Unformatted text preview:

BE6003 Physiol 6003 Cellular Electrophysiology and Biophysics Modeling of Ion Channels I CVRTI Frank B Sachse University of Utah Overview Motivation Introduction Hodgkin Huxley Modeling Background Approach Examples Group work Group work Markovian Modeling Background Approach Examples CVRTI Group work Cellular Electrophysiology and Biophysics Page 2 Motivation Mathematical ion channel models allow for of reconstruction quantitative description prediction Biophysics Electrophysiology Pharmacology electrical behavior molecular structure and dynamics of single channels and channel populations Ion channel models are frequently integrated into membrane cell and tissue models to study complex interaction in biological systems Systems biology Further applications of models are in research developing testing hypotheses development drug discovery design and safety CVRTI Cellular Electrophysiology and Biophysics Page 3 General Approach of Modeling Design or selection of initial model or set of models Parameterization Evaluation Fit to measurements or models computational efficiency Application CVRTI Cellular Electrophysiology and Biophysics Page 4 Introduction Types of Ion Channel Models Markov Models Currents through a single channel and population of channels as well as gating currents Based on states and transitions Hodgkin Huxley Models Current through a population of channels and single channel as well as gating currents Based on gating variables and rate coefficients Molecular Models Structure and dynamics Molecular interactions drug binding ion movement CVRTI Systems of ordinary differential equations ODEs Partial differential equations integration of motion in particle systems Cellular Electrophysiology and Biophysics Page 5 Hodgkin Huxley Ion Channel Model with Single Gating Variable df 1 f f dt V Rate coefficient V Rate coefficient Iion G ion max f Vm Eion f f f CVRTI f f 1 f f f 1st order ODE m m f G ion max Gating variable Maximal conductivity for ion Eion Nernst voltage Vm Transmembrane voltage Channel Environment Membrane Environment Cellular Electrophysiology and Biophysics Page 6 Molecular Structure of Phospholipid Bilayers Phospholipid hydrophilic Hydrogen not represented 6 nm hydrophobic Nitrogen Oxygen Phosphor Carbon Structure data from Heller et al J Phys Chem 1993 CVRTI Cellular Electrophysiology and Biophysics Page 7 Phospholipid Bilayers Plasma membrane Membrane of organelle Selective permeability Transmembrane proteins responsible for transport Ion Channels Pumps Exchangers Lodish et al Molecular Cell Biology Fig 7 1 2004 CVRTI Cellular Electrophysiology and Biophysics Page 8 Modeling of Membrane Nernst Equation k i Region i i e k e jD k jE k Membrane permeable for ion type k homogeneous planar infinite Region e k i Concentration of k in region i k e Concentration of k in region e i Potential in region i e Potential in region e jD k Ionic current by diffusion jE k Ionic current by electrical forces CVRTI Cellular Electrophysiology and Biophysics Page 9 Modeling of Membrane Nernst Potential In Equilibrium jE k jD k 0 Vm k i e R T k i ln z k F k e k Ion type Vm k Nernst potential V R Gas constant J mol K T Absolute temperature K z k Valence F Faraday s constant C mol k i intracellular concentration of ion type k M k e extracellular concentration of ion type k M CVRTI Cellular Electrophysiology and Biophysics Page 10 Modeling of Membrane Nernst Equation Example Nernst equation explains measured transmembrane voltage of animal and plant cells For potassium monovalent cation at temperatures of 37 C Vm K K i 310K R K i ln 61mV log 1 F K o K e For typical intra and extracellular concentrations K i 150MmM K e 5 5MmM Vm K 88mV Commonly several types of ions are contributing to transmembrane voltage CVRTI Cellular Electrophysiology and Biophysics Page 11 Modeling of Membrane Resistor Capacitor Circuit Cm Q Vm i C m membrance capacity F Region i Q electrical charge As Vm i e voltage over membrane V d d Q I Vm m dt dt C m C m Cm Rm e Membrane Region e I m Current through membrane A Rm Vm Im R m Resistance of membrane CVRTI Cellular Electrophysiology and Biophysics Page 12 Hodgkin and Huxley Measurements Measurement and mathematical modeling of electrophysiological properties of cell membrane published 1952 Nobel prize 1963 Giant axon from squid with 0 5 mm diameter Techniques Space clamp Voltage clamp Simplifications Extracellular space Salt solution Na Semi permeable membrane Intracellular space Axoplasm CVRTI K L Na K L Sodium ions Potassium ions Other ions primarily chlorine Cellular Electrophysiology and Biophysics Page 13 Group Work What are the important biophysical findings of Hodgkin and Huxley List 5 findings CVRTI Cellular Electrophysiology and Biophysics Page 14 Hodgkin Huxley Clamp Techniques Space Clamp Electrophysiological properties are independent of x Salt solution Membrane Axoplasm Internal electrode Ii d Vm dt I i Injected current A Im Ii Cm External electrode x I m Current through membrane A C m Membrane capacitor F Vm Membrane voltage V Voltage Clamp Voltage Vm is kept constant by injection of current Ii Im Ii Measurement of I V relationship Reduction of capacitive effects CVRTI Ii Salt solution Membrane Axoplasm Internal electrode Vm External electrode Cellular Electrophysiology and Biophysics Page 15 Hodgkin Huxley Voltage Clamping Clamped voltage CVRTI Measured current Cellular Electrophysiology and Biophysics Page 16 Hodgkin Huxley Measurement Protocols Protocols Measurement of I V relationship Substitution of ions in intra and extracellular space for separation of K and Na currents Analysis Based on extraction of measurement parameters in particular steady state currents time constants CVRTI Cellular Electrophysiology and Biophysics Page 17 Hodgkin Huxley Model Equivalent Circuit Diagram GNa GK GL Intracellular space i Im IC Vm i e Membrane conductivity of Na K and other ions S cm2 Cm INa IK IL GNa GK GL VNa Vk VL M e m b r a n INa IK IL Currents of Na K and other ions mA cm2 VNa VK VL Nernst voltages of Na K and other ions mV Cm Im Vm e Membrane capacitor F cm2 current mA cm2 and voltage mV Extracellular space Im C m CVRTI dVm Vm VNa GNa Vm VK GK Vm VL GL dt Cellular Electrophysiology and Biophysics Page 18 Hodgkin Huxley Model Constants Voltages are related to resting voltage Vr Conductivity and capacitance are related to membrane area Relative Na voltage Vr VNa 115 mV Relative K voltage Vr Vk 12 mV Relative voltage of other ions Vr VL 10 6 mV


View Full Document

U of U BIOEN 6003 - Modeling of Ion Channels I

Download Modeling of Ion Channels I
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Modeling of Ion Channels I and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Modeling of Ion Channels I 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?