An approximation to the Kierzek AM. et al. J Biol Chem. (2001) 276(11):8165-72 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. This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team. To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information. In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not.. To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
Equation 3 from Kierzek et al. Isomerization of closed binary complex to open complex.
Also equation 8 from Kierzek et al. Since RBS is assumed to be the rate-limiting 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.
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 792-821 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.
RNA Polymerase. Kierzek et al assume mean 35 and delta = 3.5 molecules. Turns out they assume that this buffered.
Equation 7 from Kierzek et al. Based on Draper , DE 1996 E coli and Salmonella 2nd Ed pp 902-908 ASM Press, Washington DC. This is the rate at which the RBS cleared.
Equation 8 from Kierzek et al, set equal to transcription initiaton frequency. This is the decay rate of RBS.
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.
Equations 1 and 2 from Kierzek et al. Reversible RNA binding.
Equations 5 and 6 from Kierzek et al. Association rate set to order of magnitude of diffusion-limited aggregation. Dissociation rate set to reproduce translation frequency.
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.
Equation 10 from Kierzek et al. Assume a half-life of 3 hours for beta-galactosidase in E coli, from Berquist and Truman 1978 Mol. Cell. Genet. 164, 105-108.