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.
Highlights
One major challenge in microbial physiology is determining the fundamental principles and laws underlying the regulation and coordination of cell growth and division [1]
We first test the performance of different recurrent neural network (RNN) methods by applying them to the cell size data on E . coli and S. pombe
In a previous study [24], the fully neural network (NN) model that we use in our subsequent analysis achieved a competitive or better performance compared to other RNN-based models for various synthetic and real data
Summary
One major challenge in microbial physiology is determining the fundamental principles and laws underlying the regulation and coordination of cell growth and division [1]. Simple physical and mathematical models have been developed that can explain cell growth and division with a small number of relevant variables. The assumed shape of the distribution may not always be exact for representing the unexplained components This suggests that the development of a more versatile method is helpful for elucidating the laws from the data. We can use the representation power of DL into mathematical modeling To this end, we should design an appropriate method to avoid generating artificial results by malfunctions of the high flexibility of DL. IV, we first present the performance of existing intensity-based models and show that a recently developed NN model is the best in its flexible expressiveness of data With this model, we examine how the conditional PDFs of cell sizes depend on their history.
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