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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

Results for CFFM1 and CFFM2.Shown here are the profiles of all fifty cases (top) and the resulting threshold times distributions (bottom), including the best case for A) CFFM1 and B) CFFM2. C) Threshold times distribution for the system with a nucleus (black) superimposed on CFFM1 (blue) and CFFM2 (red).
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pone.0134239.g006: Results for CFFM1 and CFFM2.Shown here are the profiles of all fifty cases (top) and the resulting threshold times distributions (bottom), including the best case for A) CFFM1 and B) CFFM2. C) Threshold times distribution for the system with a nucleus (black) superimposed on CFFM1 (blue) and CFFM2 (red).

Mentions: We are interested in making a comparison between the system shown in Fig 1B and the two versions of the CFFM of Fig 5. In particular, the temporal profiles of Yr and the protein belonging to gene C should be close. To make this comparison as fair as possible, we apply the same conditions and constraints as in the previous section. The reader should refer to this section and merely replace Eqs (3), (5) and (6) with the following equations:X˙1=r1-k1X1X˙2=r2S-k2X2X˙3=r3P2-k3X3Y˙1=K1X1-q1Y1Y˙2=K2X2-q2Y2Y˙3=K3X3-q3Y3S˙=w1(2)Y1(1-S)-w-1(2)SP˙1=w1(3)Y1(1-P1-P2)+w˜-1(3)P2-w1(3)Y2P1-w-1(3)P1P˙2=w1(3)Y2P1-w˜-1(3)P2(11)for CFFM1, andX˙1=r-k1X1X˙2=rS-k1X2X˙3=r3P-k3X3Y˙1=KX1-qY1Y˙2=KX2-qY2Y˙3=K3X3-q3Y3Z˙=aY1Y2+w-1(3)P-w1(3)Z(1-P)-(b+2q)ZS˙=w1(2)Y1(1-S)-w-1(2)SP˙=w1(3)Z(1-P)-w-1(3)P(12)for CFFM2. As before, the variables X and Y denote mRNA and protein concentrations respectively, with the subscript indicating the gene, and Z refers to the heterodimer comprising of Y1 and Y2. For CFFM1, the association and dissociation rates between the protein (either monomer or heterodimer) and a gene’s promoter are given by and respectively, with the upper index indicating the gene: i = A,B,C. The rate at which a protein encoded by gene A binds with that of gene B is represented by a, while the rate of their dissociation is given by b. In deriving Eqs (11) and (12), we made the same assumptions (those relevant to the present system) listed at the beginning of section “Deterministic model”. When all the steps of the previous section are carried out, the results are as presented in Fig 6.


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

Albert J, Rooman M - PLoS ONE (2015)

Results for CFFM1 and CFFM2.Shown here are the profiles of all fifty cases (top) and the resulting threshold times distributions (bottom), including the best case for A) CFFM1 and B) CFFM2. C) Threshold times distribution for the system with a nucleus (black) superimposed on CFFM1 (blue) and CFFM2 (red).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0134239.g006: Results for CFFM1 and CFFM2.Shown here are the profiles of all fifty cases (top) and the resulting threshold times distributions (bottom), including the best case for A) CFFM1 and B) CFFM2. C) Threshold times distribution for the system with a nucleus (black) superimposed on CFFM1 (blue) and CFFM2 (red).
Mentions: We are interested in making a comparison between the system shown in Fig 1B and the two versions of the CFFM of Fig 5. In particular, the temporal profiles of Yr and the protein belonging to gene C should be close. To make this comparison as fair as possible, we apply the same conditions and constraints as in the previous section. The reader should refer to this section and merely replace Eqs (3), (5) and (6) with the following equations:X˙1=r1-k1X1X˙2=r2S-k2X2X˙3=r3P2-k3X3Y˙1=K1X1-q1Y1Y˙2=K2X2-q2Y2Y˙3=K3X3-q3Y3S˙=w1(2)Y1(1-S)-w-1(2)SP˙1=w1(3)Y1(1-P1-P2)+w˜-1(3)P2-w1(3)Y2P1-w-1(3)P1P˙2=w1(3)Y2P1-w˜-1(3)P2(11)for CFFM1, andX˙1=r-k1X1X˙2=rS-k1X2X˙3=r3P-k3X3Y˙1=KX1-qY1Y˙2=KX2-qY2Y˙3=K3X3-q3Y3Z˙=aY1Y2+w-1(3)P-w1(3)Z(1-P)-(b+2q)ZS˙=w1(2)Y1(1-S)-w-1(2)SP˙=w1(3)Z(1-P)-w-1(3)P(12)for CFFM2. As before, the variables X and Y denote mRNA and protein concentrations respectively, with the subscript indicating the gene, and Z refers to the heterodimer comprising of Y1 and Y2. For CFFM1, the association and dissociation rates between the protein (either monomer or heterodimer) and a gene’s promoter are given by and respectively, with the upper index indicating the gene: i = A,B,C. The rate at which a protein encoded by gene A binds with that of gene B is represented by a, while the rate of their dissociation is given by b. In deriving Eqs (11) and (12), we made the same assumptions (those relevant to the present system) listed at the beginning of section “Deterministic model”. When all the steps of the previous section are carried out, the results are as presented in Fig 6.

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