# Control of noise in gene expression by transcriptional reinitiation

## TL;DR

This paper provides an analytical study of how transcriptional reinitiation influences noise in gene expression, showing it can reduce variability and serve as a fine-tuned regulatory mechanism.

## Contribution

It offers exact analytical expressions for mRNA and protein noise, demonstrating reinitiation's role in noise reduction and regulation in gene expression.

## Key findings

- Fano factor in proteins matches experimental data
- Reinitiation can produce sub-Poissonian mRNA levels
- Reinitiation allows increasing mRNA without raising noise

## Abstract

Gene expression is a random or noisy process. The process consists of several random events among which the reinitiation of transcription by RNAP is an important one. The RNAP molecules can bind the gene only after the promoter gets activated by transcription factors. Several transcription factors bind the promoter to put the gene in the active state. The gene turns into inactive state as the bound transcription factors leave the promoter. During the active period of the gene, many RNAP molecules transcribe the gene to synthesize the mRNAs. The binding event of RNAP to the active state of the gene is a probabilistic process and therefore, introduces noise or fluctuations in the mRNA and protein levels. In this paper, we analytically calculate the Fano factor in mRNA and protein levels and also the probability distribution of mRNA numbers exactly with the binding event of RNAPs in gene transcription process. The analytically calculated expression of Fano factor of proteins shows excellent agreement with an experimental result. Then we show that the Fano factor in mRNA levels can be sub-Poissonian due to the reinitiation of transcription by RNAP and the mean mRNA level can be increased without increasing the Fano factor. Our study show that the Fano factor can also be reduced keeping mRNA levels fixed. We find that the reinitiation of transcription can behave as a fine-tuned control process to regulate the mRNA/protein level in the cell.