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Bimolecular chemical reactions in crowded environments

  • Department of Polymer Science and Engineering, University of Science and Technology of China, Hefei 230026, China

Funds:  Supported by the National Natural Science Foundation of China (21225421), and the China Postdoctoral Science Foundation (2015M581998).
Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2016.08.006
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  • Author Bio:

    GAO Jing, female, born in 1990, master. Research field: soft matter physics and biological physics.

  • Corresponding author: YU Wancheng
  • Received Date: 11 April 2016
  • Accepted Date: 06 May 2016
  • Rev Recd Date: 06 May 2016
  • Publish Date: 30 August 2016
    Abstract

  • Abstract

    Using two-dimensional Langevin dynamics simulations, we investigate the kinetics of the bimolecular chemical reactions in crowded environments. An important finding is that the dependence of the mean reaction time τ on the area fraction of crowders  relies on the manner of varying . Specifically, When  is increased by adding crowders into the circular domain, a monotonic increase in τ is observed. Moreover, the growth rate of τ becomes much faster once the percolation occurs in the system. As  is tuned by varying the radius of the circular domain R, τ has a minimum as a function of , which is a result of two distinct dynamical regimes, i.e., the crowding-dominated regime and the density-dominated regime. As the size of crowders becomes larger, the reaction process is found to be accelerated. Finally, we show that distributions of the reaction time obey the exponential ones, and the degree of crowding does not alter the distribution pattern.

