×

A phenomenological approach to the dynamics of activation and clonal expansion of \(T\) cells. (English) Zbl 1211.35260

Summary: This paper deals with the modeling of the dynamics of clonal expansion and immune competition of \(T\) cells. The modeling is based on the approach of continuum mechanics, namely by conservation equations closed by phenomenological constitutive equations concerning the material behaviors. The qualitative properties of the model are analyzed in detail. A critical analysis concludes this paper with indication of research perspectives.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92C37 Cell biology
92D30 Epidemiology
Full Text: DOI

References:

[1] Personal communication of Prof. S. Gangemi of the Policlinico Hospital of the University of Messina to one of the authors (MD).; Personal communication of Prof. S. Gangemi of the Policlinico Hospital of the University of Messina to one of the authors (MD).
[2] D. Criaco, Ph.D. Thesis, University of Messina, 2010.; D. Criaco, Ph.D. Thesis, University of Messina, 2010.
[3] Fishman, M. A.; Segel, L. A., Modeling immunotherapy for allergy, Bulletin of Mathematical Biology, 58, 1099-1121 (1996) · Zbl 0878.92013
[4] Muller, I., Thermodynamics (1985), Pitman Advanced Publishing Program · Zbl 0637.73002
[5] Muller, I.; Ruggeri, T., Rational extended thermodynamics, Springer Tracts in Natural Philosophy, 37, 84-92 (1998) · Zbl 0895.00005
[6] Humphrey, J. D.; Rajagopal, K. R., A constrained mixture model for growth and remodeling of soft tissues, Mathematical Models and Methods in Applied Sciences, 12, 407-430 (2002) · Zbl 1021.74026
[7] Bellomo, N.; Li, N. K.; Maini, P. K., On the foundations of cancer modelling: selected topics, speculations and perspectives, Mathematical Models and Methods in Applied Sciences, 18, 593-646 (2008) · Zbl 1151.92014
[8] Chaplain, M. A.J., Modeling aspects of cancer growth: insight from mathematical, and numerical analysis and computational simulations, (Lecture Notes in Mathematics, vol. 1940 (2008)), 147-200 · Zbl 1264.92025
[9] Bellomo, N.; Delitala, M., From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells, Physics of Life Reviews, 5, 183-206 (2008)
[10] Bellomo, N.; Forni, G., Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory, Current Topics in Developmental Biology, 81, 485-502 (2008)
[11] Bellomo, N.; Bianca, C.; Delitala, M., Complexity analysis and mathematical tools towards the modelling of living systems, Physics of Life Reviews, 6, 144-175 (2009)
[12] C. Bianca, Mathematical modelling for keloid formation triggered by virus: malignant effects and immune system competition, Mathematical Models and Methods in Applied Sciences 21 (2) (2011) (in press).; C. Bianca, Mathematical modelling for keloid formation triggered by virus: malignant effects and immune system competition, Mathematical Models and Methods in Applied Sciences 21 (2) (2011) (in press). · Zbl 1218.35236
[13] M. Dolfin, L. Restuccia, Asymptotic waves in a mixture of biological fluids by double scale method, Preprint.; M. Dolfin, L. Restuccia, Asymptotic waves in a mixture of biological fluids by double scale method, Preprint.
