Neurons and Neuronal Potentials

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Neural Prosthetic Engineering

Neurons and Neuronal Potentials

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Neurons

• Neurons are the basic building blocks of our nervous system

• There are billions of neurons in our nervous system.

• They are electrically excitable, enabling electric stimulation.

• Once excited, they produce action potentials.

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Number of Neurons

Biological Neuron?

The basic functional unit of the nervous system.

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One estimate (published in 1988) puts the human brain at about 100 billion (10¹¹) neurons and 100 trillion (10¹⁴) synapses. A lower estimate (published in 2009) is 86 billion neurons, of which 16.3 billion are in the cerebral cortex, and 69 billion in the cerebellum (Wikipedia, neurons)

1.Williams RW, Herrup K (1988). "The control of neuron number".

Annual Review of Neuroscience. 11 (1): 423–53.

doi:10.1146/annurev.ne.11.030188.002231. PMID 3284447.

2.Azevedo FA, Carvalho LR, Grinberg LT, et al. (April 2009). "Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain". The Journal of

Comparative Neurology. 513 (5): 532–41. doi:10.1002/cne.21974.

PMID 19226510.

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Structure of neurons

Image from Addiction Science Research and Education Center, the University of Texas

Basic neuron design Connection between neurons

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Structure of neurons and Potentials they produce

• The basic neuron structure: cell body, dentrites and axons

• Synapses are the communication points between cells.

• Axon from output neuron would make synapse(s) on dendrite of input neurons.

• Pre-synapse, Post-synapse, and the post-synaptic potentials (PSP’s)

• EPSP vs. IPSP (excitatory PSP and Inhibitory PSP)

• Action potentials travel on the axons and are like fast digital pulses (All or none)- to be explained in detail.

• PSP are like analog waveforms, slow potentials.

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Synaptic potentials

• Synapse : junction across one nerve cell excites another.

1. Chemically coupled∼0.5msec delay 2. Electrically coupled

• EPSP(Excitatory Post synaptic Potential) causes depolarization (excitation) of the next cell.

• IPSP(Inhibiting~) causes hyperpolarization.

Chemical transmitter Presynaptic

terminal of previous neuron

Synaptic cleft∼150Å

Postsynaptic terminal of next neuronl

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Potentials of the neurons

spike

local field potential

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Membrane Potential of Neuron

• The neuron membrane is mostly lipid layer (insulating) except for the ion channels.

• In equilibrium, there exists an unbalance of ion concentrations across the membrane.

• These ionic imbalance across a permeable membrane causes a potential across it and this is called the

Resting Potential

• The Nernst equation is used to compute the resting potential for one ion.

• At this potential, chemical driving force (by diffusion) equals electrical driving force (by drift) on the ion.

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Equilibrium Potential:

Balancing the ion diffusion by electric field

Two forces of ion driving at resting membrane (resting ion channels)

– Chemical driving force

• Diffusion of ions by concentration gradient

– Electrical driving force

• Drift of ions by electrical potential difference

Electrical driving

force Chemical

driving force Extracellular

side

Cytoplasmic side

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K⁺ K⁺

K⁺

K⁺ K⁺ K⁺ Na⁺

Na⁺

Na⁺ Na⁺ Cl^-

Cl^- Cl^-

Cl^-

A^- A^- A^-

A^-

- - - - - - - - -

+ + + + + + + +

Siegelbaum, S. A., & Hudspeth, A. J. (2000). Principles of neural science (Vol. 4, pp. 1227-1 246). E. R. Kandel, J. H. Schwartz, & T. M. Jessell (Eds.). New York: McGraw-hill.

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Membrane Potential

• Nernst Eq.(1889)

 E : voltage inside membrane with respect to outside (outside is the ground potential)

 U : mobility of cations(+) in the membrane

 V : mobility of anions(-) in the membrane

 So for one cation system, the first term can be regarded as +1.

 For one anion system, the first term is -1.

