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Bounds on the Hausdorff dimension of random attractors for infinite-dimensional random dynamical systems on fractals
Interlocked multi-node positive and negative feedback loops facilitate oscillations
Guangdong Province Key Laboratory of Computational Science, School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China |
Positive and negative feedback loops in biological regulatory networks appear often in a multi-node manner since regulatory processes are in general multi-step. Although it is well known that interlocked positive and negative feedback loops (iPNFLs) can generate sustained oscillations, how the number of nodes in each loop affects the oscillations remains elusive. By analyzing a model of iPNFLs with multiple nodes, we find that the node number of the negative loop mainly plays a role of amplifying oscillation amplitudes whereas that of the positive loop mainly plays a role of reducing oscillatory regions, both depending on the (competitive or noncompetitive) way of interaction between the two loops. We also find that given an iPNFL network of the same structure, the noncompetitive model is more likely to produce large-amplitude oscillations than the competitive model. These results not only indicate that multi-node iPNFLs are an effective mechanism of promoting oscillations but also are helpful for the design of synthetic oscillators.
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Positive and Negative Feedback: Striking a balance between necessary antagonists, Journal of Theoretical Biology, 216 (2002), 229-241.
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Z. Darieva, A. Clancy, R. Bulmer, E. Williams, A. Pic-Taylor, B. A. Morgan and A. D. Sharrocks,
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B. Huang, X. Tian, F. Liu and W. Wang,
Impact of time delays on oscillatory dynamics of interlinked positive and negative feedback loops, Phys. Rev. E., 94 (2016), 052413.
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F. J. Jr,
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Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways, Bioessays, 29 (2007), 85-90.
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Coupled feedback loops form dynamic motifs of cellular networks, Biophysical Journal, 94 (2008), 359-365.
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W. Ma, A. Trusina, H. El-Samad, W. A. Lim and C. Tang,
Defining Network Topologies that Can Achieve Biochemical Adaptation, Cell, 138 (2009), 760-773.
doi: 10.1016/j.cell.2009.06.013. |
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K. Maeda and H. Kurata,
Long negative feedback loop enhances period tunability of biological oscillators, Journal of Theoretical Biology, 440 (2018), 21-31.
doi: 10.1016/j.jtbi.2017.12.014. |
[21] |
W. Mather, M. R. Bennett, J. Hasty and L. S. Tsimring,
Delay-induced degrade-and-fire oscillations in small genetic circuits, Physical Review Letters, 102 (2009), 068105.
doi: 10.1103/PhysRevLett.102.068105. |
[22] |
N. A. M. Monk,
Oscillatory Expression of Hes1, p53, and NF-kappaB Driven by Transcriptional Time Delays, Current Biology, 13 (2003), 1409-1413.
doi: 10.1016/S0960-9822(03)00494-9. |
[23] |
K. Montagne, R. Plasson, Y. Sakai, T. Fujii and Y. Rondelez,
Programming An In Vitro Dna Oscillator Using A Molecular Networking Strategy, Molecular Systems Biology, 7 (2011), 466-472.
doi: 10.1038/Msb.2010.120. |
[24] |
M. Monti and P. R. Wolde,
The accuracy of telling time via oscillatory signals, Physical Biology, 13 (2016), 035005.
doi: 10.1088/1478-3975/13/3/035005. |
[25] |
A. Munteanu, M. Constante, M. Isalan and R. V. Solé, Avoiding transcription factor competition at promoter level increases the chances of obtaining oscillation, BMC Systems Biology, 4 (2010), p66.
doi: 10.1186/1752-0509-4-66. |
[26] |
R. Murugan,
Theory on the dynamics of oscillatory loops in the transcription factor networks, PLoS One, 7 (2014), 3736-3739.
|
[27] |
M. Namiko, J. M. Hogh and S. Szabolcs,
Coupled positive and negative feedbacks produce diverse gene expression patterns in colonies, MBio, 6 (2015), e00059-15.
