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In experiments, the distributions of mRNA or protein numbers in single cells are often fitted to the random telegraph model which includes synthesis and decay of mRNA or protein, and switching of the gene between active and inactive states. While commonly used, this model does not describe how fluctuations are influenced by crucial biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways. Here we investigate the dynamical properties of four relatively complex gene expression models by fitting their steady-state mRNA or protein number distributions to the simple telegraph model. We show that despite the underlying complex biological mechanisms, the telegraph model with three effective parameters can accurately capture the steady-state gene product distributions, as well as the conditional distributions in the active gene state, of the complex models. Some effective parameters are reliable and can reflect realistic dynamic behaviors of the complex models, while others may deviate significantly from their real values in the complex models. The effective parameters can also be applied to characterize the capability for a complex model to exhibit multimodality. Using additional information such as single-cell data at multiple time points, we provide an effective method of distinguishing the complex models from the telegraph model. Furthermore, using measurements under varying experimental conditions, we show that fitting the mRNA or protein number distributions to the telegraph model may even reveal the underlying gene regulation mechanisms of the complex models. The effectiveness of these methods is confirmed by analysis of single-cell data forE. coliand mammalian cells. All these results are robust with respect to cooperative transcriptional regulation and extrinsic noise. In particular, we find that faster relaxation speed to the steady state results in more precise parameter inference under large extrinsic noise.

Alternative splicing (AS) significantly enriches the diversity of transcriptomes and proteomes, playing a pivotal role in the physiology and development of eukaryotic organisms. With the continuous advancement of high-throughput sequencing technologies, an increasing number of novel transcript isoforms, along with factors related to splicing and their associated functions, are being unveiled. In this review, we succinctly summarize and compare the different splicing mechanisms across prokaryotes and eukaryotes. Furthermore, we provide an extensive overview of the recent progress in various studies on AS covering different developmental stages in diverse plant species and in response to various abiotic stresses. Additionally, we discuss modern techniques for studying the functions and quantification of AS transcripts, as well as their protein products. By integrating genetic studies, quantitative methods, and high-throughput omics techniques, we can discover novel transcript isoforms and functional splicing factors, thereby enhancing our understanding of the roles of various splicing modes in different plant species.