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Ephys & Behaviour

TENSS 2025, Day 1, version 2

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  • https://tenss.github.io/TENSS_Electronics/

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Learning goals (1)

By Dhp1080, svg adaptation by Actam - Image:Neuron.svg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=4293768

How is the extracellular potential affected by neuronal activity?

How can we record these potential changes?

How do we get single neurons from these recordings?

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What we want to understand

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Electronics

FROM RESISTOR TO SPIKE

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Brains are boring

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Brains are boring until you give them a body

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Learning goals (2)

How can we measure behaviour and perform closed loop experiments?

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Building a recording setup

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Building a recording setup

https://www.kiddiwinks.co.za/news/2016/09/7-benefits-of-lego-play-for-kids-and-adults/

Recording

software

Sensor

Actuator

OpenEphys board

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Figure in the Paper

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Figure in the Paper Reality

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Real life is messy

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Fearless creativity, duck tape and a bit of solder can go a long way

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Let’s try to make something that works somehow

FROM RESISTOR TO SPIKE

BEHAVIOUR

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Learning goals (3)

How to synchronise the data streams we acquired?

How do we go from data to figure (a.k.a minimal data analysis)?

https://www.cleanpng.com/

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What will we analyse?

  • EEG?
  • LFP?
  • Head-fixed recording?
  • Freely moving recording?
  • Behaviour tracking

FROM RESISTOR TO SPIKE

ANALYSIS

BEHAVIOUR

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What is electricity?

The bunch of stuff that happens when a

kind of thing moves around

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Charge, q

  • Conserved quantity, one of only 4! (energy, angular momentum, linear momentum and charge)

The net charge of an isolated system is constant

  • Fundamental property

Proton: +e

Electron: -e

  • Positive and negative
  • Units: Coulombs (C) = 6.241509×1018 e

​

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Coulomb's inverse-square law

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Gravity vs. electric forces

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Voltage: potential difference

+

​

​

  • Electric field: Force that would be felt by a test charge at each point

+

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Voltage: potential difference

​

  • Voltage (V) = Potential difference between two points

​

​

+

​

​

  • Electric field: Force that would be felt by a test charge at each point

q

q

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Hydraulic analogy: voltage

Voltage is a difference in electrical potential.

It is measured between two distinct points.

Analog to water pressure in a pipe.

A single point has no measurable voltage.

gemini

High potential

Low potential

Intermediate potential

High voltage

Low voltage

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Current: charge in motion

Current (I): how much charge (Q) moves through a given area in time t

​

​

​

​

Units: Amperes (Amps) = Coulomb / sec

What factors will influence I?

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Hydraulic analogy: current

Hydraulic

  • Rate of water flowing through a pipe

Electrical

  • Rate of charged particles through a conductor
  • e.g. Electrons in metal
  • e.g Ions in solution

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Current: charge in motion

Current (I): how much charge (Q) moves through a given area in time t

What factors will influence I?

​

  1. Voltage/E-field: stronger means more current�
  2. Conduction medium: how good is it at allowing charge to move?

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Current paths

  • Large Voltage difference
  • Strong electrical force
  • Metal: good conductor
  • How much charge flows?���

​

~50kV

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Current paths

  • Large Voltage difference
  • Strong electrical force
  • Metal: good conductor
  • How much charge flows?��
  • None (ideally)
  • Large resistance (R)
    • Air
    • Ceramic insulators

~50kV

R

R

R

R

R

R

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Hydraulic analogy: resistance

Hydraulic

Constriction or blockage in pipe

​

​

​

Electrical

Impurities and thermal motion that disturb the flow of charged particles

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Resistance

  • Charge particles are accelerated in an electric field but slam into stuff on along their path�
  • This jiggles the stuff they slam into (heat)�
  • In some materials motion is impeded so much, that ~no charge will flow (I = 0)�
  • Units: Ohms (Ω) = Volts/Amps

​

​

​

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Resistivity

  • Resistivity (ρ): material property describing how strongly it resists current
  • Block of material with resistivity ρ, length l, and face area A
  • Perfect conductors on both faces
  • What is its total resistance?

