Action rate

For a closed chemical system witli a mass action rate law satisfying detailed balance tliese kinetic equations have a unique stable (tliennodynamic) equilibrium, In general, however, we shall be concerned witli... 

For nearly oxygen-balanced expls equilibrium (1) will dominate and control the compn of the detonation products. As already stated this equilibrium is expected to be independent of pressure if the gases behave ideally. But even for ideal gas behavior and an oxygen-balanced expl, no direct comparison can be made between theoretical detonation product calcns and observed products. This is so because measurements are made at temps much lower than detonation temps, and the products reequilibrate as the temp drops. Further complications arise because the reequilibration freezes at some rather high temp. This is a consequence of re-, action rates. At temps below some frozen equb... 

The macroscopic mass action rate law, which holds for a well-mixed system on sufficiently long time scales, may be written... 

The numerator of Eq (1) is that of a homogeneous mass action rate law. The denominator seems to have been added to account for adsorption of some of the participants. 

Action rate Irritating effect on nose and throat is intolerable after one minute at moderate concentrations, delayed blistering. 

Action rate Immediate irritation of eyes and nose delayed blistering... 

Action rate Immediate eye effect, with skin effects appearing in thirty to sixty minutes. 

Action rate Delayed action, two hours to eleven days. 

Freezing/melting point (at degrees C) -6.9 Boiling point (at degrees C) 12.8 Action rate Very rapid. 

Action rate Immediate to 3 hours, depending on concentration... 

Action rate Delayed—usually four to six hours until first symptoms appear Physiological action Blisters destroys tissue injures blood cells Required level of protection Protective mask and clothing Decontamination Bleach, fire, DS2, M258A1, M280... 

Action rate Immediate stinging of skin and redness within thirty minutes blistering delayed about thirteen hours. 

Action rate Very rapid. Death usually occurs within fifteen minutes after absorption of fatal dose. 

Action Rate Delayed twelve hours or longer... 

Action Rate On the skin, delayed twelve hours or more on the eyes, faster than HD... 

Action Rate Serious effects same as for HD (four-six hours) minor effects sooner (such as eye irritation, tearing, and light sensitivity). 

Despite its limitations, the reversible Random Bi-Bi Mechanism Eq. (46) will serve as a proxy for more complex rate equations in the following. In particular, we assume that most rate functions of complex enzyme-kinetic mechanisms can be expressed by a generalized mass-action rate law of the form... 

Drug Active Metabolites Onset of Action Rate of Elimination Primary Metabolic Route... 

Chemical kinetics govern the rate at which chemical species are created or destroyed via reactions. Chapter 9 discussed chemical kinetics of reactions in the gas phase. Reactions were assumed to follow the law of mass action. Rates are determined by the concentrations of the chemical species involved in the reaction and an experimentally determined rate coefficient (or rate constant) k. 

Synthesis chemists were very inventive when they were developing effective peptide catalysts simulating definite properties of modeled enzymes. Despite a series of successful syntheses of biomimics, their action rate and selectivity were much worse than those of natural biocatalysts. 

The mass-action assumption that j + and j do not depend on reactant concentrations can be applied to reactions other than the uni-unimolecular reaction A B. For example, the mass-action rate laws for the reaction... 

While the majority of these concepts are introduced and illustrated based on single-substrate single-product Michaelis-Menten-like reaction mechanisms, the final section details examples of mechanisms for multi-substrate multi-product reactions. Such mechanisms are the backbone for the simulation and analysis of biochemical systems, from small-scale systems of Chapter 5 to the large-scale simulations considered in Chapter 6. Hence we are about to embark on an entire chapter devoted to the theory of enzyme kinetics. Yet before delving into the subject, it is worthwhile to point out that the entire theory of enzymes is based on the simplification that proteins acting as enzymes may be effectively represented as existing in a finite number of discrete states (substrate-bound states and/or distinct conformational states). These states are assumed to inter-convert based on the law of mass action. The set of states for an enzyme and associated biochemical reaction is known as an enzyme mechanism. In this chapter we will explore how the kinetics of a given enzyme mechanism depend on the concentrations of reactants and enzyme states and the values of the mass action rate constants associated with the mechanism. 

Here, +i[S] serves as the apparent mass-action rate constant for the conversion E — ES. Each time an enzyme cycles from state E to ES and back to E again, one molecule of S is converted to P. If the rate of turnover of the catalytic cycle is significantly greater than the rate of change of reactant (S and P) concentrations, then the apparent mass-action constant +i[S] in Equation (4.2) remains effectively constant over the timescale of the catalytic cycle. This is true, for example, when the enzyme concentration is small compared to reactant concentrations, many catalytic cycles are required to produce a significant change in reactant concentrations. 

Often the key entity one is interested in obtaining in modeling enzyme kinetics is the analytical expression for the turnover flux in quasi-steady state. Equations (4.12) and (4.38) are examples. These expressions are sometimes called Michaelis-Menten rate laws. Such expressions can be used in simulation of cellular biochemical systems, as is the subject of Chapters 5, 6, and 7 of this book. However, one must keep in mind that, as we have seen, these rates represent approximations that result from simplifications of the kinetic mechanisms. We typically use the approximate Michaelis-Menten-type flux expressions rather than the full system of equations in simulations for several reasons. First, often the quasi-steady rate constants (such as Ks and K in Equation (4.38)) are available from experimental data while the mass-action rate constants (k+i, k-i, etc.) are not. In fact, it is possible for different enzymes with different detailed mechanisms to yield the same Michaelis-Menten rate expression, as we shall see below. Second, in metabolic reaction networks (for example), reactions operate near steady state in vivo. Kinetic transitions from one in vivo steady state to another may not involve the sort of extreme shifts in enzyme binding that have been illustrated in Figure 4.7. Therefore the quasi-steady approximation (or equivalently the approximation of rapid enzyme turnover) tends to be reasonable for the simulation of in vivo systems. 

Much of the present day safety evaluation follows precepts (Table VI) which were promulgated by FDA for new drugs. This requires that therapeutic and toxic doses be studied for all toxic effects, site of action, mechanism of action, rates of absorption, distribution in the body, metabolism, excretion, time of onset and duration of effects. 

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