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Is the Cell Nucleus a Necessary Component in Precise Temporal Patterning?

Albert J, Rooman M - PLoS ONE (2015)

Bottom Line: For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very similar, and whose average threshold time was approximately 150 minutes.The standard deviation of the threshold times computed over one hundred realizations were found to be between 1.8 and 7.16 minutes across both models.We found that the performance of these motifs was nowhere near as impressive as the one found in the eukaryotic cell; the best standard deviation was 6.6 minutes.

View Article: PubMed Central - PubMed

Affiliation: BioModeling, BioInformatics & BioProcesses, Université Libre de Bruxelles, Brussels, Belgium; Applied Physics Research Group, Vrije Universiteit Brussel, Brussels, Belgium.

ABSTRACT
One of the functions of the cell nucleus is to help regulate gene expression by controlling molecular traffic across the nuclear envelope. Here we investigate, via stochastic simulation, what effects, if any, does segregation of a system into the nuclear and cytoplasmic compartments have on the stochastic properties of a motif with a negative feedback. One of the effects of the nuclear barrier is to delay the nuclear protein concentration, allowing it to behave in a switch-like manner. We found that this delay, defined as the time for the nuclear protein concentration to reach a certain threshold, has an extremely narrow distribution. To show this, we considered two models. In the first one, the proteins could diffuse freely from cytoplasm to nucleus (simple model); and in the second one, the proteins required assistance from a special class of proteins called importins. For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very similar, and whose average threshold time was approximately 150 minutes. The standard deviation of the threshold times computed over one hundred realizations were found to be between 1.8 and 7.16 minutes across both models. To see whether a genetic motif in a prokaryotic cell can achieve this degree of precision, we also simulated five variations on the coherent feed-forward motif (CFFM), three of which contained a negative feedback. We found that the performance of these motifs was nowhere near as impressive as the one found in the eukaryotic cell; the best standard deviation was 6.6 minutes. We argue that the significance of these results, the fact and necessity of spatio-temporal precision in the developmental stages of eukaryotes, and the absence of such a precision in prokaryotes, all suggest that the nucleus has evolved, in part, under the selective pressure to achieve highly predictable phenotypes.

No MeSH data available.


Related in: MedlinePlus

Two models of nuclear transport.A) Simple model: the protein of gene C diffuses freely from cytoplasm into the nucleus. B) Extended model: a gene network involving importin-α (blue), importin-β (red) and cargo protein (green). The symbol ∅ indicates degraded protein and mRNA. The reactions are labeled as in Eqs (3, 2, 5, 6): r—transcription rate; λ—export rate of mRNA into the cytoplasm; K—translation rate; k—rate of mRNA degradation; q—rate of protein degradation; a (d)—rate of association (dissociation) between importins α and β; a2 (d)—rate of association (dissociation) between the importin-α−β complex and cargo protein; κ—import rate of the importin-α−β-cargo complex; γ1—rate export of importins α and β into cytoplasm; w1 (w−1)—rate of association (dissociation) between a cargo protein and a free promoter of gene C; —rate of dissociation of a cargo protein from a fully occupied promoter.
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pone.0134239.g001: Two models of nuclear transport.A) Simple model: the protein of gene C diffuses freely from cytoplasm into the nucleus. B) Extended model: a gene network involving importin-α (blue), importin-β (red) and cargo protein (green). The symbol ∅ indicates degraded protein and mRNA. The reactions are labeled as in Eqs (3, 2, 5, 6): r—transcription rate; λ—export rate of mRNA into the cytoplasm; K—translation rate; k—rate of mRNA degradation; q—rate of protein degradation; a (d)—rate of association (dissociation) between importins α and β; a2 (d)—rate of association (dissociation) between the importin-α−β complex and cargo protein; κ—import rate of the importin-α−β-cargo complex; γ1—rate export of importins α and β into cytoplasm; w1 (w−1)—rate of association (dissociation) between a cargo protein and a free promoter of gene C; —rate of dissociation of a cargo protein from a fully occupied promoter.

Mentions: For an mRNA molecule to be translated, it must find its way from the nucleus into the cytoplasm. The mRNA recruits special proteins with which it forms a complex [26] that freely diffuses into the cytoplasm [27]. Once in the cytoplasm, the mRNA rarely returns back to the nucleus, and so, from now on we will consider its transport a one way trip. Also, it is only in the cytoplasm that mRNA is actively degraded; in the nucleus, only damaged mRNA is degraded. The mechanism of intra-compartmental locomotion of proteins depends (in part) on their size: small proteins (< ∼ 40kDa) tend to diffuse freely across the membrane, while large ones need assistance from a family of proteins known as importins and exportins [28]. Those proteins that are needed back in the nucleus after translation, e.g. transcription factors, contain an amino acid sequence that the importins recognize and bind. The simplest scenario involves only one type of importin, importin-β. In another, more complex, situation two importins, importin-α and importin-β, work together to facilitate transport of cargo proteins across the nuclear membrane. In the most likely scenario, importin-α binds to importin-β before it can bind to the cargo protein. Only in this three-protein complex is import into the nucleus most efficient—though the importin-β–cargo complex, too, can sneak in but with a significantly smaller rate. Fig 1 shows in detail the essential reactions involved in synthesizing and transporting mRNA and protein. Models of this type of system have been studied previously, both theoretically and experimentally [28–30]


Is the Cell Nucleus a Necessary Component in Precise Temporal Patterning?

