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Hybrid particle-field model for DNA
Sigbjørn Løland BoreWeekley Hylleraas seminar
10.05.2019
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Primer on DNA (1)
Phosphate
Sugar
Nucleobase
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Primer on DNA (1)
Phosphate
Sugar
Nucleobase
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Primer on DNA (1)
Phosphate
Sugar
Nucleobase
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Primer on DNA (2)
I Watson and Crick pairingI Double helix formation
I Three types of helicies:I A-DNAI B-DNAI Z-DNA
A-DNA B-DNA Z-DNA
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Primer on DNA (2)
I Watson and Crick pairingI Double helix formationI Three types of helicies:
I A-DNAI B-DNAI Z-DNA
A-DNA B-DNA Z-DNA
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Primer on DNA (3)
I Human DNA: 1-3 mI Persistence length: 50 nmI Very flexible
I Environmental effectsI TemperatureI Salt
x
X
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Primer on DNA (3)
I Human DNA: 1-3 mI Persistence length: 50 nmI Very flexible
I Environmental effectsI TemperatureI Salt
x
X
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Primer on DNA (3)
I Human DNA: 1-3 mI Persistence length: 50 nmI Very flexible
I Environmental effectsI TemperatureI Salt
x
X10.05.2019 -4-
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Primer on DNA (3)
I Human DNA: 1-3 mI Persistence length: 50 nmI Very flexibleI Environmental effects
I TemperatureI Salt
x
X10.05.2019 -4-
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The project:
I Reuse established CG-representations for DNA
I Model nonbonded interactions within hybrid particle-fieldframework
I Parametrize the modelI Benchmark the modelI No excuses, parallel implementation
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The project:
I Reuse established CG-representations for DNAI Model nonbonded interactions within hybrid particle-field
framework
I Parametrize the modelI Benchmark the modelI No excuses, parallel implementation
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The project:
I Reuse established CG-representations for DNAI Model nonbonded interactions within hybrid particle-field
frameworkI Parametrize the model
I Benchmark the modelI No excuses, parallel implementation
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The project:
I Reuse established CG-representations for DNAI Model nonbonded interactions within hybrid particle-field
frameworkI Parametrize the modelI Benchmark the model
I No excuses, parallel implementation
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The project:
I Reuse established CG-representations for DNAI Model nonbonded interactions within hybrid particle-field
frameworkI Parametrize the modelI Benchmark the modelI No excuses, parallel implementation
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Coarse grain representation
I The coarse-grainedrepresentation shouldfulfill:
I Represent the structuralorganization
I 72 au per beadI 3SPN-Model of Juan de
PabloI Replace nonbonded
interactions
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Coarse grain representation
I The coarse-grainedrepresentation shouldfulfill:
I Represent the structuralorganization
I 72 au per bead
I 3SPN-Model of Juan dePablo
I Replace nonbondedinteractions
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Coarse grain representation
I The coarse-grainedrepresentation shouldfulfill:
I Represent the structuralorganization
I 72 au per beadI 3SPN-Model of Juan de
PabloI Replace nonbonded
interactions
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Coarse grain representation
I The coarse-grainedrepresentation shouldfulfill:
I Represent the structuralorganization
I 72 au per beadI 3SPN-Model of Juan de
PabloI Replace nonbonded
interactions
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Bonded interactions
H0({r}) =Natom∑
i
12
mi r2i +
Nbond∑i
12
kr (ri − ri0)2
+
Nbend∑i
12
kθ(θi − θi0)2 −
Ntor∑i
kφ exp
[− (φi − φ0i)
2
2σ2φ
],
Bond ri0/nm Bend θi0/deg Torsional φi0/degS-P 0.3899 S-P-S 94.49 P-S-P-S -154.8P-S 0.3559 P-S-P 120.15 S-P-S-P -179.2S-A 0.4670 A-S-P 112.07 A-S-P-S -32.8S-T 0.4189 P-S-A 103.53 S-P-S-A 54.8S-G 0.4829 T-S-P 116.68 T-S-P-S -44.8S-C 0.3844 P-S-T 92.06 S-P-S-T 58.0
G-S-P 110.12 G-S-P-S -29.1P-S-G 107.40 S-P-S-G 53.9C-S-P 110.33 C-S-P-S -34.1P-S-C 103.79 S-P-S-C 57.0
Equilibriumstructure
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Bonded interactions
H0({r}) =Natom∑
i
12
mi r2i +
Nbond∑i
12
kr (ri − ri0)2
+
Nbend∑i
12
kθ(θi − θi0)2 −
Ntor∑i
kφ exp
[− (φi − φ0i)
2
2σ2φ
],
Bond ri0/nm Bend θi0/deg Torsional φi0/degS-P 0.3899 S-P-S 94.49 P-S-P-S -154.8P-S 0.3559 P-S-P 120.15 S-P-S-P -179.2S-A 0.4670 A-S-P 112.07 A-S-P-S -32.8S-T 0.4189 P-S-A 103.53 S-P-S-A 54.8S-G 0.4829 T-S-P 116.68 T-S-P-S -44.8S-C 0.3844 P-S-T 92.06 S-P-S-T 58.0
G-S-P 110.12 G-S-P-S -29.1P-S-G 107.40 S-P-S-G 53.9C-S-P 110.33 C-S-P-S -34.1P-S-C 103.79 S-P-S-C 57.0
Equilibriumstructure
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Hybrid particle field methodMesoscale potentials in molecular dynamics:
Vext,i =1φ0
kbT∑
j
χijφj(r) +1κ
∑j
φj(r)− φ0
χij : Flory-Huggins parameter. κ: compressibility. φ0: system density.