[14] Burmester, G. R.; Pezzutto, A.; Wirth, J., Color Atlas of Immunology (2003), Verlag: Verlag Germany
[15] Perelson, A. S.; Weisbuch, G., Immunology for physicists, Reviews of Modern Physics, 69, 1219-1267 (1997)
[16] Pinchuk, G., (Immunology. Immunology, Schaum’s Outline Series (2002), Mc Graw-Hill)
[17] Kohler, B., Mathematically modeling dynamics of \(T\) cell responses: predictions concerning the generation of memory cells, Journal of Theoretical Biology, 245, 669-676 (2007) · Zbl 1451.92098
[18] Chao, D. L.; Davenport, M. P.; Forrest, S.; Perelson, A. S., A stochastic model of cytotoxic \(T\) cell responses, Journal of Theoretical Biology, 228, 227-240 (2004) · Zbl 1439.92057
[19] Sprent, J.; Surh, C. D., \(T\) cell memory, Annual Review of Immunology, 20, 551-579 (2002)
[20] Fife, P. C., Lecture Notes in Biomathematics, vol. 28 (1979), Springer · Zbl 0403.92004
[21] Zanlungo, F.; Rambaldi, S.; Turchetti, G., An automata based microscopic model inspired by the clonal expansion, (Deutsch, A.; etal., Mathematical Modeling of Biological Systems II (2008), Birkhauser: Birkhauser Boston)
[22] Jansen, V. A.A.; Korthals Altes, H.; Funk, G. A.; Wodarz, D., Contrasting \(B\) cell- and \(T\) cell-based protective vaccines, Journal of Theoretical Biology, 234, 39-48 (2005) · Zbl 1445.92151
[23] De Boer, R. J.; Perelson, A. S., \(T\) cell repertoires and competitive exclusion, Journal of Theoretical Biology, 169, 375-390 (1994)
[24] Grakoui, A.; Bromley, S. K.; Sumen, C.; Davis, M. M.; Shaw, A. S.; Allen, P. M.; Dustin, M. L., The immunological synapse: a molecular machine controlling \(T\) cell activation, Science, 285, 221-227 (1999)
[25] Lanzavecchia, A.; Sallusto, F.; Dustin, M. L., Dynamics of \(T\) lymphocyte responses: intermediates, effectors, and memory cells, Science, 290, 92-97 (2000)
[26] Sprent, J., Fate of H-2-activated \(T\) lymphocytes in syngeneic hosts. I. Fate in lymphoid tissues and intestines traced with 3 H-thymidine, 125 I-deoxyuridine and 51 chromium, Cell Immunology, 21, 278-302 (1976)
[27] Williams, M. A.; Bevan, M. J., Shortening the infectious period does not alter expansion of CD \(8 T\) cells but diminishes their capacity to differentiate into memory cells, The Journal of Immunology, 173, 6694-6702 (2004)
[28] Sprent, J.; Miller, J. F.A. P., Fate of H2-activated \(T\) lymphocytes in syngeneic hosts. III. Differentiation into long-lived recirculating memory cells, Cell Immunology, 21, 314-326 (1976)
[29] De Boer, R. J.; Homann, D.; Perelson, A. S., Different dynamics of CD \(4^+\) and CD \(8^+T\) cell responses during and after acute lymphocytic choriomeningitis virus infection, Journal of Immunology, 171, 3928-3935 (2003)
[30] Murray, J. D., Mathematical Biology I: An Introduction (2002), Springer, pp. 405-407 · Zbl 1006.92001
[31] Murray, J. D., Mathematical Biology II: Spatial Models and Biomedical Applications (2002), Springer
[32] Seder, R. A.; Paul, W. E., Acquisition of lymphokine-producing phenotype by CD \(4^+T\) cells, Annual Review of Immunology, 12, 635-673 (1994)
[33] Perelson, A. S., Modelling viral and immune system dynamics, Nature Reviews Immunology, 2, 8-36 (2002)
[34] Murphy, K. M.; Ouyang, W.; Farrar, J. D.; Yang, J. F.; Ranganath, S.; Asnagli, H.; Afkarian, M.; Murphy, T. L., Signaling and transcription in \(T\) helper development, Annual Review of Immunology, 18, 451-494 (2000)
[35] Nelms, K.; Keegan, A. D.; Zamorano, J.; Ryan, J. J.; Paul, W. E., The IL-4 receptor: signaling mechanisms and biologic functions, Annual Review of Immunology, 17, 701-738 (1999)
[36] Mariani, L.; Löhning, M.; Radbruch, A.; Höfer, T., Transcriptional control networks of cell differentiation: insights from helper \(T\) lymphocytes, Progress in Biophysics and Molecular Biology, 86, 45-76 (2004)
[37] Glimcher, L. H.; Murphy, K. M., Lineage commitment in the immune system: the \(T\) helper lymphocyte grows up, Genes and Development, 14, 1693-1711 (2000)
[38] Lauffenburger, D. A.; Keller, K. H., Effects of leukocyte random motility and chemotaxis in tissue inflammatory response, Journal of Theoretical Biology, 81, 475-503 (1979)
