S stical Physics Aproach to PostTranscriptional Regulation · [14] Bialek W. Biophysics: Searching for Principles. Princeton University Press, 2012. [15] Breda J, Rzepiela AJ, Gumienny

Statistical Physics Approach to Post-Transcriptional Regulation

Candidate: Araks Martirosyan

Advisors: Andrea De Martino, Enzo Marinari

Collaborator: Matteo Figliuzzi

Rome, 2015

Introduction

3

Gene Expression DNA

Protein [1]

4

Gene Expression

RNA

Transcription

DNA

Protein

5

Gene Expression

RNA mRNA

ncRNA

Transcription

DNA

Protein

6

Gene Expression

RNA mRNA

ncRNA

TranscriptionTranslation

DNA

Protein

7

ncRNA

RNA mRNA

ncRNA

Constituent RNA

tRNArRNA

...

TranscriptionTranslation

DNA

Protein [2]

8

ncRNA

RNA mRNA

ncRNA Regulatory RNA

Constituent RNA

tRNArRNA

...piRNA

siRNA

…

TranscriptionTranslation

DNA

Protein

miRNA

[3,4]

9

miRNA

RNA mRNA

ncRNA Regulatory RNA

Constituent RNA

tRNArRNA

...piRNA

siRNA

…

TranscriptionTranslation

DNA

Protein

miRNA

[5]

10

miRNA binding

3’UTR ACGACGUUCUCAUUCAGUGGUU 5’ UTR

5’UTR AAUCGCGAAGAUCUACUAGAGUAGGUCACCAGGA 3’ UTR}

}

seed

canonical sitesmRNA

miRNA28

11

mRNA cleavage

3’UTR ACGACGUUCUCAUUCAGUGGUU 5’ UTR

5’UTR AAUCGCGAAGAUCUACUAGAGUAGGUCACCAGGA 3’ UTR

5'UTR AAUCGCGAAGAUCUACUAGAGUAGGUCACCAGGA 3'UTR

cleavage

3’UTR ACGACGUUCUCAUUCAGUGGUU 5’ UTR

12

Translational repression

3’UTR ACGACGUUCUCAUUCAAUGUUU 5’ UTR

5’UTR AAUCGCGAAGAUCUACUAGAGUAGGUCACCAGGA 3’ UTR

Translational repression

3’UTR ACGACGUUCUCAUUCAAUGUUU 5’ UTR

5’UTR AAUCGCGAAGAUCUACUAGAGUAGGUCACCAGGA 3’ UTR

Ribosome

13

miRNA-Target interaction networks

* TargetScan* miRanda

16

Competing endogenous RNAs (ceRNAs)

ceRNA2

ceRNA1

miRNA

17

ceRNA effect

ceRNA2

ceRNA1

miRNA

[6]

18

DebateDenzler et al. (2014)

Mouse hepatocytes

Modulation of miRNA target abundance is unlikely to cause significant effects on gene expression through a ceRNA effect.

Bosson et al. (2014)

mouse embryonic stem cell

miRNA-target pool ratios and an affinity partitioned target pool accurately predict miRNA susceptibility to target competition.

[7, 8]

19

The goal

1. Quantify the maximal post-transcriptional regulatory power achievable by miRNA-mediated cross-talk,

2. Explore how heterogeneities in binding affinities influence the latter,

3. Compare the effectiveness miRNA-mediated control with other regulatory elements.

The model

21

ceRNA Network

miRNAceRNA1 ceRNA2

[9, 10]

22

ceRNA Network: target binding/unbinding

miRNAceRNA1 ceRNA2

C1 C2

+/- +/-k1

+ k1− k2

−k2

+

23

ceRNA Network: ceRNA cleavage

miRNAceRNA1 ceRNA2

C1 C2

+/- +/-k1

+ k1− k2

−k2

+

κ1 κ2

24

ceRNA Network: transcription

TF1

n1 miRNAceRNA1

TF2

nµ ceRNA2 n2

TFµ

C1 C2

+/- +/-

k ink ink in kout kout kout

b1 b2β

k1+ k1

− k2−

k2+

κ1 κ2

25

ceRNA Network: degradation

TF1

n1 miRNAceRNA1

TF2

nµ ceRNA2 n2

TFµ

C1 C2

+/- +/-

Ø

Ø

Ø

Ø

Øk ink ink in kout kout kout

b1 b2β

σ1 σ2

d2d1k1

+ k1− k2

−k2

+

κ1 κ2

δ

26

Dynamics ∂mi∂ t

=bini−d imi−k i+miμ+k i

− c i+ξmi−ξ++ξ−

∂μ∂ t

=βnμ−δμ−k i+miμ+(k i

−+κi)ci+ξμ−ξ++ξ−+ξκ

∂ ci∂ t

=−σimi+∑ik i

+miμ−∑i(k i

−+κi)c i+ξci+ξ+−ξ−−ξκ

∂ni ,μ∂ t

=k in f i ,μh (1−ni ,μ)−kout ni ,μ+ξni ,μ

ceRNA

miRNA

complex

TF binding site occupancy

27

Dynamics ∂mi∂ t

=bini−d imi−k i+miμ+k i

− c i+ξmi−ξ++ξ−

∂μ∂ t

=βnμ−δμ−k i+miμ+(k i

−+κi)ci+ξμ−ξ++ξ−+ξκ

∂ ci∂ t

=−σimi+∑ik i

+miμ−∑i(k i

−+κi)c i+ξci+ξ+−ξ−−ξκ

∂ni ,μ∂ t

=k in f i ,μh (1−ni ,μ)−kout ni ,μ+ξni ,μ

n̄i ,μ=k in f i ,μ

h

k in f i ,μh +kout

n̄i ,μ

f i ,μ

fast[11]

