A percolation-like model for simulating inter-cellular diffusion in the context of bystander signalling in tumour

Australasian Physical and Engineering Sciences in Medicine

Volumn 34, Issue 1, 2011, Pages 31-39

  Moulton, C R ^a,b   Fleming, A J ^b   Ebert, M A ^b,c  

^a University of Western Australia ^*  (Australia)

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^c SIR CHARLES GAIRDNER HOSPITAL   (Australia)

Author keywords

Bystander effect; Diffusion modelling; Monte carlo simulations; Percolation theory

Indexed keywords

2D STRUCTURES; 3D STRUCTURE; ANOMALOUS DIFFUSION; BYSTANDER EFFECTS; CELL DENSITY; COMMUNICATION PROCESS; COMMUNICATION RANGE; DIFFUSION LIMITED; DISORDERED MEDIA; MEAN VALUES; MONTE CARLO SIMULATION; PERCOLATION EFFECTS; PERCOLATION THEORY; RANDOM WALK; SIGNAL RANGE; SIGNALLING MOLECULES; SIMULATION PARAMETERS; SPATIAL ARRANGEMENTS; TIME-DEPENDENT DIFFUSION; TISSUE RESPONSE;

COMMUNICATION; DENSITY FUNCTIONAL THEORY; IONIZING RADIATION; MONTE CARLO METHODS; PROBABILITY; SOLVENTS; THREE DIMENSIONAL; TISSUE;

DIFFUSION;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BYSTANDER EFFECT; CELL MOTION; CELL TRANSFORMATION; COMPUTER SIMULATION; DIFFUSION; HUMAN; NEOPLASM; PATHOPHYSIOLOGY; PHYSIOLOGY; RADIATION DOSE; RADIATION EXPOSURE;

ANIMALS; BYSTANDER EFFECT; CELL MOVEMENT; CELL TRANSFORMATION, NEOPLASTIC; COMPUTER SIMULATION; DIFFUSION; HUMANS; MODELS, BIOLOGICAL; NEOPLASMS; RADIATION DOSAGE;

EID: 79961157369     PISSN: 01589938     EISSN: None     Source Type: Journal    
DOI: 10.1007/s13246-010-0048-y     Document Type: Article

References (48)

