## MA665: Introduction to Modeling and Data Analysis in Neuroscience

### Course Webpage (Fall 2012)

 Course Instructor: Mark Kramer (email, 3-4591) Course Hours: 12:30-2 PM / TTh / MCS B23 Office Hours: 2:00-3:30 PM / TTh, or by appointment Textbook: MATLAB for Neuroscientists Handouts . . .

### Course goals

In this course we will focus on the quantification and modeling of voltage data generated by the brain at a variety of spatial scales --- from single neurons to the EEG. The main goals of this course are: (1) To introduce mathematical concepts encountered in neuroscience research and more advanced neuroscience graduate courses. (2) To teach basic programming skills in MATLAB. (3) To think about neuroscience in a quantitative way.

### Syllabus

The plan - it's still flexible . . .

Week 1
Lecture: Introduction + two views of neuroscience + field trip.

• You'll need to create an AD account to use the computers in Engineering. Fill out the forms here.
Lab: Introduction to MATLAB, code.
Reading: MATLAB for Neuroscientists, Ch 2

Other introductory MATLAB resources:

Week 2
Lecture: Observations of spiking neurons and their quantification
Lab: code, d1.mat, d2.mat, d3.mat

• MATLAB for Neuroscientists, Ch 13 & 26
• A good discussion of what we'll cover in class / lab: Teich MC and Khanna SM, J Acoust Soc Am (1985) vol. 77 (3) pp. 1110-28.
• A much more advanced discussion: Kass RE, Ventura V, Brown EN, J Neurophysiol (2005) Jul;94(1):8-25.

Week 3
Lecture: Statistical models of spiking data
Lab: The Poisson model, code.

• MATLAB for Neuroscientists, Ch 13 & 26
• A good discussion of what we'll cover in class / lab: Teich MC and Khanna SM, J Acoust Soc Am (1985) vol. 77 (3) pp. 1110-28.
• Poisson or not Poisson - a short discussion: Averbeck BB, Neuron (2009) 62(3):310-311.
• A much more advanced discussion: Shadlen MN, Newsome WT, J Neurosci (1998), 18(10):3870-3896.
• The Fano factor distribution for a Poisson process: Eden UT and Kramer MA, J Neurosci Meth, 190(1):149-152, 2010.

Week 4
Lecture: Simple biophysical models of spiking data
Lab: The integrate and fire model neuron and the leaky integrate and fire model neuron, code.
Here's the my_IF_model.m we wrote in lab.

• MATLAB for Neuroscientists, Ch 11, 12, 22
• A short paper about the integrate and fire neuron: Abbott LF, Brain Research Bulletin (1999), 50(5/6):303-304.
• Gerstner and Kistler's website about the leaky integrate and fire neuron. They wrote a good book about neuron models too.
• Izhikevich's website about his popular neuron model (the Izhikevich neuron). There's a fantastic, short paper too.

Week 5
Lecture: More complicated biophysical models of spiking data
Lab: The Hodgkin Huxley neuron model code and HH0.m.

• MATLAB for Neuroscientists, Ch 20, 21
• The Hodgkin Huxley paper: Hodgkin and Huxley, J Physiol (Lond) (1952) vol. 117 (4) pp. 500-44.
• See pages 500-519 for main model derivation. BE CAREFUL: They set the resting potential to zero. To get the values accepted today, I shifted the voltage by 70 mV in class.
• Gerstner and Kistler's website about the Hodgkin-Huxley neuron. They wrote a good book about neuron models too.
• BE CAREFUL: They set the resting potential to zero (as Hodgkin-Huxley did). To get the values accepted today, I shifted the voltage by 70 mV in class.
• The dynamics of the Hodgkin-Huxley model are extremely complicated and an area of active research. Here's an example.

Week 6
Lecture: An introduction to Fourier series.
Lab: Analysis of rhythmic data. Lecture slides as pdf.
Download the lecture data set 6_data.mat and the M-file that includes MATLAB code to analyze these data.
This week's Challenge Problems.
Other data sets for challenges: lfp1.mat, lfp2.mat.

• MATLAB for Neuroscientists, Ch 7, 8
References:

Week 7
Lecture: Networks in neuroscience
Lab: Analyzing and constructing networks code and make_small_world.m.
Lab figures: net1 and net2.