Research ArticlePHYSICAL SCIENCES

Dramatic influence of patchy attractions on short-time protein diffusion under crowded conditions

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Science Advances  07 Dec 2016:
Vol. 2, no. 12, e1601432
DOI: 10.1126/sciadv.1601432
  • Fig. 1 Dynamics of crowded solutions probed by NSE.

    (A and B) Schematic description of the link between the scattering vector q and the length scale of the density fluctuations probed. Shown are the large-scale fluctuations probed at low q (A) and local dynamics probed at the nearest-neighbor length d (B), where for dense hard sphere systems, two well-separated mechanisms emerge (see text for details). (C and D) Comparison between the dynamic [D0/D(q), open symbols, left axis] and the static [S(q), from SAXS, solid line, right axis] structure factor for α-crystallin solutions at φ = 0.50 and T = 298 K (C) and for γB-crystallin solutions at φ = 0.16 and T = 308 K (D).

  • Fig. 2 Concentration dependence of the rescaled short-time diffusion at the nearest-neighbor distance Ds(q*)/D0.

    Comparison between the experimentally determined values [α-crystallin (filled black circles) and γB-crystallin (filled black squares)] and the computer simulation (open black circles) and theoretical (black line) (23) results for hard spheres. Moreover, computer simulation results are shown in (A) for the centrosymmetric potential given by Eq. 1 with the parameters b = 30, ε/εr = 3.95 (open inverse red triangles), b = 15, ε/εr = 3.45 (open blue diamonds), and b = 9, ε/εr = 2.8 (open green triangles), and in (B), the patchy particle model with b = 15, ε/εr = 2.5, and bp = 15, εpr = 9.5 and σ/σp = 6 (gray stars). In addition, the results for the centrosymmetric potential of (A) (open inverse red triangles) are displayed for comparison. Error bars are plotted for the NSE data of both proteins and are smaller than the symbols for all the γB-crystallin samples and the α-crystallin sample at the highest concentration. The insets show the respective potentials.

  • Fig. 3 Formation of transient clusters due to weak short-range attractions.

    Snapshots showing the configurations of particles at φ = 0.1 for centrosymmetric attraction (A), and with two additional attractive patches (B). The color code corresponds to the size of the cluster, Nc/N, to which the particle belongs. Here, Nc is the number of particles in a cluster, and N is the total number of particles in the system. Note that clusters are only transient and that the cluster size fluctuates in time. See movies S1 and S2 for the two simulations.

  • Fig. 4 Structural correlations in colloids with and without patchy interactions.

    Simulation results for the pair correlation function of colloids with centrosymmetric (dashed, orange) and additional patch interactions (solid, green) for φ = 0.1. For the centrosymmetric potential, the parameters are b = 30, ε/εr = 3.95, and for the patchy system b = 15, ε/εr = 2.5, bp = 15, εpr = 9.5, and σ/σp = 6.

  • Fig. 5 Distribution functions of the number of neighbors Nb of a colloidal particle.

    (A) Distribution functions for colloids interacting solely by the centrosymmetric potential at the volume fractions φ = 0.1, 0.17, 0.26, and 0.34. The potential parameters are b = 30 and ε/εr = 3.95. (B) Distribution functions for patchy colloids at φ = 0.1, 0.2, and 0.3. The potential parameters are b = 15, ε/εr = 2.5, bp = 15, and εpr = 9.5. Two colloids are considered as neighbors when their separation is smaller than the radial distance at the first minimum of the pair correlation function. (C) Relative number of patches Ncp(n) in direct contact with each other as a function of the volume fraction, where n is the number of contacts. Zero corresponds to no patch contact, unity to one, etc. Two patches are in contact when their interaction energy is half the minimal energy of the patch-patch interaction potential.

  • Table 1 Values of the second viral coefficient B2*, B2,cr*, and the relative distance to the critical point for the models used in the simulations.
    bε/εrεprB2*B2,cr*ΔB2* = (B2* − B2,cr*)/|B2,cr*|
    92.80−1.23−1.380.11
    153.450−1.12−1.290.13
    303.950−0.93−1.200.23
    152.59.5−2.60−2.870.09

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/12/e1601432/DC1

    movie S1. Transient cluster formation for particles with short-range attractions corresponding to snapshot in Fig. 3A.

    movie S2. Transient cluster formation for particles with attractive patches corresponding to snapshot in Fig. 3B.

  • Supplementary Materials

    This PDF file includes:

    • Legends for movies S1 and S2

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mp4 format). Transient cluster formation for particles with short-range attractions corresponding to snapshot in Fig. 3A.
    • movie S2 (.mp4 format). Transient cluster formation for particles with attractive patches corresponding to snapshot in Fig. 3B.

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