doi: 10.1128/mBio.00059-15. |
[28] |
B. Novák and J. J. Tyson,
Design principles of biochemical oscillators, Nat. Rev. Mol. Cell. Biol, 9 (2008), 981-991.
|
[29] |
E. L. O'Brien, E. V. Itallie and M. R. Bennett,
Modeling synthetic gene oscillators, Mathematical Biosciences, 236 (2012), 1-15.
doi: 10.1016/j.mbs.2012.01.001. |
[30] |
S. Pigolotti, S. Krishna and M. H. Jensen,
Oscillation patterns in negative feedback loops, Proc. Natl. Acad. Sci. U. S. A., 104 (2007), 6533-6537.
doi: 10.1073/pnas.0610759104. |
[31] |
J. R. Pomerening, S. Y. Kim and F. J. Jr,
Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations, Cell, 122 (2005), 565-578.
doi: 10.1016/j.cell.2005.06.016. |
[32] |
T. Shopera, W. R. Henson, A. Ng, Y. J. Lee, K. Ng and T. S. Moon,
Robust, tunable genetic memory from protein sequestration combined with positive feedback, Nucleic Acids Research, 43 (2015), 9086-9094.
doi: 10.1093/nar/gkv936. |
[33] |
H. Song, P. Smolen, E. Avron, D. A. Baxter and J. H. Byrne,
Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins, Biophysical Journal, 92 (2007), 3407-3424.
doi: 10.1529/biophysj.106.096891. |
[34] |
J. Stricker, S. Cookson, M. R. Bennett, W. H. Mather, L. S. Tsimring and J. Hasty,
A fast, robust and tunable synthetic gene oscillator, Nature, 456 (2008), 516-519.
doi: 10.1038/nature07389. |
[35] |
P. K. Tapaswi, P. Bhattacharya, An extended mathematical-model of transcription and translation during embryogenesis, Cybernetica, 24 (1981), 61-84. Available from: http://library.isical.ac.in:8080/jspui/bitstream/10263/938/1/CYB-24-1-1981-P61-84.pdf. |
[36] |
X. J. Tian, X. P. Zhang, F. Liu and W. Wang,
Interlinking positive and negative feedback loops creates a tunable motif in gene regulatory networks, Physical Review E Statistical Nonlinear and Soft Matter Physics, 80 (2009), 011926.
doi: 10.1103/PhysRevE.80.011926. |
[37] |
T. Y. Tsai, Y. S. Choi, W. Ma, J. R. Pomerening, C. Tang and J. E. Ferrell,
Robust, tunable biological oscillations from interlinked positive and negative feedback loops, Science, 321 (2008), 126-129.
doi: 10.1126/science.1156951. |
[38] |
K. Uriu and H. Tei,
Feedback loops interlocked at competitive binding sites amplify and facilitate genetic oscillations, Journal of Theoretical Biology, 428 (2017), 56-64.
doi: 10.1016/j.jtbi.2017.06.005. |
[39] |
A. Verdugo and R. Rand,
Hopf bifurcation in a DDE model of gene expression, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), 235-242.
doi: 10.1016/j.cnsns.2006.05.001. |
[40] |
Y. C. Wang, S. E. Peterson and J. F. Loring,
Protein post-translational modifications and regulation of pluripotency in human stem cells, Cell Research, 24 (2014), 143-160.
doi: 10.1038/cr.2013.151. |
[41] |
J. J. Wei and C. B. Yu,
Hopf bifurcation analysis in a model of oscillatory gene expression with delay, Proceedings of the Royal Society of Edinburgh, 139 (2009), 879-895.
doi: 10.1017/S0308210507000091. |
[42] |
X. P. Zhang, Z. Cheng, F. Liu and W. Wang,
Linking fast and slow positive feedback loops creates an optimal bistable switch in cell signaling, Physical Review E Statistical Nonlinear and Soft Matter Physics, 76 (2007), 031924.
