| dc.description.abstracteng | In the present cumulative thesis the reaction-diffusion equations modeling the signaling process of the social amoeba Dictyostelium discoideum were studied. The pattern formation process in this organism, corresponding to the production and relay of waves of the chemoattractant cAMP, was perturbed under two particular conditions: advecting flows and millimetric obstacles. The model was studied through analytical calculations, when suitable approximations were possible, and numerical simulations. The results were compared to experimental observations in such setups.
In the first part of this work, the model was modified to account for an advecting flow being applied to the system, similar to those advecting the amoebas in their natural habitat. Under these conditions the system shows a convectively unstable regime which was fully characterized. In this regime a perturbation produces downstream traveling wave trains that grow in size as they travel. These wave trains have a smaller wavelength and lower velocity on their leading front than in the center, where the peaks are more spreaded out and travel faster. Adding an absorbing boundary condition on the upstream end of the channel creates an instability capable of periodically producing wave trains which are advected downstream. This periodic process also emits an upstream traveling peak which gets absorbed by the upstream boundary and whose velocity sets the oscillation period. In a two dimensional channel this upstream traveling peak acquires a triangular shape, with its cusp at the middle of the channel. This shape becomes more elongated with increasing advecting velocities and as the peak travels along the channel.
At high flow speeds the cAMP waves acquire a very elongated parabolic shape that the model with instantaneous cAMP transfer to the extracellular media could not reproduce, but that the full 3-Component model version with a developmental path scheme successfully reproduced. The shape of the wavefront was very dependent on the location of the wave initiation point, which could only happen in the upstream boundary at high advecting flows. In our simulations a big enough group of oscillatory cells needs to be located upstream to successfully produce waves, which is consistent with experimental observations. Both in experiments and simulations the wave width increased with increasing advecting velocities and reacted very quickly to speed changes in the advecting flow. The wave period was constant along the entire range of studied flow velocities, thus providing a robust feature for aggregation across different environmental conditions.
In the second part of this work a mechanism for the creation of target patterns in D. discoideum at densities below mono-layer was uncovered. By adding a discrete cell distribution to the reaction-diffusion equations, areas of higher cell density naturally become oscillators and produce traveling waves, while areas of lower density reach a low cAMP stable steady state that can be excited. This allows the waves emanating from the target centers to be relayed through the entire system. By adding cell movement the model showed ramifying aggregation streams, similar to those observed in experiments. If in these streams the local density goes above mono-layer (confluency) a local degradation mechanism is necessary to stop them from breaking apart. This degradation can exist in the form of membrane-bounded phosphodiesterase. This work shows that the apparition of target centers is a collective phenomenon and not the work of specialized groups of cells, therefore it is consistent with recent experimental observations.
By modifying parameters in this model, the effects of adding caffeine to the cells’ buffer were successfully reproduced. Under these modifications the system showed longer oscillation periods, slower traveling waves, and fewer aggregation centers. Adding millimetric size pillars to this setup can impose specific locations for target pattern appearance, thus controlling the aggregation locations for the amoebas. For this technique to be successful the numerical simulations propose various mechanisms that might be in play acting as boundary conditions in the experimental setup. Simulations also showed an increase in sensitivity to cAMP with the addition of caffeine, thus making it easier for the amoebas to react to any possible cAMP accumulation around the pillars. These simulations provide new information on the sensitivity of D. discoideum to cAMP and open new venues for the control of multicellular aggregation. | de |