You are here: Home / Exposures / Rice, Winslow, Jafri, 1999 / Modeling Gain and Gradedness of Ca2+ Release in the Functional Unit of the Cardiac Diadic Space

Model Mathematics

Component based math viewer is available

Component: environment

Component: sarcolemma

Component: subspace

J_xfer = \frac{1.0}{tau_xfer} (Ca_SS - Ca_myo)

J_DHPR = \frac{I_DHPR DHPR_open}{2.0 F V_SS}

I_DHPR = P_Ca 4.0 \frac{V F^{2.0}}{R T} \frac{0.001 ⅇ^{\frac{2.0 V F}{R T}} - (0.341 Ca_o)}{ⅇ^{\frac{2.0 V F}{R T}} - 1.0}

DHPR_open = \{\begin{matrix} 1.0 if i = O \lor i = O_Ca \\ 0.0 otherwise \end{matrix}

J_RyR = \sum_{i = 1.0}^{8.0} (J_RyR_perm RyR_open (Ca_JSR - Ca_SS))

RyR_open = \{\begin{matrix} 1.0 if i = P_O3 \lor i = P_O4 \\ 0.0 otherwise \end{matrix}

\frac{d}{d time} (Ca_SS) = beta_SS (J_DHPR + J_RyR + \frac{V_myo}{V_SS} J_xfer)

beta_SS = {(1.0 + \frac{B_SR K_BSR}{{(K_BSR + Ca_SS)}^{2.0}} + \frac{B_SL K_BSL}{{(K_BSL + Ca_SS)}^{2.0}})}^{-1.0}

Component: sarcoplasmic_reticulum

\frac{d}{d time} (Ca_JSR) = beta_JSR (J_tr - (\frac{V_SS}{V_JSR} J_RyR))

beta_JSR = {(1.0 + \frac{CSQN_tot K_CSQN}{{(K_CSQN + Ca_JSR)}^{2.0}})}^{-1.0}

J_tr = \frac{1.0}{tau_tr} (Ca_NSR - Ca_JSR)

Component: C0

C0 = C1 beta + C_Ca0 omega - (C0 4.0 alpha + C0 gamma)

Component: C1

C1 = C0 4.0 alpha + C2 2.0 beta + C_Ca1 \frac{omega}{b} - (C1 beta + C1 3.0 alpha + C1 gamma a)

Component: C2

C2 = C1 3.0 alpha + C3 3.0 beta + C_Ca2 \frac{omega}{b^{2.0}} - (C2 2.0 beta + C2 2.0 alpha + C2 gamma a^{2.0})

Component: C3

C3 = C2 2.0 alpha + C4 4.0 beta + C_Ca3 \frac{omega}{b^{3.0}} - (C3 3.0 beta + C3 alpha + C3 gamma a^{3.0})

Component: C4

C4 = C3 alpha + O g + C_Ca4 \frac{omega}{b^{4.0}} - (C4 4.0 beta + C4 f + C4 gamma a^{4.0})

Component: O

O = C4 f - (O g)

Component: C_Ca0

C_Ca0 = C0 gamma + C_Ca1 beta_- (C_Ca0 4.0 alpha_+ C_Ca0 omega)

Component: C_Ca1

C_Ca1 = C_Ca0 4.0 alpha_+ C_Ca2 2.0 beta_+ C1 gamma a - (C_Ca1 beta_+ C_Ca1 3.0 alpha_+ C_Ca1 \frac{omega}{b})

Component: C_Ca2

C_Ca2 = C_Ca1 3.0 alpha_+ C_Ca3 3.0 beta_+ C2 gamma a^{2.0} - (C_Ca2 2.0 beta_+ C_Ca2 2.0 alpha_+ C_Ca2 \frac{omega}{b^{2.0}})

Component: C_Ca3

C_Ca3 = C_Ca2 2.0 alpha_+ C_Ca4 4.0 beta_+ C3 gamma a^{3.0} - (C_Ca3 3.0 beta_+ C_Ca3 alpha_+ C_Ca3 \frac{omega}{b^{3.0}})

Component: C_Ca4

C_Ca4 = C_Ca3 alpha_+ O_Ca g_+ C4 gamma a^{4.0} - (C_Ca4 4.0 beta_+ C_Ca4 f_+ C_Ca4 \frac{omega}{b^{4.0}})

Component: O_Ca

O_Ca = C_Ca4 f_- (O_Ca g_)

Component: P_C1

P_C1 = P_C2 k21 - (P_C1 k12)

Component: P_C2

P_C2 = P_C1 k12 + P_O3 k32 + P_C5 k52 - (P_C2 k21 + P_C2 k23 + P_C2 k25)

Component: P_O3

P_O3 = P_C2 k23 + P_O4 k43 - (P_O3 k32 + P_O3 k34)

Component: P_O4

P_O4 = P_O3 k34 + P_C5 k54 - (P_O4 k43 + P_O4 k45)

Component: P_C5

P_C5 = P_C2 k25 + P_O4 k45 + P_C6 k65 - (P_C5 k52 + P_C5 k54 + P_C5 k56)

Component: P_C6

P_C6 = P_C6 k65 - (P_C5 k56)

Component: DHPR_transition_probabilities

gamma = Ca_SS 0.1875

alpha = 0.4 ⅇ^{\frac{V + 6.0}{25.0}}

beta = 0.05 ⅇ^{\frac{- (V + 6.0)}{29.0}}

alpha_= alpha a

beta_= \frac{beta}{b}

Component: RyR_transition_probabilities

k12 = \frac{3.0E6 {Ca_SS}^{4.0}}{{2.68}^{4.0} + {Ca_SS}^{4.0}}

k23 = \frac{3.0E7 {Ca_SS}^{4.0}}{{2.68}^{4.0} + {Ca_SS}^{4.0}}

k34 = \frac{3.0E6 {Ca_SS}^{4.0}}{{2.68}^{4.0} + {Ca_SS}^{4.0}}

k54 = \frac{198.0 {Ca_SS}^{4.0}}{{2.68}^{4.0} + {Ca_SS}^{4.0}}

k25 = \frac{3.0E5 {Ca_SS}^{4.0}}{{2.68}^{4.0} + {Ca_SS}^{4.0}}

k56 = \frac{3.0E6 {Ca_SS}^{4.0}}{{2.68}^{4.0} + {Ca_SS}^{4.0}}

Source: Derived from workspace Rice, Winslow, Jafri, 1999 at changeset 8868a51f5a60.

Collaboration: To begin collaborating on this work, please use your git client and issue this command:

Downloads

Views Available

Tools

License: This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Modeling Gain and Gradedness of Ca2+ Release in the Functional Unit of the Cardiac Diadic Space