Experimental and theoretical study of mitotic spindle orientation.

The architecture and adhesiveness of a cell microenvironment is a critical factor for the regulation of spindle orientation in vivo. Using a combination of theory and experiments, we have investigated spindle orientation in HeLa (human) cells. Here we show that spindle orientation can be understood as the result of the action of cortical force generators, which interact with spindle microtubules and are activated by cortical cues. We develop a simple physical description of this spindle mechanics, which allows us to calculate angular profiles of the torque acting on the spindle, as well as the angular distribution of spindle orientations. Our model accounts for the preferred spindle orientation and the shape of the full angular distribution of spindle orientations observed in a large variety of different cellular microenvironment geometries. It also correctly describes asymmetric spindle orientations, which are observed for certain distributions of cortical cues. We conclude that, on the basis of a few simple assumptions, we can provide a quantitative description of the spindle orientation of adherent cells.

Directed percolation with incubation times.

We introduce a model for directed percolation with a long-range temporal diffusion, while the spatial diffusion is kept short ranged. In an interpretation of directed percolation as an epidemic process, this non-Markovian modification can be understood as incubation times, which are distributed accordingly to a Lévy distribution. We argue that the best approach to find the effective action for this problem is through a generalization of the Cardy-Sugar method, adding the non-Markovian features into the geometrical properties of the lattice. We formulate a field theory for this problem and renormalize it up to one loop in a perturbative expansion. We solve the various technical difficulties that the integrations possess by means of an asymptotic analysis of the divergences. We show the absence of field renormalization at one-loop order, and we argue that this would be the case to all orders in perturbation theory. Consequently, in addition to the characteristic scaling relations of directed percolation, we find a scaling relation valid for the critical exponents of this theory. In this universality class, the critical exponents vary continuously with the Lévy parameter.

Epidemic processes with immunization.

We study a model of directed percolation (DP) with immunization, i.e., with different probabilities for the first infection and subsequent infections. The immunization effect leads to an additional non-Markovian term in the corresponding field theoretical action. We consider immunization as a small perturbation around the DP fixed point in d<6, where the non-Markovian term is relevant. The immunization causes the system to be driven away from the neighborhood of the DP critical point. In order to investigate the dynamical critical behavior of the model, we consider the limits of low and high first-infection rate, while the second-infection rate remains constant at the DP critical value. Scaling arguments are applied to obtain an expression for the survival probability in both limits. The corresponding exponents are written in terms of the critical exponents for ordinary DP and DP with a wall. We find that the survival probability does not obey a power-law behavior, decaying instead as a stretched exponential in the low first-infection probability limit and to a constant in the high first-infection probability limit. The theoretical predictions are confirmed by optimized numerical simulations in 1+1 dimensions.