doi: 10.1103/PhysRevE.76.031924. |
[43] |
X. Zhao, T. Hirota, X. M. Han, H. Cho, L. W. Chong, K. Lamia, S. Liu, A. R. Atkins, E. Banayo, C. Liddle, R. T. Yu, J.R. Yates, S. A. Kay, M. Downes and R. M. Evans,
Circadian amplitude regulation via FBXW7-targeted REV-ERB $α$ degradation, Cell, 165 (2016), 1644-1657.
doi: 10.1016/j.cell.2016.05.012. |
show all references
References:
[1] |
Y. An, G. S. Xu and Z. B. Yang,
Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes, Proc. Natl. Acad. Sci. U. S. A., 106 (2009), 22002-22007.
doi: 10.1073/pnas.0910811106. |
[2] |
B. Ananthasubramaniam and H. Herzel,
Positive feedback promotes oscillations in negative feedback loops, PLoS One, 9 (2014), e104761.
|
[3] |
D. Angeli, F. J. Jr and E. D. Sontag,
Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proc. Natl. Acad. Sci. U. S. A., 101 (2004), 1822-1827.
doi: 10.1073/pnas.0308265100. |
[4] |
O. Brandman and T. Meyer,
Feedback loops shape cellular signals in space and time, Science, 322 (2008), 390-395.
doi: 10.1126/science.1160617. |
[5] |
O. Brandman, F. J. Jr, R. Li and T. Meyer,
Interlinked fast and slow positive feedback loops drive reliable cell decisions, Science, 310 (2005), 496-498.
doi: 10.1126/science.1113834. |
[6] |
C. F. Calkhoven and G. Ab,
Multiple steps in the regulation of transcription-factor level and activity, Biochemical Journal, 317 (1996), 329-342.
doi: 10.1042/bj3170329. |
[7] |
S. M. Castillo-Hair, E. R. Villota and A. M. Coronado,
Design principles for robust oscillatory behavior, Systems and Synthetic Biology, 9 (2015), 125-133.
doi: 10.1007/s11693-015-9178-6. |
[8] |
O. Cinquin and J. Demongeot,
Positive and Negative Feedback: Striking a balance between necessary antagonists, Journal of Theoretical Biology, 216 (2002), 229-241.
doi: 10.1006/jtbi.2002.2544. |
[9] |
Z. Darieva, A. Clancy, R. Bulmer, E. Williams, A. Pic-Taylor, B. A. Morgan and A. D. Sharrocks,
A competitive transcription factor binding mechanism determines the timing of late cell cycle-dependent gene expression, Molecular Cell, 38 (2010), 29-40.
doi: 10.1016/j.molcel.2010.02.030. |
[10] |
L. Giorgetti, T. Siggers, G. Tiana, G. Caprara, S. Notarbartolo, T. Corona, M. Pasparakis, P. Milani, M. L. Bulyk and G. Natoli,
Noncooperative interactions between transcription factors and clustered DNA binding sites enable graded transcriptional responses to environmental inputs, Molecular Cell, 37 (2010), 418-428.
doi: 10.1016/j.molcel.2010.01.016. |
[11] |
B. Huang, X. Tian, F. Liu and W. Wang,
Impact of time delays on oscillatory dynamics of interlinked positive and negative feedback loops, Phys. Rev. E., 94 (2016), 052413.
doi: 10.1103/PhysRevE.94.052413. |
[12] |
Z. Hui, Y. Chen and C. Yong,
Noise propagation in gene regulation networks involving interlinked positive and negative feedback loops, PLoS One, 7 (2012), e51840.
doi: 10.1371/journal.pone.0051840. |
[13] |
F. J. Jr,
Self-perpetuating states in signal transduction: Positive feedback, double-negative feedback and bistability, Current Opinion in Cell Biology, 14 (2002), 140-148.
doi: 10.1016/S0955-0674(02)00314-9. |
[14] |
D. Kim, Y. K. Kwon and K. H. Cho,
Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways, Bioessays, 29 (2007), 85-90.
