Mass action rate law for first order irreversible reactions

Reaction scheme where the products are created from the reactants and the change of a product quantity is proportional to the product of reactant activities. The reaction scheme does not include any reverse process that creates the reactants from the products. The change of a product quantity is proportional to the quantity of one reactant.

acc_rate * light(t) 2014-04-17T12:37:07Z acc_rate * acc 2011-01-07T17:28:54Z transcription(t) * (ox_toc1(t) + copies_toc1(t) *(L_toc1 + R_toc1_acc * acc) / (1 + L_toc1 + R_toc1_acc * acc + (R_toc1_cca1 * tf_output(rep_CCA1, effcopies_cca1_LHY7, cca1_n))^H_toc1_cca1)) 2011-01-07T18:14:40Z translation(t) * T * mrna proteasome(t) * (light(t) * D_l + (1 - light(t)) * D_d) * level (light(t) * Di_l + (1 - light(t)) * Di_d) * level 2011-01-07T14:30:23Z transcription(t) * (ox_cca1(t) + copies_cca1(t) * ((tf_output(rep_TOC1, effcopies_toc1_TOC8, toc1_2) * (light(t) * R_cca1_toc1_2_l + (1-light(t)) * R_cca1_toc1_2_d)) ^ H_cca1_toc1) /(( tf_output(rep_TOC1, effcopies_toc1_TOC8, toc1_2) * (light(t) * R_cca1_toc1_2_l + (1-light(t)) * R_cca1_toc1_2_d)) ^ H_cca1_toc1 + 1) ) 2011-01-07T18:05:12Z rep_pTOC1 * transcription(t) * (L_toc1 + R_toc1_acc * acc) / (1 + L_toc1 + R_toc1_acc * acc + (R_toc1_cca1 * cca1_n)^H_toc1_cca1) 2011-01-07T17:27:48Z rep_TOC1 * transcription(t) * copies_toc1(t) *(L_toc1 + R_toc1_acc * acc) / (1 + L_toc1 + R_toc1_acc * acc + (R_toc1_cca1 * cca1_n)^H_toc1_cca1) 2011-01-07T18:04:25Z rep_pCCA1 * transcription(t) * ((toc1_2 * (light(t) * R_cca1_toc1_2_l + (1-light(t)) * R_cca1_toc1_2_d)) ^ H_cca1_toc1) /((toc1_2 * (light(t) * R_cca1_toc1_2_l + (1-light(t)) * R_cca1_toc1_2_d)) ^ H_cca1_toc1 + 1) 2014-04-17T12:29:29Z rep_CCA1*transcription(t) * (copies_cca1(t) * ((tf_output(rep_TOC1, effcopies_toc1_TOC8, toc1_2) * (light(t) * R_cca1_toc1_2_l + (1-light(t)) * R_cca1_toc1_2_d)) ^ H_cca1_toc1) /(( tf_output(rep_TOC1, effcopies_toc1_TOC8, toc1_2) * (light(t) * R_cca1_toc1_2_l + (1-light(t)) * R_cca1_toc1_2_d)) ^ H_cca1_toc1 + 1) ) 2011-01-07T14:58:29Z darkpulse(tod,12) 1+0*t 2011-01-07T14:31:03Z 0*t 2011-01-07T14:30:53Z 1+0*t 2011-01-07T14:29:56Z 2000-01-01T00:00:00Z (1 + reporter * (effcopies - 1)) * tf 2011-01-07T18:14:42Z 1+0*t 1+0*t 2011-01-07T14:31:02Z 0*t 2011-01-07T14:30:50Z 1+0*t 2014-04-17T10:43:57Z ceil(0.5*tanh(12-t)) + ceil(0.5*tanh(t-12-d))
2008-01-01T23:25:42Z Carl Troein Computational Biology and Biological Physics, Lund University Millar Andrew J Institute of Molecular Plant Sciences, University of Edinburgh 2014-04-17T10:42:00

Two-gene model of the Ostreococcus circadian clock

This is a model of the circadian clock of Ostreococcus tauri, with a negative feedback loop between TOC1 and CCA1 (a.k.a. LHY) and multiple light inputs. It was used and described in Troein et al., Plant Journal (2011).

This version of the model has eliminated one light input by setting the TOC1 activation rate to its dark value, corresponding to Figure 2E of Dixon et al., New Phytologist (2014). The model has been entrained in LD 12:12 and will be given one LD cycle before going into constant light. The length of the day before LL is defined in the function called light.

