PARAMETERS (Promoter):

First of all 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.

Third and forth there 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.

The applet also incorporates the possibility for correlations between subsequent transcription initiations events. This is done by assigning a non zero probability Q that an elongating complex recruit an open complex when it leaves the promoter. When Q 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 Q is small or Q=0, subsequent firings will be governed by the statistics of the full 3 step process.

PARAMETERS (Transcription Factor)

Upper two parameters, the on- and off- rate sets the time for association and dissociation of the isolated transcription factor. When all other ``blue" parameters are <0, the transcription factor act as a repressor by simply blocking (occluding) the promoter.

When the off->C is somewhere between 0 and 1000 the dissociation rate of the closed complex is multiplied by the corresponding number each time a transcription factor is bound upstream of the promoter. At the same time the off rate for the TF is changed by the same factor, representing recruitment associated to an interaction between the TF and the RNAP.

When the C->O is somewhere between 0 and 1000, the transition from closed to open complex is modified accordingly.

When O->E is somewhere between 0 and 1000, the transition from open to elongated complex is modified accordingly. Also the off rate for the TF is changed accordingly, mimicking a model where values <1 assume that it is the binding between the TF and the RNAP which slows the rate of open complex initiation. This is obviously an idealized model, and the detailed landscape for how an RNAP goes from open to elongating complex could easily be much more complicated.

Finally the applet opens the possibility for viewing the whole process at a large scale. Setting Scale=1000 one for example view 1000bp of DNA, and thus get a better view of separation between subsequent RNAP. With the "Sim.step" button one regulate the time-step in the simulation and can speed it up (with some small cost in accuracy of occlusion effects).

1. A closed complex (C) formation.
2. An open complex (O) formation.
3. RNA polymerase (RNAP) which elongate (E) without its sigma factor.

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 upper left corner). In addition the applet incorporates the possibility for correlations between subsequent transcription initiations, modeled by allowing a recently started transcription to recruit a subsequent RNAP directly into an open complex (O) suggested by (Bar Nuham et al (2001) and Dieci et al (2003)). This modification is inspired by the bunched activity that have been observed for some promoters (Golding et al.).

The applet also includes a number of actions for a transcription factor (TF), in particular repression, activation by recruitment and more complicated effects discussed by Roy et al. (1995). These alternate actions are regulated by the blue "buttons": The first two set the binding affinity of the isolated transcription factor, and the subsequent 3 quantify its possible roles when placed upstream to the promoter: activation by recruitment (increased binding of RNAP to promoter), decreased/increased rate of going from closed to open complex (C->O), and decreased/increased rate of going from open to elongating complex (O->E). When these actions are in play, a binding (blue) TF factor is shown on any directly influenced state.

The equilibrium rates (C formation) obviously involves proportional changes of both TF dissociation and RNAP dissociation rate. The C->O transition is not associated to any change in TF dissociation rate. The transcription repression in the O->E complex is modeled by reducing the rate of O->E and at the same time decreasing the off rate of TF when also RNAP is in open complex.

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): 2712–2723.

W.R. McClure. "Mechanism and control of transcription initiation in prokaryotes." Annu Rev Biochem. 1985;54:171–204.

S. Roy, S. Garges, S. Adhya. "Activation and repression of transcription by differential contact: two sides of a coin."
J Biol Chem. 1998, 273(23): 14059-62.Click here to read

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)

G. Bar Nuham and E. Nudler. "Isolation and characterization of sigma(70)-retaining transcription elongation complexes from E.coli."
Cell 106, 443-451 (2001)

G. Dieci and A. sentenac. "Detours and shortcuts to transcription reinitiation".
trends Biochem. Sci. 28, 202-209 (2003).