A follow-up to our PNAS paper on a new theory of steroid-mediated gene induction is now available on PLoS One here. The title and abstract is below. In the first paper, we proposed a general mathematical framework to compute how much protein will be produced from a steroid-mediated gene. It had been noted in the past that the dose response curve of product given steroid amount follows a Michaelis-Menten curve or first order Hill function (e.g. Product = Amax [S]/(EC50+[S], where [S] is the added steroid concentration).. In our previous work, we exploited this fact and showed that a complete closed form expression for the dose response curve could be written down for an arbitrary number of linked reactions. The formula also indicates how added cofactors could increase or decrease the Amax or EC50. What we do in this paper is to show how this expression can be used to predict the mechanism and order in the sequence of reactions a given cofactor will act by analyzing how two cofactors affect the Amax and EC50.
Deducing the Temporal Order of Cofactor Function in Ligand-Regulated Gene Transcription: Theory and Experimental Verification
Edward J. Dougherty, Chunhua Guo, S. Stoney Simons Jr, Carson C. Chow
Abstract: Cofactors are intimately involved in steroid-regulated gene expression. Two critical questions are (1) the steps at which cofactors exert their biological activities and (2) the nature of that activity. Here we show that a new mathematical theory of steroid hormone action can be used to deduce the kinetic properties and reaction sequence position for the functioning of any two cofactors relative to a concentration limiting step (CLS) and to each other. The predictions of the theory, which can be applied using graphical methods similar to those of enzyme kinetics, are validated by obtaining internally consistent data for pair-wise analyses of three cofactors (TIF2, sSMRT, and NCoR) in U2OS cells. The analysis of TIF2 and sSMRT actions on GR-induction of an endogenous gene gave results identical to those with an exogenous reporter. Thus new tools to determine previously unobtainable information about the nature and position of cofactor action in any process displaying first-order Hill plot kinetics are now available.
Scientific Clearing House 
Very nice. I bet you had LOTS of fun deriving all 285 cases. :)
Minor quibble with the discussion, though: “It also suggests that there is just one CLS, which does not change with assay conditions.”
We don’t know what the CLS is, so if you inadvertently picked the cofactor that was concentration limiting and attempted to do an assay on it, I think in theory you could change the CLS by adding that factor (or plasmids encoding the factor) to the point where it was no longer concentration limiting. At that point a different factor (the one with the second-smallest concentration) would become the CLS. That having been said: as long as you didn’t pick the CLS to assay, it’s not a problem. If it’s not shifting between assays, then you know you didn’t pick the CLS. (I suppose if the CLS appears to change, then can you deduce that one of the factors was in fact concentration limiting?)
I guess another point would be that the approximation we made assumes that one factor is significantly lower in concentration than all the others. If all the factors in a cascade were at approximately the same concentration, I’m not sure that the approximation would hold. That having been said, at that pantoint it probably wouldn’t be Michaelis-Menten / first-order Hill anyway. So if changing the concentrations of something moves it away from being MM, the perhaps that makes a statement about the mechanism of action as well. (Not sure if you could detect that apart from experimental error, though).
As always, I am impressed at how good the data is from Stoney’s lab. It’s SCARILY quantitative, and I only now am coming to appreciate that.
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Hi Karen,
Your points are well taken. We should have qualified our statement that the CLS for this particular set of experiments seemed to be unique.
Actually, the approximation does not require a CLS. That is entirely optional. All you need is for each linking reaction to be MM. Remember that the CLS was invoked/discovered to explain the Ubc9 data because we needed post-CLS steps to explain the data.
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Right, I forgot that we don’t need a CLS. I was thinking about the case where maybe you had say two concentration-limiting factors of the same order of magnitude – then can you still make the CLS approximation, or would you just use the regular MM equations? I don’t know.
I’ve never thought of the CLS as being particularly important anyway except from a theoretical standpoint, but it was interesting to think about using it as an absolute/fixed point of orientation, whereas you only get relative order when comparing cofactors two by two. And when you can assume the CLS is the same step, that’s actually pretty useful.
I tend to think of the concentrations of cofactors as being pretty dynamic (probably because I was mostly thinking about hypothetical cofactors rather than any particular system). That’s probably why I’m so wary of associating the CLS with a particular cofactor or step all the time, because to do that we’d have to assume that the cell always makes that particular factor in a very small amount. My feeling is that perhaps the concentrations aren’t absolute but could vary dramatically with, say, different environmental stimuli. The CLS approximation is a statement about relative concentrations of cofactors, so which cofactor is the CLS is very much situation-dependent.
So rather than designating a particular cofactor “the” CLS, as it could vary in a different setup of other cofactors, it’s probably better to think of it as being concentration-limiting in a given situation. Under the same experimental conditions as done in the paper, this seems like a reasonable assumption.
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It is very important because the reactions can sum directly after the CLS. If the CLS moved later, then the MM form would break.
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