A tale of two circuits

This is a story about a fortunate coincidence.  In two papers published simultaneously last year, the Kirschner lab and the Alon lab each noticed that the signaling pathway they were studying appeared to have peculiar responses.  In both cases, the amount of output — or at least, what had previously been assumed to be the output — triggered by a given amount of signal was highly variable.  Something was clearly wrong with our assumptions.

The Kirschner lab’s pathway was the Wnt pathway, an extremely important pathway in both development and cancer.  The output of this pathway is a change in β-catenin levels.  But both modeling and experiment showed that β-catenin levels varied wildly.  There was little relationship between the amount of Wnt stimulation and the resulting absolute level of β-catenin.  Instead, the measurement that looked as if it behaved more reasonably was the ratio between the resting level of β-catenin and its level after stimulation, or the “fold change” after stimulation.  (Goentoro L & Kirschner MW 2009 Evidence that fold-change, and not absolute level, of beta-catenin dictates Wnt signaling. Mol Cell. 36 872-84. PMID: 20005849).

Now, this is very odd.  We generally don’t think of cells as being able to remember the past (though the Silver lab is working on changing this).  So if the output of an important pathway is a ratio between the current level of a protein and an earlier level, we have two problems: how does the cell create this ratio? And once the ratio has been created, how does the cell read it?

Meanwhile, the Alon lab was facing a similar puzzle, in this case while looking at the response of individual mammalian cells to EGF (epidermal growth factor).  A key output of this pathway is ERK2; it responds to EGF signaling by moving from the cytoplasm into the nucleus, where it activates the transcription of a number of genes.  Like the Kirschner lab, the Alon lab saw little relationship between the amount of EGF they used to stimulate the cells and the absolute ERK2 levels in the nucleus.  The level of ERK2 in the nucleus varies widely; the level always goes up after EGF treatment, but some cells start off so low that even after the up-tick caused by EGF they’re still below the place that other cells start.  But once again, the Alon lab found that the EGF signal was giving a constant fold change in ERK2.  (Cohen-Saidon C, Cohen AA, Sigal A, Liron Y, Alon U. 2009 Dynamics and variability of ERK2 response to EGF in individual living cells. Mol Cell. 36 885-93 PMID: 20005850).  If a cell happens to have a lot of ERK2 in the nucleus to start with, the pulse in response to EGF is large; if the starting level is low, so is the pulse.  Again, how does the cell know how big to make the pulse?  And how does a cell respond to a temporal ratio?

Let’s think about what’s happening in the simplest possible terms. In the case of β-catenin, it’s being made and degraded, and the presence of ligand reduces the rate of degradation.  (Roughly speaking).  So let’s say it’s made at a rate p and degraded at a rate q; and let’s say that a particular ligand concentration reduces the degradation rate to q/x.

The rate of change of β-catenin levels (which I will call [A] for ease of typing), dA/dt, in resting cells is then:

dA/dt = p – q[A]

and the rate in stimulated cells is

dA/dt = p – q[A]/x

At steady state dA/dt goes to zero, so for resting cells p = q[A], or [A] = p/q;

and in stimulated cells, p = q[A]/x, so [A] = xp/q.

So the level in stimulated cells is x times the level in resting cells.  The fold change is x.

It’s not so straightforward in the real world.  The real model of the Wnt pathway involves 12 different parameters that describe just the degradation machinery — all of which I have subsumed under “q”.  Synthesis is simpler, but still a lot more complicated than “p”.  Nevertheless, it turns out that this extremely complicated system behaves — for the most part — as if it were simple.  All the parameters of the system (especially the 12 parameters describing the degradation machinery) seem to be tuned to ensure that the whole pathway stays in the region where the fold change in response to a certain ligand concentration is consistent.  And, for the most part, small changes in the parameters don’t make much difference.  In the common parlance, the fold change behavior is robust to medium-sized changes in the levels of pathway components. (Note, by the way, that these are changes in what’s going on within the cell — it’s changes within the network that we’re talking about, not changes in external signals).

There is one important exception, however.  If the synthesis of β-catenin itself is increased, all bets are off*.  Increasing the rate of synthesis of β-catenin increases the resting level of β-catenin; but it also increases the fold change you get for a certain level of Wnt stimulation.  You can also change the resting level of β-catenin in other ways, for example by reducing the level of one of the proteins involved in degradation. If you do that, the fold change is unaffected.  This offers a rather elegant way to test whether the whole analysis is connected to biological reality.  If you change resting β-catenin levels by reducing degradation, you should maintain the fold change and therefore maintain the biological output that (by hypothesis) depends on fold change.  But if you make the same change in resting β-catenin levels by changing β-catenin synthesis, you should alter the fold change, and mess up your downstream results.

Goentoro and Kirschner, rather boldly, chose to test this in the context of a whole organism. In frog development, the Wnt pathway controls the formation of the dorso-ventral axis.  This should be a pretty robust process: it’s one of the things evolution cares about.  When you set out to make a frog, you should get a frog with a back and a front. They used two different methods to increase resting β-catenin levels via a change in the degradation rate.  In both cases, resting β-catenin levels went up about two-fold but frog development remained normal. But when the β-catenin synthesis rate was increased, again increasing resting β-catenin levels about two-fold, the embryos lost their dorso-ventral axis: they started to look like rather pathetic little blobs with huge heads and no tails.  This is a rather dramatic morphological difference for a small change in a protein level.  It looks as if the events downstream of Wnt really can read “fold change” in β-catenin.

