Abstract
Reactions in the intracellular medium occur in a highly organized and heterogenous environment rendering invalid modeling approaches based on the law of mass action or its stochastic counter-part. This has led to the recent development of a variety of stochastic microscopic approaches based on lattice-gas automata or Brownian dynamics. The main disadvantage of these methods is that they are computationally intensive. We propose a mesoscopic method which permits the efficient simulation of reactions occurring in the complex geometries typical of intracellular environments. This approach is used to model the transport of a substrate through a pore in a semi-permeable membrane, in which its Michaelis–Menten enzyme is embedded. We find that the temporal evolution of the substrate is a sensitive function of the spatial heterogeneity of the environment. The spatial organization and heterogeneities of the intracellular medium seem to be playing an important role in the regulation of biochemical reactions.
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A. R. Altenberger and M. Tirrell J. Chem. Phys. 80: 2208 (1984).
S. S. Andrews and D. Bray Phys. Biol. 1: 137 (2004).
G. K. Batchelor J. Fluid Mech. 74: 1 (1976).
C. W. J. Beenakker and P. Mazur Physica A 120: 388 (1983).
P. Bernado, J. G. de la Torre and M. Pons J. Mol. Recognit. 17: 397 (2004).
H. Berry Biophys. J. 83: 1891 (2002).
D. Bray Annu. Rev. Biophys. Biomol. Struct. 27: 59 (1998).
F. Brochard and P.-G. DeGennes Macromolecules 10: 1157 (1977).
D. F. Calef and J. M. Deutch Ann. Rev. Phys. Chem. 34: 493 (1983).
N. A. Campbell Biology (The Benjamin/Cummings Publishing Company, California, 1996).
B. Cheng, R. L. Fournier, and P. A. Relue Biotechnol. Bioeng. 70: 467 (2000).
R. I. Cukier Macromolecules 17: 252 (1984).
P.-G. DeGennes Macromolecules 9: 594 (1976).
P.-G. DeGennes Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).
J. M. Deutch and I. Oppenheim J. Chem. Phys. 54: 3547 (1971).
M. Doi and S. F. Edwards The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986).
S. F. Edwards J. Phys. A 8: 1670 (1975).
J. L. Eide and A. K. Chakraborty J. Phys. Chem. B. 110: 2318 (2006).
D. L. Ermak and J. A. McCammon J. Chem. Phys. 69: 1352 (1978).
B. U. Felderhof J. Phys A 11: 929 (1978).
A. R. Fersht Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, (Freeman, New York, 1999).
U. Frisch, B. Hasslacher and Y. Pomeau Phys. Rev. Letts. 56: 1505 (1986).
A. B. Fulton Cell 30: 345 (1982).
C. W. Gardiner Handbook of Stochastic Methods, 2nd edition (Springer, Berlin, 1995).
N. D. Gershon, K. R. Porter and B. L. Trus Proc. Natl. Acad. Sci USA 82: 5030 (1985).
D. A. Wolf-Gladrow Lattice-Gas Cellular Automata and Lattice-Boltzmann Models: An Introduction (Springer, Berlin, 2000).
A. Goldbeter Biochemical oscillations and cellular rhythms (Cambridge University Press, 1996).
R. Grima and T. J. Newman Phys. Rev. E 70: 036703 (2004).
R. Grima and S. Schnell Biophysical Chemistry. DOI:10.1016/j.bpc.2006.04.019.
R. Grima and S. Schnell ChemPhysChem 7: 1422 (2006).
D. Hall and A. P. Minton BBA-Proteins Proteomics 1649: 127 (2003).
J. Hardy, Y. Pomeau and O. D. Pazzis J. Math. Phys. 14: 1746 (1973).
L. Johansson and J.-E Lofroth J. Chem. Phys. 98: 7471 (1993).
R. Kapral, A. Lawniczak and P. Masiar Phys. Rev. Lett. 66: 2539 (1991).
R. Kapral, A. Lawniczak and P. Masiar J. Chem. Phys. 96: 2762 (1992).
L. B. Kier, C.-K. Cheng and P. G. Seybold Reviews in Computational Chemistry Vol. 17 (John Wiley and Sons Inc., New York, 2001), pp. 205–254.
