A Monte Carlo simulation of plasmid replication during the bacterial division cycle

Kuo, Henry; Keasling, Jay D.

doi:10.1002/(sici)1097-0290(19961220)52:6<633::aid-bit1>3.0.co;2-p

Cited by 22 publications

(11 citation statements)

References 85 publications

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“…Instead of using a model to calculate an exact result for a variable, a simulation calculates a value many times over, each time assuming new values for each input, to give an estimation of the real value (15). Monte Carlo simulation is the most widely used simulation method in biology (4,16) and has been used to study the mechanism in such biochemical procedures as cell cycle control (9) and plasmid replication (10). While many plasmid replication models have been exploited using the molecular, modeling, and simulation methods (3,12,13,20), Kuo and Keasling (10) found that the use of a Monte Carlo simulation to compare the current theories was advantageous, since the possible combinations of replication and partition theories make laboratory experiments cumbersome and time consuming.…”

mentioning

confidence: 99%

Computer Simulation of Clostridium botulinum Strain 56A Behavior at Low Spore Concentrations

Zhao

Montville

Schaffner

2003

Appl Environ Microbiol

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It is generally assumed that spore behavior is independent of spore concentration, but recently published mathematical models indicate that this is not the case. A Monte Carlo simulation was employed in this study to further examine the independence assumption by evaluating the inherent variance in spore germination data. All simulations were carried out with @Risk software. A total of 500 to 4,000 iterations were needed for each simulation to reach convergence. Lag time and doubling time from a higher inoculum concentration were used to simulate the time to detection (TTD) at a lower inoculum concentration under otherwise identical environmental conditions. The point summaries of the simulated and observed TTDs were recorded for the 26 simulations, with kinetic data at the target inoculum concentration. The ratios of the median (R m ‫؍‬ median obs / median sim ) and 90% range (R r ‫؍‬ 90% range obs /90% range sim ) were calculated. Most R m and R r values were greater than one, indicating that the simulated TTDs were smaller and more homogeneous than the observed ones. R r values departed farther from one than R m values. Ratios obtained when simulating 1 spore with 10,000 spores deviated the farthest from one. Neither ratio was significantly different from the other when simulating 1 spore with 100 spores or simulating 100 spores with 10,000 spores. When kinetic data were not available, the percent positive observed at the 95th percentile of the simulated TTDs was obtained. These simulation results confirmed that the assumption of independence between spores is not valid.Mathematical modeling is an analytical approach using calculus, algebra, and basic probability theories to obtain precise numerical values for the variables in question (11,19). Under certain conditions, when the predictor variables are known and the relationship between the predictor and response variables is simple, analytical models are an ideal solution. However, this ideal approach quickly breaks down when faced with the complexity of the real world. It is rare to be able to accurately describe a biological procedure by mathematical equations. In addition, even if it is possible to construct equations, more often than not, these equations are not solvable without using numerical iterations or making considerable approximations of the real problem. Finally, every measurement in the real world is associated with a variance and a particular degree of uncertainty (5, 18) that cannot be described by an analytical model.A simulation approach is much more suitable than an analytical approach when dealing with complicated problems with an inherent variance. Instead of using a model to calculate an exact result for a variable, a simulation calculates a value many times over, each time assuming new values for each input, to give an estimation of the real value (15). Monte Carlo simulation is the most widely used simulation method in biology (4, 16) and has been used to study the mechanism in such biochemical procedures as cell cycle control (9) and...

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confidence: 99%

Computer Simulation of Clostridium botulinum Strain 56A Behavior at Low Spore Concentrations

Zhao

Montville

Schaffner

2003

Appl Environ Microbiol

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“…The positions of the stippled squares indicate plasmid replication one generation after initiation of chromosome replication. The data of Keasling et al [8] and Finkelstein and Helmstetter [5] are consistent with plasmid replication between one half and one full generation after initiation of chromosome replication. The range of the data are indicated by the shaded trapezoidal area.…”

Section: Model For the Timing Of Plasmid Replicationmentioning

confidence: 54%

“…The proposal of cycle‐specific plasmid replication has been supported by the data of Koppes [3] and Finkelstein and Helmstetter [4]. A simulation of F‐plasmid and chromosome replication during the cell cycle supports the proposal that the F plasmid replicates in a cycle‐specific manner [5].…”

Section: Introductionmentioning

confidence: 76%

Cycle-specific replication of chromosomal and F-plasmid origins

Cooper

Keasling

1998

FEMS Microbiology Letters

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There have been various proposals for the pattern of F-plasmid replication during the division cycle. Here we show that the recent studies of Gordon et al. (Cell 90, 1113-1121, 1997) on the duplication and segregation of green fluorescent protein (GFP) labeled replication origins of the Escherichia coli chromosome and the F plasmid during the division cycle support the proposal that the F plasmid replicates with a cell-cycle-specific (artiocyclic) pattern.

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“…The discrete event view combines a continuous-time base with describing the dynamics of a system by distinguished state changes, that is, events that are triggered by the flow of time or the situation (Zeigler et al, 2000). Discrete event approaches address specific constraints of continuous and deterministic models: concentrations do not necessarily change continuously, particularly if the dynamics of a small amount of entities, like DNA molecules and plasmids, are modelled (Kuo and Keasling, 1996). In addition, the dynamics of some biological systems can be best approached in a stochastic manner, for example, if the gene regulation is to be described (Puchulka and Kierzek, 2004), where stochastic fluctuations are abundant (Cowan, 2003).…”

Section: Introductionmentioning

confidence: 99%

Discrete event modelling and simulation in systems biology

Ewald

Maus

Rolfs

et al. 2007

Journal of Simulation

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With Systems Biology, a promising new application area for modelling and simulation emerges. Today's biologists are facing huge amounts of data delivered at different levels of detail by a multitude of advanced experimentation techniques. The Systems Biology approach copes with this information by cycling through phases of forming hypotheses, constructing models, experimenting with or analysing these models, and validating the findings by wet-lab experiments. A crucial point is therefore the way in which the knowledge about a system is formalized, that is, how a biological system is described, as this constrains the perception of the system as well as the scope of possible answers the model might provide. In this article, we compare different discrete event modelling formalisms (PETRI NETS, Stochastic p-CALCULUS, STATECHARTS, and DEVS) regarding their applicability to a cell biological system of current research interest, the Wnt signalling pathway. We then introduce the popular Gillespie algorithm, which is the foundation of many discrete event simulators for molecular-biological systems, and elaborate on some interesting extensions.

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A Monte Carlo simulation of plasmid replication during the bacterial division cycle

Cited by 22 publications

References 85 publications

Computer Simulation of Clostridium botulinum Strain 56A Behavior at Low Spore Concentrations

Computer Simulation of Clostridium botulinum Strain 56A Behavior at Low Spore Concentrations

Cycle-specific replication of chromosomal and F-plasmid origins

Discrete event modelling and simulation in systems biology

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