Computational Modeling of the Cardiovascular and Neuronal System

Transcription

1 BIOEN 6900 Computational Modeling of the Cardiovascular and Neuronal System Electrophysiological Modeling of Cells Overview Recapitulation Membranes and Ion Channels Cardiac Myocytes Group Work Impact of Ion Channel Mutations on Cellular Electrophysiology Neurons Homework Summary Computational Modeling of the Cardiovascular and Neuronal System - Page 2

2 Electrophysiological Models of Cells: Motivation Description of Insights in Prediction of } electrophysiological phenomena Applications Diagnostics Electro- and magneto-cardiography Electro- and magneto-myography Electro- and magneto-neurography... Therapy Parameterization and optimization of electrical nerve stimulators, defibrillators, and pace maker electrode material, shape and position signal Development, evaluation and approval of pharmaceuticals Education and teaching in cardiology, bioengineering, and pharmacology... Computational Modeling of the Cardiovascular and Neuronal System - Page 3 Microscopic Cellular Anatomy Myocyte of ventricular myocardium cylinder-shaped length: !m diameter: ca. 8-15!m (Hoyt et al. 89) The basic shape of myocytes varies significantly for different locations, e.g.: cylinder- spindle- brick and rod-shaped Computational Modeling of the Cardiovascular and Neuronal System - Page 4

3 Electrophysiology of Cardiac Myocytes: Basics Extracellular space Membrane Intracellular space [Na] [Na] [K] [Ca] [K] [Ca] Depolarization: After reaching of threshold voltage: short term increase of g Na + Time and voltage dependent, ion selective ion channels Plateau phase: Fast increase followed by slow decrease of g Ca 2+ Fast decrease followed by slow increase of g K + Resting voltage Action voltage Upstroke Fast sodium channel Repolarization: Return of g Na +, g K + and g Ca 2+ to resting values Partly, g K + increase leads to hyperpolarization Slow calcium channel Slow potassium channel Computational Modeling of the Cardiovascular and Neuronal System - Page 5 Development of Electrophysiological Cell Models Cell 37 Measuring system Measurement results Space-, voltage- and patch-clamp Voltage sensitive dyes Channel blockers, e.g. TTX for Na channels Action voltage, membrane currents, conductivities, ion concentration, membrane capacitance length, volumes Mathematical model Commonly, system of ODEs e.g. of Hodgkin-Huxley and Markov type Computational Modeling of the Cardiovascular and Neuronal System - Page 6

4 Models of Cellular Electrophysiology 1952 today Hodgkin-Huxley axon membrane giant squid Noble Purkinje fiber - Beeler-Reuter ventricular myocyte mammal DiFrancesco-Noble Purkinje fiber mammal Earm-Hilgemann-Noble atrial myocyte rabbit Luo-Rudy ventricular myocyte guinea pig Demir, Clark, Murphey, Giles sinus node cell mammal Noble, Varghese, Kohl, Noble ventricular myocyte guinea pig Priebe, Beuckelmann ventricular myocyte human Winslow, Rice, Jafri, Marban, O Rourke ventricular myocyte canine Seemann, Sachse, Weiss, Dössel ventricular myocyte human Models describe cells by set of ordinary differential equations Equations are assigned to a whole cell and/or a small number of its compartments Computational Modeling of the Cardiovascular and Neuronal System - Page 7 Transmembrane Voltages Measured at Different Positions (from Malmivuo and Plonsey) Computational Modeling of the Cardiovascular and Neuronal System - Page 8

