Diffusion-controlled reactions of enzymes. An approximate analytic solution of Chou's model

Based on Chou's model, a criterion was derived, by which one can judge whether or not the physical picture of the critical spherical shell described by Chou for an enzyme-substrate fast reaction system can emerge. Furthermore, for those reaction systems with such a physical picture, an approximate analytical solution was presented, which can be easily handled to calculate the upper limit of the diffusion-controlled reaction and the corresponding concentration distribution of substrate molecules on the surface of the major protein outside the active site. The results thus obtained are in good agreement with those computed by Chou et al. through the approach of numerical solution. Furthermore, the physical significance of the criterion and its relation to the critical spherical shell are substantiated during the process of derivation, which is very helpful for gaining an insight into this kind of biomolecular system with surprisingly high reaction rates.

Modes of a laser resonator with a retroreflecting corner cube mirror

The self-consistent integral equation for the field distribution of the resonant modes in a resonator with a tilted retroreflecting corner cube mirror is solved. The corner cube acts like a convex lens with radius of curvature -L cot(2)theta in the rotation direction (L is the cavity length and theta the rotation angle) and like a flat plane in the direction of the rotation axis. The field distribution can be described in terms of Hermite-Gaussian functions, and these results have been confirmed experimentally using an Ar-ion laser. The equivalent beam matrix for a reflecting corner cube is also found.

Modes of a laser resonator with a retroreflecting roof mirror

The self-consistent integral equation for the field distribution of the resonant modes in a resonator with a tilted retroreflecting roof mirror is solved. The field distribution in the direction of the roof can be described in terms of Hermite-Gaussian functions. The beam matrix for a retroreflecting roof is found, and a new type of resonator which does not need precise alignment is proposed.