Protein Distributions from a Stochastic Model of the lac Operon of E. coli with DNA Looping: Analytical solution and comparison with experiments

• Published in: PloS one Vol. 9; no. 7; p. e102580
• Main Authors: Choudhary, Krishna, Oehler, Stefan, Narang, Atul
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 23.07.2014; Public Library of Science (PLoS)
• Subjects: Algorithms; Biology and Life Sciences; Biotechnology; Bursting; Bursts; Chromosomes; Deoxyribonucleic acid; DNA; DNA, Bacterial - chemistry; DNA, Bacterial - genetics; E coli; Escherichia coli; Escherichia coli - genetics; Escherichia coli - metabolism; Escherichia coli Proteins - genetics; Escherichia coli Proteins - metabolism; Experiments; Feedback, Physiological; Gene expression; Gene Expression Regulation, Bacterial; Lac Operon; Lac Repressors - genetics; Lac Repressors - metabolism; Lactose operon; Ligands; Models, Genetic; Noise; Nucleic Acid Conformation; Operator Regions, Genetic - genetics; Operators; Permease; Physical Sciences; Proteins; RNA, Messenger - genetics; RNA, Messenger - metabolism; Stochastic models; Stochastic Processes; Stochasticity; India
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0102580

Although noisy gene expression is widely accepted, its mechanisms are subjects of debate, stimulated largely by single-molecule experiments. This work is concerned with one such study, in which Choi et al., 2008, obtained real-time data and distributions of Lac permease in E. coli. They observed small and large protein bursts in strains with and without auxiliary operators. They also estimated the size and frequency of these bursts, but these were based on a stochastic model of a constitutive promoter. Here, we formulate and solve a stochastic model accounting for the existence of auxiliary operators and DNA loops. We find that DNA loop formation is so fast that small bursts are averaged out, making it impossible to extract their size and frequency from the data. In contrast, we can extract not only the size and frequency of the large bursts, but also the fraction of proteins derived from them. Finally, the proteins follow not the negative binomial distribution, but a mixture of two distributions, which reflect the existence of proteins derived from small and large bursts.