Abstract
Recently there has been significant interest in deducing the form
of the rate laws for chemical reactions occurring in the intracellular
environment. This environment is typically characterized by low-dimensionality
and a high macromolecular content; this leads to a spatial heterogeneity
not typical of the well stirred in vitro environments. For this reason,
the classical law of mass action has been presumed to be invalid
for modeling intracellular reactions. Using lattice-gas automata
models, it has recently been postulated H. Berry, Monte Carlo simulations
of enzyme reactions in two dimensions: Fractal kinetics and spatial
segregation, Biophys. J. 83 (2002) 1891-1901; S. Schnell, T.E. Turner,
Reaction kinetics in intracellular environments with macromolecular
crowding: simulations and rate laws, Prog. Biophys. Mol. Biol. 85
(2004) 235-260 that the reaction kinetics is fractal-like. In this
article we systematically investigate for the first time how the
rate laws describing intracellular reactions vary as a function of:
the geometry and size of the intracellular surface on which the reactions
occur, the mobility of the macromolecules responsible for the crowding
effects, the initial reactant concentrations and the probability
of reaction between two reactant molecules. We also compare the rate
laws valid in heterogeneous environments in which there is an underlying
spatial lattice, for example crystalline alloys, with the rate laws
valid in heterogeneous environments where there is no such natural
lattice, for example in intracellular environments. Our simulations
indicate that: (i) in intracellular environments both fractal kinetics
and mass action can be valid, the major determinant being the probability
of reaction, (ii) the geometry and size of the intracellular surface
on which reactions are occurring does not significantly affect the
rate law, (iii) there are considerable differences between the rate
laws valid in heterogeneous non-living structures such as crystals
and those valid in intracellular environments. Deviations from mass
action are less pronounced in intracellular environments than in
a crystalline material of similar heterogeneity.
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