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Kinetics of Histone Gene Expression during Early Development of Xenopus laevis.
Johanna G. Koster 1,2,3, Olivier H.J. Destree 1,3, and Hans V. Westerhoff 3
1 Department of Anatomy and Embryology, University of Amsterdam, The Netherlands, and 2 Human Genetics Branch, National Institute of Child and Human Development, National Institutes of Health, Building 10, Room 8C 429, Bethesda, Maryland 20892, U.S.A., 3 Section on Theoretical Molecular Biology, Laboratory of Molecular Biology, National Institute of Diabetes, Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland, U.S.A.
Using literature data for transcriptional and translational rate constants, gene copy numbers, DNA concentrations, and stability constants, we have calculated the expected concentrations of histones and histone mRNA during embryogenesis of Xenopus laevis. The results led us to conclude that: (i) for X. laevis the gene copy number of the histone genes is too low to ensure the synthesis of sufficient histones during very early development, inheritance from the oocyte of either histone protein or histone mRNA (but not necessarily both) is necessary; (ii) from the known storage of histones in the oocyte and the rates of histone synthesis determined by Adamson & Woodland (1977), there would be sufficient histones to structure the newly synthesized DNA up to gastrulation but not thereafter (these empirical rates of histone synthesis may be underestimates); (iii) on the other hand, the amount of H3 mRNA recently observed during early embryogenesis (Koster, 1987, Koster et al., 1988) could direct a higher and sufficient synthesis of H3 protein, also after gastrulation. We present a quantitative model that accounts both for the observed H3 mRNA concentration as a function of time during embryogenesis and for the synthesis of sufficient histones to structure the DNA throughout early embryogenesis. The model suggests that X. laevis exhibits a major (i.e. some 14-fold) reduction in transcription of histone genes approximately 11 hours after fertilization. This reduction could be due to a decrease in the number of transcribed histone genes, a decreased rate constant of transcription with continued transcription of all the histone genes, and/or a reduction in the time during the cell cycle in which histone mRNA synthesis takes place. Alternatively, the histone mRNA stability might decrease approximately 16-fold 11 hours after fertilization.
J. theor. Biol. (1988) 135, 139-167
Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.
| Name | Definition |
|---|
| Id | Name | Spatial dimensions | Size | |
|---|---|---|---|---|
| default_compartment | — | 3.0 | 1.0 |
| Id | Name | Initial quantity | Compartment | Fixed | |
|---|---|---|---|---|---|
| Prot | — | 1330000000000.0 | default_compartment | ✘ | |
| RNA | — | 570000000.0 | default_compartment | ✘ | |
| XX | — | 0.0 | default_compartment | ✔ |
Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.
| Definition |
|---|
| Id | Name | Objective coefficient | Reaction Equation and Kinetic Law | Flux bounds | |
|---|---|---|---|---|---|
| v_1 | v_1 | XX = RNA kRS * ng * DNA | |||
| v_2 | — | RNA = XX kRd*RNA | |||
| v_3 | v_3 | XX = Prot kPs * RNA | |||
| v_4 | — | Prot = XX kPd*Prot |
| Id | Value | |
|---|---|---|
| DNA | 0.0 | |
| LogDNA | 0.0 | |
| coef | 3.6 | |
| kPd | 0.0077 | |
| kPs | 343.0 | |
| kRS | 0.0 | |
| kRd | 0.231 | |
| ktranscriptionattenuation | 14.0 | |
| mDNA | 0.00000000000315 | |
| mProt | 15300.0 | |
| nA | 602000000000000000000000 | |
| nfac | 1.0 | |
| ng | 50.0 | |
| wfr | 0.236 |
| Id | Value | Reaction |
|---|
| Definition | |
|---|---|
| kRS = piecewise(540,time < 11.35, 540/ktranscriptionattenuation) | |
| DNA = piecewise(2 , time < 0.917,4*2.71828^(1.188*(-1.5 + time)), time < 8.1, 4*2.71828^(1.188*(-1.5 + time)),nfac==0,1000*(10.1 + 12.1*(-8.1 + time) + 0.0000402*(-8.1 + time)^coef)) | |
| LogDNA = log(DNA) |
| Definition |
|---|
| Definition |
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| Definition |
|---|
| Trigger | Assignments |
|---|