The model incorporates luciferase reporters, and in this SBML model the four different versions of the model for transcriptional and translational reporter lines (pTOC1::LUC, pCCA1::LUC, TOC1-LUC and CCA1-LUC) are all accessible by setting one of the rep_X parameters to 1 and the others to 0. You can also set all four to 0 to only simulate the non-reporter core of the system.

Input to the system should be provided by modifying the "light" function. Implementations of an LD cycles and transition to LL are provided as examples, but the model was also used with more complicated light regimes that vary between data sets and are not convenient to express directly in SBML.

The functions "ox_cca1" and "ox_toc1" can be altered to add overexpression of CCA1 and TOC1. Setting either to x gives additional, constitutive transcription at x times the maximal (and typically not realizable) transcription rate of the native gene. The overexpression mutant fits in Figure 7 of Troein et al. (2011) used ox_cca1 = 0.115 and oc_toc1 = 0.0584, respectively.

The functions "copies_toc1" and "copies_cca1" are normally 1 but can be lowered to simulate knockdown experiments. The functions "transcription", "translation" and "proteasome" can be modified to simulate the effects of altering the overall rate of transcription, translation and protein degradation.

The parameters were fitted specifically to data from transgenic reporter lines TOC8, pTOC3, LHY7 and pLHY7 (Corellou et al., Plant Cell 2009). Parameters that begin with "effcopies" describe the effective number of copies of CCA1 or TOC1 in the respective translational fusion lines, with anything above 1 due to the fusion proteins.

For the model fitting, the initial values were fitted to the data in the various time courses. The initial values given here correspond to the limit cycle of the system in LD 12:12. The system converges to the limit cycle in just a few days under most light conditions, so these initial values are biologically meaningful.

The species cca1luc_c and cca1luc_n have been merged into cca1luc (which corresponds to the observable luminescence signal), because Copasi refused to run the system otherwise. For TOC1-LUC, the predicted output signal is the sum of toc1luc_1 and toc1luc_2.

2011-01-07T14:19:06Z 2000-01-01T00:00:00Z 2011-01-07T14:53:26Z 2011-01-07T14:53:13Z 2011-01-07T14:53:15Z 2011-01-07T14:27:49Z 2011-01-07T14:19:16Z 2011-01-07T14:53:05Z 2011-01-07T14:52:33Z 2011-01-07T14:53:15Z 2011-01-07T14:53:19Z 2011-01-07T14:52:52Z 2011-01-07T14:19:25Z 2011-01-07T14:53:12Z 2011-01-07T14:53:08Z 2011-01-07T14:20:14Z 2011-01-07T18:18:41Z 2011-01-07T14:20:31Z 2011-01-07T15:03:45Z 2011-01-07T14:38:01Z 2011-01-07T14:20:18Z 2011-01-07T14:37:50Z 2011-01-07T14:37:55Z 2011-01-07T15:03:35Z 2011-01-07T14:53:48Z 2011-01-07T14:37:48Z 2011-01-07T14:53:49Z 2011-01-07T17:31:40Z 2011-01-07T17:30:20Z 2011-01-07T17:30:19Z 2011-01-07T18:15:26Z 2011-01-07T17:31:29Z 2011-01-07T17:30:10Z 2011-01-07T18:27:53Z 2011-01-07T14:28:08Z 2011-01-07T18:15:53Z 2011-01-07T17:30:16Z 2011-01-07T17:30:12Z 2011-01-07T17:30:57Z 2011-01-07T17:30:52Z 2011-01-07T17:29:17Z 2011-01-07T17:30:36Z 2011-01-07T17:30:42Z 2011-01-07T17:29:21Z 2011-01-07T17:30:31Z 2011-01-07T17:30:15Z 2011-01-07T14:28:14Z 2011-01-07T17:29:50Z 2011-01-07T17:30:04Z 2011-01-07T17:29:39Z 2011-01-07T17:29:26Z 0 36469256099399.63 0 856039004273047 0 0 163842909978119.9 0 46608477528557.71 75503148899064.41 75503148899064.41 189422505966251.9 0 1267952930128758 218498823243309.7 1 0.1828812174632586 1 0.08201322503032867 1.087061268589661 2.078077386923434 0.0001 0.2311070329494072 0.2921304977837297 0.7699701729778862 0.1364905833686477 0.3266194920897148 0.4615505591808016 0.3566139205511183 2.500706288063396 3.275202921038323 1.385639016822662 1.330820809545275 4.904866104286524 10 0.4241778774494377 0.2693801781540909 1.139657555086233 1 1 0 0 1 0
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