¹C2²2S + E Sk3,0 where S is a T-cell of a particular variety, E is the corresponding (free, i.e. unbound) antigen, and C is a complex consisting of a T-cell bound to an antigen. Ø indicates the loss of T-cells due to decay as described above. 1. Let s, c and e be the concentration of S, C and E, respectively, in the body at time t. Assume that the background exposure to the disease results in a constant concentration eo of the antigen (free or bound) in the body. (b) (c) Consider the T-cell system. Assuming mass action kinetics, write down a system of ODEs for Show that ds dt S + E and k-1 where KM dc dt Show (include your working) that the 2D system of ODEs has two equilibria: (s*,c*) = (0,0) == : -k₁(eo — c)s + k_1c +2k₂c - k3s k-1+k2 k₁ (s*, c*) = ( k₂e0 k3 and KM, eo k2 dt' dt and KM = k₁(eo - c)s - k_1c - k₂c.
¹C2²2S + E Sk3,0 where S is a T-cell of a particular variety, E is the corresponding (free, i.e. unbound) antigen, and C is a complex consisting of a T-cell bound to an antigen. Ø indicates the loss of T-cells due to decay as described above. 1. Let s, c and e be the concentration of S, C and E, respectively, in the body at time t. Assume that the background exposure to the disease results in a constant concentration eo of the antigen (free or bound) in the body. (b) (c) Consider the T-cell system. Assuming mass action kinetics, write down a system of ODEs for Show that ds dt S + E and k-1 where KM dc dt Show (include your working) that the 2D system of ODEs has two equilibria: (s*,c*) = (0,0) == : -k₁(eo — c)s + k_1c +2k₂c - k3s k-1+k2 k₁ (s*, c*) = ( k₂e0 k3 and KM, eo k2 dt' dt and KM = k₁(eo - c)s - k_1c - k₂c.
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
Section: Chapter Questions
Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...
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Transcribed Image Text:¹C2²2S + E
Sk3,0
where S is a T-cell of a particular variety, E is the corresponding (free, i.e. unbound) antigen, and C
is a complex consisting of a T-cell bound to an antigen. Ø indicates the loss of T-cells due to decay as
described above.
1.
Let s, c and e be the concentration of S, C and E, respectively, in the body at time t.
Assume that the background exposure to the disease results in a constant concentration eo of the antigen
(free or bound) in the body.
(b)
(c)
Consider the T-cell system.
Assuming mass action kinetics, write down a system of ODEs for
Show that
ds
dt
S + E
and
k-1
where KM
dc
dt
Show (include your working) that the 2D system of ODEs has two equilibria:
(s*,c*) = (0,0)
==
: -k₁(eo — c)s + k_1c +2k₂c - k3s
k-1+k2
k₁
(s*, c*) = (
k₂e0
k3
and
KM, eo
k2
dt' dt
and
KM
= k₁(eo - c)s - k_1c - k₂c.
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