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NENS220 Computational methods in Neuroscience. John Huguenard and Terry Sanger. Goals of the course. Overview of computational methods Mathematical techniques for creating models of neural behavior - the tools of computational methods. Computational Modeling.

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Nens220 computational methods in neuroscience

NENS220 Computational methods in Neuroscience

John Huguenard and Terry Sanger

Goals of the course
Goals of the course

  • Overview of computational methods

  • Mathematical techniques for creating models of neural behavior - the tools of computational methods

Computational modeling
Computational Modeling

  • The ultimate purpose is to relate different levels (scales) of neural behavior

    • e.g.: how do properties of ion channels determine the spiking behavior in response to synaptic input?

    • e.g.: what is the relationship between spike activity in a population of M1 neurons and movement of the arm?

Scope of the course
Scope of the course

  • This is essentially an overview of some (but not all) of the general methods

  • Intended for graduate students in neuroscience

  • In order to learn how this is done, you will have to practice

    • Necessarily involves knowledge of statistics, mathematics, and some computer programming (matlab, NEURON)

Background material
Background material

  • Probability theory

  • Information theory

  • Matrix algebra

  • Correlation integrals

  • Fourier analysis

  • Matlab programming

  • Membrane potentials

  • Cable theory

Background review
Background review

  • We will do much of this as we go.

  • Additional help in TA sessions

  • You may need to do extra reading

Two major areas
Two major areas

  • I: Neurons

    • How information is processed at the level of synapses, membranes, and dendrites

    • Relationship between inputs, membrane potentials, and spike generation

  • II: Spikes:

    • What information is carried in single spikes, temporal sequences of spikes, and spikes over populations

    • How learning results in changes in spike patterns


  • Theoretical Neuroscience, Peter Dayan and Larry Abbott, (MIT Press: Cambridge MA), 2001.

  • Available from and the Stanford bookstore, about $45

  • Other useful references:

    • Neural Engineering, Andersen and Elliasmith

    • Spikes, Bialek

    • Computational Neuroscience, Churchland and Sejnowski

    • Handbook of computational neuroscience, Arbib

    • Foundations of Cellular Neurophysiology, Johnston and Wu

  • You must have access to a workstation with matlab/NEURON.

    • Matlab available on cluster computers (firebirds, etc)

    • NEURON available for multiple platforms via free download

      • We can set up accounts on linux machines with NEURON installed.

Class structure
Class structure

  • Tuesdays and Thursdays, 3:15-5:00pm. Room H3150.

  • Tuesdays will be lectures

    • Lecture will usually follow the text chapters; you may want to read these in advance

    • A paper will be assigned, to be read before Thursday (first paper assigned next Tuesday)

  • Thursdays will be discussions of the assigned paper and the lecture, led by the TA. THESE ARE REQUIRED.

Homework assignments
Homework assignments

  • 4-6 problems sets during quarter. They will be assigned on Tuesday and due the Thursday of the following week (9 days later)

  • Will usually require simulation of some component of the paper being discussed.

  • Will require use of matlab/NEURON. You should submit the program output and source code with detailed comments

  • Should require 1-3 hours, depending on how good you are with matlab/NEURON


  • 70% weekly assignments

    • Based on output plots, code, and comments

  • 30% Class participation

    • Based on contributions to discussion groups

Part i
Part I

Modeling of realistic neurons and networks

John Huguenard

Neuroelectronics part i

Neuroelectronics, Part I

John Huguenard

The big picture a la terry sanger
The big picture, a la Terry Sanger

  • An “external signal” x(t) is something that the experimenter controls (either a sensory stimulus or a learned motor task)

  • We observe spikes that are the result of a transformation of the external signal

External World


Spike Generator



The big picture a la john huguenard
The big picture, a la John Huguenard

  • Neurons receive synaptic input

  • Neurons produce output

    • The currency of neuronal communication is spikes (action potentials)

    • Spike generation is in many cases a nonlinear function of synaptic input

External World


Spike Generator



Why it is important to consider neuronal properties
Why it is important to consider neuronal properties..

  • STDP, dendritic back propagation, dendritic signaling

  • Resonance

  • Oscillations

  • Synchronization

  • Gain control

  • Persistent activity

  • Phase precession

  • Coincidence detection vs. integration

Pyramidal Neurons in Layer V

thy1-YFP mouse

Feng et al., (2000) Neuron 28:41

200 µm

Canonical microcircuits

Canonical Microcircuits

Recurrent excitatory connections are prominent.

Function: Amplification of signals for enhanced feature detection.