1. Shuryak I, Sachs RK, Brenner DJ (2007) Biophysical models of radiation bystander effects: 1. Spatial effects in three-dimensional tissues. Radiat Res 168(6):741-749. doi:10.1667/RR1117.1 (Pubitemid 351295111)
2. Mothersill C, Seymour C (2001) Radiation-induced bystander effects: Past history and future directions. Radiat Res 155(6): 759-767 (Pubitemid 32494601)
3. Mothersill C, Seymour C (2005) Radiation-induced bystander effects: Are they good, bad or both? Med Confl Surviv 21(2):101-110. doi:10.1080/ 13623690500073398
4. Mothersill C, Seymour C (2006) Radiation-induced bystander and other non-targeted effects: Novel intervention points in cancer therapy? Curr Cancer Drug Targets 6(5):447-454. doi:10.2174/ 156800906777723976 (Pubitemid 44033392)
5. Belyakov OV, Folkard M, Mothersill C, Prise KM, Michael BD (2003) A proliferation-dependent bystander effect in primary porcine and human urothelial explants in response to targeted irradiation. Br J Cancer 88(5):767-774. doi:10.1038/sj.bjc. 6600804 (Pubitemid 36411458)
6. Belyakov OV, Mitchell SA, Parikh D, Randers-Pehrson G, Marino SA, Amundson SA, Geard CR, Brenner DJ (2005) Biological effects in unirradiated human tissue induced by radiation damage up to 1 mm away. Proc Natl Acad Sci USA 102(40):14203-14208. doi:10.1073/pnas.0505020102 (Pubitemid 41429676)
7. Mothersill C, Rea D, Wright EG, Lorimore SA, Murphy D, Seymour CB, O'Malley K (2001) Individual variation in the production of a bystander signal following irradiation of primary cultures of normal human urothelium. Carcinogenesis 22(9):1465-1471. doi:10.1093/carcin/22.9.1465 (Pubitemid 32898704)
8. Mothersill C, Lyng F, Seymour C, Maguire P, Lorimore S, Wright E (2005) Genetic factors influencing bystander signaling in murine bladder epithelium after low-dose irradiation in vivo. Radiat Res 163(4):391-399. doi:10.1667/RR3320 (Pubitemid 40404647)
9. Ballarini F, Facoetti A, Mariotti L, Nano R, Ottolenghi A (2009) Cellular communication and "non-targeted effects": Modelling approaches. Adv Space Res 44(8):917-925. doi:10.1016/ j.asr.2009.05.021
10. Prise KM, O'Sullivan JM (2009) Radiation-induced bystander signalling in cancer therapy. Nat Rev Cancer 9(5):351-360. doi: 10.1038/nrc2603
11. Facoetti A, Mariotti L, Ballarini F, Bertolotti A, Nano R, Pasi F, Ranza E, Ottolenghi A (2009) Experimental and theoretical analysis of cytokine release for the study of radiation-induced bystander effect. Int J Radiat Biol 85(8):690-699. doi:10.1080/ 09553000903020016
12. Trosko J, Ruch R (1998) Cell-cell communication in carcinogenesis. Front Biosci 3:d208-d236
13. Ballarini F, Alloni D, Facoetti A, Mairani A, Nano R, Ottolenghi A (2006) Modelling radiation-induced bystander effect and cellular communication. Radiat Prot Dosim 122(1-4):244-251. doi:10.1093/rpd/ncl446 (Pubitemid 47090458)
14. Brenner DJ, Little JB, Sachs RK (2001) The bystander effect in radiation oncogenesis: II. A quantitative model. Radiat Res 155(3):402-408. doi:10.1667/0033-7587(2001)155[0402:TBEIRO] 2.0.CO;2 (Pubitemid 32204256)
15. Khvostunov IK, Nikjoo H (2002) Computer modelling of radiation- induced bystander effect. J Radiol Prot 22(3A):A33-A37. doi:10.1088/0952-4746/22/3A/306
16. Nikjoo H, Khvostunov IK (2003) Biophysical model of the radiation-induced bystander effect. Int J Radiat Biol 79(1):43-52. doi:10.1080/ 0955300021000034701 (Pubitemid 36140236)
17. Nikjoo H, Khvostunov IK (2004) A theoretical approach to the role and critical issues associated with bystander effect in risk estimation. Hum Exp Toxicol 23(2):81-86. doi:10.1191/ 0960327104ht422oa (Pubitemid 38380018)
18. Leonard BE (2009) The range of the bystander effect signal in three-dimensional tissue and estimation of the range in human lung tissue at low radon levels. Radiat Res 171(3):374-378. doi:10.1667/RR1374.1
19. Little M, Filipe J, Prise K, Folkard M, Belyakov O (2005) A model for radiation-induced bystander effects, with allowance for spatial position and the effects of cell turnover. J Theoret Biol 232(3):329-338. doi:10.1016/j.jtbi. 2004.08.016 (Pubitemid 39575105)
20. Saxton M (1990) Lateral diffusion in a mixture of mobile and immobile particles: A Monte Carlo study. Biophys J 58(5):1303-1306. doi:10.1016/S0006- 3495(90)82470-X (Pubitemid 20363988)
21. Saxton M (1994) Anomalous diffusion due to obstacles: A Monte Carlo study. Biophys J 66(2, Part 1):394-401. doi:10.1016/ S0006-3495(94)80789-1 (Pubitemid 24058459)
22. Wedemeier A, Merlitz H, Langowski J (2009) Anomalous diffusion in the presence of mobile obstacles. EPL (Europhys Lett) 88(3):38004-p1-38004-p5. doi:10.1209/0295-5075/88/38004
