The Impact of Retroactivity on the Behavior of Biomolecular Systems

A Review of Recent Results


Modularity is a powerful property for analyzing the behavior of a system on the basis of the behavior of its components. According to this property, any two components maintain their behavior unchanged upon interconnection. Is modularity a natural property of biomolecular networks? In this review, we summarize recent theoretical and experimental results that demonstrate that the answer to this question is negative. Just as in many electrical, mechanical, and hydraulic systems, impedance-like effects, called retroactivity, arise at the interconnection of biomolecular systems and alter the behavior of connected components. Here, we illustrate the effects of retroactivity on the static characteristics and on the dynamic input/output response of biomolecular systems by employing a mixture of control theoretic tools, mathematical biology, and experimental techniques on reconstituted systems.


Modularity Retroactivity Insulation Transcriptional networks  Signaling cascades. 


  1. 1.
    Alon U (2007) An introduction to systems biology. Design principles of biological circuits. Chapman & HallGoogle Scholar
  2. 2.
    Andrianantoandro E, Basu S, Karig DK, Weiss R (2006) Synthetic biology: new engineering rules for an emerging discipline. Mol Syst Biol 2:1–14CrossRefGoogle Scholar
  3. 3.
    Asthagiri AR, Lauffenburger DA (2000) Bioengineering models of cell signaling. Annu Rev Biomed Eng 2:31–53CrossRefGoogle Scholar
  4. 4.
    Atkinson MR, Savageau MA, Meyers JT, Ninfa AJ (2003) Development of genetic circuitry exhibiting toggle switch or oscillatory behavior in Escherichia coli. Cell 113(5):597–607Google Scholar
  5. 5.
    C\(\acute{\text{ a}}\)rdenas ML, Cornish-Bowden A (1989) Characteristics necessary for an interconvertible enzyme cascade to generate a highly sensitive response to an effector. Biochem J 257(2):339–345Google Scholar
  6. 6.
    Del Vecchio D, Jayanthi S (2008) Retroactivity attenuation in transcriptional networks: design and analysis of an insulation device. In: Proceedings conference on decision and control. Cancun pp 774–780Google Scholar
  7. 7.
    Del Vecchio D, Ninfa AJ, Sontag ED (2008) Modular cell biology: retroactivity and insulation. Nature/EMBO Mol Syst Biol 4:161Google Scholar
  8. 8.
    Del Vecchio D, Ninfa AJ, Sontag ED (2008) A systems theory with retroactivity: application to transcriptional modules. In: Proceedings of American control conference. Seattle, WA pp 1368–1373Google Scholar
  9. 9.
    Elowitz MB, Liebler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403(6767):335–338CrossRefGoogle Scholar
  10. 10.
    Fell D (1997) Understanding the control of metabolism. Portland Press Ltd, LondonGoogle Scholar
  11. 11.
    Gardiner CW (1996) Handbook of stochastic methods: for physics, chemistry and the natural sciences. Springer Berlin, Heidelberg, New YorkGoogle Scholar
  12. 12.
    Gardner TS, Cantor CR, Collins JJ (2000) Construction of the genetic toggle switch in Escherichia Coli. Nature 403(6767):339–342Google Scholar
  13. 13.
    Goldbeter A, Koshland DE (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci USA 78(11):6840–6844MathSciNetCrossRefGoogle Scholar
  14. 14.
    Goldbeter A, Koshland DE Jr (1984) Ultrasensitivity in biochemical systems controlled by covalent modification. interplay between zero-order and multistep effects. J Biol Chem 259(23):14441–14447Google Scholar
  15. 15.
    Gomez-Uribe C, Verghese GC, Mirny LA (2007) Operating regimes of signaling cycles: statics, dynamics, and noise filtering. PLoS Comput Biol 3(12):2487–2497MathSciNetCrossRefGoogle Scholar
  16. 16.
    Hartwell LH, Hopfield JJ, Leibler S, Murray AW (1999) From molecular to modular cell biology. Nature 402:47–52CrossRefGoogle Scholar
  17. 17.
