A biophysically based mathematical model of unitary potential activity in interstitial cells of Cajal

Abstract

Unitary potential (UP) depolarizations are the basic intracellular events responsible for pacemaker activity in interstitial cells of Cajal (ICCs), and are generated at intracellular sites termed "pacemaker units". In this study, we present a mathematical model of the transmembrane ion flows and intracellular Ca(2+) dynamics from a single ICC pacemaker unit acting at near-resting membrane potential. This model quantitatively formalizes the framework of a novel ICC pacemaking mechanism that has recently been proposed. Model simulations produce spontaneously rhythmic UP depolarizations with an amplitude of approximately 3 mV at a frequency of 0.05 Hz. The model predicts that the main inward currents, carried by a Ca(2+)-inhibited nonselective cation conductance, are activated by depletion of sub-plasma-membrane [Ca(2+)] caused by sarcoendoplasmic reticulum calcium ATPase Ca(2+) sequestration. Furthermore, pacemaker activity predicted by our model persists under simulated voltage clamp and is independent of [IP(3)] oscillations. The model presented here provides a basis to quantitatively analyze UP depolarizations and the biophysical mechanisms underlying their production.

FIGURE 1

Schematic diagram of the ICC pacemaker unit showing all the components involved in the UP modeling framework. Displayed are the ionic conductances and their respective interactions with the intracellular organelles and cytoplasmic subspaces. The four compartmental volumes comprising the pacemaker unit are 1), the endoplasmic reticulum (ER); 2), the mitochondria; 3), the cytoplasmic subspace 1; and 4), the cytoplasmic subspace 2. The four plasma membrane currents that regulate cellular electrophysiology are 1), the inward Ca²⁺ current (I_Ca); 2), the nonselective cation conductance (I_NSCC); 3), the plasma membrane Ca²⁺-ATPase (I_PM); and 4), the outward Na⁺ current (I_Na). The five Ca²⁺ fluxes responsible for controlling intracellular Ca²⁺ movement are 1), the mitochondrial Ca²⁺ uniporter (J_MCU); 2), the mitochondrial Na⁺/Ca²⁺ exchanger (J_NCX); 3), sarcoendoplasmic reticulum Ca²⁺-ATPase (J_SERCA); 4), the IP₃R Ca²⁺ flux (J_IPR); and 5), the intercytoplasmic subspace Ca²⁺ flux (J_S1S2). All of the components included in this model are introduced in the Model framework section. The equations describing the ionic conductances and governing the model-state variables are located in Appendix A, and all model parameter and initial-state variable values are given in Table 2.

FIGURE 2

High-powered ICC electron micrograph photos showing the ultrastructural features. Note the abundance of mitochondria (M) and endoplasmic reticulum (arrowheads) in close proximity to each other and the cell membrane. Figure reprinted with permission from the Annual Review of Physiology, Volume 68 © 2006 by Annual Reviews (www.annualreviews.org).

FIGURE 3

UP membrane depolarizations produced from model simulations. (A) A single UP oscillation. (B) UPs over multiple pacemaker cycles, illustrating the spontaneous rhythmicity of model pacemaker activity.

FIGURE 4

Intracellular ionic concentrations and IP₃R open probability tracked over multiple pacemaker cycles. The plots displayed are (A) S₁ [Ca²⁺], C_S1, (B) S₂ [Ca²⁺], C_S2, (C) IP₃R open probability, P_IPR, (D) ER [Ca²⁺], C_ER, (E) mitochondrial [Ca²⁺], C_MT, and (F) S₁ [Na⁺], N_S1. Note that logarithmic values are plotted for the C_S2 (B) and P_IPR (C) traces.

FIGURE 5

Plots showing the temporal relationship between the model SVs during the ER Ca²⁺ release phase of the UP oscillatory cycle. (A) The simultaneous increase in C_S2 and P_IPR leads to (B) initiation of ER Ca²⁺ causing a sudden reduction in C_ER, which results in (C) a significant increase in C_S2. (D) The significant increase in C_S2 activates the MCU, causing mitochondrial Ca²⁺ accumulation. (E) Simultaneously, the SERCA pumps activate to replenish ER Ca²⁺ stores, hence causing a reduction in C_S1. The depletion in C_S1 activates I_NSCC, resulting in (F) a significant influx of Na⁺ into the pacemaker unit. Note that the SV on the left vertical axis is represented by the solid curve, and the SV on the right vertical axis by the dashed curve. Also note that logarithmic values are plotted for the C_S2 (B) and P_IPR (C) traces.

FIGURE 6

Schematic diagram of the pacemaking mechanism cycle as illustrated by the model response. (Step 1) Initial Ca²⁺ entry from the V_m-dependent inward Ca²⁺ current, I_Ca, which diffuses from S₁ to S₂. (Step 2) Sufficient Ca²⁺ entry into S₂ raises the IP₃R open probability to threshold and ER Ca²⁺ release occurs. (Step 3) The subsequent increase in C_S2 activates the MCU, causing rapid mitochondrial Ca²⁺ accumulation. (Step 4) ER Ca²⁺ sequestration via the SERCA pumps to replenish ER Ca²⁺ stores. (Step 5) Activation of I_NSCC, caused by C_S1 depletion from SERCA activation. The resulting Ca²⁺ and Na⁺ influx is responsible for the UP depolarization phase. (Step 6) Repolarization, caused by I_Na activation from increased N_S1 levels, and C_MT restitution, from J_NCX, resets the pacemaker unit allowing the cycle to begin again.

FIGURE 7

Pacemaker unit cytosolic [Ca²⁺] oscillations around the ER Ca²⁺ release phase of the pacemaker cycle (A) and over multiple pacemaker cycles (B). Note that there is an increase in cytosolic [Ca²⁺] over each cycle. This is despite the fact that depletion of C_S1 is required for the activation of pacemaker currents (I_NSCC) and C_S1 makes up the bulk of cytosolic [Ca²⁺].

FIGURE 8

Intracellular ionic concentrations produced under simulated voltage-clamp conditions for (A) C_S1, (B) C_S2, (C) C_ER, (D) C_MT, and (E) N_S1. Simulations were performed for V_m = −80, −70, and −60 mV. The simulations show that depolarization causes a decrease in pacemaking frequency and a decrease in the magnitude of the intracellular ionic concentrations (the effect is opposite for hyperpolarization). Note that logarithmic values are plotted for the C_S2 trace (B).

FIGURE 9

Numerical simulations showing the short-term (A–C) and long-term (D–F) effects of mitochondrial inhibition on pacemaker activity. The bar above the traces in A–C denotes MCU inhibition. UP depolarizations, which are present before MCU inhibition, are abolished after MCU block (A). This appears to be due to a build-up in C_S2 (B) which prevents the IP₃R from returning to a susceptible state (C). Long-term simulation, after pacemaker activity cessation, shows membrane hyperpolarization (D) caused by a transient increase in C_S1 (E). The increase in C_S1 is due to the emptying of mitochondrial Ca²⁺ stores over time (F). Note that logarithmic values are plotted for the C_S2 (B) and P_IPR (C) traces, and that the y axis on C_S1 trace (E) is truncated at 0.121 μM.

FIGURE 10

Trace of the aggregate plasma membrane current, I_ion, required to reproduce a UP depolarization using the UP representation of Edwards and Hirst (12) (A = 0.434 s, B = 0.077 s, 3HC_m = 1). Note the two distinct phases of transmembrane ionic flux that comprise UP depolarizations: net inward ion flux and net outward ion flux.