Network nonlinearities in drug treatment

  • David G. MíguezEmail author


Despite major achievements in the understanding of human disease, there is a general perception that the drug development industry has failed to meet the expectations that recent advances in biotechnology should drive. One of the potential sources of failure of many next generation drugs is that their targets are embedded in highly nonlinear signaling pathways and gene networks with multiple negative and positive feedback loops of regulation. There is increasing evidence that this complex network shapes the response to external perturbations in the form of drug treatment, originating bistability, hypersensitivity, robustness, complex dose-response curves or schedule dependent activity. This review focuses on the effect of nonlinearities on signaling and gene networks involved in human disease, using tools from Nonlinear Dynamics to discuss the implications and to overcome the effects of the nonlinearities on regulatory networks.

Key words

bistability mathematical modeling systems pharmacology 


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  1. [1]
    Ajo-Franklin, C.M., Drubin, D.A., Eskin, J.A., Gee, E.P.S., Landgraf, D., Phillips, I., Silver, P.A. 2007. Rational design of memory in eukaryotic cells. Genes Dev 27, 2271–2276.CrossRefGoogle Scholar
  2. [2]
    Alon, U. 2007. Network motifs: Theory and experimental approaches. Nat Rev Genet 8, 450–461.PubMedCrossRefGoogle Scholar
  3. [3]
    Alonso, S., Sagues, F., Mikhailov, A.S. 2003. Taming Winfree turbulence of scroll waves in excitable media. Science 299, 1722–1725.PubMedCrossRefGoogle Scholar
  4. [4]
    Ankers, J.M., Spiller, D.G., White, M.R., Harper, C.V. 2008. Spatio-temporal protein dynamics in single living cells. Curr Opin Biotechnol 19, 375–380.PubMedCrossRefGoogle Scholar
  5. [5]
    Baselga, J., Rothenberg, M.L., Tabernero, J., Seoane, J., Daly, T., Cleverly, A., Berry, B., Rhoades, S.K., Ray, C.A., Fill, J., Farrington, D.L., Wallace, L.A., Yingling, J.M., Lahn, M., Arteaga, C., Carducci, M. 2008. TGF-beta signalling-related markers in cancer patients with bone metastasis. Biomarkers 13, 217–236.PubMedCrossRefGoogle Scholar
  6. [6]
    Batchelor, E., Mock, C.S., Bhan, I., Loewer, A., Lahav, G. 2008. Recurrent initiation: A mechanism for triggering p53 pulses in response to DNA damage. Mol Cell 30, 277–289.PubMedCrossRefGoogle Scholar
  7. [7]
    Batchelor, E., Loewer, A., Lahav, G. 2009. The ups and downs of p53: Understanding protein dynamics in single cells. Nat Rev Cancer 9, 371–377.PubMedCrossRefGoogle Scholar
  8. [8]
    Becskei, A., Serrano, L. 2000. Engineering stability in gene networks by autoregulation. Nature 405, 590–593.PubMedCrossRefGoogle Scholar
  9. [9]
    Becskei, A., Seraphin, B., Serrano, L. 2001. Positive feedback in eukaryotic gene networks: Cell differentiation by graded to binary response conversion. EMBO J 20, 2528–2535.PubMedCrossRefGoogle Scholar
  10. [10]
    Bellacosa, A., Kumar, C.C., Di Cristofano, A., Testa, J.R. 2005. Activation of AKT kinases in cancer: Implications for therapeutic targeting. Adv Cancer Res 94, 29–86.PubMedCrossRefGoogle Scholar
  11. [11]
    Belousov, B.P. 1959. Periodically acting reaction and its mechanism. Compilation of Abstracts on Radiation Medicine 147, 145.Google Scholar
  12. [12]
    Booth, B., Zemmel, R. 2004. Prospects for productivity. Nat Rev Drug Discov 3, 451–456.PubMedCrossRefGoogle Scholar
  13. [13]
    Carracedo, A., Pandolfi, P.P. 2008. The PTEN-PI3K pathway: Of feedbacks and cross-talks. Oncogene 27, 5527–5541.PubMedCrossRefGoogle Scholar