​

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Resistivity

  • Resistivity (ρ): material property describing how strongly it resists current
  • Block of material with resistivity ρ, length l, and face area A
  • Perfect conductors on both faces
  • What is its total resistance?

​

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Resistivity

Silicon

Copper

ρ = 2.3×103 Ω⋅m

ρ = 1.7×10-8 Ω⋅m

11 orders of magnitude

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Hydraulic analogy: resistivity

Hydraulic

Density of mesh in pipe

​

​

​

Electrical

(1 / mobility) of charge carriers

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Wire

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Wire

  • In an ideal circuit a wire is connection with no resistance
  • It’s is symbolised by a line
  • Two points linked by a wire are “shorted” or have a “short circuit”

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Resistor

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Current depends on voltage and resistance

  • Current is proportional to voltage
  • Current is inversely proportional to resistance
  • Ohm’s Law

​

​

​

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Conservation of charge

  • Although charge moves, the total charge must be conserved!
  • There is only one topology that supports this: a loop.
  • All electrical circuits are loops

​

​

​

​

​

​

​

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Voltage�(10 V)

Resistor�(10 Ohms)

I

I

What happens it you replace the resistor with a wire?

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Circuit

  • Where is the loop?

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Ground

  • Where is the loop?
  • Ground and power symbols are useful for complicated schematics.
  • Used to indicate a common conductor and voltage.

Cu

I

I

Cu

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Hydraulic analogy: ground

Hydraulic

  • What is 0 potential energy?
  • “Sea level”: arbitrary potential energy level

Electrical

  • What is 0 voltage
  • “Ground”: arbitrary potential

+

0

-

+

0

-

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Charge is conserved (“Kirchhoff's Current Law”)

  • Conservation of charge
  • “Kirchhoff's current law”

​

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Energy is conserved (“Kirchhoff's Voltage Law”)

  • Conservation of energy
  • “Kirchhoff's voltage law”

​

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Voltage Divider

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Potentiometer

Vout

“Wiper”

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Voltage divider

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Voltage divider

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Voltage divider

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Voltage divider

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Voltage divider

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The recording arc

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What is an electrode?

  • Insulated wire with exposed tip
  • Bring it within the E-field / potential field produced by cell

​

​

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What is an electrode?

  • Insulated wire with exposed tip
  • Rs = Series resistance (CSF, electrode interface)
  • Rsh = Shunt resistance. Ideally large, but not in practice.

​

​

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What is an electrode?

  • What is Vout?

​

​

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Electric fields �and Ohm’s Law

Jon Newman

�TENSS 2024

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ECG - Electrocardiogram

  • Electrical activity generated by cardiac tissue
  • Surface electrode
  • V(t)

​

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EMG - Electromyogram

  • Electrical activity generated by �skeletal muscle (motor unit APs)
  • Surface electrodes
  • V(t)

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EEG - Electroencephalogram

  • Electrical activity generated by the brain
  • Summed activity of lots of neurons
  • Surface electrodes
  • V(t)

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LFP - Local field potential

  • Electrical activity generated by a neural circuit
  • Summed activity of lots of neurons
  • Intracranial electrodes
  • V(t)

​

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Spike or “Unit” Recordings

  • Electrical activity generated by individual cells
  • Small intracranial electrodes
    • Silicon probes
    • Tetrodes
    • Sharps
  • V(t)

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Electrical recordings

  • Sensing an “electric field”
  • Output is voltage, why?
  • Electrodes
    • Why 2 or more?
    • Different shapes
    • Different materials
  • Voltage as function of time
    • Amplified, why?
    • Filtered, why?
    • Digitized, why/how?

​

V

time

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Electric Fields

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Charge, q

  • Conserved quantity, one of only 4! (energy, angular momentum, linear momentum and charge)

The net charge of an isolated system is constant

  • Fundamental property

Proton: +e

Electron: -e

  • Positive and negative
  • Units: Coulombs (C) = 6.241509×1018 e

​

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Coulomb's inverse-square law

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Gravity vs. electric forces

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Electric force

Object with charge

Test charge, q0

Calculate force using inverse square law and plot arrow

Divide by q0 to get field value (why?)