[39] Tosin, A.; Ambrosi, D.; Preziosi, L., Mechanics and chemotaxis in the morphogenesis of vascular networks, Bulletin of Mathematical Biology, 68, 7, 1819-1836 (2006) · Zbl 1334.92066
[40] Keller, E. F.; Segel, L. A., Model for chemotaxis, Journal of Theoretical Biology, 30, 225-234 (1971) · Zbl 1170.92307
[41] Keller, E. F.; Segel, L. A., Traveling bands of chemotactic bacteria: a theoretical analysis, Journal of Theoretical Biology, 30, 235-248 (1971) · Zbl 1170.92308
[42] Byrne, H.; Preziosi, L., Modelling solid tumour growth using the theory of mixtures, Mathematical Medicine and Biology, 20, 341-366 (2003) · Zbl 1046.92023
[43] Ambrosi, D.; Preziosi, L., On the closure of mass balance models for tumour growth, Mathematical Models and Methods in Applied Sciences, 12, 737-754 (2002) · Zbl 1016.92016
[44] Ford, R. M.; Lauffenburger, D. A., Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients, Bulletin of Mathematical Biology, 53, 721-749 (1991) · Zbl 0729.92029
[45] Georgescu, A.; Palese, L.; Raguso, G., Biomatematica—Modelli dinamica e biforcazione (2009), Cacucci Editore
[46] Bertram, J. S., The molecular biology of cancer (review), Molecular Aspects of Medicine, 21, 167-223 (2001)
[47] Pointer, K.; Hillen, T., Volume filling and quorum sensing in models for chemosensitive movement, Canadian Applied Mathematics Quarterly, 10, 280-301 (2003)
[48] D.A. Lauffenburger, Ph.D.Thesis, University of Minnesota, 1979.; D.A. Lauffenburger, Ph.D.Thesis, University of Minnesota, 1979.
[49] Tranquillo, R. T.; Lauffenburger, D. A.; Zigmond, S. H., A stochastic model for leukocyte random motility and chemotaxis based on receptor binding fluctuations, The Journal of Cell Biology, 106, 303-309 (1988)
[50] Boyce, W. E.; DiPrima, R. C., Elementary Differential Equations and Boundary Value Problems (2009), Wiley · Zbl 0807.34002
[51] Friedl, P.; Wolf, K., Tumour-cell invasion and migration: diversity and escape mechanisms, Nature Reviews Cancer, 3, 362-374 (2003)
[52] Carini, G., Lezioni di Istituzioni di Fisica Matematica (1989), Mediterranean Press
[53] Bellouquid, A.; Delitala, M., Modelling Complex Biological Systems—A Kinetic Theory Approach (2006), Birkhäuser: Birkhäuser Boston · Zbl 1178.92002
[54] Bellomo, N.; Bellouquid, A., From a class of kinetic models to macroscopic equations for multicellular systems in biology, Discrete Continuous Dynamical System B, 4, 59-80 (2004) · Zbl 1044.92021
[55] Bellomo, N.; Bellouquid, A., On the derivation of macroscopic tissue equations from hybrid models of the kinetic theory of multicellular growing systems—the effect of global equilibrium, Nonlinear Analysis: Hybrid Systems, 3, 215-224 (2009) · Zbl 1184.93071
[56] Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J., Multicellular growing systems: hyperbolic limits towards macroscopic description, Mathematical Models and Methods in Applied Sciences, 17, 1675-1693 (2007) · Zbl 1135.92009
[57] Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J., Complexity and mathematical tools toward the modelling of multicellular growing systems, Mathematical and Computer Modelling, 51, 441-451 (2010) · Zbl 1190.92001
[58] Bellomo, N.; Bellouquid, A.; Nieto, J.; Soler, J., Multiscale biological tissue models and flux-limited chemotaxis from binary mixtures of multicellular growing systems, Mathematical Models and Methods in Applied Sciences, 20 (2010) · Zbl 1402.92065
[59] Chalub, F. A.; Markowich, P.; Perthame, B.; Schmeiser, C., Kinetic models for chemotaxis and their drift-diffusion limits, Monatshefe für Mathematik, 142, 123-141 (2004) · Zbl 1052.92005
[60] Chalub, F. A.; Dolak-Struss, Y.; Markowich, P.; Oeltz, D.; Schmeiser, C.; Soref, A., Model hierarchies for cell aggregation by chemotaxis, Mathematical Models and Methods in Applied Sciences, 16, 1173-1198 (2006) · Zbl 1094.92009
[61] Keller, E. F.; Segel, L. A., Model for chemotaxis, Journal of Theoretical Biology, 30, 225-234 (1971) · Zbl 1170.92307
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.