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Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain.

Zhang L, Radtke K, Zheng L, Cai AQ, Schilling TF, Nie Q - Mol. Syst. Biol. (2012)

Bottom Line: During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5.Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments.This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of California, Irvine, CA 92697-3875, USA.

ABSTRACT
Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5. Fluorescent in situ hybridization reveals rough edges around these gene expression domains, in which cells co-express hoxb1a and krox20 on either side of the boundary, and these sharpen within a few hours. Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments. In particular, fluctuations in RA initially induce a rough boundary that requires noise in hoxb1a/krox20 expression to sharpen. This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

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Noise in hoxb1a/krox20 expression leads to boundary sharpening. (A) Minimum Action Paths (dash lines) at [RA]in=0.1, 0.5, and 0.8 (krox20-on: blue dot, hoxb1a-on: red dot, both-off: black dot, critical point: green dot). (B) Gene switching probability estimated by MAPs reveals that noise in gene expression can drive cells from co-expressing Hoxb1/Krox20 to uniform Krox20 expression when [RA]in is high, and this coincides with the results of Monte Carlo simulations. (C–E) With noise in both [RA]in and hoxb1a/krox20 expression, a transient noisy boundary becomes sharp over time: (C) single sample; (D) gene distribution at the r4/5 boundary (1000 samples are taken to calculate the gene distributions); (E) two-dimensional simulation at the r4/5 boundary (hoxb1a: blue; krox20: red). (F) Sharpness Index versus time. ‘green dashed line': noise only in extracellular RA alone; ‘black dashed-dotted line': noise in both extracellular and intracellular RA; ‘magenta dotted line': noise in gene expression alone; ‘blue solid line': noise interactions between RA and gene expression; ‘red dashed line with green squares': mean value of the Sharpness Index for distributions of Krox20 obtained from the experimental data. The error bar represents the standard error of the mean. The times 11, 11.3, 11.7, 12, and 12.7 h.p.f. correspond 3, 4, 5, 6, and 8 somites, respectively, and are rescaled to 1, 9, 20, 29, and 50.
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f4: Noise in hoxb1a/krox20 expression leads to boundary sharpening. (A) Minimum Action Paths (dash lines) at [RA]in=0.1, 0.5, and 0.8 (krox20-on: blue dot, hoxb1a-on: red dot, both-off: black dot, critical point: green dot). (B) Gene switching probability estimated by MAPs reveals that noise in gene expression can drive cells from co-expressing Hoxb1/Krox20 to uniform Krox20 expression when [RA]in is high, and this coincides with the results of Monte Carlo simulations. (C–E) With noise in both [RA]in and hoxb1a/krox20 expression, a transient noisy boundary becomes sharp over time: (C) single sample; (D) gene distribution at the r4/5 boundary (1000 samples are taken to calculate the gene distributions); (E) two-dimensional simulation at the r4/5 boundary (hoxb1a: blue; krox20: red). (F) Sharpness Index versus time. ‘green dashed line': noise only in extracellular RA alone; ‘black dashed-dotted line': noise in both extracellular and intracellular RA; ‘magenta dotted line': noise in gene expression alone; ‘blue solid line': noise interactions between RA and gene expression; ‘red dashed line with green squares': mean value of the Sharpness Index for distributions of Krox20 obtained from the experimental data. The error bar represents the standard error of the mean. The times 11, 11.3, 11.7, 12, and 12.7 h.p.f. correspond 3, 4, 5, 6, and 8 somites, respectively, and are rescaled to 1, 9, 20, 29, and 50.

Mentions: The likelihood that a system switches from X1 to X2 relies on its ability to pass through the unstable critical point Xc that lies between X1 and X2 along the path ϕ*. The distance /ϕ*(X1)−ϕ*(Xc)/ is the minimum barrier to the stochastic transition from one state to the other. For a smooth RA gradient and a simple bistable gene expression state (Figure 2C), we calculate MAPs (E et al, 2004) at different levels of RA. At low RA concentration (e.g., at RA=0.1 μM), three MAPs connect each pair of stable states, with each MAP passing through one unstable critical point (Figure 4A). Based on MAP theory, the activation of Krox20 (Krox20-on) from a ‘both-off' state requires less action (a lower barrier) than activation of Hoxb1, which helps explain why the r3 domain of Krox20 expression expands when noise increases in our models (Figure 3C). In contrast, at intermediate RA concentrations a single MAP connects the two steady states and the action to switching from Hoxb1-on to Krox20-on decreases from RA=0.5 to 0.8 μM (Figure 4A), indicating that it becomes easier to switch in this direction as RA increases. When RA levels are high, Krox20-on is the only stable state.


Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain.

