Tau (t) Plots

As described in the previous chapters, transcription initiation is a multi-step process that starts with the binding of the RNAp to the promoter, which leads to the closed complex formation fol- lowed by isomerization to form a transcriptionally active open complex (Chamberlin 1974). The kinetics of these steps have been measured directly, using abortive initiation techniques and in

vitro transcription initiation assays (Buc and McClure 1985; McClure 1985; Lutz et al. 2001). For

instance, the rate of the open complex formation has been determined by the mean time taken by the components of transcription, namely the RNAp and the promoter, to reach a steady state rate of production of abortive products. These measurements have shown that there is a sequence- specific lag time before reaching steady state, which was interpreted as the time taken for the RNAp to bind the promoter and form the closed complex. It is the fact that this lag time changes with the concentration of RNAp that distinguishes the closed complex formation from the open complex formation (Buc and McClure 1985).

This dependence allows the construction of a ‘t plot’, which depicts the positive linear relationship between the lag times (inverse of the rate constant of closed complex formation) and the inverse of the RNAp concentration (McClure 1980). In a t plot, the slope of the line between the data points corresponds to the mean time for the completion of the closed complex formation. Mean- while, the point where the line intercepts with the y axis corresponds to the mean time for the open complex formation, since it corresponds to having an infinite concentration of RNAp’s in the sys- tem (McClure 1980).

The use of in vitro techniques to study the kinetics of the steps in transcription initiation has the advantage of allowing to measure transcription for a wide range of concentrations of RNAp. On the other hand, changing RNAp concentrations in live cells is expected to disturb the cell signifi- cantly (Gummesson et al. 2009). This makes it difficult to assess in vivo, the effect of changing RNAp levels on RNA production rates for a given promoter. However, a recent work showed that the two major impediments could be overcome, and established a method for dissecting the in vivo kinetics of the steps involved in transcription initiation (Lloyd-Price et al. 2016). Namely, first, it was shown that RNAp concentrations could be changed to a degree, without altering tangibly the cell growth rates. This not only shows that the cells are not being placed under harmful stress but also that differences in cell division rates do not disturb the estimations. Additionally, it was shown that, within this range, the rate of RNA production changed linearly with the inverse of the RNAp concentration. Second, this method assumes that the fraction of RNA polymerases free for tran- scription is approximately constant within this range of conditions and as such, the intracellular concentration of free RNAps can be assessed from the total RNAp concentration. Note that if this

condition was not valid, a Lineweaver-Burk plot of the inverse of RNAp concentration versus the rate of RNA production would result in a curve. Thus, the occurrence of a line is evidence that (i) the relative free RNAp concentrations can be assessed from the total RNAp concentrations, and that (ii) no factors other than the changes in the free RNAp concentration are affecting transcription of the target promoter (Lloyd-Price et al. 2016).

Given this, after defining which media conditions result in specific intracellular levels of RNAp, it is possible to determine, the relative RNA production rate of a promoter, which is inversely proportional to the mean duration of the time intervals between consecutive RNA production. It is then possible to fit the general model of transcription initiation to the empirical data, which ac- counts for the multi-steps comprising this process, and estimate the in vivo duration of the open and closed complex for a particular promoter.

In Publication II, we made use of this strategy to assess how the duration of the closed and open complex formation of the T7 phage Φ10 promoter change with temperature. For this, we obtained empirical data on how its transcription activity changes with varying concentration of T7 RNAp. As mentioned above, this change should affect the kinetics of the closed complex, but not of the following steps (Lloyd-Price et al. 2016). Here, instead of using media richness to change the T7 RNAp levels, we implemented different concentrations of IPTG, since the gene coding for T7 RNAp was placed under the control of the LacUV5 promoter (Studier and Moffatt 1986). Mean- while, the relative levels of T7 RNAp and the target gene were determined by qPCR.

From reaction (3.4) (Chapter 3), the mean time interval between consecutive RNA production (Δt) is: ( ' ) 1 1 1 Δt( ) CC OC CC OC OC CC OC k k K RNAp RNApk k k RNApk k + + = + = + (4.2)

In (4.2), RNAp is the concentration of T7 RNAp in the cell while K is the ratio between k’CC and

kOC. From (4.2) Δt is given by:

Δt(RNAp) =

t

t

Wheret(RNAp) is the mean time for an RNAp to commit to the open complex formation, and tOC

is the mean time for the completion of the open complex formation. From (4.3), the inverse of the interval between consecutive RNA production events changes linearly with the inverse of T7 RNAp level (1/RNAp). Also, from (4.2) and (4.3):

( )

OC t RNAp

From qPCR results, we can infer the relative rate of RNA production, given an infinite amount of T7 RNAps in the cell. This rate should correspond to the fraction of time of the transcription ini- tiation process that corresponds to the open complex formation alone (Lloyd-Price et al. 2016), as depicted in Equation (4.4). Figure 4.3 shows the resultingt-plots for each temperature assessed in

Publication II.

Figure 4.3: Tau plots for the T7 Φ 10 promoter activity at different temperatures: (A) 43⁰C, (B) 37⁰C and (C) 20⁰C. Figure from Publication IV.