Table 1. Mathematical parameters describing the functional interactions among various cell types.
Rate | 1/year | Pathway | S(Ns) | S(Nd) | S(M1) | S(M2) | Sensitivity |
α1 | 10−5 | Aq → Ns | 50000 | −50000 | −6000 | 6000 | Strong |
α2 | 10−3 | Ap → Nd | −500 | 500 | −60 | 60 | Weak |
α3 | 10−2 | M1 → Nd | −200 | 200 | −35 | 35 | Weak |
α4 | 10−4 | M2 → Aq | 500 | −500 | 150 | −150 | Weak |
α5 | 10−2 | M1 → Ap | −3 | 3 | 1 | −1 | Weak |
α6 | 10−2 | Ns → M2 | 500 | −500 | −6000 | 6000 | Weak |
α7 | 10−4 | Aq → M2 | 5000 | −5000 | −50000 | 50000 | Strong |
α8 | 10−2 | Aβ ⊥ M2 | −400 | 400 | 5000 | −5000 | Moderate |
α9 | 10−2 | M1 ⊥ M2 | −30 | 30 | 250 | −250 | Weak |
α10 | 10−2 | Nd → M1 | −8 | 8 | 90 | −90 | Weak |
α11 | 10−2 | Ns ⊥ M1 | 500 | −500 | −6000 | 6000 | Moderate |
α12 | 10−4 | Aq ⊥ M1 | 5000 | −5000 | −50000 | 50000 | Strong |
α13 | 10−2 | Aβ → M1 | −400 | 400 | 5000 | −5000 | Moderate |
α14 | 10−4 | M2 ⊥ M1 | 5000 | −5000 | −50000 | 50000 | Strong |
α15 | 1 | Ns → Aβ | −10 | 10 | 100 | −100 | Weak |
α16 | 10−2 | M2 ⊥ Aβ | 100 | −100 | −1000 | 1000 | Weak |
αr | 1 | M2 ⊥ Aβ | 8 | −8 | −100 | 100 | Weak |
The rates αi associated with the pathways of the AD mechanism, and the sensitivities of the Ns and Nd populations to variations in the values of αi. The values for the sensitivity coefficients S(Nj, j = s, d) = dNj/dαi are determined after 20 years for ±2.5% perturbations in each αi value. A cell population is more sensitive to a change in a rate that produces a larger value of |S(Nj)|. Positive S(Nj) imply that a rate contributes to an increase in Nj while a negative value entails a corresponding population decrease.