Ribosome Biogenesis in Replicating Cells: Integration of Experiment and Theory Tyler M. Earnest,1,2 John A. Cole,2 Joseph R. Peterson,3 Michael J. Hallock,4 Thomas E. Kuhlman,1,2 Zaida Luthey-Schulten1,2,3 1 Center for the Physics of Living Cells, University of Illinois, Urbana, IL 2 Department of Physics, University of Illinois, Urbana, IL 3 Department of Chemistry, University of Illinois, Urbana, IL 4 School of Chemical Sciences, University of Illinois, Urbana, IL Received 26 March 2016; revised 3 June 2016; accepted 8 June 2016 Published online 13 June 2016 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/bip.22892 ABSTRACT: simulation software. In order to determine the replication parameters, we construct and analyze a series of Esche- Ribosomes—the primary macromolecular machines richia coli strains with fluorescently labeled genes distrib- responsible for translating the genetic code into proteins— uted evenly throughout their chromosomes. By measuring are complexes of precisely folded RNA and proteins. The these cells’ lengths and number of gene copies at the single- ways in which their production and assembly are managed cell level, we could fit a statistical model of the initiation by the living cell is of deep biological importance. Here we and duration of chromosome replication. We found that for extend a recent spatially resolved whole-cell model of ribo- our slow-growing (120 min doubling time) E. coli cells, some biogenesis in a fixed volume [Earnest et al., Biophys J replication was initiated 42 min into the cell cycle and com- 2015, 109, 1117–1135] to include the effects of growth, pleted after an additional 42 min. While simulations of the DNA replication, and cell division. All biological processes biogenesis model produce the correct ribosome and mRNA are described in terms of reaction-diffusion master equa- counts over the cell cycle, the kinetic parameters for tran- tions and solved stochastically using the Lattice Microbes scription and degradation are lower than anticipated from Additional Supporting Information may be found in the online version of this article. a recent analytical time dependent model of in vivo mRNA Correspondence to: Zaida Luthey-Schulten, Department of Chemistry, University production. Describing expression in terms of a simple of Illinois at Urbana-Champaign, A544 Chemical and Life Sciences Lab, 600 South Mathews Avenue, Urbana, IL 61801; e-mail: [email protected] chemical master equation, we show that the discrepancies Tyler M. Earnest, John A. Cole, and Joseph R. Peterson contributed equally to this work. are due to the lack of nonribosomal genes in the extended Contract grant sponsor: National Science Foundation (NSF) Contract grant number: MCB-1244570 biogenesis model which effects the competition of mRNA Contract grant sponsor: NSF Center for the Physics of Living Cells for ribosome binding, and suggest corrections to parameters Contract grant number: PHY-1430124 Contract grant sponsor: NSF Graduate Research Fellowship to be used in the whole-cell model when modeling expres- Contract grant number: DGE-1144245 Contract grant sponsor: U.S. Department of Energy, Office of Science, Biological sion of the entire transcriptome. VC 2016 Wiley Periodicals, and Environmental Research, Adaptive Biosystems Imaging Scientific Focus Area Contract grant sponsor: Alfred P. Sloan Foundation Research Fellowship in Inc. Biopolymers 105: 735–751, 2016. Physics Contract grant number: FG-2015-65532 Keywords: stochastic gene expression; ribosome biogene- Contract grant sponsor: National Science Foundation sis; bacterial cell division Contract grant numbers: OCI-0725070, ACI-1238993 Contract grant sponsor: National Institutes of Health Contract grant numbers: 9 P41 GM104601-23, GM112659 VC 2016 Wiley Periodicals, Inc. Biopolymers Volume 105 / Number 10 735 736 Earnest et al. This article was originally published online as an accepted species. The use of a stochastic simulation methodology was preprint. The “Published Online” date corresponds to the pre- print version. You can request a copy of any preprints from important for a number of reasons. First and foremost, gene the past two calendar years by emailing the Biopolymers edi- expression has been shown to be highly variable from cell-to- torial office at [email protected]. cell; this is especially pronounced when the molecules involved are in low copy numbers.20–22 Ribosomal RNA is transcribed from seven operons interspersed throughout the E. coli genome, and many of the intermediate structures along the assembly pathways can exist in very few copies due to the rapid binding of INTRODUCTION 19 n Escherichia coli, ribosomes account for approximately additional proteins. Accurately modeling the random diffusive one fourth of the