Homework Assignment Cell Membrane Simulationsmacleod/bioen/be6000/homeworks/cell/comments... ·...
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Homework: AP Simulation Bioengineering 6000 CV Physiology
Homework Assignment Cell Membrane Simulations
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question 1: All or Nothing?
• What is all or nothing?– Threshold– Only two states, all, or nothing, independent of variations other than
threshold being reached.• Does the model replicate this behavior?• What consequences does the answer have on subsequent
simulations?– Where to set threshold in later questions?
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Probing the Stimulation Space
1 2 4 6 8
5
10
15
20
25
No No No No Yes
No No No No Yes
No No No No Yes
No No No No Yes
No No Yes Yes Yes
Stimulus Duration [ms]
Stim
ulus
Am
plitu
de [µ
A/c
m2 ]
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Probing the Stimulation Space
1 2 4 6 8
5
10
15
20
25
No No No No Yes
No No No No Yes
No No No No Yes
No No No No Yes
No No Yes Yes Yes
Stimulus Duration [ms]
Stim
ulus
Am
plitu
de [µ
A/c
m2 ]
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question 1: All or Nothing?Probing the 2D simulation space
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
All or Nothing Example
Stimulus fixed at 8 msVaried in amplitude
The Problem?
Stimulus carries over to the response of the membrane; it is too long.
0
10
20
30
40
0 1.25 2.5 3.75 5
y = -6.3003x + 34.033R² = 0.8477
R
2 = 0.85y = �6.3x + 34.0
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question #1: Cell Stimulation
Ith (µA/cm^2)
ΔTth
(ms)1/ΔTth
32.5 1 1.0
30 1 1.0
27.5 1.5 0.7
25 1.5 0.7
22.5 1.5 0.7
20 2 0.5
17.5 2 0.5
15 2.5 0.4
12.5 3 0.3
10 3.5 0.3
7.5 5 0.2Intensity vs. Duration
0
10
20
30
40
0 1.25 2.5 3.75 5
y = -15.973ln(x) + 30.861R² = 0.9553
R
2 = 0.96y = �16 ln(x) + 30.86
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question #1: Cell Stimulation
Intensity vs. Duration
Ith (µA/cm^2)
ΔTth
(ms)1/ΔTth
32.5 1 1.0
30 1 1.0
27.5 1.5 0.7
25 1.5 0.7
22.5 1.5 0.7
20 2 0.5
17.5 2 0.5
15 2.5 0.4
12.5 3 0.3
10 3.5 0.3
7.5 5 0.2
0
10
20
30
40
0 1.25 2.5 3.75 5
y = 1.8931x2 - 17.181x + 46.35
R² = 0.9693
R
2 = 0.97y = 1.89x
2 � 17.2x + 46.4
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question #1: Cell Stimulation
Intensity vs. Duration
Ith (µA/cm^2)
ΔTth
(ms)1/ΔTth
32.5 1 1.0
30 1 1.0
27.5 1.5 0.7
25 1.5 0.7
22.5 1.5 0.7
20 2 0.5
17.5 2 0.5
15 2.5 0.4
12.5 3 0.3
10 3.5 0.3
7.5 5 0.2
0
10
20
30
40
0 1.25 2.5 3.75 5
y = 42.559e-0.3805x
R² = 0.9507
Stim
ulus
Inte
nsity
(µA
/cm
2
Duration (ms)
R
2 = 0.95y = 42.6e
�0.38x
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question #1: Cell Stimulation
Ith (µA/cm^2)
ΔTth
(ms)1/ΔTth
32.5 1 1.0
30 1 1.0
27.5 1.5 0.7
25 1.5 0.7
22.5 1.5 0.7
20 2 0.5
17.5 2 0.5
15 2.5 0.4
12.5 3 0.3
10 3.5 0.3
7.5 5 0.2
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Membrane Voltage
E kE Na E Ca
g Na g K g Ca
C m
Outside
Inside
E
Think Charge!
