Inferring intrinsic and extrinsic noise from a dual fluorescent reporter

http://biorxiv.org/content/early/2016/04/21/049486

Hope some of you will find it useful.

]]>Interesting! I would not at all be surprised if there is a “batch” effect (I usually just call it “cell lines are just different” ðŸ™‚ ), and that’s certainly an issue. I wonder if it’s a bigger issue than the differences between CFP and YFP in the two-color ELSS-style experiments (which would lead to artificially higher intrinsic noise). I haven’t done any of these comparisons myself experimentally, just relaying what I’ve heard from others.

]]>Assuming no batch (strain) effect, then the estimation of intrinsic and extrinsic noise in Volfson et al. (2006) is actually the same as in Elowitz et al (2002). The difference is that the 2nd reporter in the two-reporter experiment is replaced with the 2nd copy in the copy number experiment. This means that, similar to the scatterplot of CFP versus YFP, one can plot the scatterplot of strain A versus (strain B – strain A) for the copy number experiment. Whereas extrinsic noise is the covariance between the two reporters in the two-reporter experiment, extrinsic noise is the covariance between the two copies in the copy number experiment.

Formulas in the supplement (sec. II on p 1) to the Volfson paper are consistent with the description above. In their notation, V1 and V2 are the variance in the 1-copy and 2-copy strains, respectively. Vi and Ve are intrinsic and extrinsic noise, respectively. Their formulas are:

Vi = 2V1 – V2 / 2; (1)

Ve = V2 / 2 – V1. (2)

To see why these formulas are used, we can again apply the hierarchical model presented in the blog post, replacing C and Y with C1 and C2 (assuming only the, say, CFP reporter is used in the copy number experiment). Then in the 1-copy strain,

V1 = Var[C1] = Vi + Ve = Var[C2]. (3)

In the 2-copy strain,

V2 = Var[C1 + C2] = Var[C1] + Var[C2] + 2Cov[C1,C2] = 2(Vi + Ve) + 2Ve. (4)

Together, (3) and (4) give rise to (1) and (2).

The other paper you mentioned in the comment, Sherman and Cohen (2015), explicitly stated that the covariance between the two copies is the extrinsic noise (equations S19 and S20 in S2.5.1 of the supplement). However, they saw large variation with the results from these formulas (they also mentioned that this experience was consistent with Steward-Ornstein et al. 2012, Molecular Cell. I haven’t looked into this ref yet). They went on to derive another approach for better estimation. I think that the large variation Sherman and Cohen saw with formulas (3) and (4) is possibly indication of the non negligible batch (strain) effect.

]]>Here is a nice recent paper on the one/two copy noise measurement from Marc Sherman and Barak Cohen (Cell Systems 2015): http://www.sciencedirect.com/science/article/pii/S2405471215001854

and here’s to my knowledge the first paper to use this approach (Volfson… Hasty, Nature 2005): http://www.nature.com/nature/journal/v439/n7078/full/nature04281.html

Very interesting idea! We’ll think about it.

]]>One experimental point that many have noted in the subsequent years is that it’s often quite hard to really ensure that the two reporters are well and truly identicalâ€“indeed, there are often differences in degradation rate, photophysical properties, etc. An alternative approach is to measure how total variability increases upon adding another copy of the *exact* same reporter. E.g., compare one copy of GFP in the cell to two copies. If variability is intrinsic, the variance goes up by a factor of two; if extrinsic, by a factor of four. I have not done those sort of experiments, but those that have feel more confident in that approach. Curious about what the statistical properties of such an experiment would be.

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