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Date
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Activity
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January
8
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Course
Organization, Introduction, Overview: Slides
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January
10
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Fall,
Chap 1: Differential equations and examples Homework
1 due Wed, January 17 Solutions
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January
12
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Fall,
Chap 1: Differential equations, fixed points, oscillations, modeling
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January
15
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No
class
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January
17
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Fall,
Chap 2: Resting potential and gates
Homework 2 due Wed, January 24: Fall, pp 50-51,
numbers 1, 2, 6, 7
Hint
for number 2b: use the formula C =
Q/V, where Q is charge in coulombs (unit symbol = C), V is potential in
volts (V), C is capacitance in farads (F), and the units satisfy F = C/V.
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January
19
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Fall,
Chap 2: Voltage activated gates
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January
22
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Fall,
Chap 2: Voltage clamp and Morris-Lecar
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January
24
|
Fall,
Chap 2: Morris-Lecar analysis; see graphs
of hyperbolic functions
NEW: Homework 3 due
Fri, February 2. Link for problem 2 (revised 1/29).
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January
26
|
Fall,
Chap 2: 2 variable odes and analysis
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January
29
|
Fall,
Appendix A4: 2 variable odes and stability
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January
31
|
Fall,
Chap 2: Morris-Lecar analysis
Formulas for Morris-Lecar system
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February
2
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Fall,
Appendix A5, 2 variable odes and bifurcations Homework 4
due Wed, February 7.
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February
5
|
Fall,
Appendix A5, Hopf bifurcations and winpp (basic
introduction and locbif
tutorial)
Here
is a link for xpp
on windows.
Some
ode files illustrating bifurcations:
saddle-node, transcritical, pitchfork, hopf.
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February
7
|
Fall,
Chapter 2: Recap and Hodgkin-Huxley
Hodgkin-Huxley
ode files: basic,
conductances, m gate
NEW: Homework 5
due Wed, February 16
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February
9
|
Ionic
models for cardiac cells
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February
12
|
Rapid
equilibrium approximation; Fall, sec 4.1
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February
14
|
Asymptotic
analysis, Fall, sec 4.2, Homework 6 due Wed,
February 21: Fall, chap 4, numbers
2, 3.
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February
16
|
Asymptotic
analysis, Fall, sec 4.2
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February
19
|
Michaelis-Menten,
Fall, sec 4.7
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February
21
|
Michaelis-Menten,
continued
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February
23
|
Cardiac
models overview
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February
26
|
Transport
mechanisms and GLUT, sec 3.1 and 3.2
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February
28
|
SERCA
pump and calcium handling, sec 3.4 and 5.1
Take
home midterm begins.
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March
2
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No
class – take home midterm due Monday, March 5.
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March
5
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Calcium
handling, continued.
Take
home midterm due in class.
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March
7
|
Calcium
oscillations.
ODE
files: BFSG
closed. BFSG open.
BFSG open reduced.
Homework 7 due Wed, March 21 (group homework): Fall,
chap 4, numbers 4, 5, 9.
For number 9, see section 3.2.3 for a discussion of the thermodynamic
constraint. Also, independent in the context of part (a) means that
the rate is the same for the binding of activating calcium whether the
inactivating calcium is bound or not, and likewise for the rate of binding
of inactivating calcium. Finally for part (b), use variables x1, x2,
x3, x4 instead of x0, x1, x3, x4.
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March
9
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Calcium
handling, sec 5.2 and discussion of projects.
Project
proposals due Friday, March 30.
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March
12-16
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Spring
break
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March
19
|
Calcium
oscillations, section 5.3. Slides
ODE
files for midterm solutions: IP3 full, IP3 reduced
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March
21
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Calcium
oscillations, section 5.3. Project proposal due March 28.
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March
23
|
Calcium
oscillations, section 5.3.
Pituitary gonadotroph closed system ode file.
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March
26
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Calcium
oscillations, section 5.3
Pituitary gonadotroph constant flux ode file.
Pituitary gonadotroph with
Morris-Lecar ode file.
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March
28
|
Intercellular
communications, section 6.1 Gap
junctions
Coupled
Morris-Lecar oscillators: original parameters, ch 6 parameters.
Homework 8, due Wednesday, April 4 (group homework): Fall, et al, chap 5, numbers 3, 6ab –
cancelled, work on project instead.
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March
30
|
Intercellular
communications, section 6.1
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April
2
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Electrical
coupling and continuous limit, section 6.1
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April
4
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Spatial
modeling, section 7.1
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April
6
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Spatial
modeling and cable equation, section 7.1
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April
9
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Spatial
modeling examples, section 7.2
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April
11
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Numerical
methods for PDE, section 7.3
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April
13
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Traveling
waves, section 7.5
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April
16
|
Traveling
waves with Fitzhugh-Nagumo
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April
18
|
ECG
basics
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April
20
|
ECG
and arrhythmias
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April
23
|
Circle
maps and arryhthymias
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|
April
25
|
Arryhthymias
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April
27
|
Project
presentation
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