Chemical modification of nanoparticles or particlelike systems is ubiquitously being used to facilitate specific pharmaceutical functionalities or physicochemical attributes of nanocrystals, proteins, enzymes, or other particlelike systems. Often the modification process is incomplete and the functional activity of the product depends upon the distribution of functional ligands among the different particles in the system. Here, the distribution function describing the spread of ligands in particlelike systems undergoing partial modification reactions is derived and validated against a conjugated enzyme model system by use of matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF). The distribution function is shown to be applicable to describe the distribution of ligands in a wide range of particlelike systems (such as enzymes, dendrimers, or inorganic nanocrystals) and is used to establish guidelines for the synthesis of uniformly modified particle systems even at low reaction efficiencies.
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