23. Lauffenburger DA, Linderman J (1996) Receptors: Models for binding, trafficking, and signaling. Oxford University Press, Oxford
24. Banks DS, Fradin C (2005) Anomalous diffusion of proteins due to molecular crowding. Biophys J 89(5):2960-2971. doi:10.1529/ biophysj.104.051078 (Pubitemid 41636053)
25. Isvoran A, Vilaseca E, Garces JL, Unipan L, Mas F (2007) Monte Carlo simulation of single-particle diffusion in two-dimensional and three-dimensional crowded media. Rom J Biophys 17(1):21-32
26. Sahimi M (1994) Applications of percolation theory, 1st edn. Taylor and Francis, London
27. Aharony A, Stauffer D (1992) Introduction to percolation theory, 2nd edn. Taylor and Francis, London
28. Sotta P, Long D (2003) The crossover from 2D to 3D percolation: Theory and numerical simulations. Eur Phys J E 11(4):375-388. doi:10.1140/epje/i2002- 10161-6
29. Huang Y, Joiner M, Zhao B, Liao Y, Burmeister J (2010) Dose convolution filter: Incorporating spatial dose information into tissue response modeling. Med Phys 37(3):1068-1074. doi: 10.1118/1.3309440
30. Nesbitt JE, Fuller GM (1992) Dynamics of interleukin-6 internalization and degradation in rat hepatocytes. J Biol Chem 267(9):5739-5742
31. Qayum N, Muschel RJ, Im JH, Balathasan L, Koch CJ, Patel S, McKenna WG, Bernhard EJ (2009) Tumor vascular changes mediated by inhibition of oncogenic signaling. Cancer Res 69(15):6347-6354. doi:10.1158/0008-5472.CAN-09-0657
32. Welter M, Bartha K, Rieger H (2008) Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor. J Theoret Biol 250(2):257-280. doi:10.1016/j.jtbi.2007. 09.031 (Pubitemid 350297316)
33. Jiang Y, Pjesivac-Grbovic J, Cantrell C, Freyer JP (2005) A multiscale model for avascular tumor growth. Biophys J 89(6):3884-3894. doi:10.1529/biophysj.105.060640 (Pubitemid 41725610)
34. Lemons DS, Gythiel A (1997) Paul Langevin's 1908 paper on the theory of Brownian motion. Am J Phys 65(11):1079-1081. doi:10.1119/1.18725
35. Newburgh R, Peidle J, Rueckner W (2006) Einstein, Perrin, and the reality of atoms: 1905 revisited. Am J Phys 74(6):478-481. doi:10.1119/1.2188962 (Pubitemid 43893482)
36. Krouglova T, Vercammen J, Engelborghs Y (2004) Correct diffusion coefficients of proteins in fluorescence correlation spectroscopy. Application to tubulin oligomers induced by Mg2? and paclitaxel. Biophys J 87(4):2635-2646. doi:10.1529/biophysj. 104.040717
37. Wu J, Berland KM (2008) Propagators and time-dependent diffusion coefficients for anomalous diffusion. Biophys J 95(4): 2049-2052. doi:10.1529/biophysj.107.121608
38. Hrabe J, Hrabětová S, Segeth K (2004) A model of effective diffusion and tortuosity in the extracellular space of the brain. Biophys J 87(3):1606-1617. doi:10.1529/biophysj.103.039495 (Pubitemid 39167018)
39. Lacks DJ (2008) Tortuosity and anomalous diffusion in the neuromuscular junction. Phys Rev E 77(4):041912-1-041912-8. doi:10.1103/PhysRevE.77.041912 (Pubitemid 351568532)
40. Francis K, Palsson BO (1997) Effective intercellular communication distances are determined by the relative time constants for cyto/chemokine secretion and diffusion. Proc Natl Acad Sci USA 94(23):12258-12262 (Pubitemid 27492515)
41. Wier M, Edidin M (1986) Effects of cell density and extracellular matrix on the lateral diffusion of major histocompatibility antigens in cultured fibroblasts. J Cell Biol 103(1):215-222. doi: 10.1083/jcb.103.1.215 (Pubitemid 16067005)
42. Eikenberry S (2009) A tumor cord model for Doxorubicin delivery and dose optimization in solid tumors. Theoret Biol Med Model 6(1):16-35. doi:10.1186/1742-4682-6-16
43. Matsumoto M and Nishimura T (1998) Mersenne twister: A 623- dimensionally equidistributed uniform pseudo-random number generator. ACM Trans Model Comput Simul 8(1):3-30. doi: 10.1145/272991.272995
44. Grima R (2007) Directed cell migration in the presence of obstacles. Theoret Biol Med Model 4(1):2-13. doi:10.1186/1742- 4682-4-2
45. Ebert MA, Suchowerska N, Jackson MA, McKenzie DR (2010) A mathematical framework for separating the direct and bystander components of cellular radiation response. Acta Oncol 49(8):1334-1343. doi:10.3109/0284186X.2010.487874
46. Langen KM, Jones DTL (2001) Organ motion and its management. Int J Radiat Oncol Biol Phys 50(1):265-278. doi:10.1016/ S0360-3016(01)01453-5
47. van Herk M (2004) Errors and margins in radiotherapy. Semin Radiat Oncol 14(1):52-64. doi:10.1053/j.semradonc.2003.10.003 (Pubitemid 38168954)
48. Magzoub M, Jin S, Verkman AS (2008) Enhanced macromolecule diffusion deep in tumors after enzymatic digestion of extracellular matrix collagen and its associated proteoglycan decorin. FASEB J 22(1):276-284. doi:10.1096/fj.07- 9150com