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Emergent Self-Organized Criticality in Gene Expression Dynamics: Temporal Development of Global Phase Transition Revealed in a Cancer Cell Line.

Tsuchiya M, Giuliani A, Hashimoto M, Erenpreisa J, Yoshikawa K - PLoS ONE (2015)

Bottom Line: Emergent properties of SOC through a mean field approach are revealed: i) SOC, as a form of genomic phase transition, consolidates distinct critical states of expression, ii) Coupling of coherent stochastic oscillations between critical states on different time-scales gives rise to SOC, and iii) Specific gene clusters (barcode genes) ranging in size from kbp to Mbp reveal similar SOC to genome-wide mRNA expression and ON-OFF synchronization to critical states.This suggests that the cooperative gene regulation of topological genome sub-units is mediated by the coherent phase transitions of megadomain-scaled conformations between compact and swollen chromatin states.In summary, our study provides not only a systemic method to demonstrate SOC in whole-genome expression, but also introduces novel, physically grounded concepts for a breakthrough in the study of biological regulation.

View Article: PubMed Central - PubMed

Affiliation: Systems Biology Program, School of Media and Governance, Keio University, Fujisawa, Japan.

ABSTRACT

Background: The underlying mechanism of dynamic control of the genome-wide expression is a fundamental issue in bioscience. We addressed it in terms of phase transition by a systemic approach based on both density analysis and characteristics of temporal fluctuation for the time-course mRNA expression in differentiating MCF-7 breast cancer cells.

Methodology: In a recent work, we suggested criticality as an essential aspect of dynamic control of genome-wide gene expression. Criticality was evident by a unimodal-bimodal transition through flattened unimodal expression profile. The flatness on the transition suggests the existence of a critical transition at which up- and down-regulated expression is balanced. Mean field (averaging) behavior of mRNAs based on the temporal expression changes reveals a sandpile type of transition in the flattened profile. Furthermore, around the transition, a self-similar unimodal-bimodal transition of the whole expression occurs in the density profile of an ensemble of mRNA expression. These singular and scaling behaviors identify the transition as the expression phase transition driven by self-organized criticality (SOC).

Principal findings: Emergent properties of SOC through a mean field approach are revealed: i) SOC, as a form of genomic phase transition, consolidates distinct critical states of expression, ii) Coupling of coherent stochastic oscillations between critical states on different time-scales gives rise to SOC, and iii) Specific gene clusters (barcode genes) ranging in size from kbp to Mbp reveal similar SOC to genome-wide mRNA expression and ON-OFF synchronization to critical states. This suggests that the cooperative gene regulation of topological genome sub-units is mediated by the coherent phase transitions of megadomain-scaled conformations between compact and swollen chromatin states.

Conclusion and significance: In summary, our study provides not only a systemic method to demonstrate SOC in whole-genome expression, but also introduces novel, physically grounded concepts for a breakthrough in the study of biological regulation.

No MeSH data available.