At this point in my story you should be convinced that it’s possible for a signaling pathway to use fold change as an output.  But you are probably still puzzled by the question of how this output gets read by the downstream targets.  I know I was.

Enter the fortunate coincidence that I promised you in my first paragraph.  While all this was going on, Uri Alon happened to be on sabbatical in our (Marc Kirschner’s) department.  This had two important consequences. First — thanks to a poster Lea Goentoro gave at the Department Retreat — the similarity between the results of the two systems was recognized early enough for both groups to describe the phenomena they were seeing using the same keyword (fold change) and coordinate publication in the same journal (Molecular Cell).  If the two groups had published separately and in different journals it might easily have taken years (or decades) for the fact that both systems are showing the same phenomenon to be recognized.  Second, because the phenomenon of fold change had popped up in two quite different contexts, both groups were encouraged to think of it as a possibly general phenomenon, and so to ask what the mechanism for “reading” a fold change might, in general, be.

Uri, as many of you know, has written a textbook on systems biology that describes (among other things) the behavior of patterns of protein interactions that he calls “network motifs”.  During a late-night brainstorming session,  the idea emerged that a very common motif — the “incoherent” feed-forward motif — could be responsible for responding to fold changes (Goentoro L, Shoval O, Kirschner MW, Alon U. 2009. The incoherent feedforward loop can provide fold-change detection in gene regulation. Mol Cell. 36 894-9. PMID: 20005851)

What is an incoherent feed-forward motif?  It’s usually drawn like this:

and what makes it “incoherent” is that the arrow from X to Z is a positive one — activation — while the arrow from Y to Z is negative (inhibition).   This motif has been shown to be capable of a range of behaviors; for example, it can generate pulses in Z, by first stimulating the output (X) and then repressing it (Y, which is delayed).

How would this circuit work as a fold change detector?  It’s a bit easier to think about this question if we re-draw the circuit like this:

The key idea here is that Y serves as the cell’s “memory” of the resting state level of X.  Provided that the synthesis of Y is sufficiently delayed relative to X (so that it can serve as a memory of X from a long enough time ago), the level of Y can act as a surrogate for the level of X in the resting state.  The cell can then compare the level of Y (resting state) with the new level of X (stimulated state), determine the fold change, and respond accordingly.  In fact, you could think of it like this:

Not every incoherent feed-forward loop (IFFL) will act as a fold change detector.  Goentoro et al. provide a parameter analysis for three possible types of X-Y interaction on the Z promoter — competitive binding, independent binding and cooperative binding.  In each case there is a range of parameters where fold-change detection occurs, and a range where it doesn’t.  The competitive binding IFFL has the broadest range for fold detection.

So if in your work you come across an IFFL, especially one where X/Y binding to the Z promoter is competitive, you might want to look at the possibility that it’s detecting a fold change. This is a type of output that hasn’t received much recognition before, partly because people haven’t known how to look for it, and my bet is that it will pop up in many places.  The (so far hypothetical) IFFLs in the Wnt and EGF cases haven’t been identified, so you could be first.  Take a look.

Oh, before I end — why would you want to detect fold changes instead of increases in absolute levels?  My take on this is that absolute protein levels are sensitive to cell-to-cell variations in parameters such as the number of ribosomes, as well as individual-to-individual variations in, for example, gene copy number.  If you want a process like development to be really reliable, you want to avoid responding to all the factors that might lead to increased or decreased resting levels of a protein — all the noise — and focus only on increases above and beyond the possible noise level. Fold changes are a good way to do this.  The authors point out that this is in some ways reminiscent of Weber’s Law, which observes that for several of our senses we don’t perceive absolute levels, but (essentially) a fold change (the logarithm of the ratio between the absolute change and the original level).  So, for example, you easily distinguish between a 1 lb weight and a 2 lb weight, but not between 11 lbs and 12 lbs.  This means that you can see dim stars on a very dark night and yet not be overwhelmed when the moon comes out.

* Update: Just to clarify: in my toy model, when the rate of production of A goes up by x-fold, you would still see a fold change of 1/x.  But it turns out that the real Wnt pathway (or at least its computational surrogate) doesn’t behave that way: the parameters are tuned such that you see a fold change in response to a decrease in degradation, but not an increase in production.

Goentoro L, & Kirschner MW (2009). Evidence that fold-change, and not absolute level, of beta-catenin dictates Wnt signaling. Molecular cell, 36 (5), 872-84 PMID: 20005849

Cohen-Saidon C, Cohen AA, Sigal A, Liron Y, & Alon U (2009). Dynamics and variability of ERK2 response to EGF in individual living cells. Molecular cell, 36 (5), 885-93 PMID: 20005850

Goentoro L, Shoval O, Kirschner MW, & Alon U (2009). The incoherent feedforward loop can provide fold-change detection in gene regulation. Molecular cell, 36 (5), 894-9 PMID: 20005851