Post-trancriptional Regulation by microRNA’s

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 • 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 Effective equations: with Effective silencing requires that αs > Qαm+, where =ms/. 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 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? Voinnet (2005) D Kosman et al, Science (2006) Iba4 vs Hoxb8 - Ronshaugen et al. Genes Dev. 2005;

Sharpening the target expression pattern. 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.

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)

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 solution No 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 • 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 Experimentally, lin-14 inhibits an inhibitor of lin-28 which is independent of lin-4; and vice versa

Positive feedback Stoichiometric mode Catalytic mode Thin lines - simple miRNA repression Thick lines - with bistable behavior due to feedback Dashed lines - reduced feedback note temporal ordering

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

Final results Solid lines: catalytic Dashed: Stoichiometric Precise temporal staging is made easier by miRNA

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??

Post-trancriptional Regulation by microRNA’s