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.

Biology: The Dynamic Science (MindTap Course List)

4th Edition

ISBN:9781305389892

Author:Peter J. Russell, Paul E. Hertz, Beverly McMillan

Publisher:Peter J. Russell, Paul E. Hertz, Beverly McMillan

Chapter45: Defenses Against Disease

Section: Chapter Questions

Problem 5TYK

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