Research ArticleBIOPHYSICS

Rapid and inefficient kinetics of sickle hemoglobin fiber growth

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Science Advances  13 Mar 2019:
Vol. 5, no. 3, eaau1086
DOI: 10.1126/sciadv.aau1086
  • Fig. 1 Semi-automated tracking of HbS fiber assembly dynamics.

    (A) Groups of HbS fibers (spherulites) imaged by DIC microscopy. Groups of HbS fibers are called spherulites. Individual spherulites are the result of homogeneous nucleation in solution, followed by heterogeneous nucleation of new fibers off of existing ones. (B) Heterogeneous nucleation of new HbS fibers off the side of existing fibers. Arrows indicate the nucleation site of the new fiber. (C) Result of function fitting within the user-defined region of interest (left; green lines) for an example HbS fiber (right). Red dots are the individual fiber backbone positions estimated as in (D). The blue line is the determined fiber axis fit to the backbone positions. The cyan dot is the position of the fiber end estimated as in (E). (D) Pixel intensity values from a cross section of an HbS fiber imaged by DIC microscopy. The line is the best-fit Gaussian first derivative to the pixel values (Eq. 7). The red dot indicates the function mean, taken to be the backbone position of the HbS fiber. (E) DIC values along the fiber axis determined from fitting the HbS fiber backbone positions. The line is the best-fit Gaussian survival function to the contrast values. The cyan dot is the function mean, taken to be the position of the fiber end. a.u., arbitrary units. (F) Kymograph showing HbS fiber growth over time. Position is along the vertical axis, while time is along the horizontal axis. Scale bars, 30 s and 5 μm for the horizontal and vertical bars, respectively. (G) Semi-automated tracking results for the HbS fiber shown in (F). (H) Growth rates (vg) as a function of HbS activity (γC). Activity coefficients were determined as described in (11). Circles are the values estimated from semi-automated tracking at 25°C (black) and 37°C (gray). Squares are reported values from (17), diamonds are reported values from (11), and the triangle is a reported value from (13). Lines are the projected trends from the data in (11). Vertical error bars are SD of the growth rate (n = 126 and 110 fibers at 25° and 37°C, respectively). Horizontal error bars are 10% uncertainty in the concentration due to pipetting. All experimental images are an average of 25 frames and were collected at 25°C and C = 3.1 mM.

  • Fig. 2 DIC signal is directly proportional to the number of HbS fibers.

    (A) HbS fibers grown at 37°C and C = 2.3 mM. Arrowheads indicate the two ends of the axis used to construct the kymograph shown in (B). The yellow line is the cross section used in (C). (B) Kymograph of the fiber bundle shown in (A). Position is on the vertical axis and time is on the horizontal axis. Scale bars, 30 s and 5 μm along the horizontal and vertical axes, respectively. Arrows indicate the time points shown in (C) to (E). (C) DIC signal along a cross section of an HbS fiber in time. Arrows are the time points corresponding to (B). (D) Normalized pixel values (circles) along the cross section at the time points indicated by the arrows in (B) and (C). Lines are the best fit of Eq. 7 to the individual pixel values. (E) DIC signal intensity along the fiber cross section as a function of time. Arrows indicate the time points corresponding to (B) to (D). Bars show the time span over which the adjacent value was calculated via averaging of the individual signal values. (F) DIC images showing an example of heterogeneous nucleation (left) and the intersection of two separate HbS fibers (right). Red and yellow arrowheads indicate the region where the intensity value was calculated for the multifiber region (nucleation or intersection) or the adjacent region, respectively. Scale bars, 2 μm. (G) Boxplot of the normalized DIC signal values for the indicated analysis regions. Values were normalized to the average DIC signal (minimum of two samples) from the regions adjacent to the corresponding nucleation or intersection site. Data include samples from a total of 70 fibers, 38 and 32 fibers at 25° and 37°C, respectively.

  • Fig. 3 Rapid kinetics of HbS fiber self-assembly.

    (A) Projected trend in the variance of the length displacement (ΔL) distribution as a function of frame averaging from the original acquisition rate (25 Hz; ti = 1/25 s). Blue and red lines are the portion contributed by the experimental noise and assembly dynamics, respectively, while the black line is the sum of the two. The dashed line marks the edge of the regimes where either experimental noise or assembly dynamics dominate the experimentally measured variance, as determined by intersection between the projected trends. (B and C) Mean (B) and variance (C) of the ΔL distribution as a function of frame averaging for samples of 3.1 mM hemoglobin at 25°C (n = 126 fibers from three samples). (D and E) Mean and variance values for all fibers at 25°C are shown (gray dots). Solid lines are the same as in (B) and (C). Dashed lines show the expected trend using the values of vg and Dp from the trends observed in (11). In (E), the experimental noise contribution is the same for both the solid and dashed lines. Values are shown on a log scale to facilitate comparison against the projected trend from the 1D model. (F and G) Mean (F) and variance (G) of the ΔL distribution as a function of frame averaging for samples of 2.3 mM hemoglobin at 37°C (n = 110 fibers from three samples). Black lines in (B) and (F) are the best fit of Eq. 5. Black lines in (C) and (G) are the best fit of Eq. 6 to the values estimated from all fibers. Blue and red lines in (C) and (G) show the portion of the fit contributed by the experimental noise and assembly dynamics, respectively. In all plots, the open circles are the median value calculated across all fibers. Error bars are 95% confidence intervals obtained from bootstrapping.

  • Fig. 4 1D model underestimates the kinetics of assembly for multistranded polymers.

    Estimated on-rate (A) and off-rate (B) constant as a function of temperature. Note that the rates shown here are per HbS fiber end, rather than per individual protofilament. Circles denote the values from this study, while diamonds are reported values from (11), squares are reported values from (12), and triangles are reported values from (13). Solid and dashed lines are the best-fit exponential trend to the data from this study and from (11), respectively. *P < 0.001 by one-way analysis of variance (ANOVA). (C) Single–time point tracking precision as a function of sampling frequency when using our semi-automated approach. Values are those extracted from the fit to the experimental noise shown in Fig. 3C for the data collected at 25°C.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/3/eaau1086/DC1

    Supplementary Discussion

    Fig. S1. HbS fiber nucleation and growth occur throughout the sample.

    Fig. S2. MSD analysis confirms variance analysis.

    Table S1. Exact values from ANOVA statistical tests.

    Movie S1. HbS fiber assembly.

    Movie S2. Bundle of HbS fibers grown along the same trajectory.

    Reference (39)

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Discussion
    • Fig. S1. HbS fiber nucleation and growth occur throughout the sample.
    • Fig. S2. MSD analysis confirms variance analysis.
    • Table S1. Exact values from ANOVA statistical tests.
    • Legends for movies S1 and S2
    • Reference (39)

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mov format). HbS fiber assembly.
    • Movie S2 (.mov format). Bundle of HbS fibers grown along the same trajectory.

    Files in this Data Supplement:

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