Representation and inference of size control laws by neural network aided point processes

Abstract

The regulation and coordination of cell growth and division is a long-standing problem in cell physiology. Recent single-cell measurements using microfluidic devices provide quantitative time-series data of various physiological parameters of cells. To clarify the regulatory laws and associated relevant parameters such as cell size, mathematical models have been constructed based on physical insights over the phenomena and tested by their capabilities to reproduce the measured data. However, such a conventional model construction by abduction faces a constant risk that we may overlook important parameters and factors especially when complicated time series data is concerned. In addition, comparing a model and data for validation is not trivial when we work on noisy multi-dimensional data. Using cell size control as an example, we demonstrate that this problem can be addressed by employing a neural network (NN) method, originally developed for history-dependent temporal point processes. The NN can effectively segregate history-dependent deterministic factors and unexplainable noise from a given data by flexibly representing functional forms of the deterministic relation and noise distribution. With this method, we represent and infer birth and division cell size distributions of bacteria and fission yeast. The known size control mechanisms such as adder model are revealed as the conditional dependence of the size distributions on history and their Markovian properties are shown sufficient. In addition, the inferred NN model provides a better data representation for the abductive model searching than descriptive statistics. Thus, the NN method can work as a powerful tool to process the noisy data for uncovering hidden dynamic laws.