neurons! (so you don’t have to watch me draw a lot of bad pictures!) image from...
TRANSCRIPT
NEURONS!
(So you don’t have to watch me draw a lot of bad pictures!)
Image from saturn.med.nyu.edu/research/mn/ganlab/
OVERVIEW
• Neural Modeling• Neural network modeling• Learning in neural networks• Modeling ischemic stroke• Self-organizing maps
OVERVIEW CONTINUED
• Examples• A computational tool for the reduction of nonlinear ODE
systems possessing multiple scales (Kopell)• The dynamic structure underlying subthreshold oscillations
and the onset of spikes in medial entorhinal cortex stellate cells (Kopell)
• Control of repetitive firing in squid axon membrane as a model for a neuron oscillator (Rinzel)
• Analysis of Competition-Based Spreading Activation in Connectionist Models (Wang)
• Feature Discovery and Classification of Doppler Umbilical Artery Blood Flow Velocity Waveforms (Baykal)
• A Connectionist Approach to Vertex Covering Problems (Peng)
OVERVIEW CONTINUED
• Mathematical Techniques• Differential equations• Dynamical Systems• Computer Science• Graph Theory and Networks• Analysis
OUR FOCUS
• Dynamics of the action potential (at a single point)• Systems of differential equations: HODGKIN-HUXLEY
EQUATIONS• Simulation of systems of differential equations (finite
difference schemes)• Dynamical systems and bifurcations (more generally, some
study of excitable systems)
A.L. HODGKIN and A. F. HUXLEY
The Nobel Prize in Physiology or Medicine 1963 (with Eccles): "for their discoveries concerning the ionic mechanisms involved in excitation and inhibition in the peripheral and central portions of the nerve cell membrane"
More about Hodgkin and Huxley
• Performed lab experiments on a squid giant axon—very large, up to 1 mm in diameter (normally a micron)
• Developed voltage clamp experimental technique• Developed differential equation model (1 PDE, 3
ODES) for an action potential based on the experiments
5 Publications!• Huxley AL and Hodgkin AF.
– Measurement of Current-Voltage Relations in the Membrane of the Giant Axon of Loligo. Journal of Physiology 1: 424-448, 1952(a).
– Currents Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo. Journal of Physiology 1:449-472, 1952 (b).
– The Components of Membrane Conductance in the Giant Axon of Loligo. Journal of Physiology 1: 473-496, 1952 (c).
– The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo. Journal of Physiology 1: 497-506,1952 (d).
– A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. Journal of Physiology 1: 500-544, 1952 (e).
3 weeks on a hand calculator to compute a single action potential!
Your first homework will involve repeating that calculation—just like they did it!
3 weeks on a hand calculator to compute a single action potential!
Your first homework will involve repeating that calculation—just like they did it!
Just kidding! It is a “repeat” in a sense—but no three week calculations for us!
Many neurons from www.pdn.cam.ac.uk/.../anatomya/opa-neuro.html
Developing cortical neuronfrom www.anatomy.wisc.edu/faculty_kalil.html
Spiny hippocampal neuron from www.ucihs.uci.edu/anatomy/stewardpix2b.html
Sample nerve cells from www.mind.ilstu.edu/.../neuro/neuron_1.html (The Mind Project)
BASIC NEURON TYPES
1. Bipolar (interneuron); 2. Unipolar (sensory neuron); 3. Multipolar (motor neuron); 4. Pyramidal Cell (excitatory cortical cell). From www.thethinkingbusiness.co.uk/brainn1.jpg
1.2.
3.
4.
Cell Body (processing center)Inside is called the SOMA
Dendrites (receptors)Take in excitatory & inhibitory stimulifrom other neurons or sensory stimuli.
Image from www.essex.ac.uk/.../sld001.htm
Cell Body
Dendrites
Dendrites
Axon
AxonSynapses
Axon Hillock
Image frompespmc1.vub.ac.be/POS/Turchap1.html
THE AXON
• Very narrow (microscopic, on the order of a single micron)
• Very long• Human sciatic nerve: nearly 1 meter in length
• Responsible for action potential propagation!
ACTION POTENTIAL
An action potential is a wave of electrical discharge that travels along the
membrane of a cell.
Image from www.learner.org/.../archive/images/1968_d.html
Image from wikipedia—under action potential
RC Circuit Model Outside of membrane
Inside of Membrane
Resistors: 2 terminal components that resist an electrical current by producing a voltage drop—the axon analogues are the ion channels. The arrow represents a variable resistance (for us, w.r.t. time)
Capacitors: Devices that store energy in the electric field created between a pair of conductors on which electrical charges of opposite charge are stored—the axon analogue is created by the membrane.
R-K+
R-Na+
R-LK+
Na+
L
Image from wikipedia under action potential
C