There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

SUMMARY An essential feature of bacterial plasmids is their ability to replicate as autonomous genetic elements in a controlled way within the host. Therefore, they can be used to explore the mechanisms involved in DNA replication and to analyze the different strategies that couple DNA replication to other critical events in the cell cycle. In this review, we focus on replication and its control in circular plasmids. Plasmid replication can be conveniently divided into three stages: initiation, elongation, and termination. The inability of DNA polymerases to initiate de novo replication makes necessary the independent generation of a primer. This is solved, in circular plasmids, by two main strategies: (i) opening of the strands followed by RNA priming (theta and strand displacement replication) or (ii) cleavage of one of the DNA strands to generate a 3′-OH end (rolling-circle replication). Initiation is catalyzed most frequently by one or a few plasmid-encoded initiation proteins that recognize plasmid-specific DNA sequences and determine the point from which replication starts (the origin of replication). In some cases, these proteins also participate directly in the generation of the primer. These initiators can also play the role of pilot proteins that guide the assembly of the host replisome at the plasmid origin. Elongation of plasmid replication is carried out basically by DNA polymerase III holoenzyme (and, in some cases, by DNA polymerase I at an early stage), with the participation of other host proteins that form the replisome. Termination of replication has specific requirements and implications for reinitiation, studies of which have started. The initiation stage plays an additional role: it is the stage at which mechanisms controlling replication operate. The objective of this control is to maintain a fixed concentration of plasmid molecules in a growing bacterial population (duplication of the plasmid pool paced with duplication of the bacterial population). The molecules involved directly in this control can be (i) RNA (antisense RNA), (ii) DNA sequences (iterons), or (iii) antisense RNA and proteins acting in concert. The control elements maintain an average frequency of one plasmid replication per plasmid copy per cell cycle and can “sense” and correct deviations from this average. Most of the current knowledge on plasmid replication and its control is based on the results of analyses performed with pure cultures under steady-state growth conditions. This knowledge sets important parameters needed to understand the maintenance of these genetic elements in mixed populations and under environmental conditions.

Replication and control of circular bacterial plasmids.

Construction of improved Escherichia-Pseudomonas shuttle vectors derived from pUC18/19 and sequence of the region required for their replication in Pseudomonas aeruginosa

On plasmid incompatibility.

Higgs Boson Theory and Phenomenology

An autonomously replicating 2,248-base-pair DNA segment of the mini-F plasmid carries nine 19-base-pair repeating sequences Five of the repeats are arranged in one direction and form the right cluster, whereas the remaining four repeats are arranged in the opposite direction and form the left cluster (Murotsu et al, Gene 15:257-271, 1981) Each cluster, cloned separately into the multicopy plasmid vector pBR322, exhibited a strong F-specific incompatibility phenotype (FIP) These clusters were thought to be responsible for the expression of IncB and IncC phenotypes, causing a switchoff function on mini-F replication Mini-F DNA fragments containing two, three, or more than four repeats were inserted into pBR322 Cells carrying these recombinant plasmids exhibited, respectively, no, intermediate, and strong FIP intensity Cloning of five repeats into pSC101, whose copy number is about 6 in contrast to 20 for pBR322, resulted in an FIP of intermediate intensity Thus, the intensity of FIP reflects the dosage of repeats in a cell The five repeats in the right cluster were eliminated from the mini-F derivative without impairing its autonomous-replicating ability (Bergquist et al, J Bacteriol 147:888-889, 1981; Kline and Palchavdhuri, Plasmid 4:281-289) Such deletion, however, caused a sixfold elevation of the copy number When the eliminated cluster of repeats was reinserted in the derivative, the copy number was lowered to the original value, viz, 1 to 2 The position and orientation of this insertion was not important in the copy number control Thus, the repeats are also related to copy number control A model to account for the role of the repeating sequences in the control of copy number and FIP is discussed

Role of Nine Repeating Sequences of the Mini-F Genome for Expression of F-Specific Incompatibility Phenotype and Copy Number Control

