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Mathematical Models of Cell Response Following Heating

  • Neil T. Wright
Chapter
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 1097)

Abstract

The cells of the cardiovascular system can experience temperature excesses of a few degrees during a diseased state or of tens of degrees during a thermal therapy treatment. These raised temperatures may be acute or of long duration. The multiple cell lines that compose each tissue then react, in approximate order of increasing thermal insult, by expressing heat shock proteins, undergoing apoptosis, or suffering necrosis. Mathematical models of the response of cells could aid in planning and designing thermal therapies. The multi-factor nature of the cell response makes it challenging to develop such models. The models most used clinically are mathematically simple and based on the response of representative tissues. The model that might provide the most fundamental understanding of the biochemical response of cells requires many parameters, some of which are difficult to measure. None of the semi-empirical models that provide improved prediction of cell fate have been widely accepted to plan therapies. There remain great opportunities for developing mathematical models cell response.

Notes

Acknowledgements

The author thanks Prof. John Pearce for his insightful comments regarding modeling of cell death.

References

  1. Akaiki H (1974) A new look at the statistical model identification. IEEE Trans Autom Control 19:716–723CrossRefGoogle Scholar
  2. Barrie PJ (2012) The mathematical origins of the kinetic compensation effect: 1. the effect of random experimental errors. Phys Chem Chem Phys 14:318–326CrossRefPubMedPubMedCentralGoogle Scholar
  3. Bauer KD, Henle KJ (1979) Arrhenius analysis of heat survival curves from normal and thermotolerant cho cells. Radiat Res 78:251–263CrossRefPubMedPubMedCentralGoogle Scholar
  4. Beck J, Arnold K (1977) Parameter estimation in engineering and science. Wiley, New YorkGoogle Scholar
  5. Benjamin IJ, McMillan DR (1998) Stress (heat shock) proteins: molecular chaperones in cardiovascular biology and disease. Circ Res 83:117–132CrossRefPubMedPubMedCentralGoogle Scholar
  6. Bessiere F, N’Djin WA, Colas EC, Chavrier F, Greillier P, Chapelon, JY, Chevalier P, Lafon C (2016) Ultrasound-guided transesophageal high-intensity focused ultrasound cardiac ablation in a beating heart: a pilot feasibility study in pigs. Ultrasound Med Biol 42(8): 1848–1861CrossRefPubMedPubMedCentralGoogle Scholar
  7. Bettaieb A, Averill-Bates DA (2008) Thermotolerance induced at a fever temperature of 40C protects cells against hyperthermia-induced apoptosis mediated by death receptor signaling. Biochem Cell Biol 86: 521–538CrossRefPubMedPubMedCentralGoogle Scholar
  8. Bettaieb A, Averill-Bates DA (2015) Thermotolerance induced at a mild temperature of 40C alleviates heat shock-induced ER stress and apoptosis in HeLa cells. Biochim Biophys Acta 1853:52–62CrossRefPubMedPubMedCentralGoogle Scholar
  9. Briones E, Lacalle JR, Marin-Leon I, Rueda JR (2015) Transmyocardial laser revascularization versus medical therapy for refractory angina. Cochrane Database Syst Rev 2:CD003712Google Scholar
  10. Brundel BJ, Henning RH, Ke L, van Gelder IC, Crijns HJ, Kampinga HH (2006a) Heat shock protein upregulation protects against pacing-induced myolysis in HL-1 atrial myocytes and in human atrial fibrillation. J Mol Cell Cardiol 41:555–562CrossRefPubMedGoogle Scholar
  11. Brundel BJ, Shiroshita-Takeshita A, Qi X, Yeh YH, Chartier D, van Gelder IC, Henning RH, Kampinga HH, Nattel S (2006b) Induction of heat shock response protects the heart against atrial fibrillation. Circ Res 99:1394–1402CrossRefPubMedGoogle Scholar
