Modeling sRNA-dependent circuits

QUANTITATIVE MODELING OF GENETIC CIRCUITS

INTEGRATING TRANSCRIPTIONAL AND SRNAMEDIATED REGULATIONS

Matteo Brilli

INRIA - RHONE-ALPESLBBE

UMR CNRS 5558UNIV-LYON1

Trento November 27, 2012

(INRIA, CNRS, UNIV-LYON1) MODELING INTEGRATED GENETIC CIRCUITS NOVEMBER 27, 2012 1 / 31

TOC

1 INTRODUCTION

2 EXAMPLES

3 BASICS OF MATHEMATICAL MODELING

4 NETWORK MOTIFS AND THEIR DYNAMICAL PROPERTIES

5 MODELING SRNA REGULATIONDynamical properties of sRNA-transcription integrated circuits


INTRODUCTION

INTRODUCTION

GENERAL FEATURES

1 sRNAs are today recognized as pivotal post-transcriptional regulators;

2 size ranges from 50 to a few hundreds nucleotides;

3 the majority modulate gene expression by direct base-pairing with targetmRNA;

4 regulation is predominantly negative;

5 increasing evidence of multiple targets per sRNA.


INTRODUCTION

WIDESPREAD OCCURRENCE


INTRODUCTION

FUNDAMENTAL ROLES IN PATHOGENESIS

FIGURE 1: Gopel2011a


INTRODUCTION

MAIN ROLES IN E. coli

FIGURE 2: Predictions from Modi2011.

A ROLE IN..Mainly stress andenvironmental relatedfunctions.


INTRODUCTION

FULLY INTEGRATED WITHIN THE GENE REGULATORY

NETWORK

FIGURE 3: sRNA are often regulated by specific transcription factors (TF) and often regulate TFsStorz2011


INTRODUCTION

MOST COMMON MECHANISMS OF ACTION

FIGURE 4: Waters2009

DIFFERENT MODES OF ACTION

1 Block translation (often bind theShine-Dalgarno) and increasedegradation;

2 Increase mRNA degradation;

3 Promote transcription termination;

4 Increase translation rate by removinginhibitory secondary structures;

5 Act in stoichiometric fashion(degraded with target);

6 Often in conjunction with Hfq.


INTRODUCTION

HFQ

FIGURE 5: Storz2011

HFQ

1 Interacts with both thesRNA and the targetmRNA;

2 Interacts with the RNAdegradosome;

3 Affects the translationand turnover rates ofspecific transcripts;

4 Distant homologues inArchaea and Eukaryotes.


INTRODUCTION

HFQ

FIGURE 6: Chao2010


INTRODUCTION

SHORT SUMMARY FOR EUKARYOTES

FIGURE 7: RNA regulation in Eukaryotes Kim2005

• Different types ofsmall RNAs;

• Different helperproteins/proteincomplexes;

• Pre-processing;• Act catalytically.


EXAMPLES

RYHB AND IRON HOMEOSTASIS

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;


EXAMPLES

QRR AND QUORUM SENSING REGULATION IN Vibrio

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.


EXAMPLES

QRR AND QUORUM SENSING REGULATION IN Vibrioharvey

FIGURE 10: Input-output relation for the WT and mutated genetic circuits of

quorum-sensing in V. harvey. [Teng2011].

Different strains with one or moreregulatory feedback destroyed and singlecell fluorescence measurements as afunction of AI-1 and AI-2 concentrations.

RESULTS

1 Feedback into LuxN allows V.harvey to actively adjust its relativesensitivity to AI signals as cellstransition from low to high celldensities;

2 The other feedback loops controlthe input and output dynamicranges and the noise in the circuit.


EXAMPLES

VIRULENCE REGULATION IN Clostridium perfringens

FIGURE 11: [Frandi2010]

HERE COMES THE QUESTION...How to study the different regulatory schemes?