  14. [14]
    Carracedo, A., Ma, L., Teruya-Feldstein, J., Rojo, F., Salmena, L., Alimonti, A., Egia, A., Sasaki, A.T., Thomas, G., Kozma, S.C., Papa, A., Nardella, C., Cantley, L.C., Baselga, J., Pandolfi, P.P. 2008. Inhibition of mTORC1 leads to MAPK pathway activation through a PI3K-dependent feedback loop in human cancer. J Clin Invest 118, 3065–3074.PubMedGoogle Scholar
  15. [15]
    Cheong, R., Hoffmann, A., Levchenko, A. 2008. Understanding. NF-kappaB signaling via mathematical modeling. Mol Syst Biol 4, 192.PubMedCrossRefGoogle Scholar
  16. [16]
    Cui, J., Zhang, M., Zhang, Y.Q., Xu, Z.H. 2007. JNK pathway: Diseases and therapeutic potential. Acta Pharmacol Sin 28, 601–608.PubMedCrossRefGoogle Scholar
  17. [17]
    Edery, I. 2000. Circadian rhythms in a nutshell. Physiol Genomics 3, 59–74.PubMedGoogle Scholar
  18. [18]
    Engelman, J.A., Luo, J., Cantley, L.C. 2006. The evolution of phosphatidylinositol 3-kinases as regulators of growth and metabolism. Nat Rev Genet 7, 606–619.PubMedCrossRefGoogle Scholar
  19. [19]
    Epshtein, V., Nudler, E. 2003. Cooperation between RNA polymerase molecules in transcription elongation. Science 300, 801–805.PubMedCrossRefGoogle Scholar
  20. [20]
    Fan, Q.W., Specht, K.M., Zhang, C., Goldenberg, D.D., Shokat, K.M., Weiss, W.A. 2003. Combinatorial efficacy achieved through two-point blockade within a signaling pathway-a chemical genetic approach. Cancer Res 63, 8930–8938.PubMedGoogle Scholar
  21. [21]
    Fan, Q.W., Cheng, C.K., Nicolaides, T.P., Hackett, C.S., Knight, Z.A., Shokat, K.M., Weiss, W.A. 2007. A dual phosphoinositide-3-kinase alpha/mTOR inhibitor cooperates with blockade of epidermal growth factor receptor in PTEN-mutant glioma. Cancer Res 67, 7960–7965.PubMedCrossRefGoogle Scholar
  22. [22]
    Garcia-Echeverria, C., Sellers, W.R. 2008. Drug discovery approaches targeting the PI3K/Akt pathway in cancer. Oncogene 27, 5511–5526.PubMedCrossRefGoogle Scholar
  23. [23]
    Gardner, T.S., Cantor, C.R., Collins, J.J. 2000. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342.PubMedCrossRefGoogle Scholar
  24. [24]
    Gual, P., Le Marchand-Brustel, Y., Tanti, J.F. 2005. Positive and negative regulation of insulin signaling through IRS-1 phosphorylation. Biochimie 87, 99–109.PubMedCrossRefGoogle Scholar
  25. [25]
    Guttridge, D.C., Albanese, C., Reuther, J.Y., Pestell, R.G., Baldwin, A.S. 1999. NF-κB controls cell growth and differentiation through transcriptional regulation of cyclin D1. Mol Cell Biol 19, 5785–5799.PubMedGoogle Scholar
  26. [26]
    Hamstra, D.A., Bhojani, M.S., Griffin, L.B., Laxman, B., Ross, B.D., Rehemtulla, A. 2006. Real-time evaluation of p53 oscillatory behavior in vivo using bioluminescent imaging. Cancer Res 66 7482–7489.PubMedCrossRefGoogle Scholar
  27. [27]
    Harrington, L.S., Findlay, G.M., Lamb, R.F. 2005. Restraining PI3K: mTOR signalling goes back to the membrane. Trends Biochem Sci 30, 35–42.PubMedCrossRefGoogle Scholar
  28. [28]
    Hasty, J., Pradines, J., Dolnik, M., Collins, J.J. 2000. Noise-based switches and amplifiers for gene expression. Proc Natl Acad Sci USA 97, 2075–2080.PubMedCrossRefGoogle Scholar
  29. [29]
    Hennessy, B.T., Smith, D.L., Ram, P.T., Lu, Y., Mills, G.B. 2005. Exploiting the PI3K/AKT pathway for cancer drug discovery. Nat Rev Drug Discov 4, 988–1004.PubMedCrossRefGoogle Scholar
  30. [30]
    Hoffmann, A., Levchenko, A., Scott, M.L., Baltimore, D. 2002. The IκB-NF-κB signaling module: Temporal control and selective gene activation. Science 298, 1241–1245.PubMedCrossRefGoogle Scholar
