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Theory on the dynamics of feedforward loops in the transcription factor networks.

Murugan R - PLoS ONE (2012)

Bottom Line: We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs.The coherent C1 type seems to be more robust against changes in other system parameters.We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs.

View Article: PubMed Central - PubMed

Affiliation: Department of Biotechnology, Indian Institute of Technology Madras, Chennai, India. rmurugan@gmail.com

ABSTRACT
Feedforward loops (FFLs) consist of three genes which code for three different transcription factors A, B and C where B regulates C and A regulates both B and C. We develop a detailed model to describe the dynamical behavior of various types of coherent and incoherent FFLs in the transcription factor networks. We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs. Detailed analysis shows that the response times of FFLs strongly dependent on the ratios (w(h) = γ(pc)/γ(ph) where h = a, b, c corresponding to genes A, B and C) between the lifetimes of mRNAs (1/γ(mh)) of genes A, B and C and the protein of C (1/γ(pc)). Under strong binding conditions we can categorize all the possible types of FFLs into groups I, II and III based on the dependence of the response times of FFLs on w(h). Group I that includes C1 and I1 type FFLs seem to be less sensitive to the changes in w(h). The coherent C1 type seems to be more robust against changes in other system parameters. We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs.

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Related in: MedlinePlus

Dependency of response times on various sets of system parameters viz. = (wa, wb, wc),  = (µab, µac, µbc, µyc, Lab) and  = (vba, vca, vcb, εab, vcy). Response times are expressed in terms of number of generation times. A. Dependency of response times of various types of FFLs under weak binding conditions. Here the simulation setting are  = 1,  = 0.0003,  = 4, Δτ = 5 x10−6, the total simulation time was set to T = 25 generation times and  was iterated in the interval (0.001, 10) with Δ = 0.001. Under weak binding condition we observe that each of the considered FFLs behaves in a different way from others. B. Dependency of response times of FFLs . Settings are same as A with  = 0.1. C. Dependency of response times of FFLs . Settings are same as A with  = 0.01. D. Dependency of response times of FFLs . Settings are same as A however with  = 0.001. Under this strong binding conditions all the considered FFLs segregate into three Groups namely I, II and III. It seems that PPP (C1) and PNP (I1) type FFLs show less variation with respect to changes in  and also their response times are comparable with that of the unregulated C. E. Influence of increase in  on the dependency of response times of FFLs on . Here  = 0.003. This is the physiological value of  for a typical yeast cell nucleus whose volume is ∼10 times higher than a bacterial cell. In this case, P-P type FLL shifts from the third subgroup of Group I to the second subgroup. F. Influence of changes in  on the dependency of response times of FFLs on . Here  = 0.03. This is the physiological value for a typical human cell nucleus whose volume is ∼100 times larger than a bacterial cell. In this case, PNP (I1) type incoherent FFL shifts to Group III.
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pone-0041027-g002: Dependency of response times on various sets of system parameters viz. = (wa, wb, wc),  = (µab, µac, µbc, µyc, Lab) and  = (vba, vca, vcb, εab, vcy). Response times are expressed in terms of number of generation times. A. Dependency of response times of various types of FFLs under weak binding conditions. Here the simulation setting are  = 1,  = 0.0003,  = 4, Δτ = 5 x10−6, the total simulation time was set to T = 25 generation times and was iterated in the interval (0.001, 10) with Δ = 0.001. Under weak binding condition we observe that each of the considered FFLs behaves in a different way from others. B. Dependency of response times of FFLs . Settings are same as A with  = 0.1. C. Dependency of response times of FFLs . Settings are same as A with  = 0.01. D. Dependency of response times of FFLs . Settings are same as A however with  = 0.001. Under this strong binding conditions all the considered FFLs segregate into three Groups namely I, II and III. It seems that PPP (C1) and PNP (I1) type FFLs show less variation with respect to changes in and also their response times are comparable with that of the unregulated C. E. Influence of increase in on the dependency of response times of FFLs on . Here  = 0.003. This is the physiological value of for a typical yeast cell nucleus whose volume is ∼10 times higher than a bacterial cell. In this case, P-P type FLL shifts from the third subgroup of Group I to the second subgroup. F. Influence of changes in on the dependency of response times of FFLs on . Here  = 0.03. This is the physiological value for a typical human cell nucleus whose volume is ∼100 times larger than a bacterial cell. In this case, PNP (I1) type incoherent FFL shifts to Group III.

Mentions: The dependency of the response times on the parameters seems to be strongly influenced by the set of binding parameters . Under weak binding conditions such as , we find that each of FFLs under consideration show different type of variations as changes. Figure 2A suggests that the response times of various FFLs under weak binding conditions seems to be in the descending order of P-P, N-P, PPP, NPP, NNP, PNP, PPN, NPN, N-N, P-N, NNN and PNN. We further observe that almost all the FFLs show similar type of variation in response time with respect to changes in in the dynamic range (0.1, 1). From Figures 2B, 2C and 2D we find that this scenario significantly changes as the binding strength increases. Under strong binding conditions such as 1, the entire set of FFLs can be approximately categorized into three subgroups (Figure 2D) based on the behavior of overall response times with respect to changes in viz. Group I: {{PPN, NNP}, {PPP, NPP, N-P}, {P-P, PNP}}, Group II: {NPN, {N-N, NNN}, PNN} and Group III: P-N. Here the order of response times of various subgroups is Group I > Group II > Group III. One can write the segregation pattern in the standard terminology of FFLs as {{I3, C4}, {C1, I4, N-P}}, {P-P, I1}}, {C2, {N-N, I2}, C3}, P-N. Though Group II and Group III type FFLs possess lesser response times than Group I their response times increase almost linearly upon an increase over the entire range of investigation on a log-log scale.


