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Model Mathematics

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Component: environment

pressure = 350.0 max {0.0, stretch - 1.0} voltage_out = \frac{current_in}{1.0} 1.0 transmembranevoltage = (voltage_out - 5) P_Open

Component: stimulus_protocol

stretch = \{\begin{matrix} stim_amplitude if time \geq stim_offset \land (time - stim_offset) mod stim_period ≦ stim_duration \\ 1.0 otherwise \end{matrix}

Component: stimulus_protocol

current = \{\begin{matrix} stim_amplitude if time \geq stim_offset \land time < stim_t_end \land (time - stim_offset) mod stim_period ≦ stim_duration \land (time - stim_offset) mod (N_period_total stim_period) < N_period_applied stim_period \\ 0 otherwise \end{matrix}

Component: kinetics

r2 = \frac{r1 r3 r5}{r4 r6} ce2 = ce1 + ce3 + ce5 - ce4 - ce6 cm2 = - cm4

p_O_I1 = r1 ⅇ^{\frac{ce1 gradmu}{140}}

p_I1_O = r2 ⅇ^{\frac{ce2 gradmu}{140} + \frac{cm2 pressure}{70}}

p_I1_C = r3 ⅇ^{\frac{ce3 gradmu}{140}}

p_C_I1 = r4 ⅇ^{\frac{ce4 gradmu}{140} + \frac{cm4 pressure}{70}}

p_C_O = r5 ⅇ^{\frac{ce5 gradmu}{140}}

p_O_C = r6 ⅇ^{\frac{ce6 gradmu}{140}}

p_I2_O = r7 ⅇ^{\frac{\frac{ce7 gradmu}{140} pressure}{70}}

p_O_I2 = r8 ⅇ^{\frac{ce8 gradmu}{140}} \frac{d}{d time} (P_Open) = (- (p_O_I1 + p_O_I2 + p_O_C)) P_Open + p_C_O P_Closed + p_I1_O P_I1 + p_I2_O P_I2 \frac{d}{d time} (P_Closed) = (- (p_C_I1 + p_C_O)) P_Closed + p_O_C P_Open + p_I1_C P_I1 \frac{d}{d time} (P_I1) = (- (p_I1_O + p_I1_C)) P_I1 + p_C_I1 P_Closed + p_O_I1 P_Open \frac{d}{d time} (P_I2) = (- p_I2_O) P_I2 + p_O_I2 P_Open

Component: parameters

r2 = \frac{r1 r3 r5}{r4 r6} ce2 = ce1 + ce3 + ce5 - ce4 - ce6 cm2 = - cm4

Component: equilibrium

Source: Derived from workspace A Simple Voltage-Modulated Markov Chain Model for the Piezo1 Ion Channel to Investigate Electromechanical Pacing at changeset 8465ce0a385c.

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ogiermann_2022_piezo1_rect_pacing.cellml