    Abstract

    Using two-dimensional Langevin dynamics simulations, we investigate the kinetics of the bimolecular chemical reactions in crowded environments. An important finding is that the dependence of the mean reaction time τ on the area fraction of crowders  relies on the manner of varying . Specifically, When  is increased by adding crowders into the circular domain, a monotonic increase in τ is observed. Moreover, the growth rate of τ becomes much faster once the percolation occurs in the system. As  is tuned by varying the radius of the circular domain R, τ has a minimum as a function of , which is a result of two distinct dynamical regimes, i.e., the crowding-dominated regime and the density-dominated regime. As the size of crowders becomes larger, the reaction process is found to be accelerated. Finally, we show that distributions of the reaction time obey the exponential ones, and the degree of crowding does not alter the distribution pattern.
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    • References(29)
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    MINTON A P. How can biochemical reactions within cells differ from those in test tubes? [J] Journal of Cell Science, 2006, 119: 2 863-2 869.
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    SUN J, WEINSTEIN H. Toward realistic modeling of dynamic processes in cell signaling: Quantification of macromolecular crowding effects [J]. The Journal of Chemical Physics, 2007, 127: 155105.
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    WIECZOREK G, ZIELENKIEWICZ P. Influence of macromolecular crowding on protein-protein association rates: A Brownian dynamics study[J]. Biophysical Journal, 2008, 95: 5 030-5 036.
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    JEON J H, MONNE H M, JAVANAINEN M, et al. Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins[J]. Physical Review Letters, 2012, 109: 188103.
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    KIM J S, YETHIRAJ A. Effect of macromolecular crowding on reaction rates: A computational and theoretical study [J]. Biophysical Journal, 2009, 96: 1 333-1 340.
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    HALL D, HOSHINO M. Effects of macromolecular crowding on intracellular diffusion from a single particle perspective[J]. Biophysical Reviews, 2010, 2: 39-53.
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    TORNEY D C, MCCONNELL H M. Diffusion-limited reaction rate theory for two-dimensional systems [J]. Proceedings of the Royal Society of London A, 1983, 387: 147-170.
    [18]
    PIAZZA F, FOFFI G, DE MICHELE C. Irreversible bimolecular reactions with inertia: from the trapping to the target setting at finite densities [J]. Journal of Physics, 2013, 25: 245101.
    [19]
    SUNG B J, YETHIRAJ A. Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions [J]. The Journal of Chemical Physics, 2005, 123: 114503.
    [20]
    PIAZZA F, DORSAZ N, DE MICHELE C. Diffusion-limited reactions in crowded environments: a local density approximation [J]. Journal of Physics, 2013, 25: 375104.
    [21]
    ISAACSON D A. Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials [J]. Physical Review E, 2009, 80: 066106.
    [22]
    CHANDLER D. Introduction to Modern Statistical Mechanics [M]. New York: Oxford University Press, 1987.
    [23]
    ERMAK D L, BUCKHOLZ H. Numerical integration of the Langevin equation: Monte Carlo simulation [J]. Journal of Computational Physics, 1980, 35: 169-182.
    [24]
    BAUMGRTNER A, MUTHUKUMAR M. A trapped polymer chain in random porous media [J]. The Journal of Chemical Physics, 1987, 87: 3 082-3 088.
    [25]
    MUTHUKUMAR M, BAUMGRTNER A. Effects of entropic barriers on polymer dynamics[J]. Macromolecules, 1989, 22: 1 937-1 941.
    [26]
    SALTZMAN E J, MUTHUKUMAR M. Conformation and dynamics of model polymer in connected chamber-pore system [J]. The Journal of Chemical Physics, 2009, 131: 214903.
    [27]
    STAUFFER D, AHARONY A. Introduction to Percolation Theory [M]. London: Taylor and Francis Press, 1985.
    [28]
    ASAKURA S, OOSAWA F. Interaction between particles suspended in solutions of macromolecules [J]. Journal of Polymer science, 1958, 33: 183-192.
    [29]
    YU W C, LUO K F. Effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure [J]. The Journal of Chemical Physics, 2015, 142: 124901.
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    [1]
    ZIMMERMAN S B, TRACH S O. Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli [J]. Journal of Molecular Biology, 1991, 222: 599-620.
    [2]
    ELLIS R J. Macromolecular crowding: obvious but under appreciated [J]. Trends in Biochemical Sciences, 2001, 26: 597-604.
    [3]
    ELLIS R J, MINTON A P. Join the crowd [J]. Nature, 2003, 425: 27-28.
    [4]
    ZIMMERMAN S B, MINTON A P. Macromolecular crowding: biochemical, biophysical, and physiological consequences [J]. Annual Review of Biophysics and Biomolecular Structure, 1993, 22: 27-65.
    [5]
    MINTON A P. The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media [J]. The Journal of Biological Chemistry, 2001, 276: 10 577-10 580.
    [6]
    RICE S A. Diffusion-Limited Reactions [M]. New York: Elsevier, 1985.
    [7]
    DORSAZ N, DE MICHELE C, PIAZZA F, et al. Diffusion-limited reactions in crowded environments [J]. Physical Review Letters, 2010, 105: 120601.
    [8]
    MINTON A P. How can biochemical reactions within cells differ from those in test tubes? [J] Journal of Cell Science, 2006, 119: 2 863-2 869.
    [9]
    SCHMIT J D, KAMBER E, KONDEV J. Lattice model of diffusion-limited bimolecular chemical reactions in confined environments [J]. Physical Review Letters, 2009, 102: 218302.
    [10]
    DONG W, BAROS F, ANDRE J C. Diffusion-controlled reactions. I. Molecular dynamics simulation of a noncontinuum model [J]. The Journal of Chemical Physics, 1989, 91: 4 643-4 650.
    [11]
    DZUBIELLA J, MCCAMMON J A. Substrate concentration dependence of the diffusion-controlled steady-state rate constant [J]. The Journal of Chemical Physics, 2005, 122: 184902.
    [12]
    SUN J, WEINSTEIN H. Toward realistic modeling of dynamic processes in cell signaling: Quantification of macromolecular crowding effects [J]. The Journal of Chemical Physics, 2007, 127: 155105.
    [13]
    WIECZOREK G, ZIELENKIEWICZ P. Influence of macromolecular crowding on protein-protein association rates: A Brownian dynamics study[J]. Biophysical Journal, 2008, 95: 5 030-5 036.
    [14]
    JEON J H, MONNE H M, JAVANAINEN M, et al. Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins[J]. Physical Review Letters, 2012, 109: 188103.
    [15]
    KIM J S, YETHIRAJ A. Effect of macromolecular crowding on reaction rates: A computational and theoretical study [J]. Biophysical Journal, 2009, 96: 1 333-1 340.
    [16]
    HALL D, HOSHINO M. Effects of macromolecular crowding on intracellular diffusion from a single particle perspective[J]. Biophysical Reviews, 2010, 2: 39-53.
    [17]
    TORNEY D C, MCCONNELL H M. Diffusion-limited reaction rate theory for two-dimensional systems [J]. Proceedings of the Royal Society of London A, 1983, 387: 147-170.
    [18]
    PIAZZA F, FOFFI G, DE MICHELE C. Irreversible bimolecular reactions with inertia: from the trapping to the target setting at finite densities [J]. Journal of Physics, 2013, 25: 245101.
    [19]
    SUNG B J, YETHIRAJ A. Molecular-dynamics simulations for nonclassical kinetics of diffusion-controlled bimolecular reactions [J]. The Journal of Chemical Physics, 2005, 123: 114503.
    [20]
    PIAZZA F, DORSAZ N, DE MICHELE C. Diffusion-limited reactions in crowded environments: a local density approximation [J]. Journal of Physics, 2013, 25: 375104.
    [21]
    ISAACSON D A. Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials [J]. Physical Review E, 2009, 80: 066106.
    [22]
    CHANDLER D. Introduction to Modern Statistical Mechanics [M]. New York: Oxford University Press, 1987.
    [23]
    ERMAK D L, BUCKHOLZ H. Numerical integration of the Langevin equation: Monte Carlo simulation [J]. Journal of Computational Physics, 1980, 35: 169-182.
    [24]
    BAUMGRTNER A, MUTHUKUMAR M. A trapped polymer chain in random porous media [J]. The Journal of Chemical Physics, 1987, 87: 3 082-3 088.
    [25]
    MUTHUKUMAR M, BAUMGRTNER A. Effects of entropic barriers on polymer dynamics[J]. Macromolecules, 1989, 22: 1 937-1 941.
    [26]
    SALTZMAN E J, MUTHUKUMAR M. Conformation and dynamics of model polymer in connected chamber-pore system [J]. The Journal of Chemical Physics, 2009, 131: 214903.
    [27]
    STAUFFER D, AHARONY A. Introduction to Percolation Theory [M]. London: Taylor and Francis Press, 1985.
    [28]
    ASAKURA S, OOSAWA F. Interaction between particles suspended in solutions of macromolecules [J]. Journal of Polymer science, 1958, 33: 183-192.
    [29]
    YU W C, LUO K F. Effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure [J]. The Journal of Chemical Physics, 2015, 142: 124901.
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