A stochastic process determines the time at which cell division begins in Escherichia coli

Central dogma at the single-molecule level in living cells

Gene expression originates from individual DNA molecules within living cells. Like many single-molecule processes, gene expression and regulation are stochastic, that is, sporadic in time. This leads to heterogeneity in the messenger-RNA and protein copy numbers in a population of cells with identical genomes. With advanced single-cell fluorescence microscopy, it is now possible to quantify transcriptomes and proteomes with single-molecule sensitivity. Dynamic processes such as transcription-factor binding, transcription and translation can be monitored in real time, providing quantitative descriptions of the central dogma of molecular biology and the demonstration that a stochastic single-molecule event can determine the phenotype of a cell.

Free RNA polymerase and modeling global transcription in Escherichia coli

Growth rate-dependent changes in the cytoplasmic concentration of free functional RNA polymerase, [R(f)], affect the activity of all bacterial genes. Since [R(f)] is not accessible to direct experimental quantitation, it can only be found indirectly from an evaluation of promoter activity data. Here, a theory has been derived to calculate [R(f)] from the concentrations of total RNA polymerase and promoters in a model system with known Michaelis-Menten constants for the polymerase-promoter interactions. The theory takes transcript lengths and elongation rates into account and predicts how [R(f)] changes with varying gene dosages. From experimental data on total concentrations of RNA polymerase and kinetic properties of different classes of promoters, the theory was developed into a mathematical model that reproduces the global transcriptional control in Escherichia coli growing at different rates. The model allows an estimation of the concentrations of free and DNA-bound RNA polymerase, as well as the partitioning of RNA polymerase into mRNA and stable RNA synthesizing fractions. According to this model, [R(f)] is about 0.4 and 1.2 microM at growth rates corresponding to 1.0 and 2.5 doublings/h, respectively. The model accurately reflects a number of further experimental observations and suggests that the free RNA polymerase concentration increases with increasing growth rate.

Activities of constitutive promoters in Escherichia coli

The in vivo activities of seven constitutive promoters in Escherichia coli have been determined as functions of growth rate in wild-type relA+ spoT+ strains with normal levels of guanosine tetraphosphate (ppGpp) and in ppGpp-deficient DeltarelADeltaspoT derivatives. The promoters include (i) the spc ribosomal protein operon promotor Pspc; (ii) the beta-lactamase gene promotor Pblaof plasmid pBR322; (iii) the PLpromoter of phage lambda; (iv) and (v) the replication control promoters PRNAIand PRNAIIof plasmid pBR322; and (vi) and (vii) the P1 and P2 promoters of the rrnB ribosomal RNA operon. Each strain carried an operon fusion consisting of one of the respective promoter regions linked to lacZ and recombined into the chromosome at the mal locus of a lac deletion strain. The amount of 5'-terminal lacZ mRNA and of beta-galactosidase activity expressed from these promoters were determined by standard hybridization or enzyme activity assays, respectively. In addition, DNA, RNA and protein measurements were used to obtain information about gene dosage, rRNA synthesis and translation rates. By combining lacZ mRNA hybridization data with gene dosage and rRNA synthesis data, the absolute activity of the different promoters, in transcripts/minute per promoter, was determined. In ppGpp-proficient (relA+ spoT+) strains, the respective activities of rrnB P1 and P2 increased 40 and fivefold with increasing growth rate between 0.7 and 3.0 doublings/hour. The activities of Pspc, PL, Pbla, and PRNAIincreased two- to threefold and reached a maximum at growth rates above 2.0 doublings/hour. In contrast, PRNAIIactivity decreased threefold over this range of growth rates. In ppGpp-deficient (DeltarelA DeltaspoT) bacterial strains, the activities of rrnB P1 and P2 promoters both increased about twofold between 1.6 and 3.0 doublings/hour, whereas the activities of Pspc, PL, Pbla, and PRNAI, and PRNAIIwere about constant. To explain these observations, we suggest that the cellular concentration of free RNA polymerase increases with increasing growth rate; for saturation the P1 and P2 rRNA promoters require a high RNA polymerase concentration that is approached only at the highest growth rates, whereas the other promoters are saturated at lower polymerase concentrations achieved at intermediate growth rates. In addition, the data indicate that the respective rrnB P1 and PRNAIIpromoters were under negative and positive control by ppGpp. This caused a reduced activity of rrnB P1 and an increased activity of PRNAIIduring slow growth in wild-type (relA+ spoT+) relative to ppGpp-deficient (DeltarelA DeltaspoT) bacterial strains.