In this paper, a significant acceleration of estimating low-failure rate in a high-dimensional SRAM yield analysis is achieved using sequential importance sampling. The proposed method systematically, autonomously, and adaptively explores failure region of interest, whereas all previous works needed to resort to brute-force search. Elimination of brute-force search and adaptive trial distribution significantly improves the efficiency of failure-rate estimation of hitherto unsolved high-dimensional cases wherein a lot of variation sources including threshold voltages, channel-length, carrier mobility, etc. are simultaneously considered. The proposed method is applicable to wide range of Monte Carlo simulation analyses dealing with high-dimensional problem of rare events. In SRAM yield estimation example, we achieved 106 times acceleration compared to a standard Monte Carlo simulation for a failure probability of 3 × 10−9 in a six-dimensional problem. The example of 24-dimensional analysis on which other methods are ineffective is also presented.

Sequential importance sampling for low-probability and high-dimensional SRAM yield analysis

Mini-F is a fragment of the F plasmid, consisting of 9,000 base pairs, which carries all of the genes and sites required for replicon maintenance and control. Its copy number is one to two per chromosome. This plasmid is joined to ColE1, whose copy number is 16 to 20. Under normal circumstances the composite plasmid replication exhibited ColE1 characteristics, maintaining a high copy number. However, when ColE1 replication was inhibited by deoxyribonucleic acid polymerase I inactivation, its replication exhibited mini-F characteristics, maintaining a low copy number. These observations are in complete agreement with those of Timmis et al. (Proc. Natl. Acad. Sci. U.S.A. 71:4556-4560, 1974), who examined the behavior of a recombinant plasmid formed between pSC101 and ColE1. The transition from high to low copy number allowed us to examine the control system acting in cells carrying plasmids exhibiting intermediate copy numbers. The initiation of the mini-F replication system as represented by deoxyribonucleic acid synthesis of the composite plasmid was completely blocked when there were multiple copies of mini-F in a cell. It was not restored until the copy number was lowered to one to two, after which replication was first detected. ppF, a mini-F replicon packaged in a phage λ head behaved similarly: its replication was completely shut off when the resident mini-F genome copy number was high and was inhibited partially when the resident mini-F genome copy number was low. These experiments clearly demonstrate that there is a switch-off mechanism acting on deoxyribonucleic acid synthesis (initiation) in a cell carrying mini-F, and its intensity is related to the plasmid copy number. This result supports the “inhibitor dilution model” proposed by Pritchard et al. (Symp. Soc. Gen. Microbiol. 19:263-297, 1969). The nature of the hypothetical inhibitor is discussed.

Replication Control and Switch-Off Function as Observed with a Mini-F Factor Plasmid

The minimal replication origin of miniF plasmid was found to lie within a region of 217 bp in length. This region contains an AT cluster and the four 19 bp direct repeats responsible for incompatibility, termed incB. Its location coincides with that of ori2 of plasmid F, previously inferred to be the replication starting point by electron microscopic analysis (Eichenlaub et al. 1981).

Identification of the minimal essential region for the replication origin of miniF plasmid

A device array suitable for efficiently collecting statistical information on bias-temperature instability (BTI) parameters of a large number of transistors is presented. The proposed array structure substantially shortens measurement time of threshold voltage shifts under BTI conditions by parallelizing stress periods of multiple devices while maintaining 0.2mV precision. An implementation of BTI array consisting of 128 devices successfully validates stress-pipelining concept. Log-normal distributions of time exponents are experimentally observed.

Hiroshi Tsutsui

Papers

Role of Nine Repeating Sequences of the Mini-F Genome for Expression of F-Specific Incompatibility Phenotype and Copy Number Control

Sequential importance sampling for low-probability and high-dimensional SRAM yield analysis

Replication Control and Switch-Off Function as Observed with a Mini-F Factor Plasmid

Identification of the minimal essential region for the replication origin of miniF plasmid

A device array for efficient bias-temperature instability measurements