 RT/F : 25mV@RT (58 mV if log is base 10)

 First applied to physiology in 1902

E =

u - v

u + v F RT

[C]i [C]o ln

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Resting membrane potential

The resting potential of a cell is determined by the relative

proportion of different types of ion channels that are open, together with the value of their equilibrium potentials

K+

Na+

Electrical driving force Chemical driving force

Siegelbaum, S. A., & Hudspeth, A. J. (2000). Principles of neural science (Vol. 4, pp. 1227-1 11

246). E. R. Kandel, J. H. Schwartz, & T. M. Jessell (Eds.). New York: McGraw-hill.

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For Membrane that is permeable to Three Ions

• If the plasma membrane were permeable only to any single ion of K⁺, Na⁺, and Cl^-, the potential difference across the membrane could be calculated by the Nernst equation.

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Goldman-Hodgkin-Katz Eq.

Cytoplasm(mM) Extracellular Fluid(mM)

Permeability ratio at resting state

Permeability ratio at active state

K⁺ 400 20 1 1

Na⁺ 50 440 0.04 20

Cl^- 52 560 0.45 0.45

 P : permeability

 Hodgkin & Katz have found

P_k : P_Na : P_Cl = 1: 0.04 : 0.45 at resting X500

= 1: 20 : 0.45 at active

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Action Potential of Neuron

• An excited (Stimulated) neuron (Above threshold) will experience change of ion permeability in short time duration.

• At resting state, the membrane is permeable mostly to the K+ and Cl- ions.

• But at excitation, the the permeability to Na+ ions increases abruptly. This causes the depolarization of the membrane (becoming more positive inside).

• Closing of Na+ gates and opening of K+ follow (hyperpolarization)

• Active pump will restore the initial state

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Action potentials (APs)

15 http://anatomytutorials.weebly.com/action-potentials.html

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Hodgkin-Huxley Model of Neuron

• Through elaborate experiments (voltage clamp experiments on Squid Axons), they were able to

explain the behavior of neurons using the voltage and time dependence of permeability (conductance).

• They received Nobel prize of Physiology or Medicine in 1963 for this work.

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Neuron membrane model

• Hodgkin Huxley model

− In an active membrane, some conductances vary with respect to time and the membrane potential.

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METANEURON

• http://www.metaneuron.org/

• ‘Free’ Interactive neural signal simulation software

• To investigate the quantitative behavior of neuron in response to different membrane properties and ion concentrations

• Current pulse stimulation with an intracellular electrode

• Based on the Hodgkin-Huxley equations

• Six lessons: resting membrane potential, membrane time constant, membrane length constant, axon action potential, axon voltage

clamp and synaptic potential

• Newman M. and Newman E., “Metal Neuron: A free neuron simulation program for teaching cellular neurophysiology”, The journal of undergraduate neuroscience education (June), Spring 2013, 12(1), A11-17

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Intracellular Recording:

Action potentials (APs)

19 http://anatomytutorials.weebly.com/action-potentials.html Electrolyte

Solution Glass Pipette Metal Wire

Electrode

cell

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Extracellular Neural Recording:

Compound Action potentials (CAPs) and Local Field Potentials (LFPs)

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• If your metal electrode is outside several neurons, the electrode will record action potentials from multiple number of neurons. This is the CAPs. In this case, the amplitude of the potentials are attenuated significantly. (Extracellular Recording)

•Together with the CAPs, the post synaptic potentials are recorded in a summated form. This is the LFP. This potential is a lot slower.

0.6 1.1

0.4

0.2

Amplitude (mV) 0

Time (s)

CAP (spikes)

LFP

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Cortical Signals Recorded from Brain using Microelectrode

Parietal Reach Region (PRR)

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Hwang, Eun Jung, and Richard A. Andersen. "Effects of visual stimulation on LFPs, spikes, and LFP-spike relations in PRR." Journal of neurophysiology105.4 (2011): 1850-1860.

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Reference

-Hodgkin, Alan L., and Andrew F. Huxley. "A quantitative description of membrane current and its application to conduction and excitation in nerve."The Journal of

physiology 117.4 (1952): 500-544.

-Newman M. and Newman E., “Metal Neuron: A free Neuron simulation program for teaching cellular

neurophysiology”, The journal of undergraduate

neuroscience education (June), Spring 2013, 12(1), A11-17

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