    Heinrich R, Neel BG, Rapoport TA (2002) Mathematical models of protein kinase signal transduction. Mol Cell 9:957–970CrossRefGoogle Scholar
  18. 18.
    Jayanthi S, Del Vecchio D (2009) On the compromise between retroactivity attenuation and noise amplification in gene regulatory networks. In: Proceedings conference on decision and control. Shangai, China, pp 4565–4571Google Scholar
  19. 19.
    Jayanthi S, Del Vecchio D (2010) Retroactivity attenuation in biomolecular systems based on timescale separation. IEEE Trans Automatic Control, DOI: 10.1109/TAC.2010.2069631MATHGoogle Scholar
  20. 20.
    Jiang P, Ninfa AJ (2007) Escherichia coli  PII signal transduction protein controlling nitrogen assimilation acts as a sensor of adenylylate energy charge in vitro. Biochemistry 46:12979–12996CrossRefGoogle Scholar
  21. 21.
    Jiang P, Mayo AE, Ninfa AJ (2007) Escherichia coli glutamine synthetase adenylyltransferase (ATase, EC kinetic characterization of regulation by PII, PII-UMP, glutamine, and alpha-ketoglutarate. Biochemistry 46(13):4133–46Google Scholar
  22. 22.
    Kholodenko BN (2006) Cell signaling dynamics in time and space. Nat Rev Mol Cell Biol 7(3):165–176CrossRefGoogle Scholar
  23. 23.
    Kholodenko BN, Kiyatkin A, Bruggeman FJ, Sontag E, Westerhoff HV, Hoek JB (2002) Untangling the wires: a strategy to trace functional interactions in signaling and gene networks. Proc Natl Acad Sci USA 99(20):12841–12846CrossRefGoogle Scholar
  24. 24.
    Kirschner MW, Gerhart JC (2005) The plausibility of life: resolving Darwin’s Dilemma. Yale University Press, New Haven and LondonGoogle Scholar
  25. 25.
    Klipp E, Herwig R, Kowald A, Wierling C, Lehrach H (2005) Systems biology in practice. Wiley, WeinheimCrossRefGoogle Scholar
  26. 26.
    Kokotovic P, Khalil HK, O’Reilly J (1999) Singular perturbation methods in control. SIAMGoogle Scholar
  27. 27.
    Kremling A, Saez-Rodriguez J (2007) Systems biology - An engineering perspective. J Biotechnol 129:329–351CrossRefGoogle Scholar
  28. 28.
    Krstić M, Kanellakopoulos I, Kokotović PV (1995) Nonlinear and Adaptive Control Design. Wiley, New YorkGoogle Scholar
  29. 29.
    Lauffenburger DA (May 2000) Cell signaling pathways as control modules: complexity for simplicity? Proc Natl Acad Sci USA 97(10):5031–5033CrossRefGoogle Scholar
  30. 30.
    Mason O, Verwoerd M (Apr 2006) Graph theory and networks in biology. Technical report.
  31. 31.
    Michel AN, Miller RK (1977) Qualitative Analysis of Large Scale Dynamical Systems. Academic Press, New YorkMATHGoogle Scholar
  32. 32.
    Moylan PJ, Hill DJ (1978) Stability criteria for large-scale systems. IEEE Trans Automat Contr 23(2):143–149MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Ninfa AJ, Jiang P (2005) PII signal transduction proteins: sensors of α-ketoglutarate that regulate nitrogen metabolism. Curr Opinion Microbiol 8:168–173CrossRefGoogle Scholar
  34. 34.
    Paulsson J (2004) Summing up the noise in gene networks. Nature 427:415–418CrossRefGoogle Scholar
  35. 35.
    Papin JA, Reed JL, Palsson BO (2004) Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. Trends Biochem Sci 29:641–647CrossRefGoogle Scholar
  36. 36.
