated binodal and spinodal, respectively, for . The two solid curves describe the calculated binodal and spinodal, respectively, where the two curves account for an additional temperature dependence of the attractive potential depth with [see Eq. (8)]. The dashed-dotted curves are the calculated fluid-crystal coexistence curves for , with the interaction parameters determined from the experimental data at the critical point as explained in the text. In region I, a stable fluid phase is observed, whereas one finds a fluid-crystal coexistence in region II, a metastable gas-liquid coexistence in region III, and a pure crystalline phase in region IV.

Image of FIG. 5.
FIG. 5.

Gas-liquid coexistence curves of a lysozyme solution obtained experimentally from temperature quenches at four different salt concentrations: , 0.4 mol/l , 0.3 mol/l , and 0.2 mol/l . The filled symbols mark the critical points estimated from the experiment. The solid curves describe the coexistence curves as calculated from our model using a fixed value .

Image of FIG. 6.
FIG. 6.

Phase diagram of lysozyme for NaCl, HEPES buffer, and . The symbols indicate the experimental data points identical to the ones in Fig. 4. The solid curves describe the equilibrium phase diagram obtained from the anisotropic model. For comparison, the dashed lines describe the gas-liquid and fluid-solid coexistence curves are obtained from a purely isotropic pair potential. In both cases, is set equal to 5.


Generic image for table
Table I.

System and pair potential parameters used in the thermodynamic perturbation calculation of the metastable gas-liquid binodal/spinodal, and the stable fluid-solid coexistence curve (for salt concentrations as indicated). The attractive potential part parameters and are determined by Eqs. (24) and (25), respectively, using . For given , the parameters , , and (with a fixed value ) are determined from the experimental values for , , and , with fixed to 5.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A simple patchy colloid model for the phase behavior of lysozyme dispersions