  12. Chen SS, Wright NT, Humphrey JD (1998) Phenomenological evolution equations for heat-induced shrinkage of a collagenous tissue. IEEE Trans Biomed Eng 45:1234 –1240CrossRefPubMedGoogle Scholar
  13. Dewey W, Hopwood L, Sapareto S, Gerweck L (1977) Cellular responses to combinations of hyperthermia and radiation. Radiology 123:463–479CrossRefPubMedGoogle Scholar
  14. Diller K, Pearce J (1999) Issues in modeling thermal alterations in tissues. Ann N Y Acad Sci 888:153–164CrossRefPubMedGoogle Scholar
  15. Doi M, Edwards SF (1986) The theory of polymer dynamics. Oxford University Press, OxfordGoogle Scholar
  16. Eißing TE, Conzelmann H, Gilles ED, Allg\(\ddot{\mathrm{o}}\) wer F, Bullinger E, Scheurich P (2004) Bistability analyses of a caspase activation model for receptor-induced apoptosis. J Biol Chem 279:36892–36897CrossRefPubMedGoogle Scholar
  17. Eißing TE, Waldherr S, Allg\(\ddot{\mathrm{o}}\) wer F, Scheurich P, Bullinger E (2007) Steady state and (bi-) stability evaluation of simple protease signalling networks. BioSyst 90:591–601CrossRefPubMedGoogle Scholar
  18. Elmore SA, Dixon D, Hailey JR, Harada T, Herbert RA, Maronpot, RR, Nolte T, Rehg JE, Rittinghausen S, Rosol TJ, Satoh H, Vidal JD, Willard-Mack CL, Creasy DM (2016) Recommendations from the INHAND apoptosis/necrosis working group. Toxicol Pathol 44:173–188CrossRefPubMedPubMedCentralGoogle Scholar
  19. Evans SS, Repasky EA (2015) Fisher DT: fever and the thermal regulation of immunity: the immune system feels the heat. Nat Rev Immunol 15(6): 335–349CrossRefPubMedPubMedCentralGoogle Scholar
  20. Feng Y, Oden JT, Rylander MN (2008) A two-state cell damage model under hyperthermic conditions: theory and in vitro experiments. J Biomech Eng 130: 041016–1–10CrossRefPubMedPubMedCentralGoogle Scholar
  21. Freed KF (2011) Entropy-enthalpy compensation in chemical reactions and adsorption: an exactly solvable model. J Phys Chem B 115:1689–1692CrossRefPubMedGoogle Scholar
  22. Fussenegger M, Bailey JE, Varner J (2000) A mathematical model of caspase function in apoptosis. Nat Biotechnol 18:768–774CrossRefPubMedGoogle Scholar
  23. Gabai VL, Sherman MY (2002) Molecular biology of thermoregulation. J Appl Physiol 92:1743–1748CrossRefPubMedGoogle Scholar
  24. Galluzzi L, Vitale I, Abrams J, Alnemri E, Baehrecke E, Blagosklonny, M, Dawson T, Dawson V, El-Deiry W, Fulda S, Gottli E, Green D, Hengartner M, Kepp O, Knight R, Kumar S, Lipton S, Lu X, Madeo, F, Malorni W, Mehlen P, Nunez G, Peter M, Piacentini M, Rubinsztein D, Shi Y, Simon HU, Vandenabeele P, White E, Yuan J, Zhivotovsky B, Melino G, Kroemer G (2012) Molecular definitions of cell death subroutines: recommendations of the nomenclature committee on cell death 2012. Cell Death Differ 19:107–120CrossRefPubMedGoogle Scholar
  25. Galluzzi L, Pedro JBS., Vitale I, Aaronson S, Abrams J, Adam D, Alnemri E, Altucci L, Andrews D, Annicchiarico-Petruzzelli M, Baehrecke E, Bazan N, Bertrand M, Bianchi K, Blagosklonny M, Blomgren K, Borner C, Bredesen D, Brenner C, Campanella M, Candi, E, Cecconi F, Chan F, Chandel N, Cheng E, Chipuk J, Cidlowski J, Ciechanover A, Dawson T, Dawson V, Laurenzi VD, Maria RD, Debatin KM, Daniele ND, Dixit V, Dynlacht B, El-Deiry W, Fimia G, Flavell R, Fulda S, Garrido C, Gougeon ML, Green D, Gronemeyer H, Hajnoczky G, Hardwick J, Hengartner M, Ichijo H, Joseph B, Jost P, Kaufmann T, Kepp O, Klionsky D, Knight R, Kumar S, Lemasters J, Levine B, Linkermann A, Lipton S, Lockshin, R., López-Otín C, Lugli E, Madeo F, Malorni W, Marine JC, Martin S, Martinou JC, Medema J, Meier P, Melino