from multiple compartments and transfers carrier (2.11) Consider a compartment with volume V and tracer from a single compartment, which we shall refer to as i's single donor ('sd'). We allow for the * to serve as donor to one or more compartments. noted Fad- Csd Fsd (a) Derive the following ordinary differential equa- tion: Fad (Cad - Ci) . Vi d. %3D dt (b) Show that Csd must be greater than C, for Ci to be increasing; that, similarly, C4 must be smaller than C; in order that C; be decreasing. to the sd compartment, or perhaps to one or mo
from multiple compartments and transfers carrier (2.11) Consider a compartment with volume V and tracer from a single compartment, which we shall refer to as i's single donor ('sd'). We allow for the * to serve as donor to one or more compartments. noted Fad- Csd Fsd (a) Derive the following ordinary differential equa- tion: Fad (Cad - Ci) . Vi d. %3D dt (b) Show that Csd must be greater than C, for Ci to be increasing; that, similarly, C4 must be smaller than C; in order that C; be decreasing. to the sd compartment, or perhaps to one or mo
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Solve and Explain a,b,c,d and e
Transcribed Image Text:compartments 'upstream' from the sd compart-
ment.
Show that Csd
= C; precisely when C;
attains its maximum. (The results of parts (b)
and (c) are known as Zilversmit's rule.)
(d) In the analysis of metabolic pathways, it is often
important to know if a certain compound (metabo-
lite) of interest is formed entirely out of one par-
ticular other compound (its precursor). Explain
how Zilversmit's rule can be used in answering this
question.
(e) Can Zilversmit's rule be generalised to several
donors? How useful is the generalized result?
Transcribed Image Text:(c) Consider an experiment in which tracer is added
The carrier flow supplying compartment i is de-
possibilities that the single donor receives carrier
from multiple compartments and transfers carrier
to as i's single donor ('sd'). We allow for the
(2.11) Consider a compartment with volume V and tracer
from a single compartment, which we shall refer
other compartments besides i; similarly we allow
* to serve as donor to one or more compartments.
noted Fed.
Csd
Fsd
(a) Derive the following ordinary differential equa-
tion:
Fad
부 (Cad-Ci).
Vi
dt
(b) Show that Csd must be greater than C, for Ci to
be increasing; that, similarly, Cad must be smaller
than C; in order that C; be decreasing.
to the sd compartment, or perhaps to one or mov
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