Theory on the dynamics of feedforward loops in the transcription factor networks.

Murugan R - PLoS ONE (2012)

Dependency of response times on various sets of system parameters viz. = (wa, wb, wc),  = (µab, µac, µbc, µyc, Lab) and  = (vba, vca, vcb, εab, vcy). Response times are expressed in terms of number of generation times. A. Dependency of response times of various types of FFLs under weak binding conditions. Here the simulation setting are  = 1,  = 0.0003,  = 4, Δτ = 5 x10−6, the total simulation time was set to T = 25 generation times and  was iterated in the interval (0.001, 10) with Δ = 0.001. Under weak binding condition we observe that each of the considered FFLs behaves in a different way from others. B. Dependency of response times of FFLs . Settings are same as A with  = 0.1. C. Dependency of response times of FFLs . Settings are same as A with  = 0.01. D. Dependency of response times of FFLs . Settings are same as A however with  = 0.001. Under this strong binding conditions all the considered FFLs segregate into three Groups namely I, II and III. It seems that PPP (C1) and PNP (I1) type FFLs show less variation with respect to changes in  and also their response times are comparable with that of the unregulated C. E. Influence of increase in  on the dependency of response times of FFLs on . Here  = 0.003. This is the physiological value of  for a typical yeast cell nucleus whose volume is ∼10 times higher than a bacterial cell. In this case, P-P type FLL shifts from the third subgroup of Group I to the second subgroup. F. Influence of changes in  on the dependency of response times of FFLs on . Here  = 0.03. This is the physiological value for a typical human cell nucleus whose volume is ∼100 times larger than a bacterial cell. In this case, PNP (I1) type incoherent FFL shifts to Group III.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3401222&req=5

pone-0041027-g002: Dependency of response times on various sets of system parameters viz. = (wa, wb, wc),  = (µab, µac, µbc, µyc, Lab) and  = (vba, vca, vcb, εab, vcy). Response times are expressed in terms of number of generation times. A. Dependency of response times of various types of FFLs under weak binding conditions. Here the simulation setting are  = 1,  = 0.0003,  = 4, Δτ = 5 x10−6, the total simulation time was set to T = 25 generation times and was iterated in the interval (0.001, 10) with Δ = 0.001. Under weak binding condition we observe that each of the considered FFLs behaves in a different way from others. B. Dependency of response times of FFLs . Settings are same as A with  = 0.1. C. Dependency of response times of FFLs . Settings are same as A with  = 0.01. D. Dependency of response times of FFLs . Settings are same as A however with  = 0.001. Under this strong binding conditions all the considered FFLs segregate into three Groups namely I, II and III. It seems that PPP (C1) and PNP (I1) type FFLs show less variation with respect to changes in and also their response times are comparable with that of the unregulated C. E. Influence of increase in on the dependency of response times of FFLs on . Here  = 0.003. This is the physiological value of for a typical yeast cell nucleus whose volume is ∼10 times higher than a bacterial cell. In this case, P-P type FLL shifts from the third subgroup of Group I to the second subgroup. F. Influence of changes in on the dependency of response times of FFLs on . Here  = 0.03. This is the physiological value for a typical human cell nucleus whose volume is ∼100 times larger than a bacterial cell. In this case, PNP (I1) type incoherent FFL shifts to Group III.
Mentions: The dependency of the response times on the parameters seems to be strongly influenced by the set of binding parameters . Under weak binding conditions such as , we find that each of FFLs under consideration show different type of variations as changes. Figure 2A suggests that the response times of various FFLs under weak binding conditions seems to be in the descending order of P-P, N-P, PPP, NPP, NNP, PNP, PPN, NPN, N-N, P-N, NNN and PNN. We further observe that almost all the FFLs show similar type of variation in response time with respect to changes in in the dynamic range (0.1, 1). From Figures 2B, 2C and 2D we find that this scenario significantly changes as the binding strength increases. Under strong binding conditions such as 1, the entire set of FFLs can be approximately categorized into three subgroups (Figure 2D) based on the behavior of overall response times with respect to changes in viz. Group I: {{PPN, NNP}, {PPP, NPP, N-P}, {P-P, PNP}}, Group II: {NPN, {N-N, NNN}, PNN} and Group III: P-N. Here the order of response times of various subgroups is Group I > Group II > Group III. One can write the segregation pattern in the standard terminology of FFLs as {{I3, C4}, {C1, I4, N-P}}, {P-P, I1}}, {C2, {N-N, I2}, C3}, P-N. Though Group II and Group III type FFLs possess lesser response times than Group I their response times increase almost linearly upon an increase over the entire range of investigation on a log-log scale.

Bottom Line: We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs.The coherent C1 type seems to be more robust against changes in other system parameters.We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs.

View Article: PubMed Central - PubMed

Affiliation: Department of Biotechnology, Indian Institute of Technology Madras, Chennai, India. rmurugan@gmail.com

ABSTRACT
Feedforward loops (FFLs) consist of three genes which code for three different transcription factors A, B and C where B regulates C and A regulates both B and C. We develop a detailed model to describe the dynamical behavior of various types of coherent and incoherent FFLs in the transcription factor networks. We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs. Detailed analysis shows that the response times of FFLs strongly dependent on the ratios (w(h) = γ(pc)/γ(ph) where h = a, b, c corresponding to genes A, B and C) between the lifetimes of mRNAs (1/γ(mh)) of genes A, B and C and the protein of C (1/γ(pc)). Under strong binding conditions we can categorize all the possible types of FFLs into groups I, II and III based on the dependence of the response times of FFLs on w(h). Group I that includes C1 and I1 type FFLs seem to be less sensitive to the changes in w(h). The coherent C1 type seems to be more robust against changes in other system parameters. We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs.

Show MeSH
Related in: MedlinePlus