S, Mizushima N, Moll U, Mu\(\tilde{\mathrm{n}}\) oz-Pinedo C, Nu\(\tilde{\mathrm{n}}\) ez G, Oberst, A, Panaretakis T, Penninger J, Peter M, Piacentini M, Pinton P, Prehn J, Puthalakath H, Rabinovich G, Ravichandran K, Rizzuto R, Rodrigues C, Rubinsztein D, Rudel T, Shi Y, Simon HU, Stockwell B, Szabadkai G, Tait S, Tang H, Tavernarakis N, Tsujimoto Y, Berghe TV, Vandenabeele P, Villunger A, Wagner E, Walczak H, White E, Wood W, Yuan J, Zakeri Z, Zhivotovsky B, Melino G, Kroemer G (2015) Essential versus accessory aspects of cell death: recommendations of the NCCD 2015. Cell Death Differ 22:58–73Google Scholar
  26. Glory A, Averill-Bates DA (2016) The antioxidant transcription factor Nrf2 contributes to the protective effect of mild thermotolerance (40C) against heat shock-induced apoptosis. Free Radic Biol Med 99:485–497CrossRefPubMedGoogle Scholar
  27. Gorczyca W, Bruno S, Darzynkiewicz R, Gong J, Darzynkiewicz Z (1992) DNA strand breaks occurring during apoptosis: their early in situ detection by terminal deoxynucleotidyl transferase and nick translation assays and prevention by serine protease inhibitors. Int J Oncol 1:639–648PubMedGoogle Scholar
  28. Hahn GM (1982) Hyperthermia and cancer. Plenum Press, New YorkCrossRefGoogle Scholar
  29. Harrington PL, Wright NT (2005) Sensitivity analysis of Arrhenius parameters for denaturation of collagen. In: Proceedings of 2005 ASME summer bioengineering conferenceGoogle Scholar
  30. Harris JL, Humphrey JD (2004) Kinetics of thermal damage to a collagenous membrane under biaxial isotonic loading. IEEE Trans Biomed Eng 51(2):371–379CrossRefPubMedPubMedCentralGoogle Scholar
  31. He X, Bischof JC (2003) Quantification of temperature and injury response in thermal therapy and cryosurgery. Crit Rev Biomed Eng 31(5):355–422CrossRefPubMedPubMedCentralGoogle Scholar
  32. He X, Bhowmick S, Bischof J (2000) Supraphysiological thermal injury in dunning at-1 prostate tumor cells. J Biomech Eng 122:51–59Google Scholar
  33. Henriques Jr FC (1947) Studies of thermal injury V. The predictability and the significance of thermally induced rate processes leading to irreversible epidermal injury. Arch Pathol 43:489–502Google Scholar
  34. Henriques Jr FC, Moritz AR (1947) Studies of thermal injury. I. The conduction of heat to and through skin and the temperatures attained therein. Am J Pathol 23:531–549Google Scholar
  35. Hesami S, Mohammadi M, Rezaee MA, Jalili A, Rahmani MR (2017) The effects of hyperthermia on the immunomodulatory properties of human umbilical cord vein mesenchymal stem cells (MSCs). Int J Hyperth 33(7):705–712. http://dx.doi.org/10.1080/02656736.2017.1309576. PMID: 28540823Google Scholar
  36. Humphrey JD (2008) Vascular adaptation and mechanical homeostasis at tissue, cellular, and sub-cellular levels. Cell Biochem Biophys 50:53–78CrossRefPubMedPubMedCentralGoogle Scholar
  37. Humphrey JD, Rajagopal R (2002) A constrained mixture model for growth and remodeling of soft tissues. Math Models Methods Appl Sci 12(3):407–430CrossRefGoogle Scholar
  38. Johnson HA, Pavelec M (1972) Thermal injury due to normal body temperature. Am J Pathol 66:557–564PubMedPubMedCentralGoogle Scholar
  39. Jung H (1986) A generalized concept for cell killing by heat. Rad Res 106:56–72CrossRefGoogle Scholar
  40. Kampinga HH (1993) Thermotolerance in mammalian cells. J Cell Sci 104:11–17PubMedPubMedCentralGoogle Scholar
  41. Kampinga HH (2006) Cell biological effects of hyperthermia alone or combined with radiation or drugs: A short introduction to newcomers in the field. Int J Hyperth 22:191–196CrossRefGoogle Scholar
  42. Kellerer A, Rossi H (1971) RBE and the primary mechanics of radiation action. Rad Res 47:15–34CrossRefGoogle Scholar
