Units

CONTENTS Passive Properties

Nernst equation: Equilibrium and reversal potential Goldman equation: Goldman-Hodgkin-Katz constant field equation Pumps: Na/K exchange pump Permeability vs Conductance

Basic RC properties Input resistance Membrane time constant Low-pass filter

Attenuation and delay: Basic cable properties Space (length) constant: : Attenuation with distance Time constant: Time delay with distance Input resistance Non-uniform diameter: A compartmental model Spatial summation

Units: Passive property units Action Potentials (Spikes) Spike Conceptual Summary

Threshold: All-or-none? Sodium Dependence Hyperkalaemia: Too much extracellular potassium Spike Currents and Conductance Molecular Events: Single-channel patch recording Strength-Duration Curve Refractory Period Threshold Accommodation Rebound Excitation: Post-inhibitory rebound Pacemaker: Continuous regular spiking

Basic Conduction Features Collision Spatial Distribution: Voltage profile along the axon Passive vs Active Conduction: A qualitative comparison Refractory Conduction Myelination and Saltatory Conduction

Theory Classic HH: How to get a Nobel prize Sodium IV Curve Potassium IV Curve Capacitive Current: Importance in voltage clamp mechanism Patch Recording: Single channel recording under voltage clamp

Endogenous Bursters Plateau Potentials A Current: Fast (transient) potassium current

Gate Voltage Dependency Channel Voltage Dependency Putting it Together: Finding the membrane potential Non-Ohmic Channels: The GHK current equation Reduced Models: Morris-Lecar and others Phase Plane Analysis

Synapses

Excitation and Inhibition Voltage Clamp: Applied to synaptic potentials Summation and Facilitation Depolarizing and Silent IPSPs Non-Spiking Synapses Voltage-Dependent Synapses: NMDA-type Hebbian Synapses: The basis of memory? Quantal Release

Frequency Matters Size Matters Rectification

Proximal and Distal Inhibtion Directional Sensitivity

Networks

Flip-Flop Circuit Reciprocal Inhibition Oscillator Multi Phase Rhythms Sensory Feedback Phase Resetting Tests Tadpole Swimming: A case study Synchronization and Entrainment

Stochastic Resonance: Noise matters Lateral Inhibition

Primary Afferent Depolarization (PAD)

Phase Ambiguity

Classical Conditioning: Pavlov's dog Associative Learning: Pattern completion Facilities for Memory Models

Theory: Population-level coding in the Wilson-Cowan model Neurosim Implementation Stable States Oscillations Multi-Unit Models

Single-Channel Kinetics

Sojourn Duration and Transition Rate Constants Sojourn Distribution is Exponential

Open-Time Distribution Closed-Time Distribution is Multi-Exponential

What's the Point?: A reminder

Open-Time Distribution Closed-Time Distribution

Acetylcholine Receptor Model Auto-Correlation Compartmental Models Active Currents Neurosim Implementation Implementation

Passive Properties Noise Spiking Properties Voltage-Dependent Channels Ca-Dependent Channels Sodium Pump

Spiking Chemical Synapses Non-Spiking Chemical Synapses Carrier Ions: Calcium and sodium Electrical Synapses

Exponential Euler Integration Integration Components Adaptive Step Size Wilson-Cowan integration

References

Contents

Passive Properties Action Potentials (Spikes) Synapses Networks Single-Channel Kinetics

Units

Note: some units vary in their meaning depending on the context (e.g. R can be resistance or the gas constant). If the meaning departs from this table, it is defined when used.

Quantity	Description	Typical units	Note
r	radius of structure	µm
V	voltage: membrane potential	mV
I	current	nA
R	resistance	MΩ
C	capacitance	µF
R_m	specific membrane resistance	kΩ cm²Specific resistance units are a bit counter-intuitive. We tend to think of it as resistance per unit area, but since the relationship is inverse (resistance goes down as area goes up) the units are actually resistance times unit area.	resistance of a patch of membrane 1 cm² in area.
r_m	membrane resistance per inverse unit length	kΩ cm	membrane resistance of 1 cm length of dendrite or axon \[r_{m}=R_{m}/2\pi r\]
C_m (upper case C)	specific membrane capacitance	µF cm^-2	capacitance of a patch of membrane 1 cm² in area.
c_m (lower case c)	membrane capacitance per unit length	µF cm^-1	membrane capacitance of 1 cm length of dendrite or axon \[c_{m}=2\pi rC_{m}\]
R_i	specific intracellular resistivity	kΩ cm	resistance across opposite faces of a 1 cm cube of intracellular fluid
r_i	intracellular resistance per unit length	MΩ	intracellular resistance of 1 cm length of dendrite or axon\[r_{i}=R_{i}/\pi r^{2}\]