It's a noisy business! Genetic regulation at the nanomolar scale

Many molecules that control genetic regulatory circuits act at extremely low intracellular concentrations. Resultant fluctuations (noise) in reaction rates cause large random variation in rates of development, morphology and the instantaneous concentration of each molecular species in each cell. To achieve regulatory reliability in spite of this noise, cells use redundancy in genes as well as redundancy and extensive feedback in regulatory pathways. However, some regulatory mechanisms exploit this noise to randomize outcomes where variability is advantageous.

Stochastic mechanisms in gene expression

In cellular regulatory networks, genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. In genetically controlled pathways, the protein product encoded by one gene often regulates expression of other genes. The time delay, after activation of the first promoter, to reach an effective level to control the next promoter depends on the rate of protein accumulation. We have analyzed the chemical reactions controlling transcript initiation and translation termination in a single such "genetically coupled" link as a precursor to modeling networks constructed from many such links. Simulation of the processes of gene expression shows that proteins are produced from an activated promoter in short bursts of variable numbers of proteins that occur at random time intervals. As a result, there can be large differences in the time between successive events in regulatory cascades across a cell population. In addition, the random pattern of expression of competitive effectors can produce probabilistic outcomes in switching mechanisms that select between alternative regulatory paths. The result can be a partitioning of the cell population into different phenotypes as the cells follow different paths. There are numerous unexplained examples of phenotypic variations in isogenic populations of both prokaryotic and eukaryotic cells that may be the result of these stochastic gene expression mechanisms.

A model of morphogenesis for protein secondary structures

This paper proposes a model for the expected probability distribution for a certain class of biological structures. In particular, a model is derived for the distribution of lengths of helices, sheets, turns, and coils as a function of the length of the structure divided by the length of the protein it is contained in. A fit between the derived lognormal function and the structures for some proteins whose three-dimensional structure is known was significant. The fit produces fundamental parameters particular to each structure type that are related to the underlying structure and its morphogenesis. The importance of the result is that a universal mathematical distribution can be used to explain certain protein morphogeneses. Also, these fundamental parameters can be used as an aid in predicting whether a given sequence is a particular secondary structure or not, without a knowledge of its three-dimensional structure.

State-structure models—A base for efficient control of fermentation processes

The imbedding of state-structure models into the framework of structured segregated models is described. A special type of state-structure models based on delay-differential equations is considered. Some results regarding the description of unbalanced growth processes and the development of efficient periodic control strategies are presented.

Changes of Escherichia coli cell cycle parameters during fast growth and throughout growth with limiting amounts of thymine

It is generally accepted that during fast growth of Escherichia coli, the time (D) between the end of a round of DNA replication and cell division is constant. This concept is not consistent with the fact that average cell mass of a culture is an exponential function of the growth rate, if it is also accepted that average cell mass per origin of DNA replication (Mi) changes with growth rate and negative exponential cell age distribution is taken into account. Data obtained from cell composition analysis of E. coli OV-2 have shown that not only Mi but also D varied with growth rate at generation times (tau) between 54 and 30 min. E. coli OV-2 is a thymine auxotroph in which the replication time (C) can be lengthened, without inducing changes in tau, by growth with limiting amounts of thymine. This property has been used to study the relationship between cell size and division from cell composition measurements during growth with different amounts of thymine. When C increased, average cell mass at the end of a round of DNA replication also increased while D decreased, but only the time lapse (d) between the end of a replication round and cell constriction initiation appeared to be affected because the constriction period remained fairly constant. We propose that the rate at which cells proceed to constriction initiation from the end of replication is regulated by cell mass at this event, big cells having shorter d times than small cells.

Stability of pBR322-derived plasmids

The stability of pBR322-derived plasmids was studied during growth of their Escherichia coli host in the absence of antibiotics. Plasmid pBR322, as well as its delta rom and delta bla derivatives, were lost from their host within 60 generations, but a number of delta tet derivatives were quite stable under the same conditions. An evaluation of the data indicated that primary plasmid loss due to random partitioning corresponds to the generation of a plasmid-free cell about every 10(4) divisions (probability P0; = "intrinsic" instability). Secondary loss of plasmid-carrying cells resulted from a growth advantage of the plasmid-free cells when bacteria die, perhaps due to unrepaired lethal damage in the DNA, under conditions of stationary incubation (= "apparent" instability). This cell death also occurred in the absence of plasmids but was accelerated by the presence of extra plasmid DNA in the cell and further accelerated by a functional tet gene. This was the reason for the differential apparent stabilities of delta bla and delta tet plasmids. There was no indication that an accumulation of plasmid multimers contributed to the plasmid instability, as has been suggested in the literature. The value of P0 = 10(-4) is 14 orders of magnitude greater than expected under the assumption of a random (Poisson) distribution of plasmid copy numbers in a population of cells.