    Pioszak AA, Jiang P, Ninfa AJ (2000) The Escherichia coli PII signal transduction protein regulates the activities of the two-component system transmitter protein NRII by direct interaction with the kinase domain of the transmitter module. Biochemistry 39(44):13450–13461CrossRefGoogle Scholar
  37. 37.
    Polderman JW, Willems JC (2007) Introduction to Mathematical Systems Theory. A Behavioral Approach, 2nd edn. Springer-Verlag, New YorkGoogle Scholar
  38. 38.
    Rosenfeld N, Young JW, Alon U, Swain PS, Elowitz MB (2005) Gene regulation at the single-cell level. Science 307(5717):1962–1965, DOI: 10.1126/science.1106914CrossRefGoogle Scholar
  39. 39.
    Rubinfeld H, Seger R (2005) The ERK cascade: a prototype of MAPK signaling. Mol Biotechnol 31(2):151–174CrossRefGoogle Scholar
  40. 40.
    Sauro HM (2004) The computational versatility of proteomic signaling networks. Curr Proteomics 1(1):67–81CrossRefGoogle Scholar
  41. 41.
    Saez-Rodriguez J, Kremling A, Gilles ED (2005) Dissecting the puzzle of life: modularization of signal transduction networks. Comput Chem Eng 29:619–629CrossRefGoogle Scholar
  42. 42.
    Seger R, Krebs EG (1995) The MAPK signaling cascade. FASEB J 9:726–735Google Scholar
  43. 43.
    Sepulchre R, Janković M, Kokotović P (1997) Constructive nonlinear control. Springer-Verlag, New YorkMATHGoogle Scholar
  44. 44.
    Snel B, Bork P, Huynen MA (2002) The identification of functional modules from the genomic association of genes. Proc Natl Acad Sci USA 99(9):5890–5895CrossRefGoogle Scholar
  45. 45.
    Sontag ED (1998) Mathematical control theory. Springer-Verlag, New YorkMATHGoogle Scholar
  46. 46.
    Sontag ED (2007) Input to state stability: Basic concepts and results. In: Nistri P, Stefani G (eds) Nonlinear and optimal control theory. Springer-Verlag, Berlin, pp 163–220Google Scholar
  47. 47.
    Stadtman ER, Chock PB (1977) Superiority of interconvertible enzyme cascades in metabolic regulation: analysis of monocyclic systems. Proc Natl Acad Sci USA 74(7):2761–2765CrossRefGoogle Scholar
  48. 48.
    Thattai M, van Oudenaarden A (2001) Intrinsic noise in gene regulatory networks. Proc Natl Acad Sci USA pp 8614–8619Google Scholar
  49. 49.
    van der Schaft AJ (2000) 2-gain and passivity techniques in nonlinear control, 2nd edn. Springer-Verlag, BerlinMATHGoogle Scholar
  50. 50.
    van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier, North HollandGoogle Scholar
  51. 51.
    Ventura AC, Jiang P, van Wassenhove L, Del Vecchio D, Merajver SD, Ninfa AJ (2010) Signaling properties of a covalent modification cycle are altered by a downstream target. Proc Natl Acad Sci USA 107(22):10032–10037CrossRefGoogle Scholar
  52. 52.
    Ventura AC, Jiang P, van Wassenhove L, Ninfa AJ, Merajver SD, Del Vecchio D (2010) The impact of retroactivity on the input/output characteristic of a signaling component. In: Dynamic systems and control conference (in press)Google Scholar
  53. 53.
    Vidyasagar M (1981) Input-Output analysis of large scale interconnected systems. Springer-Verlag, BerlinMATHCrossRefGoogle Scholar
  54. 54.
    Šiljak DD (1978) Large-Scale systems: stability and structure. Dover, New YorkMATHGoogle Scholar
  55. 55.
    Willems J (1972) Dissipative dynamical systems, Part I: General theory. Arch Ration Mech An 45:321–351MathSciNetMATHCrossRefGoogle Scholar
  56. 56.
    Willems JC (1972) Dissipative dynamical systems Part I: General theory; Part II: Linear systems with quadratic supply rates. Arch Ration Mech An 45:321–393MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations