sigbjørn løland bore weekley hylleraas seminar...

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 (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

X10.05.2019 -4-

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-

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:


frameworkI Parametrize the model

I Benchmark the modelI No excuses, parallel implementation

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The project:


frameworkI Parametrize the modelI Benchmark the model

I No excuses, parallel implementation

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The project:


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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I 72 au per bead

I 3SPN-Model of Juan dePablo

I Replace nonbondedinteractions

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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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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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Optimization procedure(1): Fitness parameter

η =1N

√√√√ N∑i=1

(ri,1 − ri,2)2

I Kabsch algorithm

Initial

TranslatedRotated

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η =1N

√√√√ N∑i=1

(ri,1 − ri,2)2

I Kabsch algorithm

InitialTranslated

Rotated

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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(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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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

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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

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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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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

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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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Problem with SS-DNA

Parameter set

χNW = 10 kJ mol−1

Both are too stiff!

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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

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Outlook


I Applications on longer doublestranded DNA

I Investigate the effect of salt on persistence lengthI Plans for applying optimization on other systems

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Outlook


I Applications on longer doublestranded DNAI Investigate the effect of salt on persistence length

I Plans for applying optimization on other systems

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Outlook


I Applications on longer doublestranded DNAI Investigate the effect of salt on persistence lengthI Plans for applying optimization on other systems

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Acknowledgements

Morten LedumMichele Cascella

10.05.2019 -20-

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