  31. [31]
    Hornung, G., Barkai, N. 2008. Noise propagation and signaling sensitivity in biological networks. PLoS Comput Biol 4, e8.PubMedCrossRefGoogle Scholar
  32. [32]
    Horváth, J., Szalai, I., De Kepper, P. 2009. An experimental design method leading to chemical turing patterns. Science 324, 772–775.PubMedCrossRefGoogle Scholar
  33. [33]
    Isaacs, F.J., Hasty, J., Cantor, C.R., Collins, J.J. 2003. Prediction and measurement of an autoregulatory genetic module. Proc Natl Acad Sci USA 100, 7714–7719.PubMedCrossRefGoogle Scholar
  34. [34]
    Kaern, M., M’guez, D.G., Munuzuri, A.P., Menzinger, M. 2004. Control of chemical pattern formation by a clock-and-wavefront type mechanism. Biophys Chem 110, 231–238.PubMedCrossRefGoogle Scholar
  35. [35]
    Kaneko, K. 2006. Life: An Introduction to Complex Systems Biology, Springer, Heidelberg.Google Scholar
  36. [36]
    Kramer, B.P., Fussenegger, M. 2005. Hysteresis in a synthetic mammalian gene network. Proc Natl Acad Sci USA 102, 9517–9522.PubMedCrossRefGoogle Scholar
  37. [37]
    Lengyel, I., Epstein, I.R. 1992. Modeling of turing structures in the chlorite-iodide-malonic Acid-starch reaction system. Proc Natl Acad Sci USA 89, 3977–3979.PubMedCrossRefGoogle Scholar
  38. [38]
    Li, F., Li, Q., Engelmann, R., Aoyama, M., Sone, S., MacMahon, H., Doi, K. 2006. Subjective similarity of patterns of diffuse interstitial lung disease on thin-section CT: An observer performance study. Acad Radiol 13, 943–950.PubMedCrossRefGoogle Scholar
  39. [39]
    Little, J. W., Shepley, D.P., Wert, D.W. 1999. Robustness of a gene regulatory circuit. EMBO J 18, 4299–4307.PubMedCrossRefGoogle Scholar
  40. [40]
    Manning, B.D., Cantley, L.C. 2007. AKT/PKB signaling: Navigating downstream. Cell 129, 1261–1274.PubMedCrossRefGoogle Scholar
  41. [41]
    Manning, B.D., Logsdon, M.N., Lipovsky, A.I., Abbott, D., Kwiatkowski, D.J., Cantley, L.C., 2005. Feedback inhibition of Akt signaling limits the growth of tumors lacking TSC2. Genes Dev 19, 1773–1778.PubMedCrossRefGoogle Scholar
  42. [42]
    Martín-Blanco, E., Gampel, A., Ring, J., Virdee, K., Kirov, N., Tolkovsky, A.M., Martinez-Arias, A. 1998. puckered encodes a phosphatase that mediates a feedback loop regulating JNK activity during dorsal closure in Drosophila. Genes Dev 12, 557–570.PubMedCrossRefGoogle Scholar
  43. [43]
    Mazzocchi, F. 2008. Complexity in biology. Exceeding the limits of reductionism and determinism using complexity theory. EMBO Rep 9, 10–14.PubMedCrossRefGoogle Scholar
  44. [44]
    Míguez, D.G., Perez-Villar, V., Munuzuri, A.P. 2005. Turing instability controlled by spatiotemporal imposed dynamics. Phys Rev E Stat Nonlin Soft Matter Phys 71, 066217.PubMedCrossRefGoogle Scholar
  45. [45]
    Míguez, D.G., Izus, G.G., Munuzuri, A.P. 2006. Robustness and stability of flow-and-diffusion structures. Phys Rev E Stat Nonlin Soft Matter Phys 73, 016207.PubMedCrossRefGoogle Scholar
  46. [46]
    Míguez, D.G., Vanag, V.K., Epstein, I.R. 2007. Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase. Proc Natl Acad Sci USA 104, 6992–6997.PubMedCrossRefGoogle Scholar
  47. [47]
    Míguez, D.G., McGraw, P., Munuzuri, A.P., Menzinger, M. 2009. Selection of flow-distributed oscillation and Turing patterns by boundary forcing in a linearly growing, oscillating medium. Phys Rev E Stat Nonlin Soft Matter Phys 80, 026208.PubMedCrossRefGoogle Scholar
  48. [48]
    Míguez, D.G. 2010a. On The Dynamics of Patterns Under External Forcing. LAP Lambert Academic Publishing AG & Co., Germany.Google Scholar