∑i<j
Vij
∑i
V ({φ(ri)})
{φ} & {∇φ}Computedon a grid
Interpolatedforces fromF = −∇Vext
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Hybrid particle field methodMesoscale potentials in molecular dynamics:
Vext,i =1φ0
kbT∑
j
χijφj(r) +1κ
∑j
φj(r)− φ0
χij : Flory-Huggins parameter. κ: compressibility. φ0: system density.
∑i<j
Vij∑
iV ({φ(ri)})
{φ} & {∇φ}Computedon a grid
Interpolatedforces fromF = −∇Vext
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Nonbonded interactions
Welec [ρ] =
∫dr VCoul(r)ρ(r)
Wnon-elec [{φ}] =1φ0
∫dr
kbT2
∑k,`
χk`φk (r)φ`(r) +1
2κ
(∑k
φk (r)− φ0
)2
P S A T C G WP χPP 0 0 0 0 0 χPWS 0 0 0 0 0 0 0A 0 0 0 χNN 0 0 χNWT 0 0 χNN 0 0 0 χNWC 0 0 0 0 0 χNN χNWG 0 0 0 0 χNN 0 χNWW χPW 0 χNW χNW χNW χNW 0
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Parametrization
I Parameters of the model:I kr , kθ, kφ, χNW , χNN , χPP , χPW
I Goals:I Reproduces well the strcuture of B-DNAI Reproduce the persistence length of SS- and DS-DNA
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Parametrization
I Parameters of the model:I kr , kθ, kφ, χNW , χNN , χPP , χPW
I Goals:I Reproduces well the strcuture of B-DNAI Reproduce the persistence length of SS- and DS-DNA
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Optimization procedure(1): Fitness parameter
η =1N
√√√√ N∑i=1
(ri,1 − ri,2)2
I Kabsch algorithm
Initial
TranslatedRotated
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Optimization procedure(1): Fitness parameter
η =1N
√√√√ N∑i=1
(ri,1 − ri,2)2
I Kabsch algorithm
InitialTranslated
Rotated
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Optimization procedure(1): Fitness parameter
η =1N
√√√√ N∑i=1
(ri,1 − ri,2)2
I Kabsch algorithm
InitialTranslatedRotated
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Optimization procedure(2): Optimization method
I Requirements:I No gradientsI Handle noisy
fitnessI Few function calls
=⇒ BayesianOptimization
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Optimization procedure(2): Optimization method
I Requirements:I No gradientsI Handle noisy
fitnessI Few function calls
=⇒ BayesianOptimization
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Optimization procedure(3): Implementation
Python interface
Shell interface
Preparesimulation
Runsimulation
Computefitness
ηχ
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Application of optimization
I 32 bp DNA, 100 mM saltI 120ns
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50
η/n
m
Nit/#
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Application of optimization
I 32 bp DNA, 100 mM saltI 120ns
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50
η/n
m
Nit/#
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Application of optimization
I 32 bp DNA, 100 mM saltI 120ns
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50
η/n
m
Nit/#
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Applications: Structural properties
I Best set:I χNW = 19.0 kJ mol−1
I χNN = −12.7 kJ mol−1
I χPW = −7.2 kJ mol−1
I χPP = −4.2 kJ mol−1
Property simulation expt.Bases per turn 9.6± 0.3 10Rise pr bp/nm 0.34(5)± 0.01 0.34Radius/nm 0.88± 0.04 0.94
2×Radius
Rise/bp
Bases/turn
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Applications: Structural properties
I Best set:I χNW = 19.0 kJ mol−1
I χNN = −12.7 kJ mol−1
I χPW = −7.2 kJ mol−1
I χPP = −4.2 kJ mol−1
Property simulation expt.Bases per turn 9.6± 0.3 10Rise pr bp/nm 0.34(5)± 0.01 0.34Radius/nm 0.88± 0.04 0.94
2×Radius
Rise/bp
Bases/turn
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Applications: Structural properties
I Best set:I χNW = 19.0 kJ mol−1
I χNN = −12.7 kJ mol−1
I χPW = −7.2 kJ mol−1
I χPP = −4.2 kJ mol−1
Property simulation expt.Bases per turn 9.6± 0.3 10Rise pr bp/nm 0.34(5)± 0.01 0.34Radius/nm 0.88± 0.04 0.94
2×Radius
Rise/bp