1

o

28

White noise

<ξ+ (t )ξ+ (t ' )>=k i+ m̄iμ̄ δ(t−t ' ) ,

<ξ−(t )ξ−(t ' )>=k i− c̄iδ(t−t ' ) ,

<ξκ(t )ξκ(t ')>=κi c̄ iδ(t−t ') ,<ξμ (t )ξμ(t ' )>=(β n̄μ+δμ̄)δ(t−t ' ),<ξmi(t )ξmi(t ' )>=(bi n̄i+d i m̄i)δ(t−t ' ) ,

m̄i=bi n̄i+k i

− c̄id i+ki

+ μ̄, μ̄=

β n̄μ+∑i(k i

−+κi) c̄iδ+∑i

k i+ m̄i

, c̄i=k i

+ μ̄ m̄iσi+k i

−+κi.

where

The method

31

Mutual Information

Channel

I ( f j ,m2)=∫df jdm2 p(f j ,m2) log2p(f j ,m2)p(f j) p(m2)

I opt=max p(f j) I (f j ,m2)

[12]

Channel Capacity

f jm2

33

Noise and information transmission

I opt=0

34

Noise and information transmission

I opt∼0

35

Noise and information transmission

I opt=log21√2π e ∫df j 1/σ f j

Popt (f j)=1Z1σ f j

37

Channels

TF1

miRNAceRNA ceRNA2 ceRNA2

TF2

ITF

miRNAceRNA

TF1 TFμTF2TFμ ImiRNA

miRNA-channel TF-channel

Results

40

The capacity of the miRNA-channel is maximal in a specific range of miRNA-ceRNA binding rates

ITF - ImiRNATF1

miRNAceRNA ceRNA2 ceRNA2

TF2

miRNAceRNA

ImiRNA ITF

41

miRNA-mediated regulation may represent the sole control mechanism in case of differential complex processing

TF1

miRNAceRNA ceRNA2 ceRNA2

TF2

miRNAceRNA

ITF - ImiRNAImiRNA ITF

42

Dependence on ∆

43

Dependence on ∆

∆σm2

44

The limit of weakly interacting high miRNA population

miRNAceRNA2miRNA

ω

ceRNA2ceRNA2ceRNA2k i+→k i

+ ω ,δ→δω .

46

Conclusions1. miRNA-mediated ceRNA effect may act as a master regulator of gene expression in the presence of the heterogeneity in target binding affinities, that is the case “in vivo” (Breda et al, 2015 [15]).

miR

NA

The density of target sites

energy of interaction between the miRNA and the target

47

Conclusions2. Target derepression may be significant even if the competitor is in low copy numbers, provided a certain heterogeneity in kinetic parameters (e.g. for a catalytically degraded target and a stoichiometrically degraded competitor) is present.

48

Thank you!

49

References

[1] Alberts B, Johnson A, Lewis J, Morgan D, Raff M, Roberts K, Walter P. Molecular Biology of the Cell. Garland Science, 2015.

[2] Cech TR, Steitz JA. The noncoding RNA revolution-trashing old rules to forge new ones. Cell 2014; 157(1): 77–94.

[3] Fire A, Xu S, Montgomery MK, Kostas SA, Driver SE, Mello CC. Potent and spe- cific genetic interference by double-stranded RNA in Caenorhabditis elegans. Nature 1998; 391(6669): 806–811.

[4] Mello CC, Darryl C Jr. Revealing the world of RNA interference. Nature 2004; 431(7006): 338–342.

[5] Bartel DP. MicroRNAs: genomics, biogenesis, mechanism, and function. Cell 2004; 116(2): 281–297.

[6] Salmena L, Poliseno L, Tay Y, Kats L, Pandolfi PP. A ceRNA hypothesis: the Rosetta Stone of a hidden, RNA language? Cell 2011; 146(3): 353–358.

[7] Denzler R, Agarwal V, Stefano J, Bartel DP, Stoffel M. Assessing the ceRNA Hypothesis with Quantitative Measurements of miRNA and Target Abundance. Molecular Cell 2014; 54(5): 766–776.

[8] Bosson AD, Zamudio JR, Sharp PA. Endogenous miRNA and target concentrations determine susceptibility to potential ceRNA competition. Molecular Cell 2015; 56(3): 347–359.

[9] Figliuzzi M, De Martino A, Marinari E. RNA-based regulation: dynamics and response to perturbations of competing RNAs. Biophysical journal 2014; 107(4): 1011–1022.

[10] Bosia C, Pagnani A, Zecchina R. Modelling Competing Endogenous RNA Networks. PLoS ONE 2013; 8(6): e66609.

[11] Alon U. An Introduction to Systems Biology: Design Principles of Biological Cir- cuits. CRC Press; 2006.

[12] Shannon CE. A Mathematical Theory of Communication. The Bell System Technical Journal 1948; 27(3): 379–423.

[13] Tkačik G, Walczak AM, Bialek W. Optimizing information flow in small genetic networks. Physical Review E 2009; 80(3): 031920.

[14] Bialek W. Biophysics: Searching for Principles. Princeton University Press, 2012.

[15] Breda J, Rzepiela AJ, Gumienny R, van Nimwegen E, Zavolan M. Quantifying the strength of miRNA-target interactions. Methods 2015; 85(1): 90–99.