​

+q

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Electric field

Object with charge

Test charge, q0

Repeat for every position around the charge

  • Arrows show the direction and magnitude of the field

​

+q

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Electric potential

Object with charge

Test charge, q0

What is the work done on the particle by the field when it comes from infinitely far away?

​

​

+q

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Electric potential field

Object with charge

Test charge, q0

Repeat for all positions in space

+q

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Voltage

Object with charge

Test charge, q0

How much work is done on test charge when it moves between positions in space�

​

Path does not matter (conservative force, no integral required!)

Unit: Volts (V) = Joules / Coulomb

+q

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Voltage

Object with charge

Test charge, q0

How much work is done on test charge when it moves between positions in space�

​

Which has a larger voltage difference?

+q

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Voltage

Object with charge

Test charge, q0

How much work is done on test charge when it moves between positions in space�

​

Which has a larger voltage difference?

+q

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Voltage

Object with charge

Test charge, q0

How much work is done on test charge when it moves between positions in space�

​

Which has a larger voltage difference?

+q

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Aside: Electron-Volt, eV

eV: The measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum

1 eV = 1.602176634×10−19 J

​

​

​

​

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Aside: Electron-Volt, eV

eV: The measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum

1 eV = 1.602176634×10−19 J

House Fly

  • 50 thousand trillion nucleons
  • 10 mg
  • 0.5 m/s

​

​

​

​

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Aside: Electron-Volt, eV

eV: The measure of an amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum

1 eV = 1.602176634×10−19 J

House Fly

  • 50 thousand trillion nucleons
  • 10 mg
  • 0.5 m/s

​

LHC

  • Single proton
  • mp/⁠me = 1836.152673
  • V = 99.9999991% * C

​

​

​

Image: https://www.warrenphotographic.co.uk/03911-houseflies-in-flight

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Superposition

Two charged objects

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Superposition

Two charged objects

�Vector addition of fields

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Superposition

Two charged objects

�Vector addition of fields

�Take gradient of combined field

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Superposition: making a voltage source

  • Two plates
  • One contains a lot of positive charge, the other negative
  • Charge is locked to each plate

​

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Superposition: making a voltage source

  • Two plates
  • One contains a lot of positive charge, the other negative
  • Charge is locked to each plate
  • Field is constant between the plates and (largely) cancels on the outside

​

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Superposition: making a voltage source

  • What happens if charge can move freely between the plates?

​

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Field inside conductor

  • What happens if charge can move freely between the plates?
  • The electric field, and therefore voltage between any two points in a perfect conductor is 0

​

Perfect conductors

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Gravity vs. electric forces

​

Gravity

Electric force

Property of Interest

Mass

Charge (+/-)

Force Law

Inverse square

Inverse square

Direction

Attraction

Repulsion or attraction

Conservative

Yes

Yes

Linear (superposition)

Yes

Yes

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Gravity vs. electric forces

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Ohm’s Law

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Current: charge in motion

Current (I): how much charge (Q) moves through a given area in time t

​

​

​

​

Units: Amperes (Amps) = Coulomb / sec

What factors will influence I?

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Current: charge in motion

Current (I): how much charge (Q) moves through a given area in time t

What factors will influence I?

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Current: charge in motion

Current (I): how much charge (Q) moves through a given area in time t

What factors will influence I?

​

  1. Voltage/E-field: stronger means more current�
  2. Conduction medium: how good is it at allowing charge to move?

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Current paths

  • Large Voltage difference
  • Strong electrical force
  • Metal: good conductor
  • How much charge flows?���

​

~50kV

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Current paths

  • Large Voltage difference
  • Strong electrical force
  • Metal: good conductor
  • How much charge flows?��
  • None (ideally)
  • Large resistance (R)
    • Air
    • Ceramic insulators

~50kV

R

R

R

R

R

R

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Resistance

  • Charge particles are accelerated in an electric field but slam into stuff on along their path�
  • This jiggles the stuff they slam into (heat)�
  • In some materials motion is impeded so much, that ~no charge will flow (I = 0)�
  • Units: Ohms (Ω) = Volts/Amps

​

​

​

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Resistivity

  • Resistivity (ρ): material property describing how strongly it resists current
  • Block of material with resistivity ρ, length l, and face area A
  • Perfect conductors on both faces
  • What is its total resistance?

