CellDynaMo–stochastic reaction-diffusion-dynamics model: Application to search-and-capture process of mitotic spindle assembly

Strength, deformability, damage and fracture toughness of fibrous material networks: Application to fibrin clots

A multiscale approach to mechanical testing in silico, which combines discrete particle-based simulations and large-deformation continuum mechanics, is developed to explore the mechanobiology, damage and fracture of fibrous materials. Combined with tensile testing in vitro of fibrin networks, the mechanical scaffold of blood clots, mechanisms of fibrin rupture are investigated that underlie embolization of intravascular blood clots (thrombi), a major cause of ischemic stroke and pulmonary embolism. At moderate strains (<50%), no network damage is observed. At larger strains, damage evolves and the network ruptures when only ∼5% of fibers and branch points break, opening a ∼150 µm rupture zone in silico. A continuum model that predicts macroscopic behavior for arbitrary states of deformation, including damage evolution, is constructed from the mesoscopic simulations with direct correlation of the damage parameter and the number of broken bonds in contrast to phenomenological damage laws. The continuum model can access length- and time-scales that are inaccessible in discrete simulations, which allows prediction of fracture toughness, the material property that determines rupture resistance in the presence of defects. This critical property for a fibrin network at physiological solid volume fraction and accounting for the dramatic decrease in volume (∼90%) under uniform tensile stressing is predicted to be 2.5-7.7 J/m2, in good agreement with experiment. These insights into mechanisms of blood clot fracture can lead to the development of new approaches to predict and prevent embolization of intravascular thrombi. The multiscale approach developed is applicable to a wide range of fibrous network-based biomaterials. STATEMENT OF SIGNIFICANCE: Dummy.

Exploring effects of platelet contractility on the kinetics, thermodynamics, and mechanisms of fibrin clot contraction

Mechanisms of blood clot contraction - platelet-driven fibrin network remodeling, are not fully understood. We developed a detailed computational ClotDynaMo model of fibrin network with activated platelets, whose clot contraction rate for normal 450,000/µl human platelets depends on serum viscosity η, platelet filopodia length l, and weakly depends on filopodia traction force f and filopodia extension-retraction speed v. Final clot volume is independent of η, but depends on v, f and l. Analysis of ClotDynaMo output revealed a 2.24 TJ/mol clot contraction free energy change, with ~67% entropy and ~33% internal energy changes. The results illuminate the "optimal contraction principle" that maximizes volume change while minimizing energy cost. An 8-chain continuum model of polymer elasticity containing platelet forces, captures clot contractility as a function of platelet count, η and l. The ClotDynaMo and continuum models can be extended to include red blood cells, variable platelet properties, and mechanics of fibrin network.

Optimal strategies for correcting merotelic chromosome attachments in anaphase

Accurate chromosome segregation in mitosis depends on proper connections of sister chromatids, through microtubules, to the opposite poles of the early mitotic spindle. Transiently, many inaccurate connections are formed and rapidly corrected throughout the mitotic stages, but a small number of merotelic connections, in which a chromatid is connected to both spindle poles, remain lagging at the spindle's equator in anaphase. Most of the lagging chromatids are eventually moved to one or the other pole, likely by a combination of microtubules' turnover and the brute force of pulling by the microtubules' majority from the one pole against the microtubules' minority from the other pole. We use computer simulations from two stochastic models (1D and full 3D CellDynaMo model) combining force balances and microtubules' dynamics for the lagging chromatids to investigate what maximizes the percentage of segregated laggards. We find that a) brute force tug-of-war with slow (< 0.0001 s-1) microtubules' detachment rate can move asymmetric laggards to the poles in limited time, b) rapid (> 0.01 s-1) microtubules' detachment rate leads to a significant loss of the laggards, and c) intermediate (~ 0.001 s-1) microtubules' detachment rate ensures higher than 90% accuracy of segregation. The simulations also shed light on the waiting time required to correct the merotelic errors in anaphase and on the roles of chromatid-attached microtubule number and Aurora B-mediated, spatially graded regulation of microtubule kinetics in anaphase.

