canonical protein dynamics
DESCRIPTION
Canonical protein dynamics. Flowchart. Differential equation. Solution. f. 0. Physical picture of protein translation and degradation. No degradation for this protein. No translations. 10. 0. 11. 1. 12. 2. 13. 3. 14. 4. 15. 5. 16. 6. 17. 7. 18. 8. 19. 9. +. +. +. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/1.jpg)
Canonical protein dynamics
1
Differential equationFlowchart
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π½πΌ
π₯ (π‘ )
π‘0
Solution
![Page 2: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/2.jpg)
2
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
No translations
Physical picture of protein translation and degradation
No degradation for this protein
+No
chan
ge
![Page 3: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/3.jpg)
Physical picture of protein translation and degradation
3
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
Chance translation
+
+
![Page 4: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/4.jpg)
Physical picture of protein translation and degradation
4
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
No
chan
ge
Neglecting to roll dice on this freshly
generated protein.
+
![Page 5: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/5.jpg)
Physical picture of protein translation and degradation
5
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+N
o ch
ange
+
![Page 6: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/6.jpg)
Physical picture of protein translation and degradation
6
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
![Page 7: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/7.jpg)
Physical picture of protein translation and degradation
7
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
No
chan
ge
Rolled dice for protein that was
already degraded!
+
![Page 8: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/8.jpg)
Physical picture of protein translation and degradation
8
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
![Page 9: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/9.jpg)
Physical picture of protein translation and degradation
9
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
![Page 10: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/10.jpg)
Physical picture of protein translation and degradation
10
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
Chance translation
+
![Page 11: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/11.jpg)
Physical picture of protein translation and degradation
11
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
+
![Page 12: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/12.jpg)
Physical picture of protein translation and degradation
12
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
+
![Page 13: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/13.jpg)
Physical picture of protein translation and degradation
17
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
+
![Page 14: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/14.jpg)
Physical picture of protein translation and degradation
18
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ + +
+
+
Chance translation
+
![Page 15: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/15.jpg)
Physical picture of protein translation and degradation
19
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ + +
+
+
+
![Page 16: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/16.jpg)
Physical picture of protein translation and degradation
20
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ + +
+
+
+
![Page 17: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/17.jpg)
Physical picture of protein translation and degradation
21
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ + +
+
+
+
![Page 18: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/18.jpg)
Physical picture of protein translation and degradation
22
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
+
β π‘
Between times and
β 2degradations
(20 time steps ) (28 proteins )(ΒΏ time steps ) (ΒΏ proteins )Proteins lost
β 3 translations20 time steps
(ΒΏ time steps )Proteins added β π½β π‘
β πΌβ π‘ π₯ (π‘ 0 )π₯ (π‘ 0+βπ‘ )β π₯ (π‘ 0 )+π½β π‘βπΌβ π‘ π₯ (π‘ 0 )
π₯ (π‘ 0+βπ‘ )βπ₯ (π‘ 0 )β π½β π‘βπΌβ π‘ π₯ (π‘ 0 )
ππ₯ππ‘ |π‘=π‘ 0β
π₯ (π‘0+β π‘ )βπ₯ (π‘0 )β π‘
β π½βπΌ π₯ ( π‘0 )
π‘ 0 +
![Page 19: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/19.jpg)
Physical picture of protein translation and degradation
23
π‘ (ππ·πΌπΆπΈ )2 3 4 5 6 7 8 90 1 12 13 14 15 16 17 18 1910 11 20
Note: Proteins can be distinguished by momentary distortions.
+ +
+
+
+
ππ₯ππ‘
=π½βπΌ π₯
+
STOPLimitation!!! (But we all do it this it this way)
x (# proteins)
28
29
30
Realistic trajectory
Unrealistically smooth trajectory
fπ½ πΌ
π₯
![Page 20: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/20.jpg)
Canonical protein dynamics
24
Differential equationFlowchart
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π½πΌ
π₯ (π‘ )
π‘0
Solution
![Page 21: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/21.jpg)
π½πΌ
Time-course and rise time
25
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
Declare initial condition, for example, βstart at time 0 with no proteinβ
π₯ (0 )=0
Look for possible steady states
0=ππ₯ππ‘
=π½βπΌ π₯ππ
π₯ (π‘ )
π‘0
π₯ππ=π½πΌ
Estimate some slopes
![Page 22: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/22.jpg)
Time-course and rise time
26
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π₯ (π‘ )
π‘
0
π½πΌ
ππ₯ππ‘
=πΌ ( π½πΌβπ₯ )π (π₯ )
π (π₯ )=βπ₯+π½πΌ
π (π₯ (0 ) )= π½πΌ
π (π₯ππ )=β π½πΌ +π½πΌ
=0
π π ππ‘
=ππ ππ₯
ππ₯π π‘
π π ππ‘
= πππ₯ (β π₯+ π½
πΌ ) ππ₯ππ‘
βππ π π‘
=πΌ π
β«π‘=0
π‘ π1π π π ππ‘
ππ‘=βπΌ β«π‘=0
π‘ π
ππ‘
β«π =π (π₯ (0 ))
π ( π₯ (π‘ π ) )1π π π =βπΌ β«
π‘=0
π‘ π
ππ‘
π π ππ‘
=βππ₯ππ‘
![Page 23: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/23.jpg)
Time-course and rise time
27
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π₯ (π‘ )
π‘
0
π½πΌ
π (π₯ )=βπ₯+π½πΌ
π (π₯ (0 ) )= π½πΌ
π (π₯ππ )=β π½πΌ +π½πΌ
=0
π π ππ‘
=ππ ππ₯
ππ₯π π‘
π π ππ‘
= πππ₯ (β π₯+ π½
πΌ ) ππ₯ππ‘
β«π =π (π₯ (0 ))
π ( π₯ (π‘ π ) )1π π π =βπΌ β«
π‘=0
π‘ π
ππ‘
ln (π (π₯ ( π‘ π )) )β ln( π½πΌ )=βπΌ [π‘ π β0 ]
π π ππ‘
=βππ₯ππ‘
ln ( π (π₯ (π‘ π ) )π½πΌ )=βπΌπ‘ ππ (π₯ (π‘ π ) )
π½πΌ
=πβπΌπ‘ π
π =π½πΌπβπΌπ‘ π
![Page 24: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/24.jpg)
π 12
Time-course and rise time
28
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π₯ (π‘ )
π‘0
π =π½πΌπβπΌπ‘ π
π½2πΌ
π½πΌ
π½2πΌ
π½πΌ
π½2πΌ
π½πΌ
π½2πΌ
π½πΌ
π½2πΌ
π½πΌ
π 12
=ln (2 )πΌ
STOPShow
![Page 25: Canonical protein dynamics](https://reader036.vdocuments.us/reader036/viewer/2022062315/56815ab7550346895dc86e7f/html5/thumbnails/25.jpg)
π 12
π 12
π 12
π 12
π 12
π½2πΌ
Time-course and rise time
29
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π₯ (π‘ )
π‘0
π =π½πΌπβπΌπ‘ π
π½πΌ
π 12
=ln (2 )πΌ