  49. [49]
    Míguez, D.G. 2010b. The role of asymmetric binding in ligand-receptor systems with 1: 2 interaction ratio. Biophys Chem 148, 74–81.PubMedCrossRefGoogle Scholar
  50. [50]
    Misra, S., Ghatak, S., Toole, B.P. 2005. Regulation of MDR1 expression and drug resistance by a positive feedback loop involving hyaluronan, phosphoinositide 3-kinase, and ErbB2. J Biol Chem 280, 20310–20315.PubMedCrossRefGoogle Scholar
  51. [51]
    Nelson, D.E., Ihekwaba, A.E.C., Elliott, M., Johnson, J.R., Gibney, C.A., Foreman, B.E., Nelson, G., See, V., Horton, C.A., Spiller, D.G., Edwards, S.W., McDowell, H.P., Unitt, J.F., Sullivan, E., Grimley, R., Benson, N., Broomhead, D., Kell, D.B., White, M.R.H. 2004. Oscillations in NF-κB signaling control the dynamics of gene expression. Science 306, 704–708.PubMedCrossRefGoogle Scholar
  52. [52]
    O’Reilly, K.E., Rojo, F., She, Q.-B., Solit, D., Mills, G.B., Smith, D., Lane, H., Hofmann, F., Hicklin, D.J., Ludwig, D.L., Baselga, J., Rosen, N. 2006. mTOR inhibition induces upstream receptor tyrosine kinase signaling and activates Akt. Cancer Res 66, 1500–1508.PubMedCrossRefGoogle Scholar
  53. [53]
    Paulsson, J. 2004. Summing up the noise in gene networks. Nature 427, 415–418.PubMedCrossRefGoogle Scholar
  54. [54]
    Pikovsky, M.R., Kurths J. 2001. Synchronization: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  55. [55]
    Ptashne, M., Jeffrey, A., Johnson, A.D., Maurer, R., Meyer, B.J., Pabo, C.O., Roberts, T.M., Sauer, R.T. 1980. Mutant lambda phage repressor with a specific defect in its positive control function. Cell 19, 1–11.PubMedCrossRefGoogle Scholar
  56. [56]
    Rosenfeld, N., Elowitz, M.B., Alon, U. 2002. Negative autoregulation speeds the response times of transcription networks. J Mol Biol 323, 785–793.PubMedCrossRefGoogle Scholar
  57. [57]
    Sakurai, T., Mihaliuk, E., Chirila, F., Showalter, K. 2002. Feedback stabilization of unstable propagating waves. Science 296, 2009–2012.PubMedCrossRefGoogle Scholar
  58. [58]
    Samuels, Y., Wang, Z., Bardelli, A., Silliman, N., Ptak, J., Szabo, S., Yan, H., Gazdar, A., Powell, S.M., Riggins, G.J., Willson, J.K., Markowitz, S., Kinzler, K.W., Vogelstein, B., Velculescu, V. E. 2004. High frequency of mutations of the PIK3CA gene in human cancers. Science 304, 554.PubMedCrossRefGoogle Scholar
  59. [59]
    Savageau, M.A. 1974. Comparison of classical and autogenous systems of regulation in inducible operons. Nature 252, 546–549.PubMedCrossRefGoogle Scholar
  60. [60]
    Schauvliege, R., Vanrobaeys, J., Schotte, P., Beyaert, R. 2002. Caspase-11 gene expression in response to lipopolysaccharide and interferon-gamma requires nuclear factor-kappa B and signal transducer and activator of transcription (STAT)1. J Biol Chem 277, 41624–41630.PubMedCrossRefGoogle Scholar
  61. [61]
    Sesti, G., Federici, M., Hribal, M.L., Lauro, D., Sbraccia, P., Lauro, R. 2001. Defects of the insulin receptor substrate (IRS) system in human metabolic disorders. FASEB J 15, 2099–2111.PubMedCrossRefGoogle Scholar
  62. [62]
    Shakhov, A.N., Kuprash, D.V., Azizov, M.M., Jongeneel, C.V., Nedospasov, S.A. 1990. Structural analysis of the rabbit TNF locus, containing the genes encoding TNF-beta (lymphotoxin) and TNF-alpha (tumor necrosis factor). Gene 95, 215–221.PubMedCrossRefGoogle Scholar
  63. [63]
    Shayesteh, L., Lu, Y., Kuo, W.L., Baldocchi, R., Godfrey, T., Collins, C., Pinkel, D., Powell, B., Mills, G.B., Gray, J.W. 1999. PIK3CA is implicated as an oncogene in ovarian cancer. Nat Genet 21, 99–102.PubMedCrossRefGoogle Scholar
  64. [64]
