Abstract. In [7] Krotov and Hopfield suggest a generalized version of the wellknown Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the "limit" as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.
It is well known that eukaryotic cells can sense oxygen (O2) and adapt their metabolism accordingly. It is less known that they can also move towards regions of higher oxygen level (aerotaxis). Using a self-generated hypoxic assay, we show that the social amoeba Dictyostelium discoideum displays a spectacular aerotactic behavior. When a cell colony is covered by a coverglass, cells quickly consume the available O2 and the ones close to the periphery move directionally outward forming a dense ring keeping a constant speed and density. To confirm that O2 is the main molecular player in this seemingly collective process, we combined two technological developments, porphyrin based O2 sensing films and microfluidic O2 gradient generators. We showed that Dictyostelium cells exhibit aerotactic and aerokinetic (increased speed at low O2) response in an extremely low range of O2 concentration (0-1.5%) indicative of a very efficient detection mechanism. The various cell behaviors under self-generated or imposed O2 gradients were modeled with a very satisfactory quantitative agreement using an in silico cellular Potts model built on experimental observations. This computational model was complemented with a parsimonious 'Go or Grow' partial differential equation (PDE) model. In both models, we found that the collective migration of a dense ring can be explained by the interplay between cell division and the modulation of aerotaxis, without the need for cell-cell communication. Explicit wave solutions of the PDE model also informed about the relative contributions of division and directed motion on the collective speed.
Using a self-generated hypoxic assay, we show that the amoeba Dictyostelium discoideum displays a remarkable collective aerotactic behavior. When a cell colony is covered, cells quickly consume the available oxygen (O2) and form a dense ring moving outwards at constant speed and density. To decipher this collective process, we combined two technological developments: porphyrin-based O2 -sensing films and microfluidic O2 gradient generators. We showed that Dictyostelium cells exhibit aerotactic and aerokinetic response in a low range of O2 concentration indicative of a very efficient detection mechanism. Cell behaviors under self-generated or imposed O2 gradients were modeled using an in silico cellular Potts model built on experimental observations. This computational model was complemented with a parsimonious ‘Go or Grow’ partial differential equation (PDE) model. In both models, we found that the collective migration of a dense ring can be explained by the interplay between cell division and the modulation of aerotaxis.
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