Related in: MedlinePlus

Coupling between fast and slow modes of coherent stochastic oscillation (CSO).CSO is appreciated in terms of Pearson correlations (x: common logarithm of minutes): A) between expression (at t = tj) and the expression change (change in expression from tj to tj+1; j = 1,..,17), P(tj;tj+1−tj)) and B) in the difference in expression between 0–10 min and tj+1−tj, P(t1−t0;tj+1−tj). In A), an opposite response is seen between the super-critical state (red line) and sub-critical (black) & near-critical (blue) states, which shows that the opposite coherent oscillatory dynamics of ABS continue, whereas B) shows the loss of the initial memory of the expression change (0–10 min), which confirms that the change in expression is stochastic. The x-axis represents log10(tj[min]). C): Temporal change in expression of the center of mass of ABSsub (x(CMsub)) shows, albeit with slight oscillation around zero, a good correlation with the Pearson correlation, P(tj;tj+1- tj) of ABSsub (upper right; x(CMsub) by red dot), which reveals an algebraic correlation to the dynamics of CMsub as a feature of SOC (see the main text for details), where the scaled motion of CMsub (upper right) is multiplied by , where α = 1.45 and N(tj) and N(tj+1 − tj) are normal to the expression vector at t = tj and the vector of the expression change: tj+1−tj. D): The long-span opposite dynamics shown in A) appear as an opposite sign of the Pearson correlation of CM between super- and sub-critical states. The average Pearson correlation (over 200 repeats; black dot) of the CM of a randomly selected temporal change in expression (tj+1−tj) from each critical state converges to r = -0.927 (x: m randomly selected mRNAs vs. y: Pearson correlation coefficient). E) Average Pearson correlation of expression (blue) and the change in expression (green) for random sampling (m = 100 with 200 repeats) between two critical states exhibits a similar singular fast/ short span correlation to the super-critical state at 15–30 min with no apparent subsequent response, which is confirmed by F): The figure reports converging Euclidean distance of two correlation points (x: time; y: correlation) between m and m+1 random samplings to zero as m is increased. This suggests the existence of coupling between a fast short span mode in the super-critical state and a long span coherent oscillation in the sub-critical state. G) and H): The emergence of coherent oscillation and stochasticity is examined in terms of G): the difference (Δ) of Pearson correlation, P(tj;tj+1−tj) between ABSsub(tj; tj+1−tj) and m randomly selected mRNAs and H): the difference in P(t1−t0;tj+1−tj) of m randomly selected mRNAs with 400 repeats for each choice, respectively (t0 = 0 min: black, t1 = 10 min: red, t2 = 15 min: green, t3 = 20 min: blue), where the standard deviation (SD) for time points (j = 1,2,3) follows  scaling: α is 0.77 and 1.0 for coherence and stochasticity (in the inset figure in the upper-right corners; red: scaling; black: SD of j = 1), respectively. The results indicate the emergence of CSO after around m = 50, which is also supported by the random sampling results given in D) and F) (marked by black vertical dashed lines).
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pone.0128565.g007: Coupling between fast and slow modes of coherent stochastic oscillation (CSO).CSO is appreciated in terms of Pearson correlations (x: common logarithm of minutes): A) between expression (at t = tj) and the expression change (change in expression from tj to tj+1; j = 1,..,17), P(tj;tj+1−tj)) and B) in the difference in expression between 0–10 min and tj+1−tj, P(t1−t0;tj+1−tj). In A), an opposite response is seen between the super-critical state (red line) and sub-critical (black) & near-critical (blue) states, which shows that the opposite coherent oscillatory dynamics of ABS continue, whereas B) shows the loss of the initial memory of the expression change (0–10 min), which confirms that the change in expression is stochastic. The x-axis represents log10(tj[min]). C): Temporal change in expression of the center of mass of ABSsub (x(CMsub)) shows, albeit with slight oscillation around zero, a good correlation with the Pearson correlation, P(tj;tj+1- tj) of ABSsub (upper right; x(CMsub) by red dot), which reveals an algebraic correlation to the dynamics of CMsub as a feature of SOC (see the main text for details), where the scaled motion of CMsub (upper right) is multiplied by , where α = 1.45 and N(tj) and N(tj+1 − tj) are normal to the expression vector at t = tj and the vector of the expression change: tj+1−tj. D): The long-span opposite dynamics shown in A) appear as an opposite sign of the Pearson correlation of CM between super- and sub-critical states. The average Pearson correlation (over 200 repeats; black dot) of the CM of a randomly selected temporal change in expression (tj+1−tj) from each critical state converges to r = -0.927 (x: m randomly selected mRNAs vs. y: Pearson correlation coefficient). E) Average Pearson correlation of expression (blue) and the change in expression (green) for random sampling (m = 100 with 200 repeats) between two critical states exhibits a similar singular fast/ short span correlation to the super-critical state at 15–30 min with no apparent subsequent response, which is confirmed by F): The figure reports converging Euclidean distance of two correlation points (x: time; y: correlation) between m and m+1 random samplings to zero as m is increased. This suggests the existence of coupling between a fast short span mode in the super-critical state and a long span coherent oscillation in the sub-critical state. G) and H): The emergence of coherent oscillation and stochasticity is examined in terms of G): the difference (Δ) of Pearson correlation, P(tj;tj+1−tj) between ABSsub(tj; tj+1−tj) and m randomly selected mRNAs and H): the difference in P(t1−t0;tj+1−tj) of m randomly selected mRNAs with 400 repeats for each choice, respectively (t0 = 0 min: black, t1 = 10 min: red, t2 = 15 min: green, t3 = 20 min: blue), where the standard deviation (SD) for time points (j = 1,2,3) follows scaling: α is 0.77 and 1.0 for coherence and stochasticity (in the inset figure in the upper-right corners; red: scaling; black: SD of j = 1), respectively. The results indicate the emergence of CSO after around m = 50, which is also supported by the random sampling results given in D) and F) (marked by black vertical dashed lines).

Mentions: Next, we investigate expression behavior around CP. Shu and colleagues [22] demonstrated, by means of density analysis of noisy gene-expression profiles, the robustness of gene expression clustering. Thus, we applied density analysis to show a hill like probability density function in expression space (see examples in Figs 3 and 7 in [18]). This hill-like function marks a dynamical stable profile of expression that in turn is defined as a 'coherent expression state (CES)' for a set of genes.