doi: 10.1002/bies.20511. |
[15] |
J. R. Kim, Y. Yoon and K. H. Cho,
Coupled feedback loops form dynamic motifs of cellular networks, Biophysical Journal, 94 (2008), 359-365.
doi: 10.1529/biophysj.107.105106. |
[16] |
K. N. Lan,
Regulation of oscillation dynamics in biochemical systems with dual negative feedback loops, Journal of the Royal Society Interface, 9 (2012), 1998-2010.
doi: 10.1098/rsif.2012.0028. |
[17] |
I. M. Lengyel, D. Soroldoni, A. C. Oates and L. G. Morelli,
Nonlinearity arising from noncooperative transcription factor binding enhances negative feedback and promotes genetic oscillations, Papers in Physics, 6 (2014), 060012.
doi: 10.4279/PIP.060012. |
[18] |
W. A. Lim, C. M. Lee and C. Tang,
Design principles of regulatory networks: Searching for the molecular algorithms of the cell, Molecular Cell, 49 (2013), 202-212.
doi: 10.1016/j.molcel.2012.12.020. |
[19] |
W. Ma, A. Trusina, H. El-Samad, W. A. Lim and C. Tang,
Defining Network Topologies that Can Achieve Biochemical Adaptation, Cell, 138 (2009), 760-773.
doi: 10.1016/j.cell.2009.06.013. |
[20] |
K. Maeda and H. Kurata,
Long negative feedback loop enhances period tunability of biological oscillators, Journal of Theoretical Biology, 440 (2018), 21-31.
doi: 10.1016/j.jtbi.2017.12.014. |
[21] |
W. Mather, M. R. Bennett, J. Hasty and L. S. Tsimring,
Delay-induced degrade-and-fire oscillations in small genetic circuits, Physical Review Letters, 102 (2009), 068105.
doi: 10.1103/PhysRevLett.102.068105. |
[22] |
N. A. M. Monk,
Oscillatory Expression of Hes1, p53, and NF-kappaB Driven by Transcriptional Time Delays, Current Biology, 13 (2003), 1409-1413.
doi: 10.1016/S0960-9822(03)00494-9. |
[23] |
K. Montagne, R. Plasson, Y. Sakai, T. Fujii and Y. Rondelez,
Programming An In Vitro Dna Oscillator Using A Molecular Networking Strategy, Molecular Systems Biology, 7 (2011), 466-472.
doi: 10.1038/Msb.2010.120. |
[24] |
M. Monti and P. R. Wolde,
The accuracy of telling time via oscillatory signals, Physical Biology, 13 (2016), 035005.
doi: 10.1088/1478-3975/13/3/035005. |
[25] |
A. Munteanu, M. Constante, M. Isalan and R. V. Solé, Avoiding transcription factor competition at promoter level increases the chances of obtaining oscillation, BMC Systems Biology, 4 (2010), p66.
doi: 10.1186/1752-0509-4-66. |
[26] |
R. Murugan,
Theory on the dynamics of oscillatory loops in the transcription factor networks, PLoS One, 7 (2014), 3736-3739.
|
[27] |
M. Namiko, J. M. Hogh and S. Szabolcs,
Coupled positive and negative feedbacks produce diverse gene expression patterns in colonies, MBio, 6 (2015), e00059-15.
doi: 10.1128/mBio.00059-15. |
[28] |
B. Novák and J. J. Tyson,
Design principles of biochemical oscillators, Nat. Rev. Mol. Cell. Biol, 9 (2008), 981-991.
|
[29] |
E. L. O'Brien, E. V. Itallie and M. R. Bennett,
Modeling synthetic gene oscillators, Mathematical Biosciences, 236 (2012), 1-15.
doi: 10.1016/j.mbs.2012.01.001. |
[30] |
S. Pigolotti, S. Krishna and M. H. Jensen,
Oscillation patterns in negative feedback loops, Proc. Natl. Acad. Sci. U. S. A., 104 (2007), 6533-6537.
