Cubatic phase for tetrapods

We investigate the phase behavior of tetrapods, hard non-convex bodies formed by 4 rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.Comment: 8 pages ReVTeX 4, including 3 EPS figure

Do cylinders exhibit a cubatic phase?

We investigate the possibility that freely rotating cylinders with an aspect ratio $L/D=0.9$ exhibit a cubatic phase similar to the one found for a system of cut-spheres. We present theoretical arguments why a cubatic phase might occur in this particular system. Monte Carlo simulations do not confirm the existence of a cubatic phase for cylinders. However, they do reveal an unexpected phase behavior between the isotropic and crystalline phase.Comment: 24 pages, 12 figures, RevTex (Submitted to J. Chem. Phys.

Confinement and crowding control the morphology and dynamics of a model bacterial chromosome

Motivated by recent experiments probing shape, size and dynamics of bacterial chromosomes in growing cells, we consider a polymer model consisting of a circular backbone to which side-loops are attached, confined to a cylindrical cell. Such a model chromosome spontaneously adopts a helical shape, which is further compacted by molecular crowders to occupy a nucleoid-like subvolume of the cell. With increasing cell length, the longitudinal size of the chromosome increases in a non-linear fashion to finally saturate, its morphology gradually opening up while displaying a changing number of helical turns. For shorter cells, the chromosome extension varies non-monotonically with cell size, which we show is associated with a radial to longitudinal spatial reordering of the crowders. Confinement and crowders constrain chain dynamics leading to anomalous diffusion. While the scaling exponent for the mean squared displacement of center of mass grows and saturates with cell length, that of individual loci displays broad distribution with a sharp maximum.Comment: 12 pages, 12 figure

Designing colloidal ground state patterns using short-range isotropic interactions

DNA-coated colloids are a popular model system for self-assembly through tunable interactions. The DNA-encoded linkages between particles theoretically allow for very high specificity, but generally no directionality or long-range interactions. We introduce a two-dimensional lattice model for particles of many different types with short-range isotropic interactions that are pairwise specific. For this class of models, we address the fundamental question whether it is possible to reliably design the interactions so that the ground state is unique and corresponds to a given crystal structure. First, we determine lower limits for the interaction range between particles, depending on the complexity of the desired pattern and the underlying lattice. Then, we introduce a `recipe' for determining the pairwise interactions that exactly satisfies this minimum criterion, and we show that it is sufficient to uniquely determine the ground state for a large class of crystal structures. Finally, we verify these results using Monte Carlo simulations.Comment: 19 pages, 7 figure

Microtubule length distributions in the presence of protein-induced severing

Microtubules are highly regulated dynamic elements of the cytoskeleton of eukaryotic cells. One of the regulation mechanisms observed in living cells is the severing by the proteins katanin and spastin. We introduce a model for the dynamics of microtubules in the presence of randomly occurring severing events. Under the biologically motivated assumption that the newly created plus end undergoes a catastrophe, we investigate the steady state length distribution. We show that the presence of severing does not affect the number of microtubules, regardless of the distribution of severing events. In the special case in which the microtubules cannot recover from the depolymerizing state (no rescue events) we derive an analytical expression for the length distribution. In the general case we transform the problem into a single ODE that is solved numerically.Comment: 9 pages, 4 figure

Microtubule organization and cell geometry

We present a systematic study of the influence of cell geometry on the orientational distribution of microtubules (MTs) nucleated from a single microtubule organizing center (MTOC). For simplicity we consider an elliptical cell geometry, a setting appropriate to a generic non-spherical animal cell. Within this context we introduce four models of increasing complexity, in each case introducing additional mechanisms that govern the interaction of the MTs with the cell boundary. In order, we consider the cases: MTs that can bind to the boundary with a fixed mean residence time (M0), force-producing MTs that can slide on the boundary towards the cell poles (MS), MTs that interact with a generic polarity factor that is transported and deposited at the boundary, and which in turn stabilizes the MTs at the boundary (MP), and a final model in which both sliding and stabilization by polarity factors is taken into account (MSP). In the baseline model (M0), the exponential length distribution of MTs causes most of the interactions at the cell boundary to occur along the shorter transverse direction in the cell, leading to transverse biaxial order. MT sliding (MS) is able to reorient the main axis of this biaxial order along the longitudinal axis. The polarization mechanism introduced in MP and MSP overrules the geometric bias towards bipolar order observed in M0 and MS, and allows the establishment of unipolar order either along the short- (MP) or the long cell axis (MSP). The behavior of the latter two models can be qualitatively reproduced by a very simple toy model with discrete MT orientations.Comment: 38 pages, 13 figure

Modeling a Cortical Auxin Maximum for Nodulation: Different Signatures of Potential Strategies

Lateral organ formation from plant roots typically requires the de novo creation of a meristem, initiated at the location of a localized auxin maximum. Legume roots can form both root nodules and lateral roots. From the basic principles of auxin transport and metabolism only a few mechanisms can be inferred for increasing the local auxin concentration: increased influx, decreased efflux, and (increased) local production. Using computer simulations we investigate the different spatio-temporal patterns resulting from each of these mechanisms in the context of a root model of a generalized legume. We apply all mechanisms to the same group of preselected cells, dubbed the controlled area. We find that each mechanism leaves its own characteristic signature. Local production by itself can not create a strong auxin maximum. An increase of influx, as is observed in lateral root formation, can result in an auxin maximum that is spatially more confined than the controlled area. A decrease of efflux on the other hand leads to a broad maximum, which is more similar to what is observed for nodule primordia. With our prime interest in nodulation, we further investigate the dynamics following a decrease of efflux. We find that with a homogeneous change in the whole cortex, the first auxin accumulation is observed in the inner cortex. The steady state lateral location of this efflux reduced auxin maximum can be shifted by slight changes in the ratio of central to peripheral efflux carriers. We discuss the implications of this finding in the context of determinate and indeterminate nodules, which originate from different cortical positions. The patterns we have found are robust under disruption of the (artificial) tissue layout. The same patterns are therefore likely to occur in many other contexts