5 Beeler-Reuter Model 1977 Electrophysiological model of mammalian ventricular myocyte membrane Parameterization by measurement with clamp techniques V m I NaI I Ca I K I NaO [Ca 2+ ] i Outside Membrane Inside I Na : Inward current of sodium I S : Inward current (primarily calcium) I K1 : Outward current of potassium I X1 : Outward current (primarily potassium) Time and voltage }dependent } } Time Time independent and voltage dependent Computational Modeling of the Cardiovascular and Neuronal System - Page 9 Beeler-Reuter: Equations for Currents ( ) "1 # i X1 = X1 0.8 e0.04 V m +77 & % e 0.04( V m $ + 35) ( ' i Na = g Na m 3 h j + g NaC 4e 0.04( V m # + 85) "1 i K1 = 0.35 e 0.08(V m + 53) + e 0.04 V m + 53) ( V m + 23) & % 1" e "0.04( V m $ + 23) ( ' i s = g s d f V m " E s ( )( V m " E Na ) ( ) E s = "82.3 " ln [ Ca 2+ ] i E Na = 50 mv i X1,i Na,i K1,i s : Stromdichten Current densities [µa / [µa/cm 2 ] 2 ] V m : Transmembranspannung Transmembrane voltage [mv] E s,e Na : Nernst i s and -sodium Spannung Nernst für an voltages i s beteiligte [mv] Ionen bzw. Natrium [mv] g s : Leitfähigkeit Conductivity für [ms/cm an i s beteiligte 2 ] Ionen [1/ cm 2 / k)] g Na : Leitfähigkeit Conductivity für of open Natrium bei channels vollständig [ms/cm offenen 2 ] Natriumkanälen [1/ cm 2 / k)] g NaC : Leitfähigkeit Conductivity für of Natrium closed Na bei channels geschlossenen [ms/cm Natriumkanälen 2 ] [1 / cm 2 / k)] d,m,x1: Aktivierungsparameter Activation state (described von Ionenkanälen by ODE) als Funktion von t und V m f,h, j: Inaktivierungsparameter Inactivation state (described als Funktion by ODE) von t und V m [ Ca 2+ ] i : Konzentration von Calcium [mmol / cm 3 ] Concentration of intracellular calcium [mmol/cm 3 ] Computational Modeling of the Cardiovascular and Neuronal System - Page 10

6 Beeler-Reuter: Equations for Currents and Concentrations dv m dt = " 1 ( i C K1 + i X1 + i Na + i Ca + i external ) m d[ Ca 2+ ] i = "10 "7 i dt s (10 "7 " [ Ca 2+ ] i ) C m = 1 µf : Membrankapazität Membrane capacitance pro Fläche cm 2 per area Results of simulations for stimulus frequency of 1 Hz Computational Modeling of the Cardiovascular and Neuronal System - Page 11 Luo-Rudy Model Electrophysiological model of ventricular myocyte membrane from guinea pig Parameterization by measurement with clamp techniques Phase I: 1991 Phase II: 1994 Motivation Improved measurement techniques (e.g. single ion channel measurements) Deficits of Beeler-Reuter, e.g. Fixed extracellular ion concentrations Neglect of calcium transport and buffering in sarcoplasmic reticulum Neglect of cell geometry Computational Modeling of the Cardiovascular and Neuronal System - Page 12

7 Luo-Rudy Model Extracellular space Pump I Ca,b I Ca I NaCa I p(ca) I Up I leak I rel Sarcoplasmic reticulum Geometry cylinder-shaped length: 100 µm radius: 11 µm I tr Myoplasm I ns(ca) I Kp I K1 I K I NaK I Na I Na,b Computational Modeling of the Cardiovascular and Neuronal System - Page 13 Cellular Electrophysiology: Normal and Failing Simulation of normal and failing human ventricular myocytes with modified Priebe-Beuckelmann model Pathology: Hypertrophy Significant changes of density of proteins relevant for calcium transport: sarcolemmal NaCa-exchanger! sarcoplasmic Ca-pump " (Sachse, Seemann, Chaisaowong, and Weiss. JCE, 2003) Calcium concentration [µm] Transmembrane voltage [mv] t [ms] Computational Modeling of the Cardiovascular and Neuronal System - Page 14