cellular dry mass and the majority of motions and reactions of the individual substrates allowed Ear- the total RNA.1 It can be tempting, then, to think of the nest et al. not only to investigate the mean behavior of the assem- bly network, but also the inherent variability in it. bacterial cell as a finely tuned machine for building ribo- Although unprecedentedly complete, the model did not somes. Their ubiquity and high sequence conservation I account for some of the most basic functions of the cell— has made them an invaluable window into the process of namely, replication of the genome, cell division, and metabo- evolution at the molecular level,2–5 and their role in protein lism. Using mRNA distributions obtained from super- synthesis involves them (either directly or indirectly) in resolution imaging experiments, recent articles by Peterson et al. essentially every process within the cell. and Jones et al. showed that mRNA copy numbers exhibit a sig- Ribosome production has evolved to be tightly regulated by nificant amount of variability simply by virtue of the fact that the cell. This is no small feat, considering that each 70S ribo- the genes that encode them are duplicated at some point during some involves the coordinated transcription, translation, fold- the cell cycle (which, in turn, depends on the genes’ positions ing, and hierarchical assembly of three strands of rRNA and on the chromosome).23,24 To quantitatively describe the replica- over four dozen proteins, all within the heterogeneous, tive dynamics of the chromosome, we have generated a series of crowded intracellular space. Starting as early as 1966, pioneer- E. coli strains with gene loci labeled by a fluorescent repressor- ing in vitro studies began to unravel some of the mechanistic operator system (FROS) distributed evenly around the chromo- details of this process.6 Work on the 30S small subunit (SSU), some. High-throughput imaging of these strains and identifica- which is largely responsible for recognizing and decoding tion and quantification of the gene copy number in each cell mRNA, showed that assembly nucleates with the folding of the allows us to fit simple models of cell growth and genome repli- so called five-way junction in the 16S rRNA of the SSU (resi- cation to extract estimates for the timing of replication of each dues 27–45 and 394–554 in E. coli), and then proceeds through gene as a function of its position on the chromosome. We use the hierarchical association of sets of ribosomal proteins, each these results to extend the ribosome biogenesis model to explic- progressively folding and stabilizing the rRNA’s growing terti- itly include cell growth, gene duplication, and division (hence- 7–12 ary structure. Interestingly, a number of in vitro studies forthreferredtoastheRBM,forribosomebiogenesismodel). have observed this process proceeding over timescales on the Although single-cell rRNA and ribosomal protein mRNA distri- 7–9 order of the cell cycle or longer, while in vivo it can take just butions are not available for direct comparison, a number of 13 a few minutes. Moreover, single cell-imaging studies on both theoretical models of mRNA statistics—including some that slow- and fast-growing cells have also shown that complete account for gene duplication—have been proposed,23,24 ribosomes are not uniformly dispersed throughout the cyto- although, importantly, they do not explicitly account for 14–18 plasm, but rather they tend to aggregate to the cell poles. mRNA–ribosome interactions. The transcription and mRNA Understanding these phenomena requires a model with both a degradation rates in the RBM differ from those generated by the complete (or nearly complete) kinetic description of the theoretical model in fitting the simulated mRNA distributions. assembly process and fine spatial resolution. We ultimately attribute this discrepancy to the fact that the 19 Recently, Earnest et al. reported the first spatially resolved RBM does not account for competition from nonribosomal stochastic simulations of ribosome biogenesis for slow-growing gene expression (e.g., genes involved in metabolism, regulation, E. coli. In that work, a model involving 251 different species etc.) We derive a simple statistical model that accounts for mes- (including the SSU, LSU, rRNA, 18 proteins that bind to it, the senger production, degradation, and interactions with the ribo- genes and mRNA that code for them, and over 140 possible somes (henceforth referred to as the SAM, for semi-analytical intermediates in the SSU assembly) and 1300 reactions for model) which we use to investigate the dependence of mRNA transcription, translation, and ribosome assembly were devel- statistics on chromosome duplication as well as the expression oped and parameterized