SummaryOuter surface lipoprotein (Osp) C is a virulence factor required for transmission of the Lyme disease agent, Borrelia burgdorferi. We have constructed an inducible promoter system to study the function and regulation of OspC by integrating regulatory elements from the Escherichia coli lac operon into the B. burgdorferi genome. An inducible promoter (flacp) was constructed by inserting a synthetic lac operator sequence between the transcriptional start site and the ribosomal binding site of the B. burgdorferi flgB promoter; flacp was then used to replace the native ospC and rpoS promoters in B. burgdorferi derivatives that constitutively express the E. coli Lac repressor protein (LacI). In vitro, the expression of ospC and rpoS from flacp was dependent on the inducer isopropyl b-D-thiogalactopyranoside and was unaffected by temperature or pH, conditions commonly used to mimic different aspects of the B. burgdorferi life cycle. Our results suggest that OspC is essential immediately upon injection into a mouse and OspC expression must be maintained during the early stages of infection. In addition, the mouse infectivity experiment indicates that this system can be used to regulate B. burgdorferi genes in vivo, within the context of an experimental tickmouse infectious cycle. RpoS is an alternative sigma factor that is required for ospC transcription. However, the role of other temperature-dependent factors has not previously been addressed. Our results with the inducible rpoS strain demonstrate that RpoS alone is sufficient to activate OspC expression, even at 23°C. This is the first functional inducible promoter system developed for use in B. burgdorferi and, for the first time, will provide researchers with the ability to artificially regulate the expression of genes in this pathogenic spirochaete.
Symbolic regression is a powerful technique to discover analytic equations that describe data, which can lead to explainable models and the ability to predict unseen data. In contrast, neural networks have achieved amazing levels of accuracy on image recognition and natural language processing tasks, but they are often seen as black-box models that are difficult to interpret and typically extrapolate poorly. In this article, we use a neural network-based architecture for symbolic regression called the equation learner (EQL) network and integrate it with other deep learning architectures such that the whole system can be trained end-to-end through backpropagation. To demonstrate the power of such systems, we study their performance on several substantially different tasks. First, we show that the neural network can perform symbolic regression and learn the form of several functions. Next, we present an MNIST arithmetic task where a convolutional network extracts the digits. Finally, we demonstrate the prediction of dynamical systems where an unknown parameter is extracted through an encoder. We find that the EQL-based architecture can extrapolate quite well outside of the training data set compared with a standard neural network-based architecture, paving the way for deep learning to be applied in scientific exploration and discovery.
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