Modeling Triggering and Repression of Competence in Bacillus

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Modeling Triggering and Repression of Competence in Bacillus Subtilis Gavin Price • • •

Modeling Triggering and Repression of Competence in Bacillus Subtilis Gavin Price • • • Gavin Price Background Recap Sensitivity analysis of the com. K/rok system Exploration of the CSF switch hypothesis Pseudo stochastic simulation of the CSF model Modeling quorum sensing with the com. K/rok system Arkin Lab 7/5/05

Background • Bacteria are called competent if they possess the ability to take up

Background • Bacteria are called competent if they possess the ability to take up extra-cellular DNA and combine it with their own • Uptake and recombination can be promiscuous or based on similarity • Some known competent species: B. subtilis, Streptococcus pneumoniae, Haemophilius influenzae • Several hypotheses regarding the reason for competence • DNA as food • Lateral gene transfer & diversification of the gene pool • DNA use as a template for repair • In B. subtilis, one of several responses to stress including degradative enzyme synthesis, chemotaxis, and sporulation. • Competence triggered by high population density and low resource levels • Small fraction of the population becomes competent for 3 -4 hrs – ~10 -20% in lab strains • Many interesting questions to be answered: • What makes the induction of competence stochastic • How does the network integrate environmental and internal signals to turn competence on and off • How do the various stress response networks interact • We can suggest answers to some of these questions via mathematical modeling of the system Gavin Price Arkin Lab 7/5/05

The Competence Signaling Pathway Gavin Price Arkin Lab 7/5/05

The Competence Signaling Pathway Gavin Price Arkin Lab 7/5/05

6 ‘Modules, ’ 5 modeled, with 31 species and 100 parameters Quorum Sensing Unknown

6 ‘Modules, ’ 5 modeled, with 31 species and 100 parameters Quorum Sensing Unknown Quorum Sensing/ Timing? Degradation Regulation Degradation Competence Commitment Signal Gavin Price Arkin Lab 7/5/05

Modules Interact to Control Competence Quorum Sensing/ Timing? Degradation Regulation Sporulation Induction Abr. B

Modules Interact to Control Competence Quorum Sensing/ Timing? Degradation Regulation Sporulation Induction Abr. B 4 Degradation Competence Commitment Signal Gavin Price Arkin Lab 7/5/05

A Recap, Gentle Readers • • • Isolated the core com. K/rok system Deg.

A Recap, Gentle Readers • • • Isolated the core com. K/rok system Deg. U required for Com. K com. K binding Abr. B 4 concentration drops as sporulation signals start, triggering a spike in Com. K Abr. B 4 releases repression on rok, which represses Com. K in turn 3 species, 19 parameters, 2 of which are known Last time showed the results of informal sensitivity analysis, i. e. twiddling parameters Gavin Price Arkin Lab 7/5/05

Sensitivity Analysis • • • Sensitivity Equation from Khalil 92 Augment set of ODEs

Sensitivity Analysis • • • Sensitivity Equation from Khalil 92 Augment set of ODEs with sensitivity equations (# of variables * # of parameters) Solve augmented set Results in sensitivity of each variable to each parameter as a function of time Divide by (x/ ) to get elasticity Gavin Price Arkin Lab 7/5/05

Sensitivity Analysis Results …this is a little hard to interpret Gavin Price Arkin Lab

Sensitivity Analysis Results …this is a little hard to interpret Gavin Price Arkin Lab 7/5/05

7 Key Parameters • Rok production and degradation rates • Com. K production and

7 Key Parameters • Rok production and degradation rates • Com. K production and degradation rates • Binding constants for Com. K, Rok, and Abr. B when Deg. U is bound Gavin Price Arkin Lab 7/5/05

The rap. C/phr. C Cassette’s Purpose is Uncertain • Solomon 96 suggests that the

The rap. C/phr. C Cassette’s Purpose is Uncertain • Solomon 96 suggests that the cassette may be a switch that turns off competence and enhances sporulation • CSF exhibits biphasic behavior in srf. A induction (activated by Com. A~P) • One hypothesis is that CSF binds to Com. P, preventing phosphorylation of Com. A Gavin Price Arkin Lab 7/5/05