  43. Laidler KJ (1987) Chemical kinetics. Harper & Row, New YorkGoogle Scholar
  44. Landry J, Chrétien P, Bernier D, Nicole LM, Marceau N, Tanguay RM (1982) Thermotolerance and heat shock proteins induced by hyperthermia in rat liver cells. Int J Radiat Oncol Biol  Phys 8:59–62CrossRefPubMedPubMedCentralGoogle Scholar
  45. Langberg JJ, Calkins H, El-Atassi R, Broganelli M, Leon A, Kalbfleisch S, Morady F (1992) Temperature monitoring during radiofrequency catheter ablation of accessory pathways. Circulation 86(5): 1469–1474CrossRefPubMedPubMedCentralGoogle Scholar
  46. Laszlo A (1992) The effects of hyperthermia on mammalian cell structure and function. Cell Prolif 25:59–87CrossRefPubMedPubMedCentralGoogle Scholar
  47. Lee L, Kassab G, Guccione J (2016) Mathematical modeling of cardiac growth and remodeling. Wiley Interdiscip Rev Syst Biol Med 8(3):211–226CrossRefPubMedPubMedCentralGoogle Scholar
  48. Lee YJ, Dewey WC (1987) Induction of heat shock proteins in Chinese hamster ovary cells and development of thermotolerance by concentrations of puromycin. J Cell Physiol 132:1–11CrossRefPubMedPubMedCentralGoogle Scholar
  49. Lepock J (2003) Cellular effects of hyperthermia: relevance to the minimum dose for thermal damage. Int J Hyperth 19(3):252–266CrossRefGoogle Scholar
  50. Li GC, Petersen NS, Mitchell HK (1982) Induced thermal tolerance and heat shock protein synthesis in Chinese hamster ovary cells. Int J Radiat Oncol Biol Phys 8:63–67CrossRefPubMedGoogle Scholar
  51. Mackey MA, Dewey WC (1988) Time-temperature analyses of cell killing of synchronous G1 and S phase Chinese hamster cells in vitro. Radiat Res 113:318–333CrossRefPubMedGoogle Scholar
  52. Mackey MA, Roti Roti JL (1992) A model of heat-induced clonogenic cell death. J Theor Biol 156(1):133–146CrossRefPubMedGoogle Scholar
  53. Mayrhauser U, Stiegler P, Stadlbauer V, Koestenbauer S, Leber B, Konrad K, Iberer F, Portucaller RH, Tscheiliessnigg K (2011a) Effect of hyperthermia on liver cell lines: important findings for thermal therapy in hepatocellular carcinoma. Anticancer Res 31:1583–1588Google Scholar
  54. Mayrhauser U, Stiegler P, Stadlbauer V, Koestenbauer S, Leber B, Konrad K, Iberer F, Tscheiliessnigg K (2011b) Cell to cell interactions influence sensitivity of liver cell lines during hyperthermia. Anticancer Res 31:3713–3718Google Scholar
  55. Miles CA, Ghelashvili M (1999) Polymer-in-a-box mechanism for the thermal stabilization of collagen molecules in fibers. Biophys J 76:3243–3252CrossRefPubMedPubMedCentralGoogle Scholar
  56. Milleron RS, Bratton SB (2006) Heat shock induces apoptosis independently of any known initiator caspase-activating complex. J Biol Chem 281(25):16991–17000CrossRefPubMedGoogle Scholar
  57. Moritz AR (1947) Studies of thermal injury. III. The pathology and pathogenesis of cutaneous burns, an experimental study. Am J Pathol 23:915–941PubMedPubMedCentralGoogle Scholar
  58. Moritz AR, Henriques Jr FC (1947) Studies of thermal injury. II. The relative importance of time and surface temperature in the causation of cutaneous burns. Am J Pathol 23:695–720PubMedPubMedCentralGoogle Scholar
  59. Okada M, Yoshida M, Tsuji Y, Horii H (2011) Clinical application of laser treatment for cardiovascular surgery. Laser Ther 20(3):217–232CrossRefPubMedPubMedCentralGoogle Scholar
  60. O’Neill DP, Peng T, Stiegler P, Mayrhauser U, Koestenbauer S, Tscheiliessnigg K, Payne SJ (2011) A three-state mathematical model of hyperthermic cell death. Ann Biomed Eng 39(1):570–579CrossRefPubMedGoogle Scholar
  61. Pearce JA (2013) Comparative analysis of mathematical models of cell death and thermal damage processes. Int J Hyperth 29(4):1464–5157CrossRefGoogle Scholar
