In vivo environments are highly crowded and inhomogeneous, which may affect reaction processes in cells. In this study we examined the effects of intracellular crowding and an inhomogeneity on the behavior of in vivo reactions by calculating the spectral dimension (ds), which can be translated into the reaction rate function. We compared estimates of anomaly parameters obtained from fluorescence correlation spectroscopy (FCS) data with fractal dimensions derived from transmission electron microscopy (TEM) image analysis. FCS analysis indicated that the anomalous property was linked to physiological structure. SubsequentTEM analysis provided an in vivo illustration; soluble molecules likely percolate between intracellular clusters, which are constructed in a self-organizing manner. We estimated a cytoplasmic spectral dimension d s to be 1.39 ±0.084. This result suggests that in vivo reactions initially run faster than the same reactions in a homogeneous space; this conclusion is consistent with the anomalous character indicated by FCS analysis. We further showed that these results were compatible with our Monte-Carlo simulation in which the anomalous behavior of mobile molecules correlates with the intracellular environment, leading to description as a percolation cluster, as demonstrated usingTEM analysis. We confirmed by the simulation that the above-mentioned in vivo like properties are different from those of homogeneously concentrated environments. Additionally, simulation results indicated that crowding level of an environment might affect diffusion rate of reactant. Such knowledge of the spatial information enables us to construct realistic models for in vivo diffusion and reaction systems.
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