2D System of Lac Operon Dynamics
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Transcript of 2D System of Lac Operon Dynamics
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2D System of Lac Operon Dynamics: mRNA and Lactose
Joaquin ReynaLanie Happ
Rohit MandeDerek Bever
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Lac Operon Background
“Adaptive enzymes” coined by André Lwoff from observing yeast (1940) Classical lac operon model developed by Francois Jacob and Jacques Monod using E.
Coli (1949 – 1950s) First genetic regulatory mechanism to be fully understood/documented The lac operon has become the foremost model/example of prokaryotic gene
regulation.
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OFF stat
e
ON stat
e
Lac Operon Activity
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Our Simplified Model
Assumption: Glucose concentration is low and the effect of cAMP is removedM′ = basal transcription rate + mRNA induction via lactose - degradation of mRNA
L′ = uptake of lactose by permease - dilution of lactose - breakdown of lactose byβ-galactosidase
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M′ = a + (b * L5)/(c + L5) - d * ML′ = e * M - f * L - (g * M * L)/(h
+ L)
Our Simplified Model
mRNA Parameters
Lactose Parametersa - basal transcription rate b - maximal transcription ratec - transcription capacity as a result of lactose activationd - mRNA degradation rate constant
e - rate constant of lactose influx as a result of mRNA (= to permease)f - lactose degradation rate constantg - maximal β-galactosidase degradation rateh - β-galactosidase activity capacity as a result of lactose activation
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M’ = 0.05 + (L5 / (1 + L5)) - ML’ = M - 0.2L - (ML / (2 + L))
Bistabilty in the Lac Operon
A
B
C
Fixed points:A: (1.0388, 2.3717) = nodal sinkLac operon is ON
B: (0.18585, 0.69071) = saddle point
C: (0.050605, 0.22721) = nodal sinkLac operon is OFF
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The Change in mRNA and Lactose over Time
mRNA vs. time
Lactose vs. time
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Changing the Dynamics by Varying the Concentration of External Lactose (e)
e << 1(e = 0.3)e = 1e >> 1(e = 3)
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Lac Operon Dynamics using Parameters from Literature1
Parameter Description Value
b maximum transcription initiation rate ~0.18 min-1
d degradation rate of mRNA in E. coli
~0.46 mRNA/min-1
e maximum rate of permease activity (lactose into cell) ~6.0X104 min-1
gmaximum rate of β-
galactosidase activity (breakdown of lactose)
~3.8x104 min-1
1Santillan, M. “Bistable Behavior in a model of the lac Operon in Escherichia coli with Variable Growth Rate.” Biophys Journal 2008 March 15. 94(6): 2065-2081
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Fixed Point:.
A: (0.5, 55003.4485) = nodal sink
Limitation:
Simple model does not seem to exhibit bistable behavior using experimentally determined parameters.
mRNA is not the cap for lactose. In reality it’s β-galactosidase production.
Lac Operon Dynamics using Parameters from Literature
A
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Further Model Development Include a glucose variable Include a protein variable Include a cell growth variable
New Research Ideas Understand the effect of
multiple operator binding sites
Research the effect of different lac operon alleles on dynamics
Future Directions
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Santillán, M. and MC Mackey. “Quantitative approaches to the study of bistability in the lac operon of Escherichia coli.” J R Source Interface 5 (2008): S29-39
Santillán, M. “Bistable Behavior in a model of the lac Operon in Escherichia coli with Variable Growth Rate.” Biophys Journal 2008 March 15. 94(6): 2065-2081
Yildirim, N. et. al. “Dynamics and bistability in a reduced model of the lac operon.” Chaos 14 (2004): 279-92
Díaz-Hernández O, Santillán M. Bistable Behavior of the Lac Operon in E. Coli When Induced with a Mixture of Lactose and TMG. Frontiers in Physiology. 2010;1:22. doi:10.3389/fphys.2010.00022.
Müller-Hill, Benno. The Lac Operon. Berlin; New York: Walter de Gruyter, 1996. Print.
References
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QQuestions???
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