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Table 17 List of model equations used in PTP Integration (modified from [21])

From: Composite mathematical modeling of calcium signaling behind neuronal cell death in Alzheimer’s disease

Equation Biological significance
τ y =1000((1000/cosh(CAM/0.1))+0.1) Time constant for secondary slow process
τ h =τ y /8 Time constant for PTP high conductance state
\( PTP_{h}^{\infty } = heav\left (y - y^{*}\right) \) Heaviside step function for PTP max value
y=heav(CAMCAM) Heaviside step function for y threshold value
dy/dt=(yy)/τ y Secondary slow process involved in opening of PTP high conductance state
\( dPTP_{h}/dt = \left (PTP_{h}^{\infty } - PTP_{h}\right)/\tau _{h} \) PTP high conductance state dynamics
\( J^{H}_{PTP} = perm_{l}^{H} * PTP_{l} * PSI * \left (H_{M} - 0.0000000398 * exp\left (-37.434 * PSI\right)/\left (1-exp\left (-37.434 * PSI\right)\right)\right) \) Proton flux through PTP in high conductance state
\( J^{Ca}_{PTP} = perm_{Ca} * PTP_{l} * J_{uni} * \left (1-postptp * PTP_{h}\right) \) Rate of Ca2+ ion transport across PTP
\( dH_{M}/dt = \left (f_{H_{M}}/\tau _{h}\right)*\left (J^{H}_{L} + J^{H}_{F1} - J^{H}_{res}+J^{H}_{PTP}\right) \) Change in mitochondrial proton concentration
τ l =p6+amp τ /cosh((H M p3)/p4) Time constant for PTP low conductance state
\( PTP_{l}^{\infty } = 0.5 * \left (1 + tanh\left (\left (p1 - H_{M}\right)/p_{2}\right)\right)\) Rate of change of polling function
\( dPTP_{l}/dt = \left (PTP_{l}^{\infty } - PTP_{l}\right)/\tau _{l} \) PTP low conductance state dynamics
\