Single progress

For a system describable with a single progress variable, we derived the Marcus equation, Eq. (5-76). 

The distortions can only be calculated from the emission spectrum of crystals at low temperature. The spectra obtained from crystals at higher temperatures or from glasses even at low temperature contain a single progression with a spacing of 500cm This effect is discussed and interpreted in terms of the MIME in Section V. 

Single Progressive Rabble (Four Arms per Hearth)... 

This rabble system produces a more uniform retention time than the single progressive method by reducing the windrow size. Sticky material may pose a bridging problem since there are no spacers between the ploughs. 

This system uses two rabble arms and accomplishes the same mixing as the four-arm single progressive method. However, the retention time is doubled compared with the four-arm configuration. 

It is theoretically possible to derive Vmax and values for an enzyme from a single progress curve (Fig. 3.11). This is certainly an attractive proposition since measuring initial velocity as a function of several substrate concentrations can be a lengthy and tedious task. The velocity of an enzyme-catalyzed reaction can be determined from the disappearance... 

Figure 3.11. Linear plot used in the determination of catalytic parameters V ax and from a single progress curve.

A plot of ln([So]/[S<]) versus [Sq —S,]/t yields a straight line with slope =-l/ T, x-intercept = Vmax, and y-intercept = V ,ax/ m (Fig. 3.11). The values of the slope and intercept can readily be obtained using linear regression. Thus, from a single progress curve (i.e., a single [Sf]-t data set) it is possible to obtain estimates of Km and kcm-... 

Features of the collision dynamics have just been discussed in terms of diagrams that simply show how potential energy varies along a single progress coordinate. Even in collinear collisions in which the system only just surmounts the barrier, inertial effects on the downhill run ensure that no trajectory exactly follows this path. Consequently, it is important that simplified explanations of collision dynamics are only given after full three-dimensional trajectory calculations. Nevertheless, such simplified descriptions, usually based on a consideration of the dynamics of collinear collisions, are frequently valid and valuable. 

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