By Kenneth H. Norwich
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Extra resources for Molecular Dynamics in Biosystems. The Kinetics of Tracers in Intact Organisms
When written in this form, there can be no doubt that the process refers only to disappearance (no source or appearance terms present) and that the concentration is at liberty to vary with 26 The Relationship Between Tracer and Tracee position within the solution. First order reactions will assume a special position in our subsequent discussion of tracer kinetics. In biochemistry we often deal with enzyme-catalyzed reactions whose kinetics are more complex than those described by the equations given above.
In time interval t, the rectangular parallelepiped of sides ~c, sy and dz is transformed into the oblique parallelepiped of sides 3x', Sy and SZ. The projections of 5y' on each of the coordinate axes is shown. The point P has coordinates (x,y,z), and Q has coordinates (x,y + y,z) etc. The first derivation was simpler and is the one commonly found in textbooks. But it required the concept of a volume fixed in space and through which the continuously distributed material passed. It is difficult to apply this concept of a fixed volume to a portion of the region close to a distensible boundary.
This element dx dy is the projection of an element of surface area onto the 42 The Biokinetics of Distributed Systems plane orthogonal to the axis of the prism (Fig. 3); thus if k is a unit vector parallel to the z-axis, k • ~ dxdy = -k • ~1 d5 1 = 2 dS 2 = -k • ~3 d5 3 = ... 10) Eq. 9) then becomes • (Yin1 dS 1 dl = ~ s J' + U2 ~2 dS2 + ... 12) where S denotes the total surface area. 14) JV y dV = ~~ where i and j are unit normal vectors parallel to the x- and y-axes respectively. 4) Speaking Practically The importance of this theorem will be to permit us to transpose our discussion of tracer and tracee fluxes from the interior of a region (volume integral) to the surface of a region (surface integral).