EXAMPLES

COMPARATIVE SYSTEMS BIOLOGY

Sinorhizobium meliloti

Caulobacter crescentus

Rhodobacter sphaeroides

CckA-RD

CckA-HK~P

CckA-RD~P

CckA-HK

CtrA

ChpT~P

CtrA~P

ChpT

CpdR~PCpdR

proteolysis(ClpX)

Phos

phor

elay

DivK~P

DivK

DivJ

DivJ~P

PleC

PleC + Pi

CckA-RD

CckA-HK~P

CckA-RD~P

CckA-HK

CtrA

ChpT~P

CtrA~P

ChpT

CpdR~PCpdR

proteolysis(ClpX)

Phos

phor

elay

CtrA GcrA DivK~P

DivK~P

DivK

DivJ

DivJ~P

PleC

PleC + Pi

CckA-RD

CckA-HK~P

CckA-RD~P

CckA-HK

CtrA

ChpT~P

CtrA~P

ChpT

CpdR~PCpdR

proteolysis(ClpX)

Phos

phor

elay

CtrA GcrA DivK~P

CtrA GcrA

Modeled circuit Dynamics

FIGURE 12: Studying the phenotypes of different regulatory circuits indifferent organisms.

1 Reconstruct circuit indifferent species;

2 Build correspondingmathematical models;

3 Compare dynamicalbehaviors;

4 Similarly: mutate thesame circuits andexplore how itsproperties change.


BASICS OF MATHEMATICAL MODELING

MODELING GENE REGULATORY NETWORKS

TF

target

Cons-tu-ve synthesis

Regulated synthesis Degrada-on and dilu-on

A) Promoter activity:

• Positive regulation: A = h+(TF, θ, n) = TFnθn+TFn ;

• Negative regulation: A = h−(TF, θ, n) = 1− h+(TF, θ, n);• Combinatorial regulation: e.g.

for an AND logic: AAND =N∏

i=1

Ai;

for OR logic: AOR =N∑

i=1

Ai .

B) Protein degradation rate γ;

C) Dilution µ.

1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

x

y=

xn

xn+

!n

Positive Hill

1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

x

y=

!n

xn+

!n

Negative Hill

n=1n=2n=3n=4n=5n=6


NETWORK MOTIFS AND THEIR DYNAMICAL PROPERTIES

NETWORK MOTIFS

FIGURE 13: Feed Forward Loops [Shoval2010].

SUMMARY ON NETWORK MOTIFS

• Transcription regulation andsignaling networks are composedof recurring patterns called networkmotifs;

• Network motifs are much moreabundant in biological networksthan would be expected by theirrandomized versions;

• The same small set of networkmotifs has been found frombacteria to plants to humans;



MODELING THE FEEDFORWARD LOOP

-1-1

I-1

SYSTEM OF EQUATIONS FOR THE FFLC-1 AND

dYdt

= By︸︷︷︸Basal

+

Regulated synthesis︷︸︸︷κY

Xn

θnXY + Xn

− (γ + µ)︸︷︷︸Degr. and dil.

Y (1)

dZdt

= Bz + κZXn

θnXZ + Xn

Yn

θnYZ + Yn︸︷︷︸

AND logic

−(γ + µ)Z. (2)

Let’s put:α = γ + µ.

SYSTEM OF EQUATIONS FOR THE FFLI-1 ANDdYdt

= By + κYXn

θnXY + Xn

− αY (3)

dZdt

= Bz + κZXn

θnXZ + Xn

θnYZ

θnYZ + Yn

− αZ. (4)



NETWORK MOTIFS HAVE SPECIFIC DYNAMICAL

PROPERTIES

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

Z(Y

)

FFLC-1 Vs Simple regulation

9.5 10 10.5 11 11.5 120

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

time

Z(Y

)

FFLI-1 Vs Simple regulation

9.5 10 10.5 11 11.5 120

0.2

0.4

0.6

0.8

1

time

Z FFLC−1Y FFLC−1Z SimpleY Simple

Z FFLI−1Y FFLI−1Z SimpleY Simple

FIGURE 14: [Shen-Orr2002,Mangan2003,Mangan2003a]

FFLC-1-1-1

• Sign-sensitive delay;• Persistence detector;• Noise reduction;

FFLI-1I-1

• Sign-sensitiveaccelerator;

• other incoherent FFL aregood pulsers;


MODELING SRNA REGULATION

INTRODUCING SRNA-MEDIATED REGULATION

FIGURE 15:

• sRNAs act stoichiometrically;• sRNAs affect mRNA

stability/translation;• most regulations are negative;

EQUATIONS OF THE SYSTEM

ds

dt= Ss −

Degr. and dil.︷︸︸︷αs − kms︸︷︷︸

Degr.complex

(5)

dm

dt= Sm − αm− kms. (6)

Note that this is the basic modeling framework for all works published on sRNA regulation e.g. from [Levine2007] on.


