BIOELECTRIC PHENOMENA

Transcription

1 Chapter 11 BIOELECTRIC PHENOMENA

2 11.3 NEURONS Membrane Potentials Resting Potential by separation of charge due to the selective permeability of the membrane to ions From C v= Q, where v=60mv and C=1μF/cm 2, the number of charges( C) equals approximately 10 8 /m 2. This charges are located within 1 μm distance of the membrane. Figure 11.1 Diagram of a typical neuron. Figure 11.2 Diagrams illustrating separation of charges across a cell membrane.

3 11.3 NEURONS Membrane Potentials Graded ddresponse and Action Potentials Neuron can change membrane potential of another neuron to which it is connected by releasing its neurotransmitter Graded response The change in membrane potential due to transfer of chemical to electrical energy from one neuron to another Varies with amount of neurotransmitter received Action potential Net result of activation of the nerve cell Large depolarizing signal of up to 100 mv that travels along axon without loss and lasts 1 5 ms When action potential ti reaches end of axon at presynaptic terminal, change in potential causes release of a packet of neurotransmitter

4 11.3 NEURONS Resting Potential, Ionic Concentrations, and Channels Resting potential is maintained through Selectively ecti e permeable eab e membrane e Active ion pump Neuron cell membrane ~ 10 nm thick Lipid bilayer (i.e., two plates separated by an insulator) Capacitive properties Extracellular fluid primarily Na + and Cl Intracellular fluid primarily K + and A (A ) large organic anions primarily amino acids and proteins Ions can only pass through membrane at ion channels

5 11.3 NEURONS Resting Potential, Ionic Concentrations, and Channels Ion channels aeio are ion specific eifi Passive responsible for resting potential Active responsible for graded response and action potential Structure (Figure not to scale) Cell membrane is 20x size of ions 10 x the size of channel Spacing between channels 10x membrane thickness Passive always open and ion specific Exist for Cl, K +, Na +, Ca 2+ Active opened or closed in response to an external electrical or chemical stimulation Also ion specific

6 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Basic Laws d[ [ I ] J(diffusion) = D dx Fick s Law J=flow of ions due to diffusion D=diffusivity constant [m 2 /s] [I] = ion concentration dx = membrane thickness Ohm s Law J=flow of ions due to drift in electric field, E μ = mobility in m 2 /sv Z=ionic valence, e.g., Z for Na+ = 1; Z for Cl = 1 [I] ion concentration V=voltage across membrane KT μ dv/dx = E = electrical field D = Einstein Relationship q Relationship between drift of particles in electric field under osmotic pressure (i.e., between diffusivity and mobility) K=Boltzmann s constant T=absolute temp q=magnitude of electrical charge = C J (drift) = μ Z [ I ] dv dx

7 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Resting Potential of a Membrane Permeable to One Ion Electric potential [K + + ] o Concentration [K + ] i the Nernst equation, named after a German physical chemist Walter Nernst, and E k = v i v o is known as the Nernst potential for K +, which can be applied other permeable ions of Na +, Cl.

8 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Donnan Equilibrium Membrane potential is due to presence of all ions and influenced by the concentration and permeability of each ion. For a 2 ion example, at equilibrium, membrane is permeable to K + and Cl but not large cation R + Donnan Equilibrium

9 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Goldman Equation Actual resting potential ld doesn t correspond to Nernst potential either for Na + or K + because Vm is affected by all permeable ions Goldman equation relates Vm and all permeable ions with following two conditions; Membrane potential or electric field must be constant Assume cell membrane of width dx=δ δ

10 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Goldman Equation V m + + kt P [ ] [ ] [ ] K K o + PNa Na o + PCl Cl i = ln + + q PK[ K ] i + PNa[ Na ] i + PCl[ Cl ] o

11 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Ion Pumps To maintain a constant resting potential, flow of charge into cell must be balanced by flow of charge out of cell. For Na +, concentration and electric gradient drives Na + into cell at rest At Vm, K + force due to diffusion is greater than due to drift and results in efflux of K + out of cell Changes in concentration gradient of K + and Na + is prevented by the Na K pump. Transports steady stream of Na + out of cell and K + into cell Active pump consumes metabolic energy

12 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Ion Pumps In general, when cell membrane is at rest, active and passive ion flows are balanced and a permanent potential exists across a membrane if 1. Membrane is impermeable to some ions 2. An active pump is present Concentrations of Na + and K + are determined by active pump, but other ions are determined by Vm using Nernst equation

