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QUANTITATIVE MODELING OF GENETIC CIRCUITS
INTEGRATING TRANSCRIPTIONAL AND SRNAMEDIATED REGULATIONS
FIGURE 8: Ferrous iron (Fe2+) is essential but itbecomes toxic in the presence of normal respiratoryby-products (H2O2):→ finely controlledhomeostasis; Salvail2012
UNDER IRON STARVATION...RyhB is a master regulator of ironhomestasis:
1 stimulates the degradationof ∼ 18 mRNAs encodingFe-proteins;
2 feedbacks on Fur;
3 promotes siderophoreproduction e.g. activatingshiA mRNA translation;
Quorum-sensing: regulation of geneexpression in response to cell density;it allows to track population density,synchronize gene expression on apopulation-wide scale, and therebycarry out collective activities.
FIGURE 9: Fenley2011
DIFFERENT ARRANGEMENTS→ DIFFERENTPHENOTYPES
1 V. harveyi produces and monitors theconcentrations of 3 autoinducers (AI), V.cholerae produces and monitors 2 AIs;
2 AI-1 and AI-2 act additively in V. harvey, butredundantly in V. cholerae;
3 ∆luxU: always bright (density-independent)in V. harveyi but not in V. cholerae.
4 ∆ sensor kinases (e.g. cqsS and luxQ)changed the luminescence phenotype in V.harveyi but not in V. cholerae.
Quorum-sensing: regulation of geneexpression in response to cell density;it allows to track population density,synchronize gene expression on apopulation-wide scale, and therebycarry out collective activities.
FIGURE 9: Fenley2011
DIFFERENT ARRANGEMENTS→ DIFFERENTPHENOTYPES
1 V. harveyi produces and monitors theconcentrations of 3 autoinducers (AI), V.cholerae produces and monitors 2 AIs;
2 AI-1 and AI-2 act additively in V. harvey, butredundantly in V. cholerae;
3 ∆luxU: always bright (density-independent)in V. harveyi but not in V. cholerae.
4 ∆ sensor kinases (e.g. cqsS and luxQ)changed the luminescence phenotype in V.harveyi but not in V. cholerae.
THIS IS AN APPROXIMATIONThe [m] and [s] concentrations are in the same order of magnitude→ the complex should not be neglected. We can overcome this limitationby using a saturation function telling which is the complexed fraction of the total form at steady state ( dx
dt = 0):
YA =AB
Atot=
Atot − Afree
Atot. (7)
ms = mtot − mfree, (8)
stot = sfree + ms, (9)
andms =
mfree · sfree
Kd, (10)
where Kd is the dissociation constant for the complex formation; the free quantities are unknown, the tot are known. After some math we getthe final form of the saturation function:
Ym =mtot + stot + Kd −
√(stot − mtot + Kd)
2 + 4Kdmtot
2mtot(11)
Using this approach we can simply model the control by the sRNA in the following way:
MODELING SRNA REGULATIONDYNAMICAL PROPERTIES OF SRNA-TRANSCRIPTION INTEGRATED
CIRCUITS
SRNA CAN PROVIDE A SWITCH-LIKE BEHAVIOR
10−2 10−1 100 10110−6
10−5
10−4
10−3
10−2
10−1
100
_s / _m
[ta
rge
t
mR
NA
]
Ultrasensitivity
a=10a=100a=1000a=10000
FIGURE 18: Ultrasensitive switch Mitarai2009.
SLIGHTLY DIFFERENT...
but comparable model from Mitarai2009:
ds
dt= α− s− γsm (13)
dm
dt= 1−
m
τ− γsm. (14)
where: α = αsαm
the relative transcription rate of s withrespect to that of m. γ = δαmτs quantifies theinactivation of the mRNA via sRNA:mRNA complexformation, and τ = τm
• Bistability: the capacity to achieve two alternative internal states in response to differentstimuli;
• ubiquitous in cellular systems;
• bistability is generated by regulatory interactions;
• fundamental biological significance e.g. cell differentiation, cell fate decision, adaptiveresponse to environmental stimuli, regulation of cell cycle oscillations and so on.
• switches involving ncRNA have been recently studied experimentally[Bumgarner2009,Iliopulos2009] and theoretically [Zhdanov2009].
MODELING SRNA REGULATIONDYNAMICAL PROPERTIES OF SRNA-TRANSCRIPTION INTEGRATED
CIRCUITS
BISTABILITY
THE MODEL
dx
dt=
Translation︷︸︸︷γy − δx︸︷︷︸
Degr.
(18)
dy
dt=
Synthesis︷ ︸︸ ︷λSy(x, p)−αy− σyz (19)
dz
dt= µSz(x, p)− βz− σyz. (20)
Where: x=protein TF, y=mRNA TF, z=sRNA.[Liu2011].
• bistability in this case only for intermediate association rates between sRNA and mRNA;
• In the monostable regimen lower degradation rates correspond to higher protein level and vice versa. On the converse, when theassociation rate is between A and B (the saddle points) the opposite can be true, depending on the initial conditions.
• the noise inherent in biological systems may induce switching between the two stable states.