8 Noble-Kohl-Varghese-Noble Model 1998 Mathematical description of ionic currents and concentrations, transmembrane voltage, and conductivities of guinea-pig ventricular myocytes extracellular space pump I Ca,stretch I bca I Ca,L,Ca I Ca,L,Ca,ds I NaCa I NaCa,ds I NaK Geometry cylinder-shaped length: 74 µm radius: 12 µm Myoplasma I Up Sarcoplasmic reticulum I rel Troponin Mechano-electrical feedback by stretch activated ion channels I tr I trop Neural influence by transmitter activated ion channels etc. I Na I p,na I b,na I Ca,L,Na I Na,stretch I K,stretch I K I K1 I Ca,L,K I b,k I K,ACh Computational Modeling of the Cardiovascular and Neuronal System - Page 15 Noble-Kohl-Varghese-Noble Model 1998 Calcium concentration [mm] Results of simulations for stimulus frequency of 1 Hz Computational Modeling of the Cardiovascular and Neuronal System - Page 16

9 Prediction of Mechano-Electrical Feedback Reduction of action potential duration (APD) by strain Increase of resting voltage by strain SL: sarcomere length Computational Modeling of the Cardiovascular and Neuronal System - Page 17 Prediction: Triggering of Action Potential by Strain Sarcomere length [µm] t=1 s: Electrical stimulus t=2 s: Strain for 5 ms Triggering of action potential for SL>2.7 µm Computational Modeling of the Cardiovascular and Neuronal System - Page 18

10 Iyer-Mazhari-Winslow Model 2004 Pump/exchanger Compartment Ca-binding protein I Na I Nab I NaCa I pca I Kv1.4,Na I NaK I Ca I up Subspace Cadmodulin I cmdn Troponin I trop I tr Sarcoplasmic reticulum Calsequestrin I rel I csqn Myoplasma I Kr I Ks I Kv4.3 I Kv1.4,K I K1 I Ca,K I Ca,b Extracellular space Computational Modeling of the Cardiovascular and Neuronal System - Page 19 Reconstructed Voltage and Currents Transmembrane voltage V m V m [mv] Hz Fast sodium current I Na I Na [pa/pf] L-type calcium current I Ca I Ca [pa/pf] Slow inward rectifying potassium current I Ks I ks [pa/pf] t [ms] Computational Modeling of the Cardiovascular and Neuronal System - Page 20

11 Electrophysiology of Mammalian Sinoatrial Node Cell Opening of Na channels Depolarization starting at resting voltage (approx. -60 mv) leads to upstroke Autorhythmicity with a frequency of ~3 Hz Computational Modeling of the Cardiovascular and Neuronal System - Page 21 Group Work Described models represent the cellular compartments with isochronous properties (0D) Under which conditions is this description appropriate and when will it fail? Computational Modeling of the Cardiovascular and Neuronal System - Page 22

12 Timothy Syndrome Computational Modeling of the Cardiovascular and Neuronal System - Page 23 Modeling of Calcium Channel Mutation Channel Modeling Differences of steady state inactivation between wild type (WT) and mutated channels Integration in Myocyte Model Prediction of course of transmembrane voltage in myocyte Changes dependent on % of mutated channels Significant increase of action potential duration (and intracellular calcium concentrations) Numerical optimization Computational Modeling of the Cardiovascular and Neuronal System - Page 24

13 Calcium Channel Defect: Timothy Syndrome Significant reduction of voltagedependent inactivation of L-type calcium channels (Ca v 1.2) Characterization with electrophysiological studies in oocytes with normal (WT) and G406R Ca v 1.2 Prolonged QT time (LQT) in patient ECGs Ion channel Prediction of cellular behavior with electrophysiological model of WT and G406R Ca v 1.2 Ventricular myocyte (Splawski, Timothy, Decher, Kumar, Sachse, Pierson, Beggs, Sanguinetti, and Keating, PNAS, 2005) Computational Modeling of the Cardiovascular and Neuronal System - Page 25 t [s] Timothy Syndrome: Increased Risk Of Arrhythmia Protocol: Stimulus frequency of 3 Hz, pause Transmembranspannung [mv] Calciumkonzentration [nm] Spontaneous opening of sarcoplasmic release channel leads to delayed afterdepolarization! Computational Modeling of the Cardiovascular and Neuronal System - Page 26

