Threshold of microvascular occlusion: injury size defines the thrombosis scenario

Damage to the blood vessel triggers formation of a hemostatic plug, which is meant to prevent bleeding, yet the same phenomenon may result in a total blockade of a blood vessel by a thrombus, causing severe medical conditions. Here, we show that the physical interplay between platelet adhesion and hemodynamics in a microchannel manifests in a critical threshold behavior of a growing thrombus. Depending on the size of injury, two distinct dynamic pathways of thrombosis were found: the formation of a nonocclusive plug, if injury length does not exceed the critical value, and the total occlusion of the vessel by the thrombus otherwise. We develop a mathematical model that demonstrates that switching between these regimes occurs as a result of a saddle-node bifurcation. Our study reveals the mechanism of self-regulation of thrombosis in blood microvessels and explains experimentally observed distinctions between thrombi of different physical etiology. This also can be useful for the design of platelet-aggregation-inspired engineering solutions.Comment: 7 pages, 5 figures + Supplementary informatio

Tubulin bond energies and microtubule biomechanics determined from nanoindentation in silico

Microtubules, the primary components of the chromosome segregation machinery, are stabilized by longitudinal and lateral non-covalent bonds between the tubulin subunits. However, the thermodynamics of these bonds and the microtubule physico-chemical properties are poorly understood. Here, we explore the biomechanics of microtubule polymers using multiscale computational modeling and nanoindentations in silico of a contiguous microtubule fragment. A close match between the simulated and experimental force-deformation spectra enabled us to correlate the microtubule biomechanics with dynamic structural transitions at the nanoscale. Our mechanical testing revealed that the compressed MT behaves as a system of rigid elements interconnected through a network of lateral and longitudinal elastic bonds. The initial regime of continuous elastic deformation of the microtubule is followed by the transition regime, during which the microtubule lattice undergoes discrete structural changes, which include first the reversible dissociation of lateral bonds followed by irreversible dissociation of the longitudinal bonds. We have determined the free energies of dissociation of the lateral (6.9+/-0.4 kcal/mol) and longitudinal (14.9+/-1.5 kcal/mol) tubulin-tubulin bonds. These values in conjunction with the large flexural rigidity of tubulin protofilaments obtained (18,000-26,000 pN*nm^2), support the idea that the disassembling microtubule is capable of generating a large mechanical force to move chromosomes during cell division. Our computational modeling offers a comprehensive quantitative platform to link molecular tubulin characteristics with the physiological behavior of microtubules. The developed in silico nanoindentation method provides a powerful tool for the exploration of biomechanical properties of other cytoskeletal and multiprotein assemblie

Ring coupler moving via the 'forced walk' mechanism [Microtubule depolymerization as a biological machine]

This video shows the microtubule-depolymerization dependent motions of a ring coupler. Although the plane of the ring oscillates slightly, it remains motionlessly on the microtubule wall until the shortening end comes by (thermal energy is not sufficient to cause Brownian 'random walks' with any appreciable frequency). Bending protofilaments, however, can push on the linkers, forcing the ring to walk in front of the protofilaments' flare. This directed motion is highly deterministic, but the exact pathway of the ring's transitions between successive minimum energy configurations is stochastic and varies in repeated calculations. A strongly bound ring retards the rate with which the protofilaments bend, so it slows the rate of microtubule shortening. Furthermore, such tight binding reduces the useful work that can be performed by the microtubule, e.g. in moving a cargo, but it ensures a stable ring's attachment to the microtubule end, even if the flared protofilaments shorten or the microtubule begins to polymerize. It has been therefore suggested that a reasonable compromise between a reduced efficiency of force transduction and an increased strength of attachment might be appropriate for the coupler in an organism like S. cerevisiae, where a kinetochore is stably attached to only one microtubule and the chromosomes do not move far during Anaphase AComponente Curricular::Educação Superior::Ciências Biológicas::Morfologi

Ring coupler moving via the 'forced walk' mechanism [Microtubule depolymerization as a biological machine]

This video shows the microtubule-depolymerization dependent motions of a ring coupler. Although the plane of the ring oscillates slightly, it remains motionlessly on the microtubule wall until the shortening end comes by (thermal energy is not sufficient to cause Brownian 'random walks' with any appreciable frequency). Bending protofilaments, however, can push on the linkers, forcing the ring to walk in front of the protofilaments' flare. This directed motion is highly deterministic, but the exact pathway of the ring's transitions between successive minimum energy configurations is stochastic and varies in repeated calculations. A strongly bound ring retards the rate with which the protofilaments bend, so it slows the rate of microtubule shortening. Furthermore, such tight binding reduces the useful work that can be performed by the microtubule, e.g. in moving a cargo, but it ensures a stable ring's attachment to the microtubule end, even if the flared protofilaments shorten or the microtubule begins to polymerize. It has been therefore suggested that a reasonable compromise between a reduced efficiency of force transduction and an increased strength of attachment might be appropriate for the coupler in an organism like S. cerevisiae, where a kinetochore is stably attached to only one microtubule and the chromosomes do not move far during Anaphase AComponente Curricular::Educação Superior::Ciências Biológicas::Morfologi

