Fig 1.
(A) One-to-one comparison of experimental images of coiled platelets marginal band (reused with permissions from: Diagouraga et al. Journal of Cell Biology. 204:177–185. DOI: 10.1083/jcb.201306085) and manually-fitted overcurved circles. Overcurvature is listed near each plotted curve. (B) Examples of the overcurved circles. (C) Illustration of circular tube modeling the initial flat peripheral ring of microtubules. (D,E) Models of coiled marginal band in platelets with different overcurvature and non-zero thickness.
Fig 2.
Overcurvature (Op)–Dimensionless volume (v) phase diagram of platelets model morphologies.
Area I corresponds to resting platelets with overcurvature = 1; Area II stands for activated platelets (hypothetically reversible activation); Area III is where platelets become sphered (irreversible activation).
Fig 3.
Possible mechanism of the overcurvature formation.
Molecular motors induce relative sliding of microtubules, which are additionally cross-linked by bridge proteins. This leads to the formation of excessive curvature in the microtubules bundle, which manifests itself by the out-of-plane coiling of marginal band.
Fig 4.
Illustration of platelet surface optimization problem.
The surface is made by the revolution of profile {x(t), y(t)} (thick line) around the ordinate axis. It consists of two parts: free (light red) and attached to the marginal band (green). Point t = u corresponds to the contact between one of the mobile subdomain and the fixed part, and points t = 0 and t = T are where the the surface intersects the axis x = 0.
Fig 5.
All possible axisymmetric profiles of resting platelets as obtained by the solution of variational problem (4).
Black circles correspond to the marginal band cross-sections. Volume increases from top to bottom, curvature increases when going from the first to the fifth row, but decreases for the last row.
Fig 6.
Scheme of the construction of blood platelet shape model (A–E) and the soap bubble supported by the overcurved wire ring (F), which presents the real-world approximation of the optimization problem solution for the mobile surface parts.
Fig 7.
Example of platelet model with 20 pseudopodia.
Their total relative volume is 0.01.
Fig 8.
A. Light scattering model obtained by filling of platelet model with dipoles; incident wave propagates from below. B. Result of light scattering simulation—controur plot of S11 element of the Mueller matrix in logarithmic scale versus polar and azimuthal scattering angles.