Pilhwa Lee, Ranjan Pradhan, Brian E. Carlson, Daniel A. Beard
1
Pilhwa Lee, Ranjan Pradhan, Brian E. Carlson, Daniel A. Beard Department of Molecular and Integrative Physiology, University of Michigan-Ann Arbor Modeling Electrical Signal Propagation in Microvascular Networks Abstract Electrical Propagation in Endothelial Tube Future Work References A bidomain formulation was developed to simulate propagation of electrical signals in endothelial cells of microvascular networks. The method is used to stimulate spatiotemporal signal propagation and attenuation in arterioles and capillaries, and analyze data from experiments on isolated vessels. A single-vessel (capillary) segment model is parameterized based on conducted response data of isolated endothelial cells tube from mouse skeletal muscle feed arteries on changes in endothelial cell membrane voltages in response graded electrical stimulation. Simulation of the resulting model facilitates determination of appropriate boundary conditions to apply along the length in simulating signal propagation in whole capillary network. The model fits well to the observed spatial attenuation of the depolarization of endothelial cells, with activated/inactivated calcium-activated potassium channels of the membrane, and predicts the electrical length constant dependency on acetylcholine. Simulations of realistic network topologies are then conducted to determine the effective time and space scales for metabolic signaling in the microvascular networks, especially with the vasodilator acetylcholine. This framework is a foundation for further study of spatiotemporal aspects of the electrical conduction in various microvascular networks. Mathematical Formulation H.S. Silva, A. Kapela, and N.M. Tsokias, A mathematical model of plasma membrane electrophysiology and calcium dynamics in vascular endothelial cells, Am. J. Physiol. Cell Physiol., 293,C277-C293, 2007 E.J. Behringer and S.S. Segal, Tuning Electrical Conduction Along Endothelial Tubes of Resistance Arteries Through Ca2+-Activated K+ channels, Circ. Res., 110, 1311-1321, 2012 Electric current in endothelial cells Change of intracellular charge in endothelial layer Cellular dynamics of chemical/ionic species Boundary condition at each segment terminal node Interface condition at each junctional node Results / Conclusion Figure 1 EC cell and tube models. A. The cellular electrophysiology is modified based on the model of Silva et al. 2007, with the addition of SK Ca /IK Ca dependency on NS309. B. The cell-cell electrical interaction is through non-selective gap junctions. In the mono-domain formulation, the electrical conductivity in EC layer is denoted . The EC membrane area per unit volume is . Figure 2 EC tube parameterization and validation. The mono-domain parameters ( , ) are parameterized from fitting experimental data in Behringer and Segal 2012. A. V m 2 at s=500 m and s=1500 m with current injection at Site 1 (±1, 2, 3nA) B. V m 2 at s=500 m with control (no NS309) and 1 μM NS309. C. V m 2 at s=50, 500, 1000, 1500 m with control (no NS309) and 1 μM NS309. Figure 3 Time course of V m 2 with NS309 and ACh. A. Time course of V m at s=500 m (V m 2) with 1 μM NS309 from t=100 sec on. Direct pharmaceutical activator NS309 directly activates IK Ca /SK Ca and hyperpolarizes membrane potential to about -60mV and attenuates response from current injection. EC tube model is simulated with current injection at Site 1 (±1, 2, 3nA) before and during NS309. B. Corresponding experiment, Behringer and Segal 2012, Figure 2A. C. Time course of V m at s=500 m (V m 2) with 3 μM ACh from t=100 sec on. ACh activates indirectly IK Ca /SK Ca via G-protein coupled receptors and hyperpolarizes membrane potential to about -60mV and attenuates electrical conduction. Endothelial tube model is simulated with current injection at Site 1 (±1, Figure 4 V m and calcium distribution with and without ACh at t=0.0, 0.05, 0.1, 21.5 sec. A - 3 nA current is injected at s=1000 m from t=0 on. Endothelial layer is most hyperpolarized at the position of current injection. The intracellular calcium is elevated with slower response than V m . A. Without ACh, from resting potential about -20mV, the steady current injection hyperpolarizes EC tube to around -50mV within 0.2 sec. B. Cytosolic calcium is elevated from baseline level of 70nM to ~130nM in 20 sec. C. With 3 μM ACh superfusion, the EC tube is hyperpolarized to -50mV, and the membrane is more hyperpolarized to about -62 mV within 2.0 sec from the steady current injection. D. At t=0.0 sec, the calcium is already elevated from ACh activated IP 3 induced calcium release, and the calcium level is lowered with