  62. Pearce JA (2015) Improving accuracy in Arrhenius models of cell death: adding a temperature-dependent time delay. J Biomech Eng 137:121006CrossRefPubMedGoogle Scholar
  63. Pearce JA, Thomsen S (1995) Rate process analysis of thermal damage. In: Welch AJ, van Germert MJC (eds) Optical and thermal response of laser-irradiated tissue. Plenum, New York, pp 561–606CrossRefGoogle Scholar
  64. Peper A, Grimbergent CA, Spaan JAE, Souren JEM, Wijk RV (1998) A mathematical model of the HSP70 regulation in the cell. J Mol Biol 14:97–124Google Scholar
  65. Purschke M, Laubach HJ, Anderson RR, Manstein D (2010) Thermal injury causes dna damage and lethality in unheated surrounding cells: active thermal bystander effect. J Invest Dermatol 130:86–92CrossRefPubMedGoogle Scholar
  66. Qin Z, Balasubramanian SK, Wolkers WF, Pearce JA, Bischof JC (2014) Correlated parameter fit of Arrhenius model for thermal denaturation of proteins and cells. Ann Biomed Eng 42:2392–2404CrossRefPubMedPubMedCentralGoogle Scholar
  67. Raffray M, Cohen GM (1997) Apoptosis and necrosis in toxicology: a continuum or distinct models of cell death. Pharmacol Ther 75(3):153–177CrossRefPubMedGoogle Scholar
  68. Roti JL, Henle KJ (1980) Comparison of two mathematical models for describing heat-induced cell killing. Rad Res 81:374–383CrossRefGoogle Scholar
  69. Rybiński M, Szymańska Z, Lasota S, Gambin A (2013) Modelling the efficacy of hyperthermia treatment. J R Soc Interface 10(88). http://dx.doi.org/10.1098/rsif.2013.0527. http://rsif.royalsocietypublishing.org/content/10/88/20130527 CrossRefPubMedCentralGoogle Scholar
  70. Rylander MN, Feng Y, Bass J, Diller KR (2005) Thermally induced injury and heat-shock protein expression in cells and tissues. Ann N Y Acad Sci 1066:222–242CrossRefPubMedPubMedCentralGoogle Scholar
  71. Rylander MN, Feng Y, Zhang Y, Bass J, Stafford RJ, Volgin A, Hazle JD, Diller KR (2006) Optimizing heat shock protein expression induced by prostate cancer laser therapy through predictive computational models. J Biomed Opt 11:11–11–16. http://dx.doi.org/10.1117/1.2241310 CrossRefPubMedPubMedCentralGoogle Scholar
  72. Rylander MN, Feng Y, Bass J, Diller KR (2007) Heat shock protein expression and injury optimization for laser therapy design. Lasers in Surgery and Medicine 39:731–746CrossRefPubMedPubMedCentralGoogle Scholar
  73. Rylander MN, Feng Y, Zimmermann K, Diller KR (2010) Measurement and mathematical modeling of thermally induced injury and heat shock protein expression kinetics in normal and cancerous prostate cells. Int J Hyperth 26(8):748–764CrossRefGoogle Scholar
  74. Samali A, Holmberg CI, Sistonen L, Orreniusa S (1999) Thermotolerance and cell death are distinct cellular responses to stress: dependence on heat shock proteins. FEBS Lett 461:306–310CrossRefPubMedPubMedCentralGoogle Scholar
  75. Santos-Marques MJ, Carvalho F, Sousa C, Remião F, Vitorino R, Amado F, Ferreira R, Duarte JA, de Lourdes Bastos M (2006) Cytotoxicity and cell signalling induced by continuous mild hyperthermia in freshly isolated mouse hepatocytes. Toxicology 224(3):210–218. https://doi.org/10.1016/j.tox.2006.04.028. http://www.sciencedirect.com/science/article/pii/S0300483X06002344 CrossRefPubMedPubMedCentralGoogle Scholar
  76. Sapareto SA, Dewey WC (1984) Thermal dose determination in cancer therapy. Int J Radiat Oncol Biol Phys 10:787–800CrossRefPubMedPubMedCentralGoogle Scholar
  77. Sapareto SA, Hopwood LE, Dewey WC, Raju MR, Gray JW (1978) Effects of hyperthermia on survival and progression of Chinese hamster ovary cells. Cancer Res 38:393–400PubMedPubMedCentralGoogle Scholar