Rodney Douglas & Kevan Martin

Inhibitory cells are sparse
Inhibitory cells are sparse







Inhibitory interneuron diversity
Inhibitory interneuron diversity

Modified From: Karube et al., (2004) J Neurosci 24:2853-65

Morphology can influence firing pattern
Morphology can influence firing pattern

Mainen & Sejnowski, 1996

Electrical properties of neurons

Electrical properties of neurons

Dominated by membrane capacitance

Neurons are integrators

whose time constant is dynamically variable

Spike output depends on voltage-dependent gating of ion channels

Passive properties of neurons

Passive properties of neurons

Semipermeable lipid bilayer membrane with high [K+]i maintained by electrogenic pump (ATPase)

Equivalent radius ~ 25 mm,

Surface Area ~ 8000 mm2=.008 mm2=8e-5cm2

Electrical capacitance



Electrical capacitance

  • Ability to store charge

    • Charge required to create potential difference between two conductors

    • A 1 Farad capacitor will store 1 Coulomb/Volt

Hille, 2001

Capacitance of cell membranes



Capacitance of cell membranes

  • Capacitance is a function of

    • Surface area (A)

    • Dielectric constant (e)

    • Distance between plates (d)

  • For membranes specific capacitance  1 mF/cm2

    • is for the most part invariant

    • for a 0.8e-5cm2 cell ~ 80 pF

Hille, 2001

Resting potential single permeant ion
Resting potential, single permeant ion

Nernst Potentials

EK = -75 mV

ENa = +50 mV

ECl = -60 mV

ECa = +100 mV

Nernst equation:

Uncompensated charge
Uncompensated charge

  • [K+]i 130 mM

  • [K+]o 3 mM

  • EK –100 mV

  • q=CV

  • = 80 pF*100mV

  • = 8pC

  • = 50e6 K+ ions

  • Total K+I = 5e12 ions

  • Fraction uncompensated = 0.001%

    • Will vary with surface to volume ratio

Membrane resistance
Membrane Resistance

  • Ion selective pores

    • Ohm’s law E = IR

      • 1V is the potential difference produced by 1A passing through 1 Ohm

    • Conductance is reciprocal of resistance,1 Siemen = 1 Ohm-1

    • Resistance is dependent on length of conductive path, cross sectional area, and resistivity of the media

    • Ion channels have conductances in the 2-250 pS range, but may open only briefly

Input resistance
Input Resistance

  • “Leak” channels are open at rest and determine the input resistance

    • i.e. the impedance to extrinsic current injection

  • Specific input resistance for neurons is in the range of 1 MW mm2 or 1 mS/mm2

    • 50,000 20 pS leak channels/mm2 = 1 channel / 20 mm2

  • Our “typical” cell of 0.008 mm2 would have an input resistance of 125 MW, or input conductance of 8 nS (equivalent to ~400 open leak channels).

Resting membrane potential 1 permeant ion
Resting membrane potential>1 permeant ion

Parallel conductance model

Ohmic channels
Ohmic channels

  • Characterized by an open channel I/V that is linear

  • I = (Vrev- Vm)/R

  • I = (Vrev- Vm) * g

g = slope


Non ohmic channels
Non-ohmic channels

  • Goldman-Hodgkin-Katz (GHK) theory

    • Ions pass independently

    • Electrical field within membrane is constant

      • sometimes known as the constant field equations

    • GHK current equation (flux in two directions)

    • GHK Voltage equation

Nonlinear driving force
Nonlinear driving force

  • GHK current equation


Better description than

ohmic for some channels

e.g. Ca2+, K+

Voltage dependent conductances
Voltage dependent conductances

  • Channel opening is a function of transmembrane voltage

Latching up and down states
Latching, up- and down-states

  • Stable systems have positive slope to I/V curve. E.g., neurons with only leak currents.

  • Voltage dependent conductances can lead to regions of negative slope conductance with two stable states.

Two types of channels
Two types of channels

  • gK:gNa =3:1, both linear


  • Synaptic input

    • Transient inputs from other sources

    • i.e. sensors or lower level neurons

  • Spike output

    • Generation of action potentials, which will then propagate the signal to the neurons at the next level, again via synapses

Chemical synapses
Chemical synapses

  • Excitatory (ES > Em)

  • Inhibitory (Es < Em)

    • shunting

  • Rapid increase in gs followed by exponential decay (tD = 1 - 100 ms)

    • Approximated by alpha function

    • Or sum of exponentials (more realistic)

Spike generation
Spike generation

  • Nonlinear, “all or none” response

    • Based on avalanche type reaction

    • Characterized by

      • Threshold

      • High conductance reset

      • Refractory period

  • Can be simulated by integrate and fire synthetic neuron