Deterministic mechanical model of T-killer cell polarization reproduces the wandering of aim between simultaneously engaged targets

T-killer cells of the immune system eliminate virus-infected and tumorous cells through direct cell-cell interactions. Reorientation of the killing apparatus inside the T cell to the T-cell interface with the target cell ensures specificity of the immune response. The killing apparatus can also oscillate next to the cell-cell interface. When two target cells are engaged by the T cell simultaneously, the killing apparatus can oscillate between the two interface areas. This oscillation is one of the most striking examples of cell movements that give the microscopist an unmechanistic impression of the cell's fidgety indecision. We have constructed a three-dimensional, numerical biomechanical model of the molecular-motor-driven microtubule cytoskeleton that positions the killing apparatus. The model demonstrates that the cortical pulling mechanism is indeed capable of orienting the killing apparatus into the functional position under a range of conditions. The model also predicts experimentally testable limitations of this commonly hypothesized mechanism of T-cell polarization. After the reorientation, the numerical solution exhibits complex, multidirectional, multiperiodic, and sustained oscillations in the absence of any external guidance or stochasticity. These computational results demonstrate that the strikingly animate wandering of aim in T-killer cells has a purely mechanical and deterministic explanation. © 2009 Kim, Maly

Structure–property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body

Biomolecular motor-driven microtubule translocation in the presence of shear flow: modeling microtubule deflection due to shear

We have previously demonstrated that shear flow aligns microtubules moving on kinesin-coated microchannels with the flow direction, and statistically analyzed the rate of microtubule alignment under different concentrations of kinesin as well as strengths of shear flow. These data qualitatively support the hypothesis that the alignment results from the leading ends of translocating microtubules bending into the direction of the flow due to viscous drag force. Here, we present a cantilever-beam model that quantitatively shows agreement between this hypothesis and observation. Specifically, the model couples the exact nonlinear solution for cantilever-beam deflection with drag coefficients determined by numerical simulations of microtubules in the presence of shear flow near a wall. Coupled with flexural rigidity results of our previous study (which used electric fields), the established model successfully predicts new experimental data for microtubule bending in response to shear flow, further supporting our hypothesis for the mechanism of microtubule alignment. We expect that the newly-calculated drag coefficients and beambending model may be useful for biophysical studies as well as interpretation of in vivo data and the design of kinesin/microtubule-based devices.close7

Leveraging Single Protein Polymers To Measure Flexural Rigidity

The micrometer-scale length of some protein polymers allows them to be mechanically manipulated in singlemolecule experiments. This provides a direct way to measure persistence length. We have used a double optical trap to elastically deform single microtubules and actin filaments. Axial extensional force was exerted on beads attached laterally to the filaments. Because the attachments are off the line of force, pulling the beads apart couples to local bending of the filament. We present a simple mechanical model for the resulting highly nonlinear elastic response of the dumbbell construct. The flexural rigidities of the microfilaments that were found by fitting the model to the experimentally observed force-distance curves are (7.1 ± 0.8) × 104 pN·n