Emergent Self-Organized Criticality in Gene Expression Dynamics: Temporal Development of Global Phase Transition Revealed in a Cancer Cell Line.

Tsuchiya M, Giuliani A, Hashimoto M, Erenpreisa J, Yoshikawa K - PLoS ONE (2015)

Coupling between fast and slow modes of coherent stochastic oscillation (CSO).CSO is appreciated in terms of Pearson correlations (x: common logarithm of minutes): A) between expression (at t = tj) and the expression change (change in expression from tj to tj+1; j = 1,..,17), P(tj;tj+1−tj)) and B) in the difference in expression between 0–10 min and tj+1−tj, P(t1−t0;tj+1−tj). In A), an opposite response is seen between the super-critical state (red line) and sub-critical (black) & near-critical (blue) states, which shows that the opposite coherent oscillatory dynamics of ABS continue, whereas B) shows the loss of the initial memory of the expression change (0–10 min), which confirms that the change in expression is stochastic. The x-axis represents log10(tj[min]). C): Temporal change in expression of the center of mass of ABSsub (x(CMsub)) shows, albeit with slight oscillation around zero, a good correlation with the Pearson correlation, P(tj;tj+1- tj) of ABSsub (upper right; x(CMsub) by red dot), which reveals an algebraic correlation to the dynamics of CMsub as a feature of SOC (see the main text for details), where the scaled motion of CMsub (upper right) is multiplied by , where α = 1.45 and N(tj) and N(tj+1 − tj) are normal to the expression vector at t = tj and the vector of the expression change: tj+1−tj. D): The long-span opposite dynamics shown in A) appear as an opposite sign of the Pearson correlation of CM between super- and sub-critical states. The average Pearson correlation (over 200 repeats; black dot) of the CM of a randomly selected temporal change in expression (tj+1−tj) from each critical state converges to r = -0.927 (x: m randomly selected mRNAs vs. y: Pearson correlation coefficient). E) Average Pearson correlation of expression (blue) and the change in expression (green) for random sampling (m = 100 with 200 repeats) between two critical states exhibits a similar singular fast/ short span correlation to the super-critical state at 15–30 min with no apparent subsequent response, which is confirmed by F): The figure reports converging Euclidean distance of two correlation points (x: time; y: correlation) between m and m+1 random samplings to zero as m is increased. This suggests the existence of coupling between a fast short span mode in the super-critical state and a long span coherent oscillation in the sub-critical state. G) and H): The emergence of coherent oscillation and stochasticity is examined in terms of G): the difference (Δ) of Pearson correlation, P(tj;tj+1−tj) between ABSsub(tj; tj+1−tj) and m randomly selected mRNAs and H): the difference in P(t1−t0;tj+1−tj) of m randomly selected mRNAs with 400 repeats for each choice, respectively (t0 = 0 min: black, t1 = 10 min: red, t2 = 15 min: green, t3 = 20 min: blue), where the standard deviation (SD) for time points (j = 1,2,3) follows  scaling: α is 0.77 and 1.0 for coherence and stochasticity (in the inset figure in the upper-right corners; red: scaling; black: SD of j = 1), respectively. The results indicate the emergence of CSO after around m = 50, which is also supported by the random sampling results given in D) and F) (marked by black vertical dashed lines).
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pone.0128565.g007: Coupling between fast and slow modes of coherent stochastic oscillation (CSO).CSO is appreciated in terms of Pearson correlations (x: common logarithm of minutes): A) between expression (at t = tj) and the expression change (change in expression from tj to tj+1; j = 1,..,17), P(tj;tj+1−tj)) and B) in the difference in expression between 0–10 min and tj+1−tj, P(t1−t0;tj+1−tj). In A), an opposite response is seen between the super-critical state (red line) and sub-critical (black) & near-critical (blue) states, which shows that the opposite coherent oscillatory dynamics of ABS continue, whereas B) shows the loss of the initial memory of the expression change (0–10 min), which confirms that the change in expression is stochastic. The x-axis represents log10(tj[min]). C): Temporal change in expression of the center of mass of ABSsub (x(CMsub)) shows, albeit with slight oscillation around zero, a good correlation with the Pearson correlation, P(tj;tj+1- tj) of ABSsub (upper right; x(CMsub) by red dot), which reveals an algebraic correlation to the dynamics of CMsub as a feature of SOC (see the main text for details), where the scaled motion of CMsub (upper right) is multiplied by , where α = 1.45 and N(tj) and N(tj+1 − tj) are normal to the expression vector at t = tj and the vector of the expression change: tj+1−tj. D): The long-span opposite dynamics shown in A) appear as an opposite sign of the Pearson correlation of CM between super- and sub-critical states. The average Pearson correlation (over 200 repeats; black dot) of the CM of a randomly selected temporal change in expression (tj+1−tj) from each critical state converges to r = -0.927 (x: m randomly selected mRNAs vs. y: Pearson correlation coefficient). E) Average Pearson correlation of expression (blue) and the change in expression (green) for random sampling (m = 100 with 200 repeats) between two critical states exhibits a similar singular fast/ short span correlation to the super-critical state at 15–30 min with no apparent subsequent response, which is confirmed by F): The figure reports converging Euclidean distance of two correlation points (x: time; y: correlation) between m and m+1 random samplings to zero as m is increased. This suggests the existence of coupling between a fast short span mode in the super-critical state and a long span coherent oscillation in the sub-critical state. G) and H): The emergence of coherent oscillation and stochasticity is examined in terms of G): the difference (Δ) of Pearson correlation, P(tj;tj+1−tj) between ABSsub(tj; tj+1−tj) and m randomly selected mRNAs and H): the difference in P(t1−t0;tj+1−tj) of m randomly selected mRNAs with 400 repeats for each choice, respectively (t0 = 0 min: black, t1 = 10 min: red, t2 = 15 min: green, t3 = 20 min: blue), where the standard deviation (SD) for time points (j = 1,2,3) follows scaling: α is 0.77 and 1.0 for coherence and stochasticity (in the inset figure in the upper-right corners; red: scaling; black: SD of j = 1), respectively. The results indicate the emergence of CSO after around m = 50, which is also supported by the random sampling results given in D) and F) (marked by black vertical dashed lines).
Mentions: Next, we investigate expression behavior around CP. Shu and colleagues [22] demonstrated, by means of density analysis of noisy gene-expression profiles, the robustness of gene expression clustering. Thus, we applied density analysis to show a hill like probability density function in expression space (see examples in Figs 3 and 7 in [18]). This hill-like function marks a dynamical stable profile of expression that in turn is defined as a 'coherent expression state (CES)' for a set of genes.

