# Plasmid segregation and accumulation

@article{Muller2017PlasmidSA, title={Plasmid segregation and accumulation}, author={Johannes Muller and K Munch and Bendix Koopmann and Eva Stadler and Louisa Roselius and Dieter Jahn and Richard Munch}, journal={arXiv: Populations and Evolution}, year={2017} }

The segregation of plasmids in a bacterial population is investigated. Hereby, a dynamical model is formulated in terms of a size-structured population using a hyperbolic partial differential equation incorporating non-local terms (the fragmentation equation). For a large class of parameter functions this PDE can be re-written as an infinite system of ordinary differential equations for the moments of its solution. We investigate the influence of different plasmid production modes, kinetic…

## 3 Citations

Eigensolutions and spectral analysis of a model for vertical gene transfer of plasmids

- BiologyJournal of mathematical biology
- 2019

The dynamics of a bacterial population carrying plasmids is studied and a simple real dominating eigenvalue with a non-negative corresponding eigen function is found and an iterative method for the numerical construction of the eigenfunction is described.

Evolutionary model for the unequal segregation of high copy plasmids

- Biology, EngineeringPLoS Comput. Biol.
- 2019

This work uses mathematical modeling to investigate the evolutionary stability of plasmid segregation for high-copy plasmids—plasmids that are present in up to several hundred copies per cell—carrying antibiotic resistance genes.

Transport equations and plasmid-induced cellular heterogeneity

- Biology, Engineering
- 2019

This thesis deals with the long-time distribution of plasmids in a bacterial population and model equations are hyperbolic transport equations with an integral term for vertical gene transfer.

## References

SHOWING 1-10 OF 42 REFERENCES

Analysis of the Stabilizing Effect of ROM on the Genetic Network Controlling ColE1 Plasmid Replication

- BiologyPacific Symposium on Biocomputing
- 1999

The rate of spontaneous plasmid loss provides an evolutionary explanation for the maintainance of Rom protein and the ability of stochastic models to link biochemical function with evolutionary considerations is discussed.

Kinetic analysis of the effects of plasmid multimerization on segregational instability of CoIE1 type plasmids in Escherichia coli B/r

- Biology, EngineeringBiotechnology and bioengineering
- 1991

The results suggest that when the ColE1‐type plasmid does not encode and express any large or disruptive foreign proteins, the copy number of 45 per cell may be the threshold at which only growth rate–dependent instability is responsible for overall plasmids instability.

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

- Biology, EngineeringBiotechnology and bioengineering
- 1996

A Monte Carlo simulation of plasmid replication and partition was developed, with a specific mechanism to mediate the transfer from mother to daughter cells, whereas the high‐copy plasmids were partitioned passively with cell mass.

Analysis of a Population Model Structured by the Cells Molecular Content

- Mathematics
- 2008

We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the…

An abstract delay-differential equation modelling size dependent cell growth and division

- Mathematics
- 1985

A two-phase model for the growth of a single cell population structured by size is formulated and analysed. The model takes the form of a delay-differential equation in a Banach space. Using…

EXISTENCE OF A SOLUTION TO THE CELL DIVISION EIGENPROBLEM

- Mathematics
- 2006

We consider the cell division equation which describes the continuous growth of cells and their division in two pieces. Growth conserves the total number of cells while division conserves the total…

Stochastic switching as a survival strategy in fluctuating environments

- BiologyNature Genetics
- 2008

It is found that fast-sw switching populations outgrow slow switchers when the environment fluctuates rapidly, whereas slow-switching phenotypes outgrow fast switcher when the environments changes rarely.

Links between deterministic and stochastic approaches for invasion in growth-fragmentation-death models

- MathematicsJournal of mathematical biology
- 2016

It is proved that the two approaches to study invasion in growth-fragmentation-death models lead to the same criterion of possible invasion, and a proof of the existence of a solution to the eigenproblem is given which satisfies the conditions needed for the study of the stochastic model, hence providing a set of assumptions under which both approaches can be carried out.