Quantitative Methods in Neuroscience
NEUBEH545/PBIO545
Course instructors: Wyeth Bair, Adrienne Fairhall, Fred Rieke
Teaching Assistants: Dean Pospisil
Office hours: TBA
Course Website:
http://rieke-server.physiol.washington.edu/People/Fred/Classes/545/545.html
The course is organized into 2 week modules, each consisting of 4 class sessions. The
first session of each module provides an introduction to a mathematical topic. The format
is didactic. The second session provides more “hands on” exposure to the same topic. It
will follow a less didactic format, with an agenda determined by student questions and
interest. Emphasis in the second session will be questions based on the didactic lecture
and Matlab tutorials. The success of this session depends on your questions! Sessions 3
and 4 consists of student-led discussion of scientific papers in which the mathematical
concepts are applied to problems in neuroscience.
Grades
Class Project (due last week of class): 25%
Class Presentation: 25%
Class Participation: 25%
Tutorial Questions: 25%
We know students will come into the class with a wide range of mathematical
backgrounds and experience with Matlab (see below). We will base grades as much as
possible on effort. Class participation is a large part of the grade in the course; this will
be based on questions asked during lecture, on questions you send in to help us organize
the second class session of each module, and participation in discussion of in-class
presentations by other students.
Matlab tutorials
We will use Matlab-based tutorials throughout the course. These require only a basic
understanding of how to run functions in Matlab (no programming is required to run the
tutorials). We will help those of you unfamiliar with Matlab by holding a brief
introduction after the first lecture, by Dean holding a help session Wed specifically to run
through the tutorial, and by being available during the first week. We highly recommend
starting the tutorials early – before the first lecture of each module of the course.
Project
An important part of the course is the independent project. Successful projects will
require substantial effort, and thus starting early is highly encouraged. Projects should
build on the mathematical concepts introduced in class; this could include extensions of
items introduced in papers we read in class or items in the tutorials. We will suggest
topics throughout the course and feel free to ask at any point about potential projects.
The project will consist of the following:
Short (~1/2 page) project proposal due by March 2
Discuss project with one of instructors or TA and get approval by March 4
Final project due by noon March 10, to include:
- project writeup (2-4 pages)
- Matlab code and any associated data files
- brief project presentation (normal class time March 10)
Journal Club Presentations
In the 2nd week of each 2 week block students will present papers illustrating the use
(and perhaps misuse) of the mathematical concepts. Papers to be covered are listed on
the course website.
Week 1. Ordinary Differential Equations (ODE)
Primary Reading:
Berg, Random Walks in Biology, Appendix B
Wilson, Spikes, Decisions and Actions, Chapter 2
Wilson, Chapter 5 (numerical methods)
Week 2. Applications of ODE to enzyme kinetics (phototransduction) and eye
movements
Phototransduction:
Baylor, D.A. Photoreceptor Signals and Vision. Proctor Lecture (a very good review
that is not overly dense)
Rieke and Baylor. Single-photon detection by rod cells of the retina. Rev of Mod
Phys Vol 70 No. 3 1998. (review emphasizing modeling of single photon
responses)
Nikonov S, Lamb TD, Pugh EN Jr. The role of steady phosphodiesterase activity in
the kinetics and sensitivity of the light-adapted salamander rod photoresponse.
J Gen Physiol. 2000 Dec;116(6):795-824.
Schnapf JL, Nunn BJ, Meister M, Baylor DA. Visual transduction in cones of the
monkey Macaca fascicularis. J Physiol. 1990 Aug;427:681-713.
Eye Movements:
Fuchs AF, Kaneko CR, Scudder CA (1985) Brainstem control of saccadic eye
movements. Annu Rev Neurosci 8:307-337.
Fuchs AF, Scudder CA, Kaneko CR (1988) Discharge patterns and recruitment order
of identified motoneurons and internuclear neurons in the monkey abducens
nucleus. J Neurophysiol 60:1874-1895.
Others:
Hodgkin and Huxley (1952) A quantitative description of membrane current and its
application to conduction and excitation in nerve. J Physiol 117:500-544
Week 3. Fourier Analysis, Filters and Convolution
Primary Readings:
Press et al., Numerical Recipes, pages 496-508 (2nd edition, this is beginning of Ch.
12); Ch. 13
Koch, Biophysics of Computation, Appendix B
Wandell, Foundations of Vision, Appendix A (but Brian mixes linear algebra and
linear systems stuff there).
Week 4. Applications of Linear Systems Theory and Fourier Analysis to problems
in visual and auditory neuroscience.
Graham N, Nachmias J (1971) Detection of grating patterns containing two spatial
frequencies: a comparison of single channel and multichannel models. Vision Res
11:251-259.
Morrone MC, Burr DC, Ross J (1983) Added noise restores recognizability of coarse
quantized images. Nature 305:226-228.
Adelson EH, Bergen JR (1985) Spatio-temporal energy models for the perception of
motion. J Opt Soc Am A 2:284-299.
Watson AB, Ahumada AJ, Jr. (1983) A look at motion in the frequency domain. In:
Motion: perception and representation (Tsotsos JK, ed), pp 1-10. New York:
Association for Computing Machinery.
Fahle, M., and Poggio, T. (1981). Visual hyperacuity: Spatio-temporal interpolation
in human vision. Proc R Soc Lond B 213, 451-477.
Watson, A. B., and Ahumada, A. J. (1985). Model of human visual-motion sensing. J
Opt Soc Am A 2, 322-341.
Art JJ and Fettiplace R (1987) Variation of membrane properties in hair cells isolated
from the turtle cochlea. J Physiol 385:207-242
Week 5. Introduction to the Theory of Stochastic Processes
Primary Reading:
Berg, Apendix A
Koch, Chapter 15
Duda, Hart and Stork, Pattern Classification (2nd edition), Appendix 4
Week 6. Applications of Stochastic Processes to neuronal spike discharge and ion
channels.
Softky & Koch
Berry and Meister, Refractoriness and Neural Precision, J Neurosci. 1998 Mar
15;18(6):2200-11.
Barlow H. B., Levick, W. R., and Yoon M. Responses to single quanta of light
in retinal ganglion cells of the cat, Vision Res. 1971 Suppl 3. pp. 87-101.
Week 7. Linear Algebra
Primary Reading:
Eero’s primer
Dayan and Abbott, Theoretical Neuroscience, Appendix A
Duda, Hart and Stork, Appendix 2
Week 8. Application of linear algebra to color vision
Baylor, Nunn and Schnapf (1987)
Chichilnisky and Wandell. Trichromatic opponent color classification.
Vision Res. 1999 Oct;39(20):3444-58.
Chichilnisky and Wandell. Seeing gray through the ON and OFF pathways.
Vis Neurosci. 1996 May-Jun;13(3):591-6.
Wandell, Chapter 4
Week 9. Dimension reduction (PCA)
Primary Readings:
Duda, Hart and Stork, pages 107-117
Week 10. Application of PCA to neural responses
Touryan J, Lau B, Dan Y (2002) Isolation of relevant visual features from random
stimuli for cortical complex cells. J Neurosci 2002 Dec 15;22(24):10811-8
Chapin JK, Nicolelis MA (1999) Principal component analysis of neuronal ensemble
activity reveals multidimensional somatosensory representations. J Neurosci
Methods. 94:121-40.
Schwartz, Chichilnisky and Simoncelli gain paper