Love

In sequencing-based ribosome footprinting, the RF read count is naturally confounded by mRNA abundance (Fig. 1A). We seek a strategy to compare RF measurements taking mRNA abundance into account in order to accurately discern the translation effect in case–control experiments. We model the vector of RNA-Seq and RF read counts $y_{\text{mRNA}}^i$ and $y_{\text{RF}}^i$ , respectively, for gene i with Negative Binomial (NB) distributions, as described before (for instance, Love et al., 2014 (link); Drewe et al., 2013 (link); Robinson et al., 2010 (link)): $y^i\hspace{0.17em}\sim \hspace{0.17em}NB({\mu }^i,{\kappa }^i),$ where μⁱ is the expected count and κⁱ is the estimated dispersion across biological replicates. Here yⁱ denotes the observed counts normalized by the library size factor (Supplementary Section A). Formulating the problem as a generalized linear model (GLM) with the logarithm as link function, we can express expectations on read counts as a function of latent quantities related to mRNA abundance β_C in the two conditions ( $C=\{0,1\}$ ), a quantity ${\beta }_{\text{RNA}}$ that relates mRNA abundance to RNA-Seq read counts, a quantity ${\beta }_{\text{RF}}$ that relates mRNA abundance to RF read counts and a quantity ${\beta }_{\Delta ,C}$ that captures the effect of the treatment on translation. In particular, the expected RNA-Seq read count ${\mu }_{\text{mRNA},C}^i$ is given by the equation $\text{log}({\mu }_{\text{mRNA},C}^i)={\beta }_C^i+{\beta }_{\text{RNA}}^i$ .
We assume that transcription and translation are successive cellular processing steps and that abundances are linearly related. The expected RF read count, ${\mu }_{\text{RF},C}^i$ , is given by $\text{log}({\mu }_{\text{RF},C}^i)={\beta }_C^i+{\beta }_{RF}^i+{\beta }_{\Delta ,C}^i$ . A key point to note is that ${\beta }_C^i$ is revealed to be a shared parameter between the expressions governing the expected RNA-Seq and RF counts. It can be considered to be a proxy for shared transcriptional/translation activity under condition C in this context. Then, ${\beta }_{\Delta ,C}^i$ indicates the deviation from that activity under condition C, with ${\beta }_{\Delta ,C}^i=0$ for C = 0 and free otherwise (See Supplementary Section B for more details).
Fitting the GLM consists of learning the parameters βⁱ and dispersions κⁱ given mRNA and RF counts for the two conditions $C=\{0,1\}$ . We perform alternating optimization of the parameters βⁱ given dispersions κⁱ and the dispersion parameters κⁱ given βⁱ, similar to the EM algorithm (Supplementary Sections B and C):
${\beta }^i=\underset{{\beta }^i}{\text{arg}\hspace{0.17em}\text{max}}{\ell }_{glm}({\beta }^i|y^i,{\kappa }^i)\hspace{1em}\text{and}\hspace{1em}{\kappa }^i=\underset{{\kappa }^i}{\text{arg}\hspace{0.17em}\text{max}}{\ell }_{NB}({\kappa }^i|y^i,{\mu }^i).$
As experimental procedures for measuring mRNA counts and RF counts differ, we enable the estimating of separate dispersion parameters for the data sources of RNA-Seq and RF profiling to account for different characteristics (Supplementary Section E).
As in Anders et al. (2012) (link), with raw dispersions estimated from previous steps, we regress all κⁱ given the mean counts to obtain a mean-dispersion relationship $f(\mu )={\lambda }_1/\mu +{\lambda }_0$ . We perform empirical Bayes shrinkage (Love et al., 2014 (link)) to shrink κⁱ towards $f(\mu )$ to stabilize estimates (see Supplementary Section D). The proposed model in RiboDiff with a joint dispersion estimate is conceptually identical to using the following GLM design matrix $\text{protocol}+\text{condition}+\text{condition}:\text{protocol}$ (for instance, in conjunction with edgeR or DESeq1/2).
In a treatment/control setting, we can then evaluate whether a treatment (C = 1) has a significant differential effect on translation efficiency compared to the control (C = 0). This is equivalent to determining whether the parameter ${\beta }_{\Delta ,1}$ differs significantly from 0 and whether the relationship denoted by the dashed arrow in Figure 1A is needed or not. We can compute significance levels based on the ${\chi }^2$ distribution by analyzing $\text{log}$ -likelihood ratios of the Null model ( ${\beta }_{\Delta ,1}^i=0$ ) and the alternative model ( ${\beta }_{\Delta ,1}^i\cancel{=}0$ ).

Generation of items: The 35 items from the CEBQ were changed from the “My child …” format to a self-complete “I ...” format (e.g. “My child loves food” was changed to “I love food”) and the original response options (‘never’, ‘rarely’, ‘sometimes’, ‘often’ and ‘always’) were retained. Ten researchers working in the area of Energy Balance completed the self-report version of the CEBQ and discussed their experiences. The researchers described how the Desire to Drink scale was difficult to complete. Items from the CEBQ such as “My child is always asking for a drink” had been adapted to “I am always asking for a drink” for the AEBQ and it became unclear what type of drink (i.e. alcoholic versus non-alcoholic) was being referred to. Additionally, the item “My child is always asking for food” from the FR construct in the CEBQ, which became “I am always asking for food” in the AEBQ, was difficult for adults to relate to. It was therefore agreed that the 3 items from the Desire to Drink scale, and the “I am always asking for food item” from the FR scale should be eliminated.
Further refinement of the questionnaire took place in 3 group discussions with a panel of clinical psychologists, behavioural scientists, dieticians, and authors of the original CEBQ. The panel initially reviewed the remaining items from the original CEBQ for any obvious gaps or additional problem areas. It was suggested that a measure of hunger experience (H), which could not be captured by the CEBQ because parents are unable to accurately determine their child’s experienced level of hunger, should be added (Wardle et al., 2013 ). It was also agreed that aspects of Food Responsiveness that related to food cues a parent would not have been able to comment on should also be included. Following this discussion, potential items for the Hunger scale were identified for review, and additional items for the Food Responsiveness scale were developed by the authors for piloting. Finally the panel reviewed all included and excluded items to ensure no further additions/removals were felt to be required. A group consensus was reached and the total number of items following these additions, and the removal of the Desire to Drink scale, was 49.
Piloting. The extended version of the AEBQ was piloted online in an opportunity sample of 49 adults (21–73 years old), 36 women (79.6%) and 13 men (20.4%). Colleagues at University College London were asked to circulate a link to the questionnaire to their friends and family from a range of professional backgrounds. Participants were invited to comment on each individual item and on the questionnaire as a whole. Piloting led to changes in the response options from ‘never’, ‘rarely’, ‘sometimes’, ‘often’ and ‘always’, to ‘strongly disagree’, ‘disagree’, ‘neither agree not disagree’, ‘agree’ and ‘strongly agree’ because participants commented that the original response options did not fit with the questions. The new response options were tested with a small convenience sample (two females and three males, aged 31 ± 7 years). This answer format appeared to be more meaningful and better understood by this sample.
Piloting also led to the deletion of the item “Given the choice, I would always have food in my mouth” because several participants commented that it “sounded a bit odd” or was “over the top”. A second item (“I am interested in food”) was eliminated because participants reported they found the meaning ambiguous. The remaining 47 item version of the AEBQ was included in the Principal Component Analysis (PCA).