Post-trancriptional Regulation by microRNA’s

Herbert Levine

Center for Theoretical Biological Physics, UCSD

with: E. Levine, P. Mchale, and E. Ben Jacob (Tel-Aviv)

Outline: Introduction

Basic model

Spatial sharpening

Temporal Sequencing

What are MicroRNA’s?

• MicroRNA’s (miRNA’s) are small noncoding RNA molecules that regulate eukaryotic gene expression at the translation level

RISC = RNA-induced Silencing Complex

MicroRNA formation

miRNA’s are processed from several precursor stages

Mammalian genomes seem to have 100’s of miRNA’s

This talk

• Basic molecular model

• Local vs global parameters

• Spatial sharpening

• Temporal control

Basic silencing model

Bare messenger RNA

Bound miRNA-mRNA

Processed state

Second step reflects the fact that complex is not just degraded directly, but is targeted to a specialized location (a cytoplasmic P-body) to stop translation

Binding- local rates; transport - global rates

Basic silencing model II

€

dm

dt=α m + κ −m

* −κ +sm( ) − λmm

dm*

dt= κ +sm −κ −m

*( ) + η−m** −η +m*( ) − λm

* m*

dm**

dt= η +m* −η−m

**( ) − λm**m**

ds

dt=α s − λ sμ + κ −m

* −κ +sm( ) + (1 − q)λm**m** + λm

* m*

•Simple to analyze this in steady-state•Critical parameter q - how much miRna is degraded per degraded mRNA (in processed state)

• q=0 miRNA is completely recycled (catalytic mode)• q>0 miRNA is partially degraded (stoichiometeric)• q<0 amplification (occurs for siRNA)

Results

€

0 =α m − λm(1 + s / K eq )m ≡α m − λmm −γsm

0 =α μ − λ ss −Qλmms / K eq ≡α s − λ ss −Qγsm,

Effective equations:

with

€

Q = qλm** /(λm

** +θ λm )

Effective silencing requires that αs > Qαm+, where =ms/.

Sharp silencing threshold

Threshold Effect

Cartoon vs Reality

•RyhB miRNA regulation of sodB•Threshold-linear units, similar to some neuron models•Also, fluctuations reduced in silenced state•From E. Levine, T. Hwa lab

Local vs. Global parameters

• Data on silencing has been very controversial, with disagreements as to whether there is both mRNA and protein repression or only protein repression

• In our model, the repression ratio can be altered by cell state (global) variables such as the transport into and out of the processed state, and miRNA loss (q)

Local vs. Global parameters

€

wM = λm /θ λm

* + λm**

θ +1

⎛

⎝ ⎜ ⎞

⎠ ⎟ , wP = wM

θ

1 +θ ⎛ ⎝ ⎜

⎞ ⎠ ⎟ .€

θ ≡(λm** + η−)/η +

Global control through the effective parameter

Gives different repression ratios for same system of miRNA and target, different cellular context

Local vs. Global parameters

• Different protocols can give opposite answers if these are not carefully controlled– Simple physics but complex biology

Complex interplay of local and global parameters

Spatial sharpening• What happens if we have a miRNA expressed with

the opposite spatial pattern from its target mRNA? – Motivation: Complementary expression patterns

• And, the miRNA might diffuse from cell to cell– Motivation - intercellular transport of siRNA in plants– Could this be an actively maintained front with q<0?

Iba4 vs Hoxb8 - Ronshaugen et al. Genes Dev. 2005;

Voinnet(2005)

D Kosman et al, Science (2006)

Conceptual idea

The model predicts that mobile microRNA (red) fine-tune this pattern by establishing a sharp interface in the target expression profile (green).

Morphogens set up a poorly defined expression domain, where mRNA levels (green) vary smoothly across the length of the embryo.

Sharpening the target expression

pattern.

Spatial model

• Note - eq has been rescaled using

We will assume that the transcription profiles are 1d functions, decaying in opposite directions, and investigate what are the resultant mRNA and miRNA

The relevant parameters are the annihilation rate k and the miRNA diffusion constant D (compared to the scale established by transcription)

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αs = Qα μ ,λ s = Qλ μ

Zero diffusion, large k

Crossing point at

Adding miRNA diffusion

• K=10000• Dark line is

analytic calculation

• Interface is sharpened

• Crossing point is shifted to left

Effect of increasing rate k

In the large k and/or small D limit, there is a sharp transition layer

Diffusion of miRNA eats into m profile, and m has a sharp drop

Analytic solutionNo miRNA flux is allowed into the region x<xt

The zero flux Green’s function is clearly

The miRNA profile is given by

And the interface is determined by setting miRNa = 0 (no fluctuations). Once this position is determined, we still have to the left

Comments

• Sharp stripes are also possible

Comments

• Can be tested with genetic mosaics

Stability Analysis

• Can extend analysis to time-dependent case• Now, miRNA equation becomes

• Linearizing around steady-state gives simple result

implies

Response to 2d quenched noise

Analytically: Low-pass filter due to diffusion

C. Elegans development

Lin4 and Let7 miRNAs control differentiation

As usual, they act by silencing targets

Is there any good reason why miRNA’s are used for this task?

miRNA as temporal regulator

• Lin-28 needed for start of L2 phase; needs to be turned off later than Lin-14

• Basic idea - one miRNA target has 5 binding sites (lin-14) and one has only 1 (lin-28)

• If miRNA act stoichiometrically, first target will soak up all the miRNA’s and the second one will not be repressed until later

The complete circuit

Experimentally, lin-14 inhibits an inhibitor of lin-28 which is independent of lin-4; and vice versa

•Direct positive feedback•Indirect positive feedback•Double-negative feedback

•miRNA switches g5 into off state and this then makes g1 also switch to off state

•This works better in stoichiometric mode, as g1 is not repressed until g5 stops absorbing s

Positive feedback

Thin lines - simple miRNA repressionThick lines - with bistable behavior due to feedbackDashed lines - reduced feedback

note temporal ordering

Catalytic mode Stoichiometric mode

The complete circuit

Experimentally, lin-14 inhibits an inhibitor of lin-28 which is independent of lin-4; and vice versa

•Direct positive feedback•Indirect positive feedback•Double-negative feedback

•miRNA switches g5 into off state and this then makes g1 also switch to off state

•This works better in stoichiometric mode, as g1 is not repressed until g5 stops absorbing s

Final results

Precise temporal staging is made easier by miRNA

Solid lines: catalyticDashed: Stoichiometric

Summary

• microRNA’s are yet another level of genetic regulation

• In nature, miRNA’s seem to be able to regulate both spatial and temporal aspects of development

• We have argued that the stoichiometric mode of operation seems to be an enabling factor

• Is this easier to arrange and control (via cell state) than equivalent transcription circuits?? Is it easier to target many genes simultaneously??