  78. Sharp K (2001) Entropy–enthalpy compensation: fact or artifact? Protein Sci 10:661–667CrossRefPubMedPubMedCentralGoogle Scholar
  79. Song AS, Najjar AM, Diller KR (2014) Thermally induced apoptosis, necrosis, and heat shock protein expression in three-dimensional culture. J Biomech Eng 136(071006-1)CrossRefGoogle Scholar
  80. Spiro IJ, Sapareto SA, Raaphorst GP, Dewey WC (1982) The effect of chronic and acute heat conditioning on the development of thermal tolerance. Int J Radiat Oncol Biol Phys 8:53–58CrossRefPubMedPubMedCentralGoogle Scholar
  81. Sriram K, Rodriguez-Fernandez M, III FD (2012) A detailed modular analysis of heat-shock protein dynamics under acute and chronic stress and its implication in anxiety disorders. PLoS ONE 7(8):e42958CrossRefPubMedPubMedCentralGoogle Scholar
  82. Stege GJJ., Brunstinc JF, Kampinga HH, Konings AWT (1995) Thermotolerance and nuclear protein aggregation: protection against initial damage or better recovery. J Cell Physiol 164:579–586CrossRefPubMedPubMedCentralGoogle Scholar
  83. Syntichaki P, Tavernarakis N (2002) Death by necrosis. EMBO reports 3(7):604–609. http://dx.doi.org/10.1093/embo-reports/kvf138 CrossRefPubMedPubMedCentralGoogle Scholar
  84. Takata AN, Zaneveld L, Richter W (1977) Laser-induced thermal damage of skin. Final report SAM-TR-77-38, USAF School of aerospace medicine, Warminster, PAGoogle Scholar
  85. Taylor RP, Starnes JW (2003) Age, cell signalling and cardioprotection. Acta Physiol Scand 178: 107–116CrossRefPubMedPubMedCentralGoogle Scholar
  86. Wang S, Diller KR, Aggarwal SJ (2003) Kinetics study of endogenous heat shock protein 70 expression. J Biomech Eng 125:794–797CrossRefPubMedPubMedCentralGoogle Scholar
  87. Wang S, Xie W, Rylander MN, Tucker PW, Aggarwal S, Diller KR (2008) HSP70 kinetics study by continuous observation of HSP-GFP fusion protein expression on a perfusion heating stage. Biotechnol Bioeng 99: 146–154CrossRefPubMedPubMedCentralGoogle Scholar
  88. Wang S, Chen PC, Berthiaume F, Toner M, Jayaraman A, Yarmush ML (2009) Dynamic effect of heat shock pretreatment on apoptotic responses to TNF-α in liver cells. J Biomech Eng 131:071003CrossRefPubMedPubMedCentralGoogle Scholar
  89. Westra A, Dewey WC (1971) Variation in sensitivity to heat shock during the cell cycle of Chinese hamster cells in vitro. Int J Rad Bio 19:467–477Google Scholar
  90. Wright NT (2003) On a relationship between the Arrhenius parameters from thermal damage studies. J Biomech Eng 125:300–304CrossRefPubMedGoogle Scholar
  91. Wright NT (2013) Comparison of models of post-hyperthermia cell survival. J Biomech Eng 135:051001CrossRefGoogle Scholar
  92. Würstle M, Zink E, Prehn J, Rehm M (2014) From computational modelling of the intrinsic apoptosis pathway to a systems-based analysis of chemotherapy resistance: achievements, perspectives and challenges in systems medicine. Cell Death Dis 5:e1258. https://doi.org/10.1038/cddis.2014.36 CrossRefPubMedPubMedCentralGoogle Scholar
  93. Xin M, Olson EN, Bassel-Duby R (2013) Mending broken hearts: cardiac development as a basis for adult heart regeneration and repair. Nat Rev Mol Cell Biol 14: 529–541CrossRefPubMedPubMedCentralGoogle Scholar
  94. Zou Y, Zhu W, Sakamoto M, Qin Y, Akazawa H, Toko H, Mizukami M, Takeda N, Minamino T, Takano H, Nagai T, Nakai A, Komuro I (2003) Heat shock transcription factor 1 protects cardiomyocytes from ischemia/reperfusion injury. Circulation 108: 3024–3030CrossRefPubMedGoogle Scholar

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Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMichigan State UniversityEast LansingUSA

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