Mechanical - Chemical Analogy

It is convenient to analyse tliese rate equations from a dynamical systems point of view similar to tliat used in classical mechanics where one follows tire trajectories of particles in phase space. For tire chemical rate law (C3.6.2) tire phase space , conventionally denoted by F, is -dimensional and tire chemical concentrations, CpC2,- are taken as ortliogonal coordinates of F, ratlier tlian tire particle positions and velocities used as tire coordinates in mechanics. In analogy to classical mechanical systems, as tire concentrations evolve in time tliey will trace out a trajectory in F. Since tire velocity functions in tire system of ODEs (C3.6.2) do not depend explicitly on time, a given initial condition in F will always produce tire same trajectory. The vector R of velocity functions in (C3.6.2) defines a phase-space (or trajectory) flow and in it is often convenient to tliink of tliese ODEs as describing tire motion of a fluid in F with velocity field/ (c p). 

Many reactions that fit the definition of an organic chemical redox reaction (Section 17.1) have already been presented in Chapters 1-16. The presentation of these reactions in various other places—without alluding at all to their redox character—was done because they follow mechanisms that were discussed in detail in the respective chapters or because these reactions showed chemical analogies to reactions discussed there. Tables 17.3 and 17.4 provide cross-references to all oxidations and reductions discussed thus far. 

Bioisosteres are defined as groups or molecules that have chemical and physical properties producing broadly similar biological properties. " Bioisosteres likely affect the same receptor site or pharmacological mechanism. This analog design principle was apphed to our DCK modification, and thio-DCK and DCK lactam derivatives were developed. 

A range of chemical analogs of the catalytic centers of Mo and W dithiolene-containing enzymes (pterins) have been prepared. In particular, the rich chemistry of multisulfur transition metal systems allows ligand redox, internal electron transfer, and intermediate redox states. Such redox flexibility may facihtate coupled proton/electron transfer and/or 0x0-transfer mechanisms, which are employed by Mo and W enzymes. 

Chemical reaction and mass transfer are two unique phenomena that help define chemical engineering. Chapter 8 described problems involving chemical reaction and mass transfer in a porous catalyst, and how to model chemical reactors when the flow was well defined, as in a plug-flow reactor. Those models, however, did not account for the complicated flow situations sometimes seen in practice, where flow equations must be solved along with the transport equation. Microfluidics is the chemical analog to microelectro-mechanical systems (MEMS), which are small devices with tiny gears, valves, and pumps. The generally accepted definition of microfluidics is flow in channels of size 1 mm or less, and it is essential to include both distributed flow and mass transfer in such devices. 

Two groups, those of Corey and Sih, have reported studies on chemical analogs of the proposed biochemical mechanism, in which they activated the hydroperoxide function by forming the corresponding mesylate or trifluoromethanesulfonate (triflate). In no case were the peroxy esters isolated as they underwent elimination under the conditions of formation, even at -110 C. 

The kinetic description of enzyme-catalyzed reactions in vitro has allowed their rates to be expressed as a function of reactant and enzyme concentrations, and a set of empirically defined kinetic parameters. Enzymologists also have sought to modify this basic relationship in systematic ways so as to reveal something about the mechanism by which the enzyme acts. Traditionally, in such studies the enzymologist has been concerned primarily with the enzyme, its proper substrates and products, and closely related chemical analogs of these proper reactants (Jencks, 1969). 

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