Recent experimental advances in single-molecule enzymology stimulated many efforts to develop singlemolecule kinetic theories of enzyme catalysis, especially for the classic Michaelis-Menten mechanism. Our group recently studied redox catalysis by single metal nanoparticles at single-turnover resolution. Compared with enzymes, which are homogeneous catalysts and have well-defined active sites, nanoparticles are heterogeneous catalysts and have many different surface sites for catalysis. To provide a theoretical framework to understand nanoparticle catalysis at the single-molecule level, here we formulate in detail the singlemolecule kinetic theory of a Langmuir-Hinshelwood mechanism for heterogeneous catalysis, which includes the multitude of surface sites on one nanoparticle. We consider two parallel product dissociation pathways that give complex single-molecule kinetics of the product dissociation reaction. We derive the probability density functions of the stochastic waiting times for both the product formation and the product dissociation reactions and describe their complex behaviors at different kinetic limiting conditions. We also obtain a singlemolecule Langmuir-Hinshelwood equation that describes the saturation kinetics of the product formation rate over substrate concentrations and evaluate the randomness parameter of single-turnover waiting times. We further compare the single-molecule kinetics between the Langmuir-Hinshelwood mechanism for heterogeneous catalysis and the Michaelis-Menten mechanism for enzyme catalysis and formulate the modified single-molecule Michaelis-Menten kinetics with multiple product dissociation pathways. In the end, we suggest that the Langmuir-Hinshelwood mechanism is also applicable to describe the single-molecule kinetics of oligomeric enzymes that contain multiple catalytic sites. We expect that these theories will enable quantitative analysis of single-turnover kinetics of heterogeneous and enzyme catalysis and provide a theoretical foundation to understand the catalytic dynamics of nanoparticles and enzymes at the single-molecule level.

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Glycine soja (BB52) is a wild soybean cultivar grown in coastal saline land in Yellow River Delta, China. In order to reveal the physiological mechanisms adapting to salinity, we examined photosynthesis, ion flux, antioxidant system and water status in Glycine soja under NaCl treatments, taking a cultivated soybean, ZH13, as control. Upon NaCl exposure, higher relative water content and water potential were maintained in the leaf of BB52 than ZH13, which might depend on the more accumulation of osmotic substances such as glycinebetaine and proline. Compared with ZH13, activities of antioxidant enzymes including superoxide dismutase, catalase, ascorbate peroxidase and contents of ascorbate, glutathione and phenolics were enhanced to a higher level in BB52 leaf under NaCl stress, which could mitigate the salt-induced oxidative damage in BB52. Consistently, lipid peroxidation indicated by malondialdehyde content was lower in BB52 leaf. Photosynthetic rate (Pn) was decreased by NaCl stress in BB52 and ZH13, and the decrease was greater in ZH13. The decreased Pn in BB52 was mainly due to stomatal limitation. The inhibited activation of rubisco enzyme in ZH13 due to the decrease of rubisco activase content became an important limiting factor of Pn, when NaCl concentration increased to 200 mM. Rubisco activase in BB52 was not affected by NaCl stress. Less negative impact in BB52 derived from lower contents of Na+ and Cl- in the tissues, and non-invasive micro-test technique revealed that BB52 roots had higher ability to extrude Na+ and Cl-. Wild soybean is a valuable genetic resource, and our study may provide a reference for molecular biologist to improve the salt tolerance of cultivated soybean in face of farmland salinity.