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E. coli chemotactic motion in the presence of a chemoattractant field hasbeen extensively studied using wet laboratory experiments, stochasticcomputational models as well as partial differential equation-based models(PDEs). The most challenging step in bridging these approaches, is establishinga closed form of the so-called chemotactic term, which describes how bacteriabias their motion up chemonutrient concentration gradients, as a result of acascade of biochemical processes. Data-driven models can be used to learn theentire evolution operator of the chemotactic PDEs (black box models), or, in amore targeted fashion, to learn just the chemotactic term (gray box models). Inthis work, data-driven Machine Learning approaches for learning the underlyingmodel PDEs are (a) validated through the use of simulation data fromestablished continuum models and (b) used to infer chemotactic PDEs fromexperimental data. Even when the data at hand are sparse (coarse in spaceand/or time), noisy (due to inherent stochasticity in measurements) or partial(e.g. lack of measurements of the associated chemoattractant field), we canattempt to learn the right-hand-side of a closed PDE for an evolving bacterialdensity. In fact we show that data-driven PDEs including a short history of thebacterial density field (e.g. in the form of higher-order in time PDEs in termsof the measurable bacterial density) can be successful in predicting furtherbacterial density evolution, and even possibly recovering estimates of theunmeasured chemonutrient field. The main tool in this effort is the effectivelow-dimensionality of the dynamics (in the spirit of the Whitney and Takensembedding theorems). The resulting data-driven PDE can then be simulated toreproduce/predict computational or experimental bacterial density profile data,and estimate the underlying (unmeasured) chemonutrient field evolution.

Data-driven Discovery of Chemotactic Migration of Bacteria via Machine Learning