doi: 10.1073/pnas.0610759104. |
[31] |
J. R. Pomerening, S. Y. Kim and F. J. Jr,
Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations, Cell, 122 (2005), 565-578.
doi: 10.1016/j.cell.2005.06.016. |
[32] |
T. Shopera, W. R. Henson, A. Ng, Y. J. Lee, K. Ng and T. S. Moon,
Robust, tunable genetic memory from protein sequestration combined with positive feedback, Nucleic Acids Research, 43 (2015), 9086-9094.
doi: 10.1093/nar/gkv936. |
[33] |
H. Song, P. Smolen, E. Avron, D. A. Baxter and J. H. Byrne,
Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins, Biophysical Journal, 92 (2007), 3407-3424.
doi: 10.1529/biophysj.106.096891. |
[34] |
J. Stricker, S. Cookson, M. R. Bennett, W. H. Mather, L. S. Tsimring and J. Hasty,
A fast, robust and tunable synthetic gene oscillator, Nature, 456 (2008), 516-519.
doi: 10.1038/nature07389. |
[35] |
P. K. Tapaswi, P. Bhattacharya, An extended mathematical-model of transcription and translation during embryogenesis, Cybernetica, 24 (1981), 61-84. Available from: http://library.isical.ac.in:8080/jspui/bitstream/10263/938/1/CYB-24-1-1981-P61-84.pdf. |
[36] |
X. J. Tian, X. P. Zhang, F. Liu and W. Wang,
Interlinking positive and negative feedback loops creates a tunable motif in gene regulatory networks, Physical Review E Statistical Nonlinear and Soft Matter Physics, 80 (2009), 011926.
doi: 10.1103/PhysRevE.80.011926. |
[37] |
T. Y. Tsai, Y. S. Choi, W. Ma, J. R. Pomerening, C. Tang and J. E. Ferrell,
Robust, tunable biological oscillations from interlinked positive and negative feedback loops, Science, 321 (2008), 126-129.
doi: 10.1126/science.1156951. |
[38] |
K. Uriu and H. Tei,
Feedback loops interlocked at competitive binding sites amplify and facilitate genetic oscillations, Journal of Theoretical Biology, 428 (2017), 56-64.
doi: 10.1016/j.jtbi.2017.06.005. |
[39] |
A. Verdugo and R. Rand,
Hopf bifurcation in a DDE model of gene expression, Communications in Nonlinear Science and Numerical Simulation, 13 (2008), 235-242.
doi: 10.1016/j.cnsns.2006.05.001. |
[40] |
Y. C. Wang, S. E. Peterson and J. F. Loring,
Protein post-translational modifications and regulation of pluripotency in human stem cells, Cell Research, 24 (2014), 143-160.
doi: 10.1038/cr.2013.151. |
[41] |
J. J. Wei and C. B. Yu,
Hopf bifurcation analysis in a model of oscillatory gene expression with delay, Proceedings of the Royal Society of Edinburgh, 139 (2009), 879-895.
doi: 10.1017/S0308210507000091. |
[42] |
X. P. Zhang, Z. Cheng, F. Liu and W. Wang,
Linking fast and slow positive feedback loops creates an optimal bistable switch in cell signaling, Physical Review E Statistical Nonlinear and Soft Matter Physics, 76 (2007), 031924.
doi: 10.1103/PhysRevE.76.031924. |
[43] |
X. Zhao, T. Hirota, X. M. Han, H. Cho, L. W. Chong, K. Lamia, S. Liu, A. R. Atkins, E. Banayo, C. Liddle, R. T. Yu, J.R. Yates, S. A. Kay, M. Downes and R. M. Evans,
Circadian amplitude regulation via FBXW7-targeted REV-ERB $α$ degradation, Cell, 165 (2016), 1644-1657.
doi: 10.1016/j.cell.2016.05.012. |








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