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.

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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 nonMarkovian 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 neighbourhood of the DP critical point. In order to investigate the dynamical critical behaviour 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 behaviour, 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.

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