Team:Newcastle/Stochasticity

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Contents 1 Stochastic Modelling Tools 1.1 Matlab 1.2 Stocks 2 2 Stochastic Switch Examples 2.1 Natural switches 2.1.1 Sin (Sporulation Inhibition) operon 2.1.1.1 Sin operon details 2.1.2 ComK positive autoregulation 2.1.2.1 Mathematical Modelling of comK 2.1.3 Sigma D 2.2 Synthetic Switches 2.3 Some useful links for bistability

Stochastic Modelling Tools

Matlab

Matlab can be used for stochastic modelling. Glasgow team used Matlab implementing Gillespie algorithm to incorporate noise among cells. They also used deterministic modelling using ODEs and compared their results. When the number of cells increase two approaches become similar since the noise is cancelled out.

Stocks 2

Stocks 2 is another stochastic simulation tool which also uses Gillespie’s direct method and supports SBML.

Stochastic Switch Examples

Natural switches

Sin (Sporulation Inhibition) operon

Sin (Sporulation Inhibition) operon can be used as the stochastic switch. It is a natural bistable switch.

File:SinOperon.jpg

During normal conditions, SinR is expressed constitutively from P3 and keeps its concentration at a constant level repressing promoter 1. When transcription of promoter1 is activated by phosphorylated Spo0A, both sinI and sinR are expressed from promoter 1. SinI inactivates SinR by forming a complex with sinR upregulating both proteins from promoter1. This cross repression, inhibition of SinR by SinI and the transcriptional represion of sinI by SinR, forms the basis of the bistability. While the positive feedback in the production of SinI enhances the bistability, it also causes increase in sinR levels because of the expression from promoter 1 hence causing oscillations.[1]

Sin operon controls the early stages of sporulation and has a key role to control the sporulation without disturbing its regulation. The threshold of this switch to progress into sporulation can be controlled by varying some parameters, hence providing population heterogeneity. Tight binding of SinR to the first promoter region with fewer sinR molecules increases this heterogeneity. By mutating the first promoter, the binding affinity of sinR the promoter can be increased. With variations on SinI:SinR interaction strength, transcription rate of sinR from the third promoter and the expression rate of SinR, dynamics of the system can be altered.[1]

SinI can be tuned with the paremeters. SinR and SinI can be used to regulate the heavy metal sequestration. Only in a sub population of the bacteria, sinI will be expressed at sufficient levels to trigger our system. Whereas sinR will be expressed in all cells. We can engineer the bacteria so that, when SinI is expressed, it binds to SinR which inhibits heavy metal intake. SinI levels will be sufficient to derepress the intake of heavy metals only in a small population of the cells since it is regulated by spo0A which is active only in a subset of the cells. Spo0A phosplation itself is also a bitsable switch so that a subset of the population will be on spo0A ON state. [2,3] So with this approach we can say that only a small population of the cells will get the heavy metals. If we want the other way we can switch the roles of SinI and sinR.With the normal conditions only 2% of the population express enough sinI.[2]

1. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1449569
2. http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2430929&blobtype=pdf
3. http://arjournals.annualreviews.org/doi/pdf/10.1146/annurev.micro.62.081307.163002

Sin operon details

[http://www.ncbi.nlm.nih.gov/nuccore/143546?ordinalpos=1&itool=EntrezSystem2.PEntrez.Sequence.Sequence_ResultsPanel.Sequence_RVDocSum#sequence_143546 Sin operon in GenBank]

sinR: Positive regulation of comK; negative regulation of aprE, kinB, sigD, spo0A, spoIIA, spoIIE, spoIIG

http://www.ncbi.nlm.nih.gov/entrez/viewer.fcgi?val=NC_000964.2&from=2551885&to=2552220&dopt=gb

sinI:Antagonist of SinR

http://www.ncbi.nlm.nih.gov/entrez/viewer.fcgi?val=NC_000964.2&from=2551678&to=2551851&dopt=gb

ComK positive autoregulation

The positive feedback in comK regulation provides the bistability in B. subtilis. we can either knock out the competence system in B. subtilis or use a homolog system from another bacteria.

[http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=2041856&blobname=NIHMS25553-supplement-01.pdf ClustalW aligment of comK genes] (Figure 2)

• Streptococcus pneumoniae:

There is no evidence of bistability in in pneumococcal competence so we can not use the genes from S.pneumoniae (http://dx.doi.org/10.1038/nrmicro1613 )

• H. influenzae

Again, nearly all the cells become competent. (http://dx.doi.org/10.1016/0168-9525(96)10014-7)

• B. cereus

It has two homologues of B. subtilis comK gene. comK1(BC1134, 62%), comK2(BC5250, 48%). But the regulation and function of these two comK genes are unknown. B. cereus showd competence when comK gene from B. subtilis is placed into B. cereus (http://gbb.eldoc.ub.rug.nl/root/2008/MicrobBiotnMironczuk/)

Mathematical Modelling of comK

-[http://www.nature.com/nature/journal/v440/n7083/full/nature04588.html An excitable gene regulatory circuit induces transient cellular differentiation]

-[http://www.nature.com/nature/journal/v440/n7083/extref/nature04588-s1.pdf And its supplementary information with math equations and parameters]

• Related Links:

1. [http://www3.interscience.wiley.com/cgi-bin/fulltext/118659803/HTMLSTART Bistability using positive autoregulation of ComK]
2. [http://www.ncbi.nlm.nih.gov/pubmed/8878039 Regulatory inputs for the synthesis of ComK]
3. [http://mic.sgmjournals.org/cgi/content/full/152/2/473 Functional analysis of the competence transcription factor ComK of Bacillus subtilis by characterization of truncation variants]

[http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2041856#SD2 ClustalW aligment of comK genes]

Sigma D

It was porposed that perhaps sigma D could be used to make a stochastic switch however perhaps not enough is known about how it is regulated?

The factors that are responsible for the stationary-phase elevation in sigD levels are unknown. sigD-dependent transcription declines after the onset of sporulation, and inactivation of sigD itself causes no overt defect in sporulation, therefore sigD’s contribution to sporulation, if any, is modest. Present evidence demonstrates that sigD is primarily involved in the expression of flagellar, motility, and autolysin genes and their regulators.

The Sigma Factors of Bacillus subtilis, WILLIAM G. HALDENWANG MICROBIOLOGICAL REVIEWS, Mar. 1995, p. 1–30

Synthetic Switches

Synthetic bistable toggle switches constructed from LacI and Cl repressors can also be used. Theese repressors repress each other creating a bistable switch with two negative feedback loops. Bistable switch with two positive feedback can also be considered.

Some useful links for bistability

• [http://dx.doi.org/10.1016/S0955-0674(02)00314-9 Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability]
• [http://www3.interscience.wiley.com/cgi-bin/fulltext/118630112/HTMLSTART Bistability in Bacteria]
• [http://www3.interscience.wiley.com/journal/118659872/abstract?CRETRY=1&SRETRY=0 Initiation of sporulation]
• [http://www.sciencemag.org/cgi/content/full/320/5872/65 Stochasticity and Cell Fate]