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

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium _Escherichia coli_, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the _in vivo_ MinDE localization dynamics by accounting for the established properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally

Equilibria of Idealized Confined Astral Microtubules and Coupled Spindle Poles

Positioning of the mitotic spindle through the interaction of astral microtubules with the cell boundary often determines whether the cell division will be symmetric or asymmetric. This process plays a crucial role in development. In this paper, a numerical model is presented that deals with the force exerted on the spindle by astral microtubules that are bent by virtue of their confinement within the cell boundary. It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable. Asymmetric stable equilibria also exist, and two or more stable positions can exist simultaneously. The theory poses new types of questions for experimental research. Regarding the cases of symmetric spindle positioning, it is necessary to ask whether the microtubule parameters are controlled by the cell so that the bending mechanics favors symmetry. If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry. Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton

Actomyosin-Dependent Cortical Dynamics Contributes to the Prophase Force-Balance in the Early Drosophila Embryo

embryo mitotic spindle during prophase depends upon a balance of outward forces generated by cortical dynein and inward forces generated by kinesin-14 and nuclear elasticity. Myosin II is known to contribute to the dynamics of the cell cortex but how this influences the prophase force-balance is unclear. mutants displaying abnormally small actin caps but normal prophase spindle length in late prophase, myosin II inhibition produced very short spindles.These results suggest that two complementary outward forces are exerted on the prophase spindle by the overlying cortex. Specifically, dynein localized on the mechanically firm actin caps and the actomyosin-driven contraction of the deformable soft patches of the actin cortex, cooperate to pull astral microtubules outward. Thus, myosin II controls the size and dynamic properties of the actin-based cortex to influence the spacing of the poles of the underlying spindle during prophase

An Experimental and Computational Study of Effects of Microtubule Stabilization on T-Cell Polarity

T-killer cells eliminate infected and cancerous cells with precision by positioning their centrosome near the interface (immunological synapse) with the target cell. The mechanism of centrosome positioning has remained controversial, in particular the role of microtubule dynamics in it. We re-examined the issue in the experimental model of Jurkat cells presented with a T cell receptor-binding artificial substrate, which permits controlled stimulation and reproducible measurements. Neither 1-µM taxol nor 100-nM nocodazole inhibited the centrosome positioning at the “synapse” with the biomimetic substrate. At the same time, in micromolar taxol but not in nanomolar nocodazole the centrosome adopted a distinct peripheral rather than the normally central position within the synapse. This effect was reproduced in a computational energy-minimization model that assumed no microtubule dynamics, but only a taxol-induced increase in the length of the microtubules. Together, the experimental and computational results indicate that microtubule dynamics are not essential for the centrosome positioning, but that the fit of the microtubule array in the deformed body of the conjugated T cell is a major factor. The possibility of modulating the T-cell centrosome position with well-studied drugs and of predicting their effects in silico appears attractive for designing anti-cancer and antiviral therapies

A global bifurcation and the appearance of a one-dimensional spiral wave in excitable media

It is well known that excitable media can sustain "fast" stable traveling pulses of excitation. In models for which analysis is tractable, the fast pulse solution is known to appear through a saddlenode bifurcation accompanied by a "slow" unstable traveling pulse. Furthermore, the uniform rest state is also a stable solution. It is generally assumed that the boundary between the basins of attractions of the rest state and fast pulse (i.e., threshold) consists of the stable manifold of the slow pulse. We use numerical experiments to explore this issue. Our results indicate that, near the saddle-node bifurcation, the stable manifold of the slow pulse does indeed act as the threshold between the rest state and fast pulse. However, further away from the saddle-node bifurcation, a global bifurcation involving the heteroclinic connections between slow and fast pulses occurs. This bifurcation gives rise to an unstable periodic solution that has been referred to as a one-dimensional spiral wave. Beyond the bifurcation point, the stable manifold of the one-dimensional spiral wave appears to act as the threshold between the rest state and fast pulse. © 2009 Society for Industrial and Applied Mathematics

Get round and stiff for mitosis

Cell rounding is a common feature of cell division. The spherical shape that cells adopt during mitosis is apparently neither a simple detachment nor a global softening or stiffening that allows cells to adopt what seems to be a mechanical equilibrium. It is a highly complex mechanical transformation by which membrane folding and peripheral signals focusing can match spindle size in order to ensure a proper cell division. Recent new insight into the mechanism involved will prompt the scientific community to focus on the regulation of the physical links that exist between the lipid bilayer membrane and the underlying actin cytoskeleton since it now appears that these will strongly influence some crucial cellular events such as the spatial organization of cell division

Springs, clutches and motors : driving forward kinetochore mechanism by modelling

As a mechanical system, the kinetochore can be viewed as a set of interacting springs, clutches and motors; the problem of kinetochore mechanism is now one of understanding how these functional modules assemble, disassemble and interact with one another to give rise to the emergent properties of the system. The sheer complexity of the kinetochore system points to a future requirement for data-driven mathematical modelling and statistical analysis based on quantitative empirical measurement of sister kinetochore trajectories. Here, we review existing models of chromosome motion in the context of recent advances in our understanding of kinetochore molecular biology