    Sheth, R., Marcon, L., Bastida, M.F., Junco, M., Quintana, L., Dhan, R., Kmita, M., Sharp, J., Ros, M.A. 2012. Hox genes regulate digit patterning by controlling the wavelength of a turing-type mechanism. Science 338, 1476.PubMedCrossRefGoogle Scholar
  65. [65]
    Spencer, S.L., Gaudet, S., Albeck, J.G., Burke, J.M., Sorger, P.K. 2009. Non-genetic origins of cell-to-cell variability in trail-induced apoptosis. Nature 459, 428–432.PubMedCrossRefGoogle Scholar
  66. [66]
    Strogatz, S.H. 1994. Non-Linear Dynamics and Chaos. Perseus Books Publishers, Cambridge.Google Scholar
  67. [67]
    Swain, P.S., Elowitz, M.B., Siggia, E.D. 2002. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Natl Acad Sci USA 99, 12795–12800.PubMedCrossRefGoogle Scholar
  68. [68]
    Swinburne, I.A., Míguez, D.G., Landgraf, D., Silver, P.A. 2008. Intron length increases oscillatory periods of gene expression in animal cells. Genes Dev 22, 2342–2346.PubMedCrossRefGoogle Scholar
  69. [69]
    Tamburini, J., Chapuis, N., Bardet, V., Park, S., Sujobert, P., Willems, L., Ifrah, N., Dreyfus, F., Mayeux, P., Lacombe, C., Bouscary, D. 2008. Protein synthesis is resistant to rapamycin and constitutes a promising therapeutic target in acute myeloid leukemia. Blood 111, 379–382.PubMedCrossRefGoogle Scholar
  70. [70]
    Thieffry, D., Huerta, A.M., Pérez-Rueda, E., Collado-Vides, J. 1998. From specific gene regulation to genomic networks: A global analysis of transcriptional regulation in Escherichia coli. Bioessays 20, 433–440.PubMedCrossRefGoogle Scholar
  71. [71]
    Vanag, V., Yang, L., Dolnik, M., Zhabotinsky, A., Epstein, I. 2000. Oscillatory cluster patterns in a homogeneous chemical system with global feedback. Nature 406, 389–391.PubMedCrossRefGoogle Scholar
  72. [72]
    Vanag, V.K., Míguez, D.G., Epstein, I.R. 2006. Designing an enzymatic oscillator: Bistability and feedback controlled oscillations with glucose oxidase in a continuous flow stirred tank reactor. J Chem Phys 125, 194515.PubMedCrossRefGoogle Scholar
  73. [73]
    Vazquez, F., Sellers, W.R. 2000. The PTEN tumor suppressor protein: An antagonist of phosphoinositide 3-kinase signaling. Biochim Biophys Acta 1470, M21–M35.PubMedGoogle Scholar
  74. [74]
    Wang, H.Q., Altomare, D.A., Skele, K.L., Poulikakos, P.I., Kuhajda, F.P., Di Cristofano, A., Testa, J.R. 2005. Positive feedback regulation between AKT activation and fatty acid synthase expression in ovarian carcinoma cells. Oncogene 24, 3574–3582.PubMedCrossRefGoogle Scholar
  75. [75]
    Weiner, O.D., Neilsen, P.O., Prestwich, G.D., Kirschner, M.W., Cantley, L.C., Bourne, H.R. 2002. A PtdInsP(3)- and Rho GTPase-mediated positive feedback loop regulates neutrophil polarity. Nat Cell Biol 4, 509–513.PubMedCrossRefGoogle Scholar
  76. [76]
    Weissman, T.A., Riquelme, P.A., Ivic, L., Flint, A.C., Kriegstein, A.R. 2004. Calcium waves propagate through radial glial cells and modulate proliferation in the developing neocortex. Neuron 43, 647–661.PubMedCrossRefGoogle Scholar
  77. [77]
    Zhabotinsky, A.M. 1964. Periodical process of oxidation of malonic acid solution. Biofizika 9, 306–311.Google Scholar

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© International Association of Scientists in the Interdisciplinary Areas and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Depto. de Física de la Materia Condensada and Instituto Nicolás Cabrera Universidad Autónoma de MadridMadridSpain
  2. 2.Condensed Matter Physics Center (IFIMAC)Universidad Autónoma de MadridMadridSpain

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