Ring coupler moving via the 'forced walk' mechanism: a view of a single protofilament and its associated ring-subunit

This video shows configurations for a single protofilament and an associated ring subunit (Dam1 heterodecamer) for a ring-microtubule pair. Here, tubulin monomers are shown as green bars (separated with dots) that correspond to their vertical axes, so each linker ends approximately 2 nm away from the green line at the monomer's surface (shown as spheres on the first image only). The ring subunit and its linker move in 3D, but the movie shows only their 2D projection onto the plane of this protofilament. Each linker is predicted to walk in 8 nm steps along the same PF, just like a kinesin. In the current case, however, the energy for linker stepping comes from the protofilament bending to its equilibrium configuration. Although the individual linkers occasionally step backwards, the whole ring moves unidirectionally towards the MT minus endComponente Curricular::Educação Superior::Ciências Biológicas::Morfologi

Model of a depolymerizing microtubule [Microtubule depolymerization as a biological machine]

This video shows the shortening plus end of a microtubule polymer with 13 protofilaments, which are arranged in a 3-start left handed helix (the most common configuration in cells). Tubulin dimers, consisting of alpha-tubulin (dark green) and beta-tubulin (light green), form a hollow tube 25 nm in a diameter. In this molecular-mechanical model of a microtubule each tubulin interacts via defined energy relationships with its longitudinal and lateral neighbors. The calculations begin with an initial configuration in which all protofilaments are perfectly straight. However, the minimum energy configuration for each pair of longitudinally attached tubulins is when they form roughly 22 degree angle. As a result, each protofilament tends to curl and form a 'ram's horn'. Tubulin dimers begin to dissociate from the protofilaments ends soon after they loose their lateral bonds (in the model the dissociation of the terminal dimer takes place when it bends greater than 90 degrees away from the microtubule axis)Componente Curricular::Educação Superior::Ciências Biológicas::Morfologi

Ring coupler moving via a biased-diffusion mechanism [Microtubule depolymerization as a biological machine]

This video shows a shortening microtubules end 'Depolymerizing microtubule' and a ring coupler (red), which was modeled after the Dam1/DASH kinetochore complex from budding yeast. Each ring subunit binds to the middle of the outer surface of beta-tubulin with a flexible linker 4 nm in length (blue). This calculation shows a ring with 13 subunits, but the rings with more subunits are expected to behave similarly because the number of bonds that the ring can establish with the microtubule wall is determined by the symmetry of the microtubule lattice (13-fold). In this calculation, the energy of interaction between each linker and tubulin is low (3 kBT, where kB is Boltzmann constant) relative to the thermal energy, so the ring diffuses rapidly on the MT wall (the video stops when the ring moves beyond the microtubule segment that was used for this calculation). As the plus end of the microtubule disassembles, the ring's displacements become biased, i.e. they occur on average away from the shortening end and towards the bottom of the screen. This is because the ring motion in the opposite direction is interrupted by a mechanical barrier formed by the flared protofilaments. The energy necessary to straighten protofilaments is so high that the ring's thermal energy is not sufficient to pass this barrier. Although technically, the bending protofilaments push on the weakly bound ring when it comes in contact, this aspect of their interactions is mechanically insignificant, due to the low resistance of ring sliding. As a result, such a ring is expected to have no impact on the rate at which the microtubule shortensComponente Curricular::Educação Superior::Ciências Biológicas::Morfologi

Model of a depolymerizing microtubule [Microtubule depolymerization as a biological machine]

This video shows the shortening plus end of a microtubule polymer with 13 protofilaments, which are arranged in a 3-start left handed helix (the most common configuration in cells). Tubulin dimers, consisting of alpha-tubulin (dark green) and beta-tubulin (light green), form a hollow tube 25 nm in a diameter. In this molecular-mechanical model of a microtubule each tubulin interacts via defined energy relationships with its longitudinal and lateral neighbors. The calculations begin with an initial configuration in which all protofilaments are perfectly straight. However, the minimum energy configuration for each pair of longitudinally attached tubulins is when they form roughly 22 degree angle. As a result, each protofilament tends to curl and form a 'ram's horn'. Tubulin dimers begin to dissociate from the protofilaments ends soon after they loose their lateral bonds (in the model the dissociation of the terminal dimer takes place when it bends greater than 90 degrees away from the microtubule axis)Componente Curricular::Educação Superior::Ciências Biológicas::Morfologi