The CSF Com. P Binding Model Gavin Price Arkin Lab 7/5/05

The CSF Com. P Binding Model Gavin Price Arkin Lab 7/5/05

Cell Density Effects • Relative Density affects the concentration of molecules that are excreted

Cell Density Effects • Relative Density affects the concentration of molecules that are excreted from the cell Gavin Price Arkin Lab 7/5/05

CSF can shut off competence given appropriate parameters • Com. K to Mec. A

CSF can shut off competence given appropriate parameters • Com. K to Mec. A binding speed is probably overdone. Corrected in next version Gavin Price Arkin Lab 7/5/05

Pseudo Stochastic Analysis of the CSF System • Added Gaussian noise to the com.

Pseudo Stochastic Analysis of the CSF System • Added Gaussian noise to the com. S transcription rate parameter • Tried several parameter update frequencies, with and without Gaussian noise in the update time • Monitored Com. K 4 concentration Gavin Price Arkin Lab 7/5/05

The System Filters High Frequency Noise 0. 01 Hz 0. 001 Hz 0. 0001

The System Filters High Frequency Noise 0. 01 Hz 0. 001 Hz 0. 0001 Hz • Adding noise to the parameter update time doesn’t make a noticeable difference Gavin Price Arkin Lab 7/5/05

At 0. 001 Hz, Gaussian com. S Noise Produces Population Diversity Gavin Price Arkin

At 0. 001 Hz, Gaussian com. S Noise Produces Population Diversity Gavin Price Arkin Lab 7/5/05

Modeling Quorum Sensing With the com. K/rok Module Gavin Price Arkin Lab 7/5/05

Modeling Quorum Sensing With the com. K/rok Module Gavin Price Arkin Lab 7/5/05

Hypotheses and Data • Both starvation (represses Abr. B 4) and overpopulation (quorum sensing)

Hypotheses and Data • Both starvation (represses Abr. B 4) and overpopulation (quorum sensing) are necessary to induce competence • One or the other should not trigger competence • Competence lasts for about 4 hours (Nester 1963, Stocker 1963, Mc. Carthy 1967) • Com. K 4 transcription increases from undectectable concentrations and levels off in 2 hours (Hahn 1994, Turgay 1998) • Only one datapoint after the 2 hr mark in these experiments, but repeated 5 times • Com. K 4 from a competent culture degrades in about 2 hours, and is stable without the Clp. CP degradation mechanism (Turgay 1998) WT mec. A- WT clp. C- Gavin Price Arkin Lab Com. S overexpression 7/5/05

So We Should Expect to See Something Like… Overpopulation only Starvation and overpopulation Starvation

So We Should Expect to See Something Like… Overpopulation only Starvation and overpopulation Starvation only Gavin Price Arkin Lab 7/5/05

Current Model Doesn’t Quite Fit • Small difference between overpopulation response and starvation/overpopulation response

Current Model Doesn’t Quite Fit • Small difference between overpopulation response and starvation/overpopulation response • Difficult to increase S/O curve without also increasing O curve Gavin Price Arkin Lab 7/5/05

Add CSF to Control Overpopulation Response Gavin Price Arkin Lab 7/5/05

Add CSF to Control Overpopulation Response Gavin Price Arkin Lab 7/5/05

CSF Limits Com. K Overproduction in Overpopulation Scenario Gavin Price Arkin Lab 7/5/05

CSF Limits Com. K Overproduction in Overpopulation Scenario Gavin Price Arkin Lab 7/5/05

Next Steps • • Continue expansion/correction of model Stochastic simulation with Gillespie algorithm Parameter

Next Steps • • Continue expansion/correction of model Stochastic simulation with Gillespie algorithm Parameter estimation for more differentiated response curves Measure time series of key species in lab (Com. K, Rok, Abr. B, Com. P) Acknowledgements Adam Arkin Denise Wolf Pat Flaherty Gavin Price Matt Onsum Arkin Lab 7/5/05