Team:Nanjing-China/Model/h2s
The Signalling Cascade
sdSQR is a NAD(P)/FAD-dependent oxidoreductase, which oxidizes S2- to zero-valent S0. SqrR, encoded by sqrR, is a constitutively expressed suppressor protein of sqr promotor. When there is no H2S in the environment, SqrR combines with the sqr promotor and keeps the expression of the enzyme at a low level; while in the case where H2S exists, it will be oxidized by the small amount of expressed enzyme, and the product will interact with SqrR, forming a tri- or tetrasulfide cross-links linking C41 and C107 on the same subunit of SqrR. The change in the structure of SqrR makes it fall off from the sqr promotor and thus the expression of sqr turns on. Overall, SQR promotes the expression of itself by producing substances that help with disinhibition[1,2].
Signalling Kinetics
In cell signaling, the enzyme sqr, catalyzes the oxidation of S2- to zero-valent S0, We model this rate using the Law of Michaelis–Menten kinetics, this model involves an enzyme, E, binding to a substrate, S, to form a complex, ES, which in turn releases a product, P, regenerating the original enzyme. This may be represented schematically as
where (forward rate), (reverse rate), and (catalytic rate) denote the rate constants, the double arrows between S (substrate) and ES (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).
Under certain assumption– such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by[3]
Applying these principles to the reaction:
Signalling Cascade Model Parameters |
Value |
Units |
| kcat | the turnover number |
1.5X10^2（est） |
| km | The substrate concentration at which the reaction rate is half of |
0.015（est） |
In cell signalling, . S will interact with SqrR, forming a tri- or tetrasulfide cross-links linking C41 and C107 on the same subunit of SqrR. The change in the structure of SqrR makes it fall off from the sqr promotor and thus the expression of sqr turns on.
We model this rate using the Law of Mass Action kinetics. This principle governs that the rate of a reaction (d/dt) is proportional to the concentrations of the substrates.
For a particular reaction, for example:
the rate can be written mathematically as:
But most biological reactions are reversible, like this:
so
Applying these principles to the interaction betw
een S and sqrR:
Model Parameters |
Value |
Units |
Kf1 |
sqrR binding constant |
13000（est） |
Kr1 |
SqrR dissociation |
220 |
Transcription
Transcription is a complex procession. However, it is well established that initiation of transcription is the major factor in determining overall rate of mRNA production. Transcription initiation is a process influenced by a number of key steps including: promoter escape, binding of the RNA Polymerase onto the promoter, isomerization, and formation of the closed RNA Pol complex from the open complex, and your Escherichia coli strain. In this model, we will assume that binding of the RNA polymerase is the rate determining step in transcription initiation.
Thus, our key assumptions for transcription are:
1. For the constitutively expressed gene sqrR, we can assume that they are at maximal transcription.
2. transcription rate is determined primarily by the disassociation of SqrR.
3. Promoter strength (in Polymerases per second) is a constant, and represents the rate of transcription at maximal expression.
We modeltranscription rate using Mass Action kinetics..
Model Parameters |
Value |
Units |
PsqrR strength |
0.12 |
mRNA molecules/sec |
| kf2 | S binding constant |
970(est) |
kr2 |
S dissociation |
25（est） |
Translation
After transcription, it must be translated into a functional chromo protein. Translation involves 3 main stages: initiation, elongation of the polypeptide, and termination. The key molecular machinery driving this process are ribosomes, who's binding and movements determine the overall rate of transcription.
Translation rate can be affected by 3 major processes:
a) the binding of the ribosome to the RBS,
b) formation of initiation complexes,
c) speed of the ribosome across the mRNA transcript.
we will assume that the movement of the ribosome (in amino acids formed per second) is the rate determining step in the translation of the proteins, and the average translation rate of 17.1 amino acids/sec.[4]
Product |
Length (amino acids) |
Translation rate (1/s) |
Sqr |
427 |
0.040 |
sqrR |
124 |
0.137 |
Mrfp |
236 |
0.072 |
Degradation and Dilution
The concentrations of each species in the model is affected by it’s degradation (inherent to the molecule) and dilution (due to cell growth). While these processes are completely unrelated, they have the same net effect: Decreasing the concentration of the species. Therefore, we represent the two rates as a combined degradation/dilution parameter in our model. we assume only the degradation/dilution of mrfp mRNA and mrfp.
Name |
Value |
Units |
Mrfp mRNA degradation/dilution |
0.0022 |
molecules/sec |
Mrfp protein degradation/dilution |
0.0013（est） |
molecules/sec |
Cellular Equations
Using the parameters found above, we can construct a series of ordinary differential equations:
The system described by these equations can be represented diagramatically by SimBiology:
Results
We assume the initial sqrR protein concentration was 0.2 mM, and the initial concentration of binding complex was 0.1mM, and the sqr mRNA as well as mecherry rfp mRNA was 0.01mM. The initial concentration was 20 mM for a 10 hour period of time.
Reference:
[1] Takayuki Shimizu, Jiangchuan Shen, Mingxu Fang, Yixiang Zhang, Koichi Hori, Jonathan C. Trinidad, Carl E. Bauer, David P. Giedroc, and Shinji Masuda. (2017). Sulfide-responsive transcriptional repressor SqrR functions as a master regulator of sulfide-dependent photosynthesis. PNAS, 114(9):2355-2360.
[2] Christoph Griesbeck, Günter Hauska and Michael Schütz. (2000). Biological Sulfide-Oxidation: Sulfide-Quinone Reductase (SQR), the Primary Reaction. Recent Research Developments in Microbiology, 4:179-203.
[3] Nelson, David L.; Cox, Michael M. (2013). Lehninger principles of biochemistry (6th ed.). New York: W.H. Freeman. pp. 158–162. ISBN 978-1429234146.
[4] Young, R and H Bremer: Polypeptide-Chain-Elongation Rate In Escherichia Coli B/R As A Function Of Growth Rate. Biochem. J. 160.2 (1976): 185-194. Web.
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