calcium uptake and IP 3 degradation. Figure 5 Electrical length constant vs. [ACh]. A. The steady state IP 3 generation rate 6.6 x 10 -5 mM/s corresponds to [ACh] = 3 μM in a linear relationship. The electrical length constant is obtained from at s=50, 500, 1000, 1500 m. In the black curve, the acetylcholine is assumed to be uniformly superfused to the whole EC tube. The blue curve represents the electrical propagation with local acetylcholine infusion from s=100 to 500 m along the tube. The red curve shows the suppressed attenuation of electrical propagation with SK/IKCa channel blockers. The current 3nA is injected at s=250 m from t=32 sec to t=34 sec. B. Spatial distribution of V m with locally infused ACh at t=1, 20, 34 sec. Figure 6 Propagation of hyperpolarization in a capillary model network. In the whole simulation, 6 μM acetylcholine is locally infused in a local zone of one bifurcation node as indicated in panel A. The current -5nA is injected at a position indicated in panel B from t=20 sec to t=28 sec. Panel A and B show the spatial distribution of Vm at t=20 sec and t=28 sec; the propagated hyperpolarization from locally infused acetylcholine, and further hyperpolarization from injected current to the upstream, respectively. Panel C and D show the spatial distribution of [Ca 2+ ] at t=20 sec and t=28 sec; the local elevation of calcium level from the locally infused acetylcholine, and the calcium wave propagation to the upstream with the additionally injected current. Vasodilation response to hypoxia/ischemia Presentation number : 678.12 Contact: [email protected]
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Modeling Electrical Signal Propagation in Microvascular Networks. Pilhwa Lee, Ranjan Pradhan, Brian E. Carlson, Daniel A. Beard Department of Molecular and Integrative Physiology, University of Michigan-Ann Arbor. Presentation number : 678.12. Contact: [email protected]. Abstract. - PowerPoint PPT Presentation
Transcript of Pilhwa Lee, Ranjan Pradhan, Brian E. Carlson, Daniel A. Beard
Pilhwa Lee, Ranjan Pradhan, Brian E. Carlson, Daniel A. BeardDepartment of Molecular and Integrative Physiology, University of Michigan-Ann Arbor
Modeling Electrical Signal Propagation in Microvascular Networks
Abstract
Electrical Propagation in Endothelial Tube
Future Work
References
A bidomain formulation was developed to simulate propagation of electrical signals in endothelial cells of microvascular networks. The method is used to stimulate spatiotemporal signal propagation and attenuation in arterioles and capillaries, and analyze data from experiments on isolated vessels. A single-vessel (capillary) segment model is parameterized based on conducted response data of isolated endothelial cells tube from mouse skeletal muscle feed arteries on changes in endothelial cell membrane voltages in response graded electrical stimulation. Simulation of the resulting model facilitates determination of appropriate boundary conditions to apply along the length in simulating signal propagation in whole capillary network. The model fits well to the observed spatial attenuation of the depolarization of endothelial cells, with activated/inactivated calcium-activated potassium channels of the membrane, and predicts the electrical length constant dependency on acetylcholine. Simulations of realistic network topologies are then conducted to determine the effective time and space scales for metabolic signaling in the microvascular networks, especially with the vasodilator acetylcholine. This framework is a foundation for further study of spatiotemporal aspects of the electrical conduction in various microvascular networks.
Mathematical Formulation
H.S. Silva, A. Kapela, and N.M. Tsokias, A mathematical model of plasma membrane electrophysiology and calcium dynamics in vascular endothelial cells, Am. J. Physiol. Cell Physiol., 293,C277-C293, 2007
E.J. Behringer and S.S. Segal, Tuning Electrical Conduction Along Endothelial Tubes of Resistance Arteries Through Ca2+-Activated K+ channels, Circ. Res., 110, 1311-1321, 2012
Electric current in endothelial cells
Change of intracellular charge in endothelial layer
Cellular dynamics of chemical/ionic species
Boundary condition at each segment terminal node
Interface condition at each junctional node
Results / Conclusion
Figure 1 EC cell and tube models. A. The cellular electrophysiology is modified based on the model of Silva et al. 2007, with the addition of SKCa/IKCa dependency on NS309. B. The cell-cell electrical interaction is through non-selective gap junctions. In the mono-domain formulation, the electrical conductivity in EC layer is denoted . The EC membrane area per unit volume is .