0
10
20
30
40
0 0.25 0.5 0.75 1
y = 30.123x + 2.9395
R² = 0.9387
Stim
ulus
Inte
nsity
(µs/
cm2)
1/Duration (1/ms)
y = mx + b Ith = K(1/Tth) + I0
K = IthTth = Qth
Qth � 30 nC/cm2
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question #1: Cell Stimulation
Ith (µA/cm^2)
ΔTth
(ms)1/ΔTth
32.5 1 1.0
30 1 1.0
27.5 1.5 0.7
25 1.5 0.7
22.5 1.5 0.7
20 2 0.5
17.5 2 0.5
15 2.5 0.4
12.5 3 0.3
10 3.5 0.3
7.5 5 0.2
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question 2: Effect of [Na+]e
• Interpretation of low [Na+]e– Think of driving
force; even is concentration gradient eliminated potential gradient exists!
– Hypothesis about ICa
– Both hypotheses are easy to test with simulation
0 100 200 300 400−100
−50
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100
mV AP
0 100 200 300 400−400
−300
−200
−100
0
uA/cm2 INa
0 100 200 300 400−6
−4
−2
0
uA/cm2 Isi
0 100 200 300 400−1
0
1
2
uA/cm2
IK
0 100 200 300 4000
1
2
3
uA/cm2
IK1
0 100 200 300 400−5
0
5
uA/cm2
IKp
Ib
0 50 100 150 200 250 300 350 400��
0
100
AP
0 50 100 150 200 250 300 350��
�
0
400
INa
0 50 100 150 200 250 300 350 400ï�
ï�
ï�
0
Isi
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
When in Doubt, Check the Simulation
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Be Careful with Axes
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Scale is Essential
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Scale is Essential
HumanHair
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Creating Clear Graphs/Figures
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Generating Secondary Results
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
More Secondary Results
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Question 3• Question #3
– Try to motivate with some physiology or pathophysiology– Examine all parameters to try and identify mechanisms– Use the simulations to explore mechanisms--they reveal the
answers many times in a way the experiments cannot!!E.g., Vary Ca+2 concentration
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Cell Simulation: General I
• Organize simulations– Develop a strategy to answer the question– Vary as few parameters at a time as possible– Use reasonable (physiological) ranges of values– Examine the relevant parameters (often good to start by looking
at all and identify relevant ones)• Develop second order results where appropriate
– e.g., plot of stimulus duration vs. stimulus– e.g., APD vs concentration
• Use results of analysis to motivate more simulations– Use to uncover mechanisms
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Cell Simulation: General II
• Organization of report– Mimic the flow of the questions and answer all parts
• Plots and graphs– Include axes with labels– Include legends– Include concise captions– Export figures rather than screen capture– Embed all figures into the running text
• Text– Use past tense to report all methods and results– Adopt formal scientific prose style– Strive for concise, clear, accurate descriptions
• Use tables to show sets of results
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
What is Wrong with this Plot?
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
And this one...
Pixelated, especially text
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
And this one...
Rule of thumb: Figure fonts should be approximately the same as surrounding text.
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
And one more... No titles for figures
Caption should not contain interpretation.
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Mastering MATLAB Plots
Bioengineering 6000 CV PhysiologyHomework: AP Simulation
Including Only What is Useful
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uA/cm2 INa
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uA/cm2 Isi
0 100 200 300 400−1
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uA/cm2
IK
0 100 200 300 4000
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uA/cm2
IK1
0 100 200 300 400−5
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uA/cm2
IKp
Ib
0 100 200 300 400−100
−50
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mV AP
0 100 200 300 400−400
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uA/cm2 INa
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uA/cm2 Isi
0 100 200 300 400−1
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uA/cm2
IK
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uA/cm2
IK1
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IKp
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mV AP
0 100 200 300 400−400
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uA/cm2 INa
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uA/cm2 Isi
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IK1
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IKp
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mV AP
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uA/cm2 INa
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uA/cm2 Isi
0 100 200 300 400−1
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IK
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uA/cm2
IK1
0 100 200 300 400−5
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uA/cm2
IKp
Ib
Replace all this with this!
Include only What you Refer To!