R. Kopelman J. Stat. Phys. 42: 185 (1986).
R. Kopelman Science 241: 1620 (1988).
H. Kuthan Prog. Biophys. Mol. Biol. 75: 1 (2001).
D. Langevin and F. Rondelez Polymer 19: 875 (1978).
J. L. Lebowitz and E. Rubin Phys. Rev. 131: 2381 (1963).
R. J. LeVeque Numerical Methods for Conservation Laws (Birkhauser, Basel, 1990).
K. Lipkow, S. S. Andrews and D. Bray J. Bact. 187: 45 (2005).
K. Luby-Phelps Int. Rev. Cytol. 192: 189 (2000).
P. Mazur and I. Oppenheim Physica 50: 241 (1970).
S. C. Merriam and G. D. J. Phillies J. Poly. Sci. Part B 42: 1663 (2004).
A. P. Minton Biopolymers 20: 2093 (1981).
A. P. Minton J. Biol. Chem. 276: 10577 (2001).
T. J. Murphy and J. L. Aguirre J. Chem. Phys. 57: 2098 (1972).
T. J. Newman and R. Grima Phys. Rev. E. 70: 051916 (2004).
P. A. Netz and T. Dorfmuller J. Chem. Phys. 107: 9221 (1997).
B. Novak, Z. Pataki, A. Ciliberto and J. J. Tyson Chaos 11: 277 (2001).
A. G. Ogston, B. N. Preston and J. D. Wells Proc. R. Soc. London, Ser. A 333: 297 (1973).
J. M. Petit, B. Roux, X. X. Zhu and P. M. Macdonald Macromolecules 29: 6031 (1996).
G. D. J. Phillies J. Phys. Chem. 93: 5029 (1989).
G. D. J. Phillies Macromolecules 20: 558 (1987).
G. D. J. Phillies Macromolecules 31: 2317 (1998).
G. D. J. Phillies Macromolecules 19: 2367 (1986).
G. D. J. Phillies J. Phys. Chem. 96: 10061 (1992).
C. G. Phillips and K. M. Jansons Macromolecules 23: 1717 (1990).
C. G. Phillips J. Chem. Phys. 95: 4593 (1991).
D. C. Rapaport The Art of Molecular Dynamics Simulation, 2nd edition (Cambridge University Press, 2004).
H. Risken The Fokker-Planck Equation (Springer, Berlin, 1989).
J. M. Rohwer, P. W. Postma, B. N. Kholodenko, and H. V. Westerhoff Proc. Natl. Acad. Sci. U.S.A. 95: 10547 (1998).
J. J. Rottler and A. C. Maggs Phys. Rev. Lett. 93: 170201 (2004).
M. A. Savageau J. Theor. Biol. 176: 115 (1995).
S. Schnell and T. E. Turner Prog. Biophys. Mol. Biol. 85: 235 (2004).
M. Thellier, J.-C. Vincent, S. Alexandre, J.-P. Lassalles, B. Deschrevel, V. Norris and C. Ripoll C. R. Biologies 326: 149 (2003).
M. Thellier, G. Legent, V. Norris, C. Baron and C. Ripoll C. R. Biologies 327: 1017 (2004).
M. Tokita, T. Miyoshi, K. Takegoshi and K. Hikichi Phys. Rev. E 53: 1823 (1996).
M. Tokuyama and I. Oppenheim Physica A 94: 501 (1978).
T. E. Turner, S. Schnell and K. Burrage Comp. Biol. Chem. 28: 165 (2004).
V. Zehnle and G. Searby J. Phys. Paris 50: 1083 (1989)
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Grima, R., Schnell, S. A Mesoscopic Simulation Approach for Modeling Intracellular Reactions. J Stat Phys 128, 139–164 (2007). https://doi.org/10.1007/s10955-006-9202-z
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DOI: https://doi.org/10.1007/s10955-006-9202-z