1,687 research outputs found
Dynamic model of gene regulation for the lac operon
Gene regulatory network is a collection of DNA which interact with each other and with other matter in the cell. The lac operon is an example of a relatively simple genetic network and is one of the best-studied structures in the Escherichia coli bacteria. In this work we consider a deterministic model of the lac operon with a noise term, representing the stochastic nature of the regulation. The model is written in terms of a system of simultaneous first order differential equations with delays. We investigate an analytical and numerical solution and analyse the range of values for the parameters corresponding to a stable solution
Phenotypic Variation and Bistable Switching in Bacteria
Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.
Network Topology as a Driver of Bistability in the lac Operon
The lac operon in Escherichia coli has been studied extensively and is one of
the earliest gene systems found to undergo both positive and negative control.
The lac operon is known to exhibit bistability, in the sense that the operon is
either induced or uninduced. Many dynamical models have been proposed to
capture this phenomenon. While most are based on complex mathematical
formulations, it has been suggested that for other gene systems network
topology is sufficient to produce the desired dynamical behavior.
We present a Boolean network as a discrete model for the lac operon. We
include the two main glucose control mechanisms of catabolite repression and
inducer exclusion in the model and show that it exhibits bistability. Further
we present a reduced model which shows that lac mRNA and lactose form the core
of the lac operon, and that this reduced model also exhibits the same dynamics.
This work corroborates the claim that the key to dynamical properties is the
topology of the network and signs of interactions.Comment: 15 pages, 13 figures, supplemental information include
Boolean Models of Bistable Biological Systems
This paper presents an algorithm for approximating certain types of dynamical
systems given by a system of ordinary delay differential equations by a Boolean
network model. Often Boolean models are much simpler to understand than complex
differential equations models. The motivation for this work comes from
mathematical systems biology. While Boolean mechanisms do not provide
information about exact concentration rates or time scales, they are often
sufficient to capture steady states and other key dynamics. Due to their
intuitive nature, such models are very appealing to researchers in the life
sciences. This paper is focused on dynamical systems that exhibit bistability
and are desc ribedby delay equations. It is shown that if a certain motif
including a feedback loop is present in the wiring diagram of the system, the
Boolean model captures the bistability of molecular switches. The method is
appl ied to two examples from biology, the lac operon and the phage lambda
lysis/lysogeny switch
A Type System for a Stochastic CLS
The Stochastic Calculus of Looping Sequences is suitable to describe the
evolution of microbiological systems, taking into account the speed of the
described activities. We propose a type system for this calculus that models
how the presence of positive and negative catalysers can modify these speeds.
We claim that types are the right abstraction in order to represent the
interaction between elements without specifying exactly the element positions.
Our claim is supported through an example modelling the lactose operon
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