Bottom Line: Emergent properties of SOC through a mean field approach are revealed: i) SOC, as a form of genomic phase transition, consolidates distinct critical states of expression, ii) Coupling of coherent stochastic oscillations between critical states on different time-scales gives rise to SOC, and iii) Specific gene clusters (barcode genes) ranging in size from kbp to Mbp reveal similar SOC to genome-wide mRNA expression and ON-OFF synchronization to critical states.This suggests that the cooperative gene regulation of topological genome sub-units is mediated by the coherent phase transitions of megadomain-scaled conformations between compact and swollen chromatin states.In summary, our study provides not only a systemic method to demonstrate SOC in whole-genome expression, but also introduces novel, physically grounded concepts for a breakthrough in the study of biological regulation.

View Article: PubMed Central - PubMed

Affiliation: Systems Biology Program, School of Media and Governance, Keio University, Fujisawa, Japan.

ABSTRACT

Background: The underlying mechanism of dynamic control of the genome-wide expression is a fundamental issue in bioscience. We addressed it in terms of phase transition by a systemic approach based on both density analysis and characteristics of temporal fluctuation for the time-course mRNA expression in differentiating MCF-7 breast cancer cells.

Methodology: In a recent work, we suggested criticality as an essential aspect of dynamic control of genome-wide gene expression. Criticality was evident by a unimodal-bimodal transition through flattened unimodal expression profile. The flatness on the transition suggests the existence of a critical transition at which up- and down-regulated expression is balanced. Mean field (averaging) behavior of mRNAs based on the temporal expression changes reveals a sandpile type of transition in the flattened profile. Furthermore, around the transition, a self-similar unimodal-bimodal transition of the whole expression occurs in the density profile of an ensemble of mRNA expression. These singular and scaling behaviors identify the transition as the expression phase transition driven by self-organized criticality (SOC).

Principal findings: Emergent properties of SOC through a mean field approach are revealed: i) SOC, as a form of genomic phase transition, consolidates distinct critical states of expression, ii) Coupling of coherent stochastic oscillations between critical states on different time-scales gives rise to SOC, and iii) Specific gene clusters (barcode genes) ranging in size from kbp to Mbp reveal similar SOC to genome-wide mRNA expression and ON-OFF synchronization to critical states. This suggests that the cooperative gene regulation of topological genome sub-units is mediated by the coherent phase transitions of megadomain-scaled conformations between compact and swollen chromatin states.

Conclusion and significance: In summary, our study provides not only a systemic method to demonstrate SOC in whole-genome expression, but also introduces novel, physically grounded concepts for a breakthrough in the study of biological regulation.

No MeSH data available.


Related in: MedlinePlus