Microtubule search-and-capture model evaluates the effect of chromosomal volume conservation on spindle assembly during mitosis

Variation in the chromosome numbers can arise from the erroneous mitosis or fusion and fission of chromosomes. While the mitotic errors lead to an increase or decrease in the overall chromosomal substance in the daughter cells, fission and fusion keep this conserved. Variations in chromosome numbers are assumed to be a crucial driver of speciation. For example, the members of the muntjac species are known to have very different karyotypes with the chromosome numbers varying from 2n=70+3B in the brown brocket deer to 2n=46 in the Chinese muntjac and 2n=6/7 in the Indian muntjac. The chromosomal content in the nucleus of these closely related mammals is roughly the same and various chromosome fusion and fission pathways have been suggested as the evolution process of these karyotypes. Similar trends can also be found in lepidoptera and yeast species which show a wide variation of chromosome numbers. The effect of chromosome number variation on the spindle assembly time and accuracy is still not properly addressed. We computationally investigate the effect of conservation of the total chromosomal substance on the spindle assembly during prometaphase. Our results suggest that chromosomal fusion pathways aid the microtubule-driven search and capture of the kinetochore in cells with monocentric chromosomes. We further report a comparative analysis of the site and percentage of amphitelic captures, dependence on cell shape, and position of the kinetochore in respect to chromosomal volume partitioning.

Mechanical fatigue testing in silico: Dynamic evolution of material properties of nanoscale biological particles

Biological particles have evolved to possess mechanical characteristics necessary to carry out their functions. We developed a computational approach to "fatigue testing in silico", in which constant-amplitude cyclic loading is applied to a particle to explore its mechanobiology. We used this approach to describe dynamic evolution of nanomaterial properties and low-cycle fatigue in the thin spherical encapsulin shell, thick spherical Cowpea Chlorotic Mottle Virus (CCMV) capsid, and thick cylindrical microtubule (MT) fragment over 20 cycles of deformation. Changing structures and force-deformation curves enabled us to describe their damage-dependent biomechanics (strength, deformability, stiffness), thermodynamics (released and dissipated energies, enthalpy, and entropy) and material properties (toughness). Thick CCMV and MT particles experience material fatigue due to slow recovery and damage accumulation over 3-5 loading cycles; thin encapsulin shells show little fatigue due to rapid remodeling and limited damage. The results obtained challenge the existing paradigm: damage in biological particles is partially reversible owing to particle's partial recovery; fatigue crack may or may not grow with each loading cycle and may heal; and particles adapt to deformation amplitude and frequency to minimize the energy dissipated. Using crack size to quantitate damage is problematic as several cracks might form simultaneously in a particle. Dynamic evolution of strength, deformability, and stiffness, can be predicted by analyzing the cycle number (N) dependent damage, [Formula: see text] , where α is a power law and Nf is fatigue life. Fatigue testing in silico can now be used to explore damage-induced changes in the material properties of other biological particles. STATEMENT OF SIGNIFICANCE: Biological particles possess mechanical characteristics necessary to perform their functions. We developed "fatigue testing in silico" approach, which employes Langevin Dynamics simulations of constant-amplitude cyclic loading of nanoscale biological particles, to explore dynamic evolution of the mechanical, energetic, and material properties of the thin and thick spherical particles of encapsulin and Cowpea Chlorotic Mottle Virus, and the microtubule filament fragment. Our study of damage growth and fatigue development challenge the existing paradigm. Damage in biological particles is partially reversible as fatigue crack might heal with each loading cycle. Particles adapt to deformation amplitude and frequency to minimize energy dissipation. The evolution of strength, deformability, and stiffness, can be accurately predicted by analyzing the damage growth in particle structure.