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2011, 8(2): 515-528. doi: 10.3934/mbe.2011.8.515

Adaptive response and enlargement of dynamic range

1. 

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

2. 

Department of Chemical Engineering and Laboratory of Network Biology Research, Technion - Israel Institute of Technology, Haifa 32000, Israel

Received  March 2010 Revised  August 2010 Published  April 2011

Many membrane channels and receptors exhibit adaptive, or desensitized, response to a strong sustained input stimulus, often supported by protein activity-dependent inactivation. Adaptive response is thought to be related to various cellular functions such as homeostasis and enlargement of dynamic range by background compensation.
   Here we study the quantitative relation between adaptive response and background compensation within a modeling framework. We show that any particular type of adaptive response is neither sufficient nor necessary for adaptive enlargement of dynamic range. In particular a precise adaptive response, where system activity is maintained at a constant level at steady state, does not ensure a large dynamic range neither in input signal nor in system output. A general mechanism for input dynamic range enlargement can come about from the activity-dependent modulation of protein responsiveness by multiple biochemical modification, regardless of the type of adaptive response it induces. Therefore hierarchical biochemical processes such as methylation and phosphorylation are natural candidates to induce this property in signaling systems.
Citation: Tamar Friedlander, Naama Brenner. Adaptive response and enlargement of dynamic range. Mathematical Biosciences & Engineering, 2011, 8 (2) : 515-528. doi: 10.3934/mbe.2011.8.515
References:
[1]

B. N. Kholodenko, Cell signaling dynamics in time and space, Nature Reviews Molecular Cell Biology, 7 (2006), 165-176. doi: 10.1038/nrm1838.

[2]

B. Wark, B. N. Lundstrom and A. Fairhall, Sensory adaptation, Current Opinion in Neurobiology, 17 (2007), 423-429. doi: 10.1016/j.conb.2007.07.001.

[3]

J. E. Keymer, R. G. Endres, M. Skoge, Y. Meir and N. S. Wingreen, Chemosensing in Escherichia coli: Two regimes of two-state receptors, Proceedings of the National Academy of Sciences, 103 (2006), 1786-1791. doi: 10.1073/pnas.0507438103.

[4]

B. A. Mello and Y. Tu, Effects of adaptation in maintaining high sensitivity over a wide range of backgrounds for Escherichia coli chemotaxis, Biophysical Journal, 92 (2007), 2329-2337. doi: 10.1529/biophysj.106.097808.

[5]

C. H. Hansen, R. G. Endres and N. S. Wingreen, Chemotaxis in Escherichia coli: A molecular model for robust precise adaptation, PLoS Computational Biology, 4 (2008), e1. doi: 10.1371/journal.pcbi.0040001.

[6]

M. J. Tindall, S. L. Porter, P. K. Maini, G. Gaglia and J. P. Armitage, Overview of mathematical approaches used to model bacterial chemotaxis i: The single cell, Bulletin of Mathematical Biology, 70 (2008), 1525-1569. doi: 10.1007/s11538-008-9321-6.

[7]

J. J. Tyson, K. C. Chen and B. Novak, Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, 15(2003), 221-231. doi: 10.1016/S0955-0674(03)00017-6.

[8]

M. Behar, N. Hao, H. G. Dohlman and T. C. Elston, Mathematical and computational analysis of adaptation via feedback inhibition in signal transduction pathways, Biophysical Journal, 93 (2007), 806-821. doi: 10.1529/biophysj.107.107516.

[9]

P. Francois and E. D. Siggia, A case study of evolutionary computation of biochemical adaptation, Physical Biology, 5 (2008), 026009. doi: 10.1088/1478-3975/5/2/026009.

[10]

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.

[11]

R. B. Bourret, K. A. Borkovich and M. I. Simon, Signal transduction pathways involving protein phosphorylation in prokaryotes, Annual Review of Biochemistry, 60 (1991), 401-441. doi: 10.1146/annurev.bi.60.070191.002153.

[12]

E. N. Pugh Jr. and T. D. Lamb, Phototransduction in vertebrate rods and cones: Molecular mechanisms of amplification, recovery and light adaptation, in "Molecular Mechanisms of Visual Transduction," volume 3, 2000.

[13]

N. Barkai and S. Leibler, Robustness in simple biochemical networks, Nature, 387 (1997), 913-917. doi: 10.1038/43199.

[14]

T.Friedlander and N. Brenner, Adaptive response by state-dependent inactivation, Proceedings of the National Academy of Sciences, 106 (2009), 22558-22563. doi: 10.1073/pnas.0902146106.

