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

Abstract

The regulation and coordination of cell growth and division are long-standing problems in cell physiology. Recent single-cell measurements that use microfluidic devices have provided quantitative time-series data on various physiological parameters of cells. To clarify the regulatory laws and associated relevant parameters, such as cell size, simple mathematical models have been constructed and tested based on their capabilities to reproduce the measured data. However, the models may fail to capture some aspects of data due to presumed assumptions or simplification, especially when the data are multidimensional. Furthermore, comparing a model and data for validation is not trivial when we handle noisy multidimensional data. Thus, to extract hidden laws from data, a novel method, which can handle and integrate noisy multidimensional data more flexibly and exhaustively than the conventional ones, is necessary and helpful. By using cell size control as an example, we demonstrate that this problem can be addressed by using 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 given data by flexibly representing the functional forms of the deterministic relation and noise distribution. By using this method, we represent and infer the birth and division cell size distributions of bacteria and fission yeast. Known size control mechanisms, such as the adder model, are revealed as the conditional dependence of the size distributions on history. Further, we show that the inferred NN model provides a better data representation for model searching than conventional descriptive statistics. Thus, the NN method can work as a powerful tool for processing noisy data to uncover hidden dynamic laws.