Albert J, Rooman M - PLoS ONE (2015)

Two models of nuclear transport.A) Simple model: the protein of gene C diffuses freely from cytoplasm into the nucleus. B) Extended model: a gene network involving importin-α (blue), importin-β (red) and cargo protein (green). The symbol ∅ indicates degraded protein and mRNA. The reactions are labeled as in Eqs (3, 2, 5, 6): r—transcription rate; λ—export rate of mRNA into the cytoplasm; K—translation rate; k—rate of mRNA degradation; q—rate of protein degradation; a (d)—rate of association (dissociation) between importins α and β; a2 (d)—rate of association (dissociation) between the importin-α−β complex and cargo protein; κ—import rate of the importin-α−β-cargo complex; γ1—rate export of importins α and β into cytoplasm; w1 (w−1)—rate of association (dissociation) between a cargo protein and a free promoter of gene C; —rate of dissociation of a cargo protein from a fully occupied promoter.
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pone.0134239.g001: Two models of nuclear transport.A) Simple model: the protein of gene C diffuses freely from cytoplasm into the nucleus. B) Extended model: a gene network involving importin-α (blue), importin-β (red) and cargo protein (green). The symbol ∅ indicates degraded protein and mRNA. The reactions are labeled as in Eqs (3, 2, 5, 6): r—transcription rate; λ—export rate of mRNA into the cytoplasm; K—translation rate; k—rate of mRNA degradation; q—rate of protein degradation; a (d)—rate of association (dissociation) between importins α and β; a2 (d)—rate of association (dissociation) between the importin-α−β complex and cargo protein; κ—import rate of the importin-α−β-cargo complex; γ1—rate export of importins α and β into cytoplasm; w1 (w−1)—rate of association (dissociation) between a cargo protein and a free promoter of gene C; —rate of dissociation of a cargo protein from a fully occupied promoter.
Mentions: For an mRNA molecule to be translated, it must find its way from the nucleus into the cytoplasm. The mRNA recruits special proteins with which it forms a complex [26] that freely diffuses into the cytoplasm [27]. Once in the cytoplasm, the mRNA rarely returns back to the nucleus, and so, from now on we will consider its transport a one way trip. Also, it is only in the cytoplasm that mRNA is actively degraded; in the nucleus, only damaged mRNA is degraded. The mechanism of intra-compartmental locomotion of proteins depends (in part) on their size: small proteins (< ∼ 40kDa) tend to diffuse freely across the membrane, while large ones need assistance from a family of proteins known as importins and exportins [28]. Those proteins that are needed back in the nucleus after translation, e.g. transcription factors, contain an amino acid sequence that the importins recognize and bind. The simplest scenario involves only one type of importin, importin-β. In another, more complex, situation two importins, importin-α and importin-β, work together to facilitate transport of cargo proteins across the nuclear membrane. In the most likely scenario, importin-α binds to importin-β before it can bind to the cargo protein. Only in this three-protein complex is import into the nucleus most efficient—though the importin-β–cargo complex, too, can sneak in but with a significantly smaller rate. Fig 1 shows in detail the essential reactions involved in synthesizing and transporting mRNA and protein. Models of this type of system have been studied previously, both theoretically and experimentally [28–30]

Bottom Line: For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very similar, and whose average threshold time was approximately 150 minutes.The standard deviation of the threshold times computed over one hundred realizations were found to be between 1.8 and 7.16 minutes across both models.We found that the performance of these motifs was nowhere near as impressive as the one found in the eukaryotic cell; the best standard deviation was 6.6 minutes.

View Article: PubMed Central - PubMed

Affiliation: BioModeling, BioInformatics & BioProcesses, Université Libre de Bruxelles, Brussels, Belgium; Applied Physics Research Group, Vrije Universiteit Brussel, Brussels, Belgium.

ABSTRACT
One of the functions of the cell nucleus is to help regulate gene expression by controlling molecular traffic across the nuclear envelope. Here we investigate, via stochastic simulation, what effects, if any, does segregation of a system into the nuclear and cytoplasmic compartments have on the stochastic properties of a motif with a negative feedback. One of the effects of the nuclear barrier is to delay the nuclear protein concentration, allowing it to behave in a switch-like manner. We found that this delay, defined as the time for the nuclear protein concentration to reach a certain threshold, has an extremely narrow distribution. To show this, we considered two models. In the first one, the proteins could diffuse freely from cytoplasm to nucleus (simple model); and in the second one, the proteins required assistance from a special class of proteins called importins. For each model, we generated fifty parameter sets, chosen such that the temporal profiles they effectuated were very similar, and whose average threshold time was approximately 150 minutes. The standard deviation of the threshold times computed over one hundred realizations were found to be between 1.8 and 7.16 minutes across both models. To see whether a genetic motif in a prokaryotic cell can achieve this degree of precision, we also simulated five variations on the coherent feed-forward motif (CFFM), three of which contained a negative feedback. We found that the performance of these motifs was nowhere near as impressive as the one found in the eukaryotic cell; the best standard deviation was 6.6 minutes. We argue that the significance of these results, the fact and necessity of spatio-temporal precision in the developmental stages of eukaryotes, and the absence of such a precision in prokaryotes, all suggest that the nucleus has evolved, in part, under the selective pressure to achieve highly predictable phenotypes.

No MeSH data available.


Related in: MedlinePlus