Ee above and “Results”). Since in our procedure , and koff parameters
Ee above and “Results”). Since in our procedure , and koff parameters cannot be separated, we aggregate them into a single parameter /koff .Temperature dependence of kinetic parametersProteins and mRNAs Bayer 41-4109MedChemExpress Bay 41-4109 half-life was measured as previously described [9]. Briefly, to determine the mRNA half-life, the cells were first treated with actinomycin D and the mRNA concentration was measured with a quantitative-reverse-transcription-Polymerase Chain Reaction (qRT-PCR) assay. Regarding the mCherry halflife, the cells PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/28993237 were first treated with the cycloheximide and the mCherry concentration was determined by flow cytometry.Twostate model of gene expressionWe previously showed [9] that in the considered system, protein distributions are well reproduced by a two-state model of gene expression, where mRNAs are produced during short transcription bursts (“on” state), separated by long inactive periods (“off “). Here, we took advantage of this behavior to simplify the fitting procedure by considering the limit of infinitely short bursts (i.e. by considering that for a given transcription burst, all mRNAs are produced simultaneously). The formalism is then mathematically equivalent to a “one-state model” (Eq. 8 in [23]), except that the burst duration is given by 1/koff rather than the RNA lifetime. This approximation is relevant here since the mCherry reporter protein half-life is much longer than (1) the burst duration and (2) the RNA half-life, and it is further validated by the good agreement of the model with experimental curves (see below). In this case the fluorescence distribution is a negative binomial [23] that be computed analytically. It only depends on two parameters: the burst size (b; number of proteins produced per burst) that gives the distribution shape and the burst frequency normalized by the protein lifetime (f) that gives the scale of the distribution:We describe the temperature dependence of the computed kinetic parameters in analogy to classical kinetic theories [24]. A reaction-limited elementary process is characterized by an activation energy EA, which can be estimated from an Arrhenius plot (log(k) vs. 1/T ). For small temperature variations around T0, T T0 this energy can be simply computed from the slope of the graph log(k) vs. T (Fig. 6b): log(k(T0 + T )) = log(k(T0 )) + (EA /kB T ) ?(T /T0 ) . For diffusion-limited reactions, the same graph would yield a slope corresponding to the case EA = kB T . Importantly, in both regimes, the kinetics increases with temperature. Here, the burst processes likely involve a complex combination of elementary processes, and the resulting temperature dependence could thus be increasing or decreasing. We compute “effective activation energies” for the inferred parameters, in analogy to the classical theories, and later discuss the signification of these quantities in terms of molecular events. Importantly, for combined kinetic processes [e.g. k = (k1 ?k2 /k3 )], the total effective activation energy is the sum of the single ones: EA = EA1 + EA2 – EA3. In contrast to the usual version, the effective activation energy can thus be negative if the reaction is inversely dependent on the limiting process.ResultsCharacteristic relaxation timeb=kofff =konwhere and are the RNA production and degradation rates, and the protein production and degradationOur first goal was to establish how fast an isolated fraction of cells could recapitulate their initial distribution. For this, we sorted ce.