[15]

S. Marom and I. B. Levitan, State-dependent inactivation of Kv3 potassium channels, Journal of Biophysics, 67 (1994), 579-589. doi: 10.1016/S0006-3495(94)80517-X.

[16]

T. M. Yi, Y. Huang, M. I. Simon and J. Doyle, Robust perfect adaptation in bacterial chemotaxis through integral feedback control, Proceedings of the National Academy of Sciences, 97 (2000), 4649-4653. doi: 10.1073/pnas.97.9.4649.

[17]

A. Csikász-Nagy and O. S. Soyer, Adaptive dynamics with a single two-state protein, Journal of The Royal Society Interface, 5 (2008), S41-S47. doi: 10.1098/rsif.2008.0099.focus.

[18]

K. Ogata, "Modern Control Engineering," Prentice Hall, fourth edition, 2002.

[19]

P. Dunten and D. E. Koshland Jr., Tuning the responsiveness of a sensory receptor via covalent modifications, Journal of Biological Chemistry, 266 (1991), 1491-1496.

[20]

T. C. Terwilliger, J. Y. Wang and D. E. Koshland Jr., Kinetics of receptor modification, Journal of Biological Chemistry, 261 (1986), 10814-10820.

[21]

S. Asakura and H. Honda, Two-state model for bacterial chemoreceptor proteins: The role of multiple methylation, Journal of Molecular Biology, 176 (1984), 349-367. doi: 10.1016/0022-2836(84)90494-7.

[22]

M. N. Levit and J. B. Stock, Receptor methylation controls the magnitude of stimulus-response coupling in bacterial chemotaxis, Journal of Biological Chemistry, 277 (2002), 36760-36765. doi: 10.1074/jbc.M204325200.

[23]

Y. Tu, T. S. Shimizu and J. C. Berg, Modeling the chemotactic response of E. coli to time-varying stimuli, Proceedings of the National Academy of Sciences, 105 (2008), 14855-14860. doi: 10.1073/pnas.0807569105.

[24]

G. L. Hazelbauer, J. J. Falke and J. S. Parkinson, Bacterial chemoreceptors: High-performance signaling in networked arrays, Trends in Biochemical Sciences, 33 (2008), 9-19. doi: 10.1016/j.tibs.2007.09.014.

[25]

V. Sourjik and H. C. Berg, Receptor sensitivity in bacterial chemotaxis, Proceedings of the National Academy of Sciences, 99 (2002), 123-127. doi: 10.1073/pnas.011589998.

[26]

R. A. Normann and I. Perlman, The effects of background illumination on the photoresponse of red and green cones, Journal of Physiology, 286 (1979), 491-507.

[27]

A. Lupas and J. Stock, Phosphorylation of an N-terminal regulatory domain activates the CheB methylesterase in bacterial chemotaxis, Journal of Biological Chemistry, 264 (1989), 17337-17342.

[28]

S. A. Simms, A. M. Stock and J. B. Stock, Purification and characterization of the S-adenosylmethionine: Glutamyl methyltransferase that modifies membrane chemoreceptor proteins in bacteria, Journal of Biological Chemistry, 262 (1987), 8537-8543.

show all references

References:
[1]

B. N. Kholodenko, Cell signaling dynamics in time and space, Nature Reviews Molecular Cell Biology, 7 (2006), 165-176. doi: 10.1038/nrm1838.

[2]

B. Wark, B. N. Lundstrom and A. Fairhall, Sensory adaptation, Current Opinion in Neurobiology, 17 (2007), 423-429. doi: 10.1016/j.conb.2007.07.001.

[3]

J. E. Keymer, R. G. Endres, M. Skoge, Y. Meir and N. S. Wingreen, Chemosensing in Escherichia coli: Two regimes of two-state receptors, Proceedings of the National Academy of Sciences, 103 (2006), 1786-1791. doi: 10.1073/pnas.0507438103.

[4]

B. A. Mello and Y. Tu, Effects of adaptation in maintaining high sensitivity over a wide range of backgrounds for Escherichia coli chemotaxis, Biophysical Journal, 92 (2007), 2329-2337. doi: 10.1529/biophysj.106.097808.

[5]

C. H. Hansen, R. G. Endres and N. S. Wingreen, Chemotaxis in Escherichia coli: A molecular model for robust precise adaptation, PLoS Computational Biology, 4 (2008), e1. doi: 10.1371/journal.pcbi.0040001.

[6]

M. J. Tindall, S. L. Porter, P. K. Maini, G. Gaglia and J. P. Armitage, Overview of mathematical approaches used to model bacterial chemotaxis i: The single cell, Bulletin of Mathematical Biology, 70 (2008), 1525-1569. doi: 10.1007/s11538-008-9321-6.