Figure 2 EC tube parameterization and validation. The mono-domain parameters ( , ) are parameterized from fitting experimental data in Behringer and Segal 2012. A. Vm2 at s=500 m and s=1500 m with current injection at Site 1 (±1, 2, 3nA) B. Vm2 at s=500 m with control (no NS309) and 1 μM NS309. C. Vm2 at s=50, 500, 1000, 1500 m with control (no NS309) and 1 μM NS309.
Figure 3 Time course of Vm2 with NS309 and ACh. A. Time course of Vm at s=500 m (Vm2) with 1 μM NS309 from t=100 sec on. Direct pharmaceutical activator NS309 directly activates IKCa/SKCa and hyperpolarizes membrane potential to about -60mV and attenuates response from current injection. EC tube model is simulated with current injection at Site 1 (±1, 2, 3nA) before and during NS309. B. Corresponding experiment, Behringer and Segal 2012, Figure 2A. C. Time course of Vm at s=500 m (Vm2) with 3 μM ACh from t=100 sec on. ACh activates indirectly IKCa/SKCa via G-protein coupled receptors and hyperpolarizes membrane potential to about -60mV and attenuates electrical conduction. Endothelial tube model is simulated with current injection at Site 1 (±1, 2, 3nA) before and during ACh infusion. D. The corresponding experiment, Behringer and Segal 2012, Figure 7A.
Figure 4 Vm and calcium distribution with and without ACh at t=0.0, 0.05, 0.1, 21.5 sec. A -3 nA current is injected at s=1000 m from t=0 on. Endothelial layer is most hyperpolarized at the position of current injection. The intracellular calcium is elevated with slower response than Vm. A. Without ACh, from resting potential about -20mV, the steady current injection hyperpolarizes EC tube to around -50mV within 0.2 sec. B. Cytosolic calcium is elevated from baseline level of 70nM to ~130nM in 20 sec. C. With 3 μM ACh superfusion, the EC tube is hyperpolarized to -50mV, and the membrane is more hyperpolarized to about -62 mV within 2.0 sec from the steady current injection. D. At t=0.0 sec, the calcium is already elevated from ACh activated IP3 induced calcium release, and the calcium level is lowered with calcium uptake and IP3 degradation.
Figure 5 Electrical length constant vs. [ACh]. A. The steady state IP3 generation rate 6.6 x 10-5 mM/s corresponds to [ACh] = 3 μM in a linear relationship. The electrical length constant is obtained from at s=50, 500, 1000, 1500 m. In the black curve, the acetylcholine is assumed to be uniformly superfused to the whole EC tube. The blue curve represents the electrical propagation with local acetylcholine infusion from s=100 to 500 m along the tube. The red curve shows the suppressed attenuation of electrical propagation with SK/IKCa channel blockers. The current 3nA is injected at s=250 m from t=32 sec to t=34 sec. B. Spatial distribution of Vm with locally infused ACh at t=1, 20, 34 sec.
Figure 6 Propagation of hyperpolarization in a capillary model network. In the whole simulation, 6 μM acetylcholine is locally infused in a local zone of one bifurcation node as indicated in panel A. The current -5nA is injected at a position indicated in panel B from t=20 sec to t=28 sec. Panel A and B show the spatial distribution of Vm at t=20 sec and t=28 sec; the propagated hyperpolarization from locally infused acetylcholine, and further hyperpolarization from injected current to the upstream, respectively. Panel C and D show the spatial distribution of [Ca2+] at t=20 sec and t=28 sec; the local elevation of calcium level from the locally infused acetylcholine, and the calcium wave propagation to the upstream with the additionally injected current.
Vasodilation response to hypoxia/ischemia
Presentation number : 678.12 Contact: [email protected]