Zhang L, Radtke K, Zheng L, Cai AQ, Schilling TF, Nie Q - Mol. Syst. Biol. (2012)

Noise in hoxb1a/krox20 expression leads to boundary sharpening. (A) Minimum Action Paths (dash lines) at [RA]in=0.1, 0.5, and 0.8 (krox20-on: blue dot, hoxb1a-on: red dot, both-off: black dot, critical point: green dot). (B) Gene switching probability estimated by MAPs reveals that noise in gene expression can drive cells from co-expressing Hoxb1/Krox20 to uniform Krox20 expression when [RA]in is high, and this coincides with the results of Monte Carlo simulations. (C–E) With noise in both [RA]in and hoxb1a/krox20 expression, a transient noisy boundary becomes sharp over time: (C) single sample; (D) gene distribution at the r4/5 boundary (1000 samples are taken to calculate the gene distributions); (E) two-dimensional simulation at the r4/5 boundary (hoxb1a: blue; krox20: red). (F) Sharpness Index versus time. ‘green dashed line': noise only in extracellular RA alone; ‘black dashed-dotted line': noise in both extracellular and intracellular RA; ‘magenta dotted line': noise in gene expression alone; ‘blue solid line': noise interactions between RA and gene expression; ‘red dashed line with green squares': mean value of the Sharpness Index for distributions of Krox20 obtained from the experimental data. The error bar represents the standard error of the mean. The times 11, 11.3, 11.7, 12, and 12.7 h.p.f. correspond 3, 4, 5, 6, and 8 somites, respectively, and are rescaled to 1, 9, 20, 29, and 50.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC3472692&req=5

f4: Noise in hoxb1a/krox20 expression leads to boundary sharpening. (A) Minimum Action Paths (dash lines) at [RA]in=0.1, 0.5, and 0.8 (krox20-on: blue dot, hoxb1a-on: red dot, both-off: black dot, critical point: green dot). (B) Gene switching probability estimated by MAPs reveals that noise in gene expression can drive cells from co-expressing Hoxb1/Krox20 to uniform Krox20 expression when [RA]in is high, and this coincides with the results of Monte Carlo simulations. (C–E) With noise in both [RA]in and hoxb1a/krox20 expression, a transient noisy boundary becomes sharp over time: (C) single sample; (D) gene distribution at the r4/5 boundary (1000 samples are taken to calculate the gene distributions); (E) two-dimensional simulation at the r4/5 boundary (hoxb1a: blue; krox20: red). (F) Sharpness Index versus time. ‘green dashed line': noise only in extracellular RA alone; ‘black dashed-dotted line': noise in both extracellular and intracellular RA; ‘magenta dotted line': noise in gene expression alone; ‘blue solid line': noise interactions between RA and gene expression; ‘red dashed line with green squares': mean value of the Sharpness Index for distributions of Krox20 obtained from the experimental data. The error bar represents the standard error of the mean. The times 11, 11.3, 11.7, 12, and 12.7 h.p.f. correspond 3, 4, 5, 6, and 8 somites, respectively, and are rescaled to 1, 9, 20, 29, and 50.
Mentions: The likelihood that a system switches from X1 to X2 relies on its ability to pass through the unstable critical point Xc that lies between X1 and X2 along the path ϕ*. The distance /ϕ*(X1)−ϕ*(Xc)/ is the minimum barrier to the stochastic transition from one state to the other. For a smooth RA gradient and a simple bistable gene expression state (Figure 2C), we calculate MAPs (E et al, 2004) at different levels of RA. At low RA concentration (e.g., at RA=0.1 μM), three MAPs connect each pair of stable states, with each MAP passing through one unstable critical point (Figure 4A). Based on MAP theory, the activation of Krox20 (Krox20-on) from a ‘both-off' state requires less action (a lower barrier) than activation of Hoxb1, which helps explain why the r3 domain of Krox20 expression expands when noise increases in our models (Figure 3C). In contrast, at intermediate RA concentrations a single MAP connects the two steady states and the action to switching from Hoxb1-on to Krox20-on decreases from RA=0.5 to 0.8 μM (Figure 4A), indicating that it becomes easier to switch in this direction as RA increases. When RA levels are high, Krox20-on is the only stable state.

Bottom Line: During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5.Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments.This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of California, Irvine, CA 92697-3875, USA.

ABSTRACT
Morphogens provide positional information for spatial patterns of gene expression during development. However, stochastic effects such as local fluctuations in morphogen concentration and noise in signal transduction make it difficult for cells to respond to their positions accurately enough to generate sharp boundaries between gene expression domains. During development of rhombomeres in the zebrafish hindbrain, the morphogen retinoic acid (RA) induces expression of hoxb1a in rhombomere 4 (r4) and krox20 in r3 and r5. Fluorescent in situ hybridization reveals rough edges around these gene expression domains, in which cells co-express hoxb1a and krox20 on either side of the boundary, and these sharpen within a few hours. Computational analysis of spatial stochastic models shows, surprisingly, that noise in hoxb1a/krox20 expression actually promotes sharpening of boundaries between adjacent segments. In particular, fluctuations in RA initially induce a rough boundary that requires noise in hoxb1a/krox20 expression to sharpen. This finding suggests a novel noise attenuation mechanism that relies on intracellular noise to induce switching and coordinate cellular decisions during developmental patterning.

Show MeSH
Related in: MedlinePlus