Calcium spiking can be used for drug screening studies in pharmaceutical industries. However, performing experiments for multiple drugs and doses are highly expensive. The oscillatory behavior of calcium spiking data demonstrates extreme nonlinearity and phase singularity. This makes it more challenging to construct physics-based models for the experimental observations. In this scenario, data based modelling, such as Artificial Neural Networks (ANN), and thereafter the model based prediction of calcium profiles may offer a cost-effective and time saving solution. Therefore, a novel ANN building algorithm is presented in the current work, where data based simultaneous estimation of ANN architecture and nonlinear activation function stands out as the main highlight. The resultant ANN was then used to learn the oscillatory behavior in calcium ion concentration data, obtained from hippocampal neurons of rats by fluorescent labelling and confocal imaging. The paper shows that the novel technique can be used in general for emulating biochemical oscillations (with or without drug injection) and can be implemented to predict the cell-drug responses for intermediated doses. The proposed algorithm can also be used for obtaining high resolution data from low resolution experimental measurements.