14 Cellular Electrophysiology: Calcium Regulation Transversal Tubule Cell Membrane Ca Na Sarcoplasmic Reticulum Ca Troponin Mitochondrion Ca Na NCX: Sodium-calcium exchanger ATP: Ionic pump driven by ATP-hydrolysis RyR: Calcium channel (ryanodine receptor) PLB: Phospholamban (Bers, Nature Insight Review Articles, 2002, modified) Computational Modeling of the Cardiovascular and Neuronal System - Page 27 Genetic Disease: Mutation of KCNQ1 Slow Inward Rectifying Potassium Current I Ks KCNQ1 KCNE1 KCNQ1 Mutations S140G Serine Glycine found in family with hereditary atrial fibrillation (Chen et al., Science, 2003) * V141M Valine Methionine found in new born child with atrial fibrillation and short QT syndrome de novo Location of Mutation S4: Voltage sensing subunit (Kong et al., Cardiovasc. Res., 2005) Computational Modeling of the Cardiovascular and Neuronal System - Page 28

15 Patient ECGs: Atrial Fibrillation I II AVF V1 HRA HBE I, II, AVF, V1: Body surface leads HRA: High right atrium HBE: His-Bundle ECG Computational Modeling of the Cardiovascular and Neuronal System - Page 29 Mutation of Slow Inward Rectifying K-Current I Ks WT KCNQ1 + KCNE1 50 % WT / 50 % mutation KCNQ1 with gain of function mutation + KCNE1 (S140G, V141M) Computational Modeling of the Cardiovascular and Neuronal System - Page 30

16 Prediction of Ventricular and Atrial Myocyte Behavior Human ventricular myocyte at 1 Hz Modified Iyer-Mazhari-Winslow model APD " - short QT syndrome high risk for sudden cardiac death (Hong, Piper, Diaz-Valdecantos, Brugada, Burashnikov, Santos de Soto, Grueso-Montero, Brugada, Sachse, Sanguinetti, and Brugada, Cardiovasc. Res., 2005) Human atrial myocyte at 1, 2, and 3 Hz WT Modified Courtemanche-Ramirez-Nattel model APD "" - facilitates atrial fibrillation (Seemann, Weiß, Sachse, and Dössel, Proc. CinC, 2004) WT/ S140G Computational Modeling of the Cardiovascular and Neuronal System - Page 31 Prediction of Sinus Node Behavior WT/V141M cells exhibit no autorhythmicity and a constant resting voltage of -37 mv Computational Modeling of the Cardiovascular and Neuronal System - Page 32

17 Modeling of Cardiac Myocytes and Neurons Geometry Spatial extend of neurons can be significantly larger than extend of myocytes Geometrical complexity of neurons can be significantly larger than complexity of myocytes Assumption of isochronous properties of membrane typically used for single cardiac myocytes. Commonly, 0D models. 1-3D models typically used for single neurons Membrane properties and transmembrane proteins Similar approaches applied for membrane modeling of myocytes and neurons Similar channels found, but significant differences of densities and properties Adjustment by re-parameterization of conductivities and rate coefficients Computational Modeling of the Cardiovascular and Neuronal System - Page 33 Model of GT1 Neuron F. V. Goor, A. P. LeBeau, L. Z. Krsmanovic, A. S., K. J. Catt and S. S. Stojikovic, Biophysical Journal, 2000 Computational Modeling of the Cardiovascular and Neuronal System - Page 34

18 Summary Recapitulation Membranes and Ion Channels Cardiac Myocytes Group Work Impact of Ion Channel Mutations on Cellular Electrophysiology Neurons Homework Computational Modeling of the Cardiovascular and Neuronal System - Page 35