System identification of signaling dependent gene expression with different time-scale data

Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we used compressed sensing technology and developed a system identification method using data of different time scales by recovering signals of missing time points. We measured phosphorylation of ERK and CREB, immediate early gene expression products, and mRNAs of decoder genes for neurite elongation in PC12 cell differentiation and performed system identification, revealing the input–output relationships between signaling and gene expression with sensitivity such as graded or switch-like response and with time delay and gain, representing signal transfer efficiency. We predicted and validated the identified system using pharmacological perturbation. Thus, we provide a versatile method for system identification using data with different time scales.
Author summary The key points of this study are two-fold: The first point is the decoding mechanism for cell differentiation. We previously demonstrated the encoding mechanism of cell fate decision information by transient and sustained ERK activation in PC12 cells, and also identified the decoding genes essential for cell differentiation in PC12 cells, including Metrnl, Dclk1, and Serpinb1a, denoted as LP (latent process) genes, which are the decoders of neurite length information. Importantly, the expression levels of the LP genes, but not the phosphorylation level of ERK, correlate with neurite length. Thus, the decoding mechanism of signaling activities by LP gene expression is a key issue for understanding the mechanism of cell differentiation. Here we identified a selective NGF- and PACAP-signaling decoding system by LP gene expression for neurite extension by developing a system identification method. The second point is the modeling. Cells decode information of signaling activation at a scale of tens of minutes by downstream gene expression with a scale of hours to days, leading to cell fate decisions such as cell differentiation. However, no system identification method with such different time scales exists. Here we developed a signal recovery technique in the field of compressed sensing originally developed for image analysis to biological sparse data of different time scales of signaling and gene expression.