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Component: environment

rho = \frac{24.0}{6.5} \ln 2.0 d = 12.0 \ln 2.0

Component: recycling_probability

pr = 0.6 + 0.2 \frac{{Ag}^{n}}{{Ag}^{n} + {Ag_min}^{n}} pr1 = 0.95 pr2 = 0.7 eta eta = \{\begin{matrix} \frac{K_AgAb}{C1 + C2} if \frac{K_AgAb}{C1 + C2} < 1.0 \\ 1.0 otherwise \end{matrix}

Component: antigens

\frac{d}{d time} (Ag) = (- (u k C + u Cs (1.0 - k))) Ag - (k_on Ag Ab)

Component: antibodies

\frac{d}{d time} (Ab) = beta AFC - (k_on Ag Ab)

Component: antigen_antibody_complexes

\frac{d}{d time} (K_AgAb) = k_on Ag Ab theta = 0.3 \frac{Ag}{C1 + C2} \frac{Ag}{Ag + K_AgAb}

Component: selection_probability_of_centrocytes

s = sc - (h + f \frac{{Ag_min}^{n}}{{Ag_min}^{n} + {Ag}^{n}}) sc = \frac{delta_c}{d (2.0 pr m - 1.0) + delta_c} s1 = 0.01 + 0.09 zeta s2 = 0.1 + 0.85 zeta zeta = \frac{Ag}{C1 + C2}

Component: centroblasts

\frac{d}{d time} (B) = rho B \frac{d}{d time} (B1) = pr1 rho Cs1 - (rho B1) \frac{d}{d time} (B2) = pr2 rho Cs2 - (rho B2)

Component: centrocytes

\frac{d}{d time} (C) = 2.0 rho m B - (mu C) \frac{d}{d time} (C1) = 2.0 rho m (M11 + B1) (M12 + B2) - (mu1 C1) \frac{d}{d time} (C2) = 2.0 rho m (M21 + B1) (M22 + B2) - (mu2 C2) mu = d s + delta_c (1.0 - s) mu1 = d s1 + delta_c (1.0 - s1) mu2 = d s2 + delta_c (1.0 - s2) delta_c = 1.5 \ln 2.0 M11 = 1.0 - M21 M12 = 1.0 - M22

Component: selected_centrocytes

\frac{d}{d time} (Cs) = d s C - (rho Cs) \frac{d}{d time} (Cs1) = d s1 C1 - (rho Cs1) \frac{d}{d time} (Cs2) = d s2 C2 - (rho Cs2)

Component: memory_cells

\frac{d}{d time} (M) = (1.0 - theta) rho (1.0 - pr) Cs \frac{d}{d time} (M1) = (1.0 - pr1) Cs1 \frac{d}{d time} (M2) = (1.0 - pr2) Cs2

Component: antibody_forming_cells

\frac{d}{d time} (AFC) = theta rho (1.0 - pr) Cs

Source: Derived from workspace Iber, Maini, 2002 at changeset 1fbe2844e1a6.

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A Mathematical Model for Germinal Centre Kinetics and Affinity Maturation