Systems Biomechanics of the Cell - Systems Biomechanics of the Cell - page 40

equilibrium centrosome position for the given microtubule length. In contrast, the
microtubules in the two-dimensional (flat) equilibrium aster can be bent in both
directions from the unstrained direction of their emanation from the centrosome
(Figs. 18 and 19 ). This gives the aster an “uncombed” appearance and is at the
source of the memory effects exhibited by such an aster. Its structure depends on
past perturbations, and the equilibrium position of the centrosome depends on the
history of the microtubule length changes.
Another theoretical demonstration of irreversibility is provided by the model
(Kim and Maly 2009 ) for the reorientation of the cell body in cytotoxic lympho-
cytes toward target cells engaged sequentially. The ability of lymphocytes to destroy
sequentially engaged targets relies on reorientation of the secretory apparatus that
directs secretion of cytotoxic granules and is associated with the centrosome and
the microtubules (Valitutti et al. 1996 ; Depoil et al. 2005 ). From the experimental
observations by Kuhn and Poenie ( 2002 ) of the movement and structure in the cyto-
toxic T lymphocytes, Kim and Maly ( 2009 ) derive the following idealizations on
which they base their numerical model. The cell boundary has a constant shape that
consists of an unattached round part and a flat part which is attached to the target
cell. The flat part is referred to as the synapse, and is said to lie in the synaptic
plane. The large rigid nucleus is coupled to the aster of microtubules converging
near its surface. Together they comprise the cell body in this comparatively more
complete model of the cellular structure. Like in the models considered heretofore,
the cell boundary constrains the cell body, causing its deformation and limiting its
mobility. Additionally, microtubules in this more complete model slide actively
along the cell outline in the areas of contact with the targets. The movements of the
cell body that are caused by the active sliding are opposed by microtubule bending
elasticity and by viscous drag. The physical specification on the active sliding
forces idealizes what should happen when microtubules come in contact with the
cell boundary on whose inner surface (cell cortex) dynein molecules are anchored
(Kuhn and Poenie 2002 ; Combs et al. 2006 ). It is assumed that the unit length of the
contacting part of the microtubule will experience a constant tangential force
directed to the distal end. The boundary in the synapse area is thus characterized by
a certain force density that is by itself nondirectional. The magnitude of the force
experienced by microtubules depends linearly on the length of the segment in con-
tact with the boundary, and the direction of the force is determined entirely by the
orientation of the said segment.
Figure 24 shows a numerical simulation in which the centrosome is initially
oriented at 90° to the developing cell-cell interface. This angle has the highest like-
lihood if the spherical T cell comes in contact with the target surface in a random
orientation. The model reproduces the experimental observations (e.g., Kuhn and
Poenie 2002 ) that the centrosome becomes reoriented to the interface. Interestingly,
stabilization of the centrosome orientation in the model is soon followed by devel-
opment of pulse-like oscillations in its position (Fig. 24 ). These will be discussed in
the next section. The prediction that concerns the subject of the present section is
that the long-range reorientation results in an arrangement of microtubules that is
very asymmetrical. On the side of the microtubule aster that was leading in the