Model of cell signal transduction in a three-dimensional domain
Tóm tắt
Intracellular signalling molecules form pathways inside the cell. These pathways carry a signal to target proteins which results in cellular responses. We consider a spherical cell with two internal compartments containing localized activating enzymes where as deactivating enzymes are spread uniformly through out the cytosol. Two diffusible signalling molecules are activated at the compartments and later deactivated in the cytosol due to deactivating enzymes. The two signalling molecules are a single link in a cascade reaction and form a self regulated dynamical system involving positive and negative feedback. Using matched asymptotic expansions we obtain approximate solutions of the steady state diffusion equation with a linear decay rate. We obtain three-dimensional concentration profiles for the signalling molecules. We also investigate an extension of the above system which has multiple cascade reactions occurring between multiple signalling molecules. Numerically, we show that the speed of the signal is an increasing function of the number of links in the cascade.
Tài liệu tham khảo
Barton G (1989) Elements of Green’s functions and propagation. Oxford Science Publications/The Clarendon Press/Oxford University Press, New York
Bray D (1998) Signaling complexes: biophysical constraints on intracellular communication. Annu Rev Biophys Biomol Struct 27: 59–75
Brown G, Kholodenko B (1999) Spatial gradients of cellular phospho-proteins. FEBS Lett 457: 452–457
Chen W, Levine H, Rappel WJ (2009) Compartmentalization of second messengers in neurons: a mathematical analysis. Phys Rev E 80(4): 041901
COMSOL Multiphysics (v3.4). COMSOL AB, Stockholm 2007
Heinrich R, Neel B (2002) Mathematical models of protein kinase signal transduction. Mol Cell 9: 957–970
Hill A (1910) The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J Physiol 70: 1–7
Kath W, Murray J (1985) Analysis of a model biological switch. SIAM J Appl Math 45(6): 943–955
Kholodenko B (2003) Four-dimensional organization of protein kinase signaling cascades: the roles of diffusion, endocytosis and molecular motors. J Exp Biol 206: 2073–2082
Kholodenko B (2006) Cell-signalling dynamics in time and space. Nat Rev Mol Cell Biol 7: 165–176
Meyers J, Craig J, Odde D (2006) Potential for control of signaling pathways via cell size and shape. Curr Biol 16: 1685–1693
Qu Z, Vondriska T (2009) The effects of cascade length, kinetics and feedback loops on biological signal transduction dynamics in a simplified cascade model. Phys Biol 6: 1–10
Sear R, Howard M (2006) Modeling dual pathways for the metazoan spindle assembly checkpoint. Proc Natl Acad Sci USA 103: 16758–16763
Smith G, Dai L, Miura R, Sherman A (2001) Asymptotic analysis of buffered calcium diffusion near a point source. SIAM J Appl Math 61(5): 1816–1838 (electronic)
Stelling J, Kholodenko B (2009) Signaling cascades as cellular devices for spatial computations. J Math Biol 58(1–2): 35–55
Straube R, Ward M (2009) An asymptotic analysis of intracellular signaling gradients arising from multiple small compartments. SIAM J Appl Math 70(1): 248–269
Thul R, Falcke M (2004) Release currents of IP 3 receptor channel clusters and concentration profiles. Biophys J 86: 2660–2673
Van Dyke M (1964) Perturbation methods in fluid mechanics. Appl Math Mech, vol 8. Academic Press, New York
Weng G, Bhalla U, Iyengar R (1999) Complexity in biological signaling systems. Sci Mag 284: 92–96