{'fraction_non_alphanumeric': 0.011658031088082901, 'fraction_numerical': 0.0012953367875647669, 'mean_word_length': 5.3884297520661155, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Ligand binding in a spherical region randomly crowded by receptors

This paper reports on some results concerning the binding of diffusing ligands in a spherical 3D region randomly filled by free receptors. It is shown that commonly accepted mean-field theory which is successfully used for bulk diffusion-controlled reactions cannot describe the behavior of ligand concentration in the diffusion layer close to the region boundary. To eliminate this drawback of the theory, we introduce a new complementary diffusion equation in the boundary layer with an appropriate matching condition. Using this equation, we find the characteristic ligand penetration length and total time-dependent flux of ligand binding to free receptors randomly distributed in a spherical region.