[7]

J. J. Tyson, K. C. Chen and B. Novak, Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, 15(2003), 221-231. doi: 10.1016/S0955-0674(03)00017-6.

[8]

M. Behar, N. Hao, H. G. Dohlman and T. C. Elston, Mathematical and computational analysis of adaptation via feedback inhibition in signal transduction pathways, Biophysical Journal, 93 (2007), 806-821. doi: 10.1529/biophysj.107.107516.

[9]

P. Francois and E. D. Siggia, A case study of evolutionary computation of biochemical adaptation, Physical Biology, 5 (2008), 026009. doi: 10.1088/1478-3975/5/2/026009.

[10]

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.

[11]

R. B. Bourret, K. A. Borkovich and M. I. Simon, Signal transduction pathways involving protein phosphorylation in prokaryotes, Annual Review of Biochemistry, 60 (1991), 401-441. doi: 10.1146/annurev.bi.60.070191.002153.

[12]

E. N. Pugh Jr. and T. D. Lamb, Phototransduction in vertebrate rods and cones: Molecular mechanisms of amplification, recovery and light adaptation, in "Molecular Mechanisms of Visual Transduction," volume 3, 2000.

[13]

N. Barkai and S. Leibler, Robustness in simple biochemical networks, Nature, 387 (1997), 913-917. doi: 10.1038/43199.

[14]

T.Friedlander and N. Brenner, Adaptive response by state-dependent inactivation, Proceedings of the National Academy of Sciences, 106 (2009), 22558-22563. doi: 10.1073/pnas.0902146106.

[15]

S. Marom and I. B. Levitan, State-dependent inactivation of Kv3 potassium channels, Journal of Biophysics, 67 (1994), 579-589. doi: 10.1016/S0006-3495(94)80517-X.

[16]

T. M. Yi, Y. Huang, M. I. Simon and J. Doyle, Robust perfect adaptation in bacterial chemotaxis through integral feedback control, Proceedings of the National Academy of Sciences, 97 (2000), 4649-4653. doi: 10.1073/pnas.97.9.4649.

[17]

A. Csikász-Nagy and O. S. Soyer, Adaptive dynamics with a single two-state protein, Journal of The Royal Society Interface, 5 (2008), S41-S47. doi: 10.1098/rsif.2008.0099.focus.

[18]

K. Ogata, "Modern Control Engineering," Prentice Hall, fourth edition, 2002.

[19]

P. Dunten and D. E. Koshland Jr., Tuning the responsiveness of a sensory receptor via covalent modifications, Journal of Biological Chemistry, 266 (1991), 1491-1496.

[20]

T. C. Terwilliger, J. Y. Wang and D. E. Koshland Jr., Kinetics of receptor modification, Journal of Biological Chemistry, 261 (1986), 10814-10820.

[21]

S. Asakura and H. Honda, Two-state model for bacterial chemoreceptor proteins: The role of multiple methylation, Journal of Molecular Biology, 176 (1984), 349-367. doi: 10.1016/0022-2836(84)90494-7.

[22]

M. N. Levit and J. B. Stock, Receptor methylation controls the magnitude of stimulus-response coupling in bacterial chemotaxis, Journal of Biological Chemistry, 277 (2002), 36760-36765. doi: 10.1074/jbc.M204325200.

[23]

Y. Tu, T. S. Shimizu and J. C. Berg, Modeling the chemotactic response of E. coli to time-varying stimuli, Proceedings of the National Academy of Sciences, 105 (2008), 14855-14860. doi: 10.1073/pnas.0807569105.

[24]

G. L. Hazelbauer, J. J. Falke and J. S. Parkinson, Bacterial chemoreceptors: High-performance signaling in networked arrays, Trends in Biochemical Sciences, 33 (2008), 9-19. doi: 10.1016/j.tibs.2007.09.014.

[25]

V. Sourjik and H. C. Berg, Receptor sensitivity in bacterial chemotaxis, Proceedings of the National Academy of Sciences, 99 (2002), 123-127. doi: 10.1073/pnas.011589998.

[26]

R. A. Normann and I. Perlman, The effects of background illumination on the photoresponse of red and green cones, Journal of Physiology, 286 (1979), 491-507.

[27]

A. Lupas and J. Stock, Phosphorylation of an N-terminal regulatory domain activates the CheB methylesterase in bacterial chemotaxis, Journal of Biological Chemistry, 264 (1989), 17337-17342.

[28]

S. A. Simms, A. M. Stock and J. B. Stock, Purification and characterization of the S-adenosylmethionine: Glutamyl methyltransferase that modifies membrane chemoreceptor proteins in bacteria, Journal of Biological Chemistry, 262 (1987), 8537-8543.

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