An approximation to the <a href = "http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=11062240 ">Kierzek AM. et al. J Biol Chem. (2001) 276(11):816572</a> model of LacZ gene expression in E. coli. They use stochastic simulation and model cell growth. Despite these discrepancies, the continuous fixed size model is within a factor of 3 of their results. Parameter values identical.
Thu Nov 9 17:30:28 2006
pathway
Deepak Kumar Sinha, Jaffar Ali, Upinder S. Bhalla, NCBS
Kierzek, Zaim and Zielenkiewicz
E. Coli

Internal
Qualitative
Approximate implementation
Approximates original data
Ribosome pool The language in the paper is a little ambiguous, but from simulation it turns out that they assume that the number of free ribosomes is held fixed at 350. In other buffered.
RNA Polymerase. Kierzek et al assume mean 35 and delta = 3.5 molecules. Turns out they assume that this buffered.
Equations 5 and 6 from Kierzek et al. Association rate set to order of magnitude of diffusionlimited aggregation. Dissociation rate set to reproduce translation frequency.
kf*LacZ_slash_RBS*LacZ_slash_Ribosomekb*LacZ_slash_RibRBS
$\mathrm{kf}\mathrm{LacZ\_slash\_RBS}\mathrm{LacZ\_slash\_Ribosome}\mathrm{kb}\mathrm{LacZ\_slash\_RibRBS}$
Equation 9 from Kierzek et al. They say that this step should be RibRBS> Protein, but based on text and the logic of the synthesis, it should really be ElRIB, the Ribosome elongating protein chain, that should give rise to the protein. The calculation is: ribosome moves at 15 AAs /sec. The protein is 1024 AAs long. So protein is formed 0.015/sec.
kf*LacZ_slash_elRIBkb*LacZ_slash_Ribosome*LacZ_slash_Protein
$\mathrm{kf}\mathrm{LacZ\_slash\_elRIB}\mathrm{kb}\mathrm{LacZ\_slash\_Ribosome}\mathrm{LacZ\_slash\_Protein}$
Equation 10 from Kierzek et al. Assume a halflife of 3 hours for betagalactosidase in E coli, from Berquist and Truman 1978 Mol. Cell. Genet. 164, 105108.
kf*LacZ_slash_Proteinkb*LacZ_slash_AAs
$\mathrm{kf}\mathrm{LacZ\_slash\_Protein}\mathrm{kb}\mathrm{LacZ\_slash\_AAs}$
Equations 1 and 2 from Kierzek et al. Reversible RNA binding.
kf*LacZ_slash_P*LacZ_slash_RNAPkb*LacZ_slash_P_RNAP
$\mathrm{kf}\mathrm{LacZ\_slash\_P}\mathrm{LacZ\_slash\_RNAP}\mathrm{kb}\mathrm{LacZ\_slash\_P\_RNAP}$
Equation 4 from Kierzek et al. They say: To clear the promoter region, active RNA polymerase must move 30 to 60 nucleotides (ref Record et al 1996 E coli and Salmonella 2nd ed pp 792821 ASM Press, Washington DC) Since rate of polymerase movement is about 40 nucleotides/sec, this step takes about 1 sec. The length of the mRNA chain that is synthesized during this time corresponds roughly to the length of the leader region containing the ribosome binding site (RBS). Therefore the synthesis of the RBS and promotor clearance occur at approximately the same rate of 1 per sec. .... Therefore we modeled these two processes by the single first order reaction with a rate constant of 1 sec.
kf*LacZ_slash_TrRNAPkb*LacZ_slash_P*LacZ_slash_RBS*LacZ_slash_ElRNAP*LacZ_slash_RNAP
$\mathrm{kf}\mathrm{LacZ\_slash\_TrRNAP}\mathrm{kb}\mathrm{LacZ\_slash\_P}\mathrm{LacZ\_slash\_RBS}\mathrm{LacZ\_slash\_ElRNAP}\mathrm{LacZ\_slash\_RNAP}$
Equation 8 from Kierzek et al, set equal to transcription initiaton frequency. This is the decay rate of RBS.
kf*LacZ_slash_RBSkb*LacZ_slash_nucleotides
$\mathrm{kf}\mathrm{LacZ\_slash\_RBS}\mathrm{kb}\mathrm{LacZ\_slash\_nucleotides}$
Equation 7 from Kierzek et al. Based on Draper , DE 1996 E coli and Salmonella 2nd Ed pp 902908 ASM Press, Washington DC. This is the rate at which the RBS cleared.
kf*LacZ_slash_RibRBSkb*LacZ_slash_elRIB*LacZ_slash_RBS
$\mathrm{kf}\mathrm{LacZ\_slash\_RibRBS}\mathrm{kb}\mathrm{LacZ\_slash\_elRIB}\mathrm{LacZ\_slash\_RBS}$
Equation 3 from Kierzek et al. Isomerization of closed binary complex to open complex.
kf*LacZ_slash_P_RNAPkb*LacZ_slash_TrRNAP
$\mathrm{kf}\mathrm{LacZ\_slash\_P\_RNAP}\mathrm{kb}\mathrm{LacZ\_slash\_TrRNAP}$
Also equation 8 from Kierzek et al. Since RBS is assumed to be the ratelimiting part of the protein synthesis, we don\'t really need to worry about the fate of the ElRNAP. For balance we degrade it at the same rate as the RBS.
kf*LacZ_slash_ElRNAPkb*LacZ_slash_nucleotides
$\mathrm{kf}\mathrm{LacZ\_slash\_ElRNAP}\mathrm{kb}\mathrm{LacZ\_slash\_nucleotides}$