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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

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 interneuron diversity
Inhibitory interneuron diversity

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

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).
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