Bases/turn
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Applications: Hairpin-formation
0 200 400 600 800 1000
t/ns
0
5
10
15
20
Bas
epa
irnu
mbe
r
0
2
4
6
8
10
12
14
16
dbp/n
m
Initial
Final
10.05.2019 -16-
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Applications: Hairpin-formation
0 200 400 600 800 1000
t/ns
0
5
10
15
20
Bas
epa
irnu
mbe
r
0
2
4
6
8
10
12
14
16
dbp/n
m
Initial
Final
10.05.2019 -16-
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Applications: Hairpin-formation
0 200 400 600 800 1000
t/ns
0
5
10
15
20
Bas
epa
irnu
mbe
r
0
2
4
6
8
10
12
14
16
dbp/n
m
Initial Final
10.05.2019 -16-
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Persistence length DS-DNA⟨
t · tl
⟩= e−l/lp , t ≡ rP,i+10 − rP,i
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
〈t·t
l〉
l/nm
I Experimental: lP =40-60 nmI Simulation: lP =43 nm
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Persistence length DS-DNA⟨
t · tl
⟩= e−l/lp , t ≡ rP,i+10 − rP,i
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
〈t·t
l〉
l/nm
I Experimental: lP =40-60 nm
I Simulation: lP =43 nm
10.05.2019 -17-
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Persistence length DS-DNA⟨
t · tl
⟩= e−l/lp , t ≡ rP,i+10 − rP,i
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
〈t·t
l〉
l/nm
I Experimental: lP =40-60 nm
I Simulation: lP =43 nm
10.05.2019 -17-
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Persistence length DS-DNA⟨
t · tl
⟩= e−l/lp , t ≡ rP,i+10 − rP,i
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
〈t·t
l〉
l/nm
I Experimental: lP =40-60 nm
I Simulation: lP =43 nm
10.05.2019 -17-
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Persistence length DS-DNA⟨
t · tl
⟩= e−l/lp , t ≡ rP,i+10 − rP,i
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
〈t·t
l〉
l/nm
I Experimental: lP =40-60 nmI Simulation: lP =43 nm
10.05.2019 -17-
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Problem with SS-DNA
Parameter set
χNW = 10 kJ mol−1
Both are too stiff!
10.05.2019 -18-
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Problem with SS-DNA
Parameter set
χNW = 10 kJ mol−1
Both are too stiff!
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Problem with SS-DNA
Parameter set
χNW = 10 kJ mol−1
Both are too stiff!
10.05.2019 -18-
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Problem with SS-DNA
Parameter set
χNW = 10 kJ mol−1
Both are too stiff!
10.05.2019 -18-
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Outlook
I Redo optimization to get better SS-strand behaviourI Less stiff kφI Limit χNW ≤ 10 kJ mol−1
I Applications on longer doublestranded DNAI Investigate the effect of salt on persistence lengthI Plans for applying optimization on other systems
10.05.2019 -19-
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Outlook
I Redo optimization to get better SS-strand behaviourI Less stiff kφI Limit χNW ≤ 10 kJ mol−1
I Applications on longer doublestranded DNA
I Investigate the effect of salt on persistence lengthI Plans for applying optimization on other systems
10.05.2019 -19-
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Outlook
I Redo optimization to get better SS-strand behaviourI Less stiff kφI Limit χNW ≤ 10 kJ mol−1
I Applications on longer doublestranded DNAI Investigate the effect of salt on persistence length
I Plans for applying optimization on other systems
10.05.2019 -19-
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Outlook
I Redo optimization to get better SS-strand behaviourI Less stiff kφI Limit χNW ≤ 10 kJ mol−1
I Applications on longer doublestranded DNAI Investigate the effect of salt on persistence lengthI Plans for applying optimization on other systems
10.05.2019 -19-
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Acknowledgements
Morten LedumMichele Cascella
10.05.2019 -20-