Dynamics of Transcription Initiation and Promoter-mediated Noize

Instructions
If you don't see a picture above with DNA and various regulatory buttons, please install newest version of Java.

Applet:

This applet allows one to simulate stocastic transcription initiation. In the middle, there are three redio buttons: "Standard", "Recruit", and "Dead-end".

"Standard" is the standard 3-step model for the initiation: RNAP bind to DNA to form a closed complex (which can fall off), then changed into an open complex, and finally start to elongate.

"Recruit" is a model to make correlation in successive transcription initiation, by taking into account the possibility that an elongating complex may recruit new RNAP to form open complex directly by changing the supercoiling of the DNA.

"Dead-end" is a model to consider the pathway that an open complex fails to elongate but go into dead-end complex, which occlude next RNAP until it is removed after some time.

PARAMETERS (Promoter):

In the "Standard" model, there is the total strength of the promoter, ``Strength", quantified by the average time in seconds between two subsequent transcription initiation events. E.coli promoters can here have widely different strengths, from about 1 second for some Ribosomal promoters to for example 360 second for the lysogeny maintenance gene in the P2 phage. The promoter strength, or its reciprok namely the time between two subsequent RNAP's is:

1/Strength = time(off)+time(closed)+time(open)+time(self-occlusion)

Second there is the aspect ratio, which is the ratio of effective rate for forming an open complex formation all the way from free RNAP, to the rate of initiating an elongating complex from an already formed open complex:

Aspect ratio = rate(off->Open)/rate(Open->Elongation)

A low aspect ratio means a slow on-rate, and a relatively fast elongation initiation. Thus a low aspect ratio imply that the RNAP spend a short time on the promoter. A low aspect ratio also means that the promoter activity is limited by the rate of open complex formation. The aspect ratio have large implications for transcriptional interference (Sneppen et al. (2005)), as well as for the most efficient ways that the promoter can be regulated by transcription factors. P2 lysogeny maintenance promoter have aspect ratio 0.04 whereas 186 lysogeny maintenance promoter have aspect ration of 1.

[Off--> Closed] and [Closed-->off] are equilibrium rates of forming and dissociating from the closed complex. The ratio between these rates sets the average time spent in the closed state.

If one choose "Recruit", the applet also incorporates the possibility for correlations between subsequent transcription initiations events. This is done by assigning a non zero probability P that an elongating complex recruit an open complex when it leaves the promoter. When P approaches 1, each elongating complex will tend to recruit an open complex and subsequent transcription initiations will have exponentially distributed waiting times with mean set by the rate at which open complexes becomes elongating. When P is small or P=0, subsequent firings will be governed by the statistics of the full 3 step process.

If one choose "Dead-end", an open complex can elongate normally with a probability Q (given in a box "Q(Succeed elongation)", or go into a dead-end complex with a probability (1-Q) which cannot elongate any more but prevent new RNAPs to comes in: The dead-end complex is removed stocastically with a given average decay time (In the box "Decay time (sec)"). The dead-end complex will be shown by Black and grey.

The applet allows you to change parameter. One can change the equilibrium rates and recruitment rate. To control the transition between the close complex to the open complex and the open complex to the elongating complex, one can choose to (i) give the strength of the promotor and the aspect ratio, and then the transition rates are calculated, or (ii) controle the transition rates, and then the strength of the promotor and the aspect ratio is calculated. (i) is applied when one choose the buttom "Control Strength", while (ii) is applied when the button "Control rates" is chosen. The background of the parameters that one is controling appears light blue, while the one that is calculated (and cannot be changed) appears pink. In the rectuitment model or the dead-end model, there is some restriction in possible combinations of parameters. For example, in the dead-end model, if one gives very long decay time of the dead-end complex with high probability to go into the dead-end complex, it is impossible to get high strength. If one chose "Control Strength" but gave impossible strength, the value of the strength is refused and go back to the previous value.

Finally the applet opens the possibility for viewing the whole process at a large scale. Change the scroll bar with "Small" and "Large"; "Small" means you see smally regision (but magnified), while "Large" means you see large scale structure of DNA, and thus get a better view of separation between subsequent RNAP. With the scroll bar with "Slow" and "Fast", one regulate the speed of the simulation.

Philosophy
Transcription initiation modeled as a 3 step process (McClure 1985):
  1. A closed complex (C) formation.
  2. An open complex (O) formation.
  3. RNA polymerase (RNAP) which elongate (E) without its sigma factor.
Of these processes, step 1 is an equilibrium process with an on- and an off- rate that sets the affinity of the RNAP to the promoter. Step 2 and 3 are considered one way reactions, and each is therefore characterized by one one-way reaction rate.

In the applet we visualize the 3-step process with transitions between 3 representations of the same piece of DNA. The ``1-position" of the promoter is illustrated with the arrow, whereas the -10 and -35 positions are indicated with green bars across the double stranded DNA.

We quantify the promoter in terms of 4 numbers, ordered after decreasing practical implications. In addition the applet incorporates the possibility for correlations between subsequent transcription initiations. This modification is inspired by the bunched activity that have been observed for some promoters (Golding et al.).

References:

H. Buc, W.R. McClure. "Kinetics of open complex formation between Escherichia coli RNA polymerase and the lac UV5 promoter. Evidence for a sequential mechanism involving three steps."
Biochemistry. 1985 24(11): 27122723.

W.R. McClure. "Mechanism and control of transcription initiation in prokaryotes." Annu Rev Biochem. 1985;54:171204.

Sneppen K, Dodd IB, Shearwin KE, Palmer AC, Schubert RA, Callen BP, Egan JB. "A mathematical model for transcription interference"
J. Mol. Biol. 346 399 (2005).

I. Golding, J. Paulsson, S.M.Zawilski and E.C. Cox, "Real time kinetics of gene activity in individual bacteria"
Cell 123, 1025 (2005)