1. Neural Modeling - Fall 13861 Single Neuron vs Neural population Strategy to discover the Brain Functionality Biomedical engineering Group School of Electrical Engineering Sharif University of Technology

2. Neural Modeling - Fall 13862 The Single Neuron What kind of physical devices are neurons? Neurons are electro-chemical devices. Well-characterized in terms of their electrical properties.

3. Neural Modeling - Fall 13863 Synapse

4. Neural Modeling - Fall 13864

5. 5 STRUCTURE They have three distinct parts: (1) Cell body, (2) Dendrites, and (3) the Axon The particular type of neuron that stimulates muscle tissue is called a motor neuron. Dendrites receive impulses and conduct them toward the cell body.

6. Neural Modeling - Fall 13866 Myelinated Axons The axon is a single long, thin extension that sends impulses to another neuron. They vary in length and are surrounded by a many-layered lipid and protein covering called the myelin sheath, produced by the schwann cells.

7. Neural Modeling - Fall 13867 Resting Potential In a resting neuron (one that is not conducting an impulse), there is a difference in electrical charges on the outside and inside of the plasma membrane. The outside has a positive charge and the inside has a negative charge.

8. Neural Modeling - Fall 13868 Contribution of Active Transport There are different numbers of potassium ions (K + ) and sodium ions (Na + ) on either side of the membrane. Even when a nerve cell is not conducting an impulse, for each ATP molecule that’s hydrolysed, it is actively transporting 3 molecules Na + out of the cell and 2 molecules of K + into the cell, at the same time by means of the sodium-potassium pump.

9. Neural Modeling - Fall 13869 Contribution of facilitated diffusion The sodium-potassium pump creates a concentration and electrical gradient for Na + and K +, which means that K + tends to diffuse (‘leak’) out of the cell and Na + tends to diffuse in. BUT, the membrane is much more permeable to K +, so K + diffuses out along its concentration gradient faster. Conversely, the electric field causes both ions tend to come in.

10. Neural Modeling - Fall 138610 RESULTS IN: a net positive charge outside & a net negative charge inside. Such a membrane is POLARISED

11. Neural Modeling - Fall 138611 Action Potential When the cell membranes are stimulated, there is a change in the permeability of the membrane to sodium ions (Na + ). The membrane becomes more permeable to Na + and K +, therefore sodium ions diffuse into the cell down a concentration gradient. The entry of Na + disturbs the resting potential and causes the inside of the cell to become more positive relative to the outside.

12. Neural Modeling - Fall 138612 All-or-None Principle Throughout depolarisation, the Na+ continues to rush inside until the action potential reaches its peak and the sodium gates close. If the depolarisation is not great enough to reach threshold, then an action potential and hence an impulse are not produced. This is called the All-or-None Principle. Neuron is a physical device that converts an ‘input’ voltage change on their dendrites into an ‘output’ voltage spike train that travels down their axon.

13. Neural Modeling - Fall 138613 Speed of Nerve Impulses Impulses travel very rapidly myelin sheath greatly increases the velocity In unmyelinated fibres, the entire axon membrane is exposed and impulse conduction is slower. A low-precision electrical device

14. Neural Modeling - Fall 138614 Equivalent Model for Dendrites and Axons Rdx dx Cdx

15. Neural Modeling - Fall 138615 Equivalent Model for an excited Neuron Rdx dx Cdx v 0 (t) The passive membrane time constant in the soma is on the order of about 10 ms.

16. Neural Modeling - Fall 138616 Transmission of Action Potential/ Dendrite potential

17. Neural Modeling - Fall 138617 Neuron: Transistor Electrical devices Highly nonlinear Signal/information processors Short memories: Long Memories Output voltage spikes: proportional Heterogeneous : Homogeneous Biological : Manufactured

18. Neural Modeling - Fall 138618 Beyond the single neuron Population of Neurons Mainly ‘population-temporal’ representation Ch2,3 ch4 ch5

19. Neural Modeling - Fall 138619 Neural population Benefits Varying degrees of detail. Extract the information that was nonlinearly encoded using a linear decoder Allows many of the tools of linear signals and systems theory Ability to better observation

20. Neural Modeling - Fall 138620 NEURAL TRANSFORMATION Neural representation paves the way for a useful understanding of neural transformation Can be characterized using linear decoding.