Two‐dimensional reactive systems: Rapid bimolecular processes on spherical surfaces

Formation of Large Hypericin Aggregates in Giant Unilamellar Vesicles-Experiments and Modeling

The incorporation of hypericin (Hyp) from aqueous solutions into giant unilamellar vesicle (GUV) membranes has been studied experimentally and by means of kinetic Monte Carlo modeling. The time evolution of Hyp fluorescence originating from Hyp monomers dissolved in the GUV membrane has been recorded by confocal microscopy and while trapping individual GUVs in optical tweezers. It was shown that after reaching a maximum, the fluorescence intensity gradually decreased toward longer times. Formation of oversized Hyp clusters has been observed on the GUV surface at prolonged time. A simplified kinetic Monte Carlo model is presented to follow the aggregation/dissociation processes of Hyp molecules in the membrane. The simulation results reproduced the basic experimental observations: the scaling of the characteristic fluorescence decay time with the vesicle diameter and the buildup of large Hyp clusters in the GUV membrane.

Diffusion influenced binary reactive processes in membranes involving identical particles: a Monte Carlo study

Simple random walk simulations on triangular lattices were performed in order to obtain a basic quantitative understanding of the kinetics of diffusion influenced binary reactive processes of membrane associated peptides or proteins within the two dimensionality of lipid bilayers. The results of the Monte Carlo simulations are compared with various formal approximate steady-state approaches, such as presented by Keizer [Acc. Chem. Res., 18 (1985) 235-241] in the context of statistical nonequilibrium thermodynamics or by Hardt [Biophys. Chem., 10 (1979) 239-243], based on the well known work of Delbrück and Adam. For diffusion controlled binary reactions of identical particles, nice agreement with the numerically simulated values is found in the low concentration limit for both Hardt's and Keizer's approach. For the latter a fluctuating steady-state particle source has to be considered. The dependence of the steady-state rate coefficient on system size is investigated, and the results are compared to the work of Swartz and Peacock-López [J. Chem. Phys., 95 (4) (1991) 2727-2731]. In order to elucidate the results, a practical application is considered. An application to a dimerization reaction on vesicles of typical experimental dimensions is given.

Effect of linear reinsertion of receptor on the distribution of receptors around coated pits

We consider a linear receptor reinsertion step in our kinetic model of the primary steps occurring in receptor-mediated endocytosis. In contrast with our previous zeroth order receptor reinsertion assumption, here we consider a first order process, and we study the effect of receptor diffusion on the trapping rate constant (k+) and the radial distribution of receptors around coated pits (grp). Using experimental data for low density lipoproteins (LDL) receptors on fibroblast cells, we find that the trapping of receptors by coated pits is diffusion-controlled for any value of the escaping rate constant (k-). This result is significantly different from our previous findings. In fact, for a zeroth order process, we find that either diffusion has no effect on k+ or, at the most, receptor trapping is 84% diffusion-controlled. Moreover, we find values for the receptor reinsertion rate constant (kappa), which range between 15% of the pit's invagination rate constant, lambda, and three halves lambda. In addition, the ratio kappa/lambda is equal to the ratio of the concentration of receptors in pits with respect to the internalized receptors. Comparison between the experimental radial distribution of receptors around pits and the theoretical should provide an indication of the diffusion effect on k+.

A theoretical model of LDL-receptor trapping on a spherical cell

The kinetics of the trapping of LDL-receptor complexes by coated pits on the surface of fibroblasts is examined in this paper. We have recently developed a mathematical formalism to extend Keizer's non-linear, non-equilibrium fluctuation-dissipation theory to the kinetics of chemical systems constrained to a spherical surface. Keizer's theory is ideally suited to the study of open biological systems. In the past it has been used to investigate endocytosis on fibroblasts. However, these applications have modeled the cell membrane with an infinite plane. As such, the finite size of the cellular membrane, as well as its precise symmetry, could not be incorporated into the previous studies. Thus in this paper we use our recently developed methodology to reexamine the trapping step in endocytosis on spherical cells. For cell surface processes, the theoretical consideration of a spherical symmetry or an infinite plane, in model calculations, will depend on the experimental or in vivo conditions of the processes of interest. For a spherical symmetry, we find that the finite size of the cell surface does not significantly affect the rate of the trapping step given the empirically determined values for the relevant parametes on fibroblasts. This result supports the approximation used in the previous investigation. However, this and other analyses indicate that the finitie size of the biological surface probably is an important parameter for processes which occur on smaller biological surfaces such as those found on organelles.