Spatial constraints and the organization of the cytoskeleton

The shape of animal cells is in controlled by a network of filamentous polymers called the cytoskeleton. The two main components of the cytoskeleton are actin filaments and microtubules. These polymers continuously reorganize in order to performed their diverse cellular functions. For example, in processes such as cell migration actin filaments grow against the membrane, creating flat protrusions called lamellipodia. The lamellipodia enable the cells to move over surfaces. Microtubules are a key player in the cell division mechanism. There, the proper separation of the genetic material between the two daughter cells is controlled by two microtubule asters. The positioning of these two asters also determines the location where the cells will physically separate. Both migration and division are crucial processes for the cell, however the mechanisms underlying these processes are still poorly understood. The organization of the cytoskeleton in cells, and thus their functioning as cell shapers, is an interplay between mutual interaction, confinement and protein mediated interactions. Since cells are exquisitely complex systems, experimentally, the bottom-up approach proves useful in understanding the contribution of each of these interactions on the cytoskeleton organization. This approach is based on the idea of reconstructing a minimal system and adding more complexity to it as our understanding of this system increases. Starting by a bottom-up approach, as it is done in experimental systems, we study various aspects of confinement and mutual interactions on cytoskeleton organization. The simplest system in which these two interactions are expected to compete is when dense enough rigid cytoskeletal polymers are confined. Experimentally, this question is addressed by confining these polymers in microchambers which are small compared to the persistence length of the enclosed polymers. In Chapter 2, using Monte Carlo simulations, we investigate the organization of rigid polymers confined in shallow square containers, this geometry being simplified model of a lamellipodium. We find that, in the regime where the confinement effect, which causes wall alignment of the polymers, competes with the self-aligning tendency of the polymers, the organization is characterized by a nematic droplet aligned along a diagonal and wall aligned polymers. The pattern is stabilized by linear defect structures. By the same methods, in Chapter 3, we study rigid polymers in curved wall confinement, finding that the bipolar structure appearing in the disk geometry is drastically modified by the opening of a hole in the middle of the container. Unexpectedly, in this annular geometry, the organization is characterized by highly aligned domains separated by radial defect walls. The patterns observed are the result of the finite size of the particles. When the rigid polymers are small compared to the confining volume, their orientation is expected to vary over lengths which are much larger than the length of the polymer. In this regime the system is well described by continuum theories. Since currently employed continuum models either exclude the emergence of singularities by the way they are constructed (Oseen-Frank model) or are valid only in for a limited density range around the transition from an unordered to an ordered system (Landau-De Gennes model), in Chapter 4, we construct a mean-field model combining the virtues of these two models. We apply this model to a system of rigid small polymers enclosed in rectangular shallow container (geometry similar to the one in Chapter 2), finding that patterns which are minimizing the energy of the system are characterized by continuum variation of the orientation. However, our model also yields patterns containing point defects which have slightly higher energy. So far we have considered only rigid cytoskeletal polymers, however at the length scale of the cell the polymers are better described by an elastic rod. In Chapter 5 we study the configurations adopted by a cytoskeletal polymers when enclosed by a rigid ellipsoidal membrane. We find that, compared to the spherical confinement, the change in shape of the confining membrane leads to non-trivial organization of the enclosed polymers. Among the patters observed are single bundles, planar asters, circular and elliptical rings. In reconstructed systems such as emulsion droplets the cytoskeletal polymers push against the membrane, deforming it but, since the membrane is under tension, it also constrains them to bend. Determining the polymeric configurations as a function of the confining surface is the first step towards understanding this mechanical interplay between the cytoskeleton and the membrane. For proper cell division, a precise positioning of the two microtubule asters involved is required. The positioning of the two asters is based on pushing and pulling forces generated by the microtubule-membrane interaction. Experimental evidence shows that, in reconstructed systems, a spatial separation between the two asters in always present. Therefore, in Chapter 6, we investigate the steric repulsion between two asters finding that it indeed leads to a spatial separation. The models that we developed in this thesis are a starting point for understanding the cytoskeletal organization and its role in the cell. In the last Chapter of this thesis we give some directions that the present work opens.