Fig 1.
Biophysical models for ICCs and SM cells involved in gastric motility.
Schematics showing (A) anatomical divisions of the stomach and the arrangement of various cell types in the stomach wall, (B) membrane ionic currents and intracellular Ca2+-IP3 components included in an interstitial cell of Cajal (ICC) model, and (C) membrane ionic currents in a smooth muscle (SM) cell model. See Table 1 for symbols and details of ionic currents. [Ca]i = Intracellular Ca2+, ER = endoplasmic reticulum, Na+/Ca2+ = Sodium/Calcium exchange pump, SR = Sarcoplasmic reticulum, SS = Submembrane space, (D) Simulated rhythmic membrane potential dynamics in an ICC (left panel) and an SM cell (right panel), respectively.
Fig 2.
Gastric Motility Network model architecture.
The GMN is constituted of a chain of nearest-neighbor coupled interstitial cells of Cajal (ICC) and associated smooth muscle (SM) cells. The ICCs have electrical and second messenger (Ca2+ and IP3) based coupling, while the ICC to SM and SM to SM couplings are only electrical. There is a negative gradient in enteric neural innervation (β) that modulates IP3 production rate along the rostrocaudal ICC chain (ICC index). Key variables and their interconnections impacting the functionality of an ICC are illustrated in the enlarged inset. The bold arrows in the inset show the inflows and outflows of key variables. The dashed arrows indicate dependency of the sink variable on the source variable. The dashed arrows with (+) sign highlight the positive feedback pathways important for intrinsic pacemaking by an ICC. See Table 1 and text for further details.
Table 1.
Ionic currents in the ICC model.
Fig 3.
Slow-wave propagation and entrainment in the GMN.
(A) Spatiotemporal plot of the SM cell membrane potential along the length of the stomach (vertical axis) and time (horizontal axis) of all 42 SM cells of the network. The direction of slow-wave propagation occurs from the rostral end of the network (representing the mid-corpus) to the caudal end (representing the terminal antrum). (B) The membrane potential of 7 equidistant SM cells in the 42-cell network. (C) Total Lag for the first 7 cycles of simulation and the last 7 cycles of simulation. (D) Relative Lag (RL) between the 1st SM cell and ith SM cell in the network for the last 20 cycles, where i = 2, 3, 4,…, 42. (E) Spatiotemporal map of periods of all 42 SM cells in the network for the last 20 cycles. The inset plots for the Relative Lag (Fig 3D) and SM Cell Period (Fig 3E) were generated from the in vitro recordings of SM activity at different locations along the length of the cat stomach [45], where location 1 is the rostral-most recording.
Fig 4.
Enhanced longitudinal entrainment. Synergy of electrical coupling and second messenger exchange preserve longitudinal entrainment along the entire length of the stomach.
(A1, A2 and A3) Structure of the network, when only electrical coupling is present (A1), when only exchange of second messengers is present (A2), and when both electrical coupling and exchange of second messengers are present (A3). (B) The Relative Lags for the three different cases shown in Fig 4A are measured from the last 20 cycles of respective simulations. (C) Spatiotemporal maps of SM Cell Periods in the three different cases respectively.
Fig 5.
Electrical gap junction and second messenger coupling strengths. The inter-ICC coupling strengths impact GMN entrainment, gastric slow-wave velocity and pacemaker frequency.
(A, E) GICC−ICC and PIP3 are altered for the simulations in Fig 5B–5D and Fig 5F–5H, respectively. (B) Spatiotemporal map of membrane potential (B1), Relative Lags (B2), and spatiotemporal map of SM Cell Periods (B3) for the network when GICC−ICC = 0.35 nS (left panels, partially entrained) and 1.4 nS (right panels, entrained). (C) The Total Lag for changes in GICC−ICC is shown for the last 7 cycles of 900-sec simulations for different conductance values (nS) indicated by the color legend. The two distinct classes of responses are enlarged in the right panels (lower ones entrained, upper ones partially entrained). An increase in Total Lag indicates decrease in slow-wave velocity. (F) Spatiotemporal maps of membrane potential (F1), Relative Lags (F2), and spatiotemporal maps of SM Cell Periods (F3) for the network when PIP3 = 4.0 sec-1 (left panels, partially entrained) and 16.0 sec-1 (right panels, entrained). The spatiotemporal membrane potential diagrams are shown for the last 120 seconds of the respective simulation, whereas the Relative Lag and the SM Cell Period diagrams are shown for the last 20 cycles of the respective simulation. (G) The Total Lag for changes in PIP3 is shown for the last 7 cycles of 900-sec simulations for different conductance values (nS) indicated by the color legend. (D, H) For several networks, the mean Total Lag (odd numbered panels) and the SM Cell Period (even numbered panels) of the last 7 cycles for each network with respect to its GICC−ICC and PIP3 can be fit by individual exponential function, respectively. For increasing values of GICC−ICC, an exponential fit (, where a1 = 8.65, β1 = 0.75, a2 = 18.23, β2 = 17.87) has been drawn along the mean value of Total Lag and for increasing values of PIP3, another exponential fit (
, where a1 = 7.44, β1 = 1.70e5, a2 = 32.07, β2 = 9.37) has been drawn along the mean values of Total Lag. Partially entrained networks have not been considered for equation fitting. For SM Cell Period calculation, the last cell (42nd cell) has been considered as the representative cell of the network. An increase in Total Lag indicates decrease in slow-wave velocity while a decrease in SM Cell Period indicates increase in pacemaking frequency.
Fig 6.
Entrainment in GMN is resilient to variability in inter-ICC coupling strengths.
(A,G) The variability in only GICC−ICC (A) and both GICC−ICC and PIP3 (G) (20%, 50%, and 100% variability) are shown around their mean values. (B, H) Total Lag of the network without inter-ICC IP3 exchange for three different variabilities in GICC−ICC (B) and of the network with inter-ICC IP3 exchange for three different variabilities in GICC−ICC and PIP3 (H). The latency to entrainment cannot be inferred from any of the panels in (B), since the networks were only partially entrained. However, the latency to entrainment can be measured from the first two panels in (H), since the Total Lag has attained constant value in these two cases. (C, I) Total Lag is shown for each case for the last 7 cycles using violin plot. The asterisk (*) symbol represents a statistically significant difference between the corresponding quantities. Spatiotemporal diagrams of membrane potential (D, J), Relative Lags, (E, K) and spatiotemporal maps of SM Cell Periods (F, L) for the network are shown for three different variabilities in GICC−ICC for the network without inter-ICC IP3 exchange and in GICC−ICC and PIP3 for the network with inter-ICC IP3 exchange, respectively. The spatiotemporal membrane potential diagrams are shown for the last 120 seconds of the respective simulation, whereas the Relative Lag and the SM Cell Period diagrams are shown for the last 20 cycles of the respective simulation.