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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

Importins in a steady state at t = 0.A) Average protein concentrations for Yn. The red curve corresponds to the best case discussed in Fig 4. The black curve is the profile obtained when the concentrations Xαn, Xαc, Xβn, Xβc, Yαn, Yαc, Yβn, Yβc and Z2 start out in a steady state, and q → q/2.4 and a2 → a2/50. B) 100 profiles generated by the Gillespie algorithm. At t = 150, Δt/tav = 0.017.
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pone.0134239.g008: Importins in a steady state at t = 0.A) Average protein concentrations for Yn. The red curve corresponds to the best case discussed in Fig 4. The black curve is the profile obtained when the concentrations Xαn, Xαc, Xβn, Xβc, Yαn, Yαc, Yβn, Yβc and Z2 start out in a steady state, and q → q/2.4 and a2 → a2/50. B) 100 profiles generated by the Gillespie algorithm. At t = 150, Δt/tav = 0.017.

Mentions: We note that the results of the extended model rely on the requirement that all three genes are turned on at the same time. In real systems this may not always be the case. In many situations the importins may have reached steady state well before the gene of interest is turned on. In fact, experimental studies reveal that neither case is strictly true; the importins themselves are regulated by other molecules, making their concentration vary over time [31–33]. For the sake of completion, however, we did consider a situation where, at time t = 0, all the gene products pertaining to importins are in a steady state. As an example, we took the parameters corresponding to the best case scenario, shown in Fig 4D, and modified them such that the temporal profile of Yn under the new conditions matches the reference profile Yr according to the constraints of section “Stochastic model”. To have a good match, we only had to let q → q/2.4 and a2 → a2/50. Fig 8 shows the result. The temporal precision, while still very good, is diminished by about 30%. This result does not necessarily mean that the precision is always diminished for the latter, as the parameters for the best case scenario may be completely different. An analysis similar to the one carried out in section “Stochastic model” will be necessary in order to determine whether starting out with importins, and the mRNAs from which they are translated, already in a steady state follow the distribution similar to the ones in Fig 4C. We leave this analysis for the future. The proven capability to control importins experimentally [42] makes our results testable.


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

Albert J, Rooman M - PLoS ONE (2015)

Importins in a steady state at t = 0.A) Average protein concentrations for Yn. The red curve corresponds to the best case discussed in Fig 4. The black curve is the profile obtained when the concentrations Xαn, Xαc, Xβn, Xβc, Yαn, Yαc, Yβn, Yβc and Z2 start out in a steady state, and q → q/2.4 and a2 → a2/50. B) 100 profiles generated by the Gillespie algorithm. At t = 150, Δt/tav = 0.017.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4520485&req=5

pone.0134239.g008: Importins in a steady state at t = 0.A) Average protein concentrations for Yn. The red curve corresponds to the best case discussed in Fig 4. The black curve is the profile obtained when the concentrations Xαn, Xαc, Xβn, Xβc, Yαn, Yαc, Yβn, Yβc and Z2 start out in a steady state, and q → q/2.4 and a2 → a2/50. B) 100 profiles generated by the Gillespie algorithm. At t = 150, Δt/tav = 0.017.
Mentions: We note that the results of the extended model rely on the requirement that all three genes are turned on at the same time. In real systems this may not always be the case. In many situations the importins may have reached steady state well before the gene of interest is turned on. In fact, experimental studies reveal that neither case is strictly true; the importins themselves are regulated by other molecules, making their concentration vary over time [31–33]. For the sake of completion, however, we did consider a situation where, at time t = 0, all the gene products pertaining to importins are in a steady state. As an example, we took the parameters corresponding to the best case scenario, shown in Fig 4D, and modified them such that the temporal profile of Yn under the new conditions matches the reference profile Yr according to the constraints of section “Stochastic model”. To have a good match, we only had to let q → q/2.4 and a2 → a2/50. Fig 8 shows the result. The temporal precision, while still very good, is diminished by about 30%. This result does not necessarily mean that the precision is always diminished for the latter, as the parameters for the best case scenario may be completely different. An analysis similar to the one carried out in section “Stochastic model” will be necessary in order to determine whether starting out with importins, and the mRNAs from which they are translated, already in a steady state follow the distribution similar to the ones in Fig 4C. We leave this analysis for the future. The proven capability to control importins experimentally [42] makes our results testable.

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