13 11.4 BASIC BIOPHYSICS TOOLS AND RELATIONSHIPS Ion Pumps Example Problem 11.3 Consider membrane with an active K+ pump, passive channels for K + and Cl and nonequilibrium initial concentration of [KCl] on both sides of the membrane and find an expression for flux from active K + pump From J cl =0, From [Cl ]=[K + ] [K + ] o [K + ] i Concentration [K + ] i [Cl - ] o Electric potential [Cl - ] i [Cl - ] i Without pump, concentration would be equal inside and outside of membrane

14 11.5 EQUIVALENT CIRCUIT MODEL FOR THE CELL MEMBRANE Electromotive and Resistive Properties Electromotive Force Properties : The Nernst potential for each ion is the electrical potential difference across the ion channel and modeled as a battery. Resistive Properties : Each channel has resistance R ( or conductance G = 1/R ) to the movement of electrical charge through it. Conductance is related to membrane permeability. Na K Pump Current generators

15 11.5 EQUIVALENT CIRCUIT MODEL FOR THE CELL MEMBRANE Capacitance Capacitive Properties Electrical conductors (cytoplasm and extracellular fluid) separated by an insulating material (lipid bilayer of the membrane) 1μF/cm 2 C m

16 11.5 EQUIVALENT CIRCUIT MODEL FOR THE CELL MEMBRANE Example Problem Capacitive Properties since

17 11.5 EQUIVALENT CIRCUIT MODEL FOR THE CELL MEMBRANE Capacitive Properties Vm due to a series of 15 ma current pulses of 6ms duration with the onsets occurring at 0, 2, 4, 6, and 8 ms. Since the pulses occur within 5τ of the previous pulses, the effect of each on Vm is additive, allowing the membrane to depolarize to approximately 45mV. If the pulses were spaced at intervals greater than 5τ, then Vm would be a series of pulse responses as previously illustrated.

18 11.5 EQUIVALENT CIRCUIT MODEL FOR THE CELL MEMBRANE Change in Membrane Potential with Distance Equivalent circuit i of series of membrane sections; connected with axial resistance, Ra resistance to the flow of current in the cytoplasm from one membrane section to the next Change in the membrane potential Vm, Vm, due to the current injection with relatively long time duration; Determined by current through the resistance only The resistance seen in n sections from the injection site = R th + n R a Decreases exponentially with distance;

19 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Action Potentials and the Voltage Clamp Experiment Hodgkin and Huxley published 5 papers in 1952 that t described d a series of experiments and empirical model of an action potential in a squid giant axon; Once Vm reaches threshold, h time and voltage dependent d t conductance changes occur in the active N a+ and K + gates that drive Vm toward E Na, then back to E K, and finally to the resting potential. Hodgkin and Huxley used two experimental techniques; Space Clamp : to produce a constant Vm over a large region of the membrane by inserting a silver wire inside the axon and thus eliminating Ra. Voltage Clamp : to allow the control of Vm by eliminating the effect of further depolarization due to the influx I Na and efflux of I K as membrane permeability changed. Figure Illustration of the conductance gate for sodium.

20 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Action Potentials and the Voltage Clamp Experiment Voltage Clamp First select a clamp voltage and then records the resultant First select a clamp voltage and then records the resultant membrane current, Im, that is necessary to keep Vm at the clamp voltage

21 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Action Potentials and the Voltage Clamp Experiment I Na + I K = I m initial capacitive current constant leakage current Let I Na =0 by substituting a large impermeable cation for N a+ in the external solution, then measure I K and calculate I Na

22 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Action Potentials and the Voltage Clamp Experiment Reconstructing of the Action Potential

23 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Equations Describing G Na and G K h l d b d k d l The empirical equation used by Hodgkin and Huxley to model G Na and G K ;

24 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Equation for the Dependence of the Membrane Potential A model of the cell membrane stimulated via an external stimulus, Im; R l E l Figure Circuit model of an unmyelinated section of squid giant axon. The channels for K + and Na + are represented using the variable voltage time conductances given in Equations and The passive gates for Na +, K +, and Cl are given by a leakage channel with resistance, R l, and Nernst potential, E l. The Na K pump is not drawn for ease in analysis since it does not contribute any current to the rest of the circuit.

25 11.6 HODGKIN-HUXLEY MODEL OF THE ACTION POTENTIAL Equation for the Dependence of the Membrane Potential SIMULINK I program

26 11.7 MODEL OF THE WHOLE NEURON A model for entire neuron including the dendrite, soma, axon, and presynaptic terminal; Figure A segment of the axon with active and passive compartments.

27 11.7 MODEL OF THE WHOLE NEURON Figure SIMULINK model for two adjacent neurons.