​

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Resistivity

  • Resistivity (ρ): material property describing how strongly it resists current
  • Block of material with resistivity ρ, length l, and face area A
  • Perfect conductors on both faces
  • What is its total resistance?

​

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Resistivity

Silicon

Copper

ρ = 2.3×103 Ω⋅m

ρ = 1.7×10-8 Ω⋅m

11 orders of magnitude

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Current depends on voltage and resistance

  • Current is proportional to voltage
  • Current is inversely proportional to resistance
  • Ohm’s Law

​

​

​

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Conservation of charge

  • Although charge moves, the total charge must be conserved!
  • There is only one topology that supports this: a loop.
  • All electrical circuits are loops

Voltage�(10 V)

Resistor�(10 Ohms)

I

I

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Circuit

  • Where is the loop?

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Ground

  • Where is the loop?
  • Ground and power symbols are useful for complicated schematics.
  • Used to indicate a common conductor and voltage.

Cu

I

I

Cu

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Charge is conserved (“Kirchhoff's Current Law”)

  • Conservation of charge
  • “Kirchhoff's current law”

​

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Energy is conserved (“Kirchhoff's Voltage Law”)

  • Conservation of energy
  • “Kirchhoff's voltage law”

​

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Hydraulic Analogies

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Hydraulic analogy: current

Hydraulic

  • Rate of water flowing through a pipe

Electrical

  • Rate of charged particles through a conductor
  • e.g. Electrons in metal
  • e.g Ions in solution

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Hydraulic analogy: voltage

Hydraulic

  • Potential energy

​

Electrical

  • “Electrical potential energy”

​

High potential energy compared to �sea level

+9V compared to the other terminal

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Hydraulic analogy: ground

Hydraulic

  • What is 0 potential energy?
  • “Sea level”: arbitrary potential energy level

Electrical

  • What is 0 voltage
  • “Ground”: arbitrary potential

+

0

-

+

0

-

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Hydraulic analogy: resistance

Hydraulic

Constriction or blockage in pipe

​

​

​

Electrical

Impurities and thermal motion that disturb the flow of charged particles

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Hydraulic analogy: resistivity

Hydraulic

Density of mesh in pipe

​

​

​

Electrical

(1 / mobility) of charge carriers

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Voltage Divider

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Resistor circuit

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Potentiometer

Vout

“Wiper”

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Voltage divider

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Voltage divider

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Voltage divider

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Voltage divider

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Voltage divider

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What is an electrode?

  • Insulated wire with exposed tip
  • Bring it within the E-field / potential field produced by cell

​

​

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What is an electrode?

  • Insulated wire with exposed tip
  • Rs = Series resistance (CSF, electrode interface)
  • Rsh = Shunt resistance. Ideally large, but not in practice.

​

​

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What is an electrode?

  • What is Vout?

​

​

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Questions

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Parallel Resistors

  • We saw above that series resistors add
  • When resistors are in parallel, they pass a fraction of the incoming current in inverse proportion to their respective resistances.

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Intuitive origins of inverse-square law

  • Imagine some point source for gravitational force (a “mass”).
  • Draw a sphere around it
  • As sphere radius increases, strength is distributed over area

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​

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Newton’s universal law of gravitation

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Gravitational Field

Object with mass M

Test mass, m = 1

Gravitational force field

  • Arrows show direction test mass will move

M

M

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Gravitational Potential

Object with mass M

Test mass, m = 1

How much work is done on test mass when it moves between positions in space�

​

​

Path does not matter (conservative force)

M

M

M

Φ1

Φ2

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Superposition

To find the combined field, add the fields produced by each mass

​