Convergence of Catalytic Antibody and Terpene Cyclase Mechanisms: Polyene Cyclization Directed by Carbocation-π...

Carbocations are one of the reaction intermediates formed during several nucleophilic substitutions or elimination reactions. A carbocation is an electron-deficient species with the central carbon atom having six electrons and three bonded atoms. The central carbon in a carbocation is sp2 hybridized with trigonal planar geometry. It has an empty p orbital perpendicular to the plane of the structure that can accept electrons. Thus, carbocations act as strong electrophiles and may react with any...

Evolution shapes the features of organisms over time, ensuring that they are suited for the environments in which they live. Sometimes, selection pressure leads to the rise of similar but unrelated adaptations in organisms with no recent common ancestors, a process known as convergent evolution.

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is a crucial tool in the analysis of discrete-time systems, but its convergence is limited to specific values of the complex variable z. This range of values, known as the Region of Convergence (ROC), is fundamental in determining the behavior and stability of a system or signal. The ROC defines the region in the complex plane where the z-transform converges, which can take various...

Overview
Antibodies, also known as immunoglobulins (Ig), are essential players of the adaptive immune system. These antigen-binding proteins are produced by B cells and make up 20 percent of the total blood plasma by weight. In mammals, antibodies fall into five different classes, which each elicits a different biological response upon antigen binding.
The Y-Shaped Structure of Antibodies Consists of Four Polypeptide Chains
Antibodies consist of four polypeptide chains: two identical heavy...

The turnover number of an enzyme is the maximum number of substrate molecules it can transform per unit time. Turnover numbers for most enzymes range from 1 to 1000 molecules per second. Catalase has the known highest turnover number, capable of converting up to 2.8×106 molecules of hydrogen peroxide into water and oxygen per second. Lysozyme has the lowest known turnover number of half a molecule per second.
Chymotrypsin is a pancreatic enzyme that breaks down proteins during digestion....

The theory of catalytically perfect enzymes was first proposed by W.J. Albery and J. R. Knowles in 1976. These enzymes catalyze biochemical reactions at high-speed. Their catalytic efficiency values range from 108-109 M-1s-1. These enzymes are also called 'diffusion-controlled' as the only rate-limiting step in the catalysis is that of the substrate diffusion into the active site. Examples include triose phosphate isomerase, fumarase, and superoxide dismutase.
 
Most enzymes...