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
Canonical protein dynamics
1
Differential equationFlowchart
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π½πΌ
π₯ (π‘ )
π‘0
Solution
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
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
+
+
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.
+
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
+
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.
+ +
+
+
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!
+
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.
+ +
+
+
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.
+ +
+
+
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
+
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.
+ +
+
+
+
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.
+ +
+
+
+
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.
+ +
+
+
+
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
+
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.
+ + +
+
+
+
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.
+ + +
+
+
+
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.
+ + +
+
+
+
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 +
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₯
Canonical protein dynamics
24
Differential equationFlowchart
ππ₯ππ‘
=π½βπΌ π₯f
π½ πΌπ₯
π½πΌ
π₯ (π‘ )
π‘0
Solution
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
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‘
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
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
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