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![Page 1: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/1.jpg)
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
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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
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MicroRNA formation
miRNA’s are processed from several precursor stages
Mammalian genomes seem to have 100’s of miRNA’s
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This talk
• Basic molecular model
• Local vs global parameters
• Spatial sharpening
• Temporal control
![Page 5: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/5.jpg)
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
![Page 6: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/6.jpg)
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)
![Page 7: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/7.jpg)
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
![Page 8: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/8.jpg)
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
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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)
![Page 10: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/10.jpg)
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
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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
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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)
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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.
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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)
€
αs = Qα μ ,λ s = Qλ μ
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Zero diffusion, large k
Crossing point at
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Adding miRNA diffusion
• K=10000• Dark line is
analytic calculation
• Interface is sharpened
• Crossing point is shifted to left
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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
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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
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Comments
• Sharp stripes are also possible
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Comments
• Can be tested with genetic mosaics
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Stability Analysis
• Can extend analysis to time-dependent case• Now, miRNA equation becomes
• Linearizing around steady-state gives simple result
implies
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Response to 2d quenched noise
Analytically: Low-pass filter due to diffusion
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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?
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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
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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
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Positive feedback
Thin lines - simple miRNA repressionThick lines - with bistable behavior due to feedbackDashed lines - reduced feedback
note temporal ordering
Catalytic mode Stoichiometric mode
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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
![Page 28: Post-trancriptional Regulation by microRNA’s Herbert Levine Center for Theoretical Biological Physics, UCSD with: E. Levine, P. Mchale, and E. Ben Jacob.](https://reader036.fdocuments.us/reader036/viewer/2022062719/56649ee15503460f94bf2650/html5/thumbnails/28.jpg)
Final results
Precise temporal staging is made easier by miRNA
Solid lines: catalyticDashed: Stoichiometric
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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??