MODELING SRNA REGULATION

BUT...

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:

dmtot

dt= Sm −

degr. free form︷︸︸︷γ · (mtot − Ym · mtot)−

degr. complex︷︸︸︷γ2 · Ym · mtot −µ · mtot. (12)


MODELING SRNA REGULATIONDYNAMICAL PROPERTIES OF SRNA-TRANSCRIPTION INTEGRATED

CIRCUITS

THRESHOLD LINEAR RESPONSE

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7

mRNA synthesis rate.

[m

RN

A]S

S

plus: Levine et al., 2007 modelcircles: Our modificated model

other parameters are:m=0.2

s=0.1k=3.5354e 01Kd=0.01

A THRESHOLD LINEARRESPONSE:

• When αm � αs,translatable targetmRNA is very small;

• When αm � αs, thetarget mRNA starts to beavailable for translation.



CIRCUITS

THRESHOLD LINEAR RESPONSE

0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

m

X SS

=0.5

=1.0

=4.0=2.0

FIGURE 16:

0 0.2 0.4 0.6 0.8 10

0.05

0.1

0.15

0.2

m SS / µ m SS

m

FIGURE 17:

A THRESHOLD LINEAR RESPONSE:

• The threshold depends only onthe two transcription rates;

• The smoothness of the transitiondepends on the degradation rateof the complex (half-life given bylog2γ

h);

• Around the crossover regiondifferences in steady state levelsof the target are much moredependent on the interactionstrength Kd .

• This gives an easy way forordering the expression ofdifferent genes by tuning αm andKd .



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

τsis the ratio of the mRNA

lifetime to the sRNA lifetime.



CIRCUITS

TARGET PRIORITIZATION

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

sRNA synthesis rate

norm

alized

steady

state

[mR

NA

]

sRNA mediated regulation

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Repressor synthesis rate

norm

alized

steady

state

[mR

NA

]

Transcriptional repression

PRIORITIZATION

• Multistep switch-like degradationupon changing the rate ofsynthesis of the sRNA;

• Separation of the level betweenthe (k + 1)th mRNA and the kth

mRNA becomes clearerincreasing the difference in thedegradation rate.

• Separation between mRNAlevels following transcriptionalregulation is not as sharp as withsRNA regulation;

• prioritization through sRNA ismuch more effective especiallyfor small changes in the sRNAsynthesis rate.



CIRCUITS

BISTABILITY

sRNA

TF

THE MODEL

dx

dt=

Translation︷︸︸︷γy − δx︸︷︷︸

Degr.

(15)

dy

dt=

Synthesis︷︸︸︷λSy(x, p)−αy− σyz (16)

dz

dt= µSz(x, p)− βz− σyz. (17)

Where: x=protein TF, y=mRNA TF, z=sRNA. [Liu2011].

• 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].



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.



CIRCUITS

CONCLUSIONS

• sRNAs provide an efficient regulatory mechanism;• integration of transcriptional and sRNA mediated regulations generates a

wide variety of interesting dynamical behaviors, such as threshold linearresponse, prioritization of targets and even bistability (and oscillations);

• modeling genetic circuits may provide information on both functionalityand evolution of genetic circuits.



CIRCUITS

COLLABORATORS AND ACKNOWLEDGEMENTS

A SPECIAL THANKS TO

Equipe Baobab (MF Sagot),LBBE, INRIA; Daniel Kahn(LBBE, INRA).

AND FOR YOUR ATTENTION,Thank you!

contact me: [email protected]

By the way...looking for a dog? 6 Labrador Chocolate available, contact me!


APPENDIX BIBLIOGRAPHY


Modeling sRNA-dependent circuits

Science

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