resolving the structure of viral genomes with atomic

Resolving the Structure of Viral Genomes with Atomic

ResolutionAleksei Aksimentiev

Department of PhysicsUniversity of Illinois at Urbana-Champaign

I use Blue Waters to …

… understand molecular underpinnings of life … build biologically inspired systems

DNA, the blueprint

Viral genome, the program of infection

Cryoem reconstruction with concentric rings (Evilevitch et al, UIUC)

http://darwin.bio.uci.edu/~faculty/wagner/hsv2f.html

Herpes virus (HSV)

Open questions:- What is the 3D structure of the genome?- How genome ejection is triggered and sustained?- Can it be used as a drug target?

DNA is a highly

charged polymer!

Samesigncharges….

- -Samesignchargescana0ract(inamedium)

FF

- -Samesignchargesrepel

(invacuum)

FF

DNAissurroundedbycounterions +1e, sodium or potassium

+2e, magnesium or calcium

+4e,spermine

+3e,spermidine

EffecBvea0racBonbetweenDNAisobservedwhencounterionshavecharge≥2e

All-Atom Molecular Dynamics Simulation of DNA Condensates

Classical Force Field

U(r) =X

bonds

kb(b� b0)2 +

X

angles

k✓(✓ � ✓0)2 +

X

dihedrals

k�(1 + cos(n�� 0))

U(r) =X

bonds

kb(b� b0)2 +

X

angles

k✓(✓ � ✓0)2 +

X

dihedrals

k�(1 + cos(n�� 0))

+X

non-bonded pairs i,j

4✏ij

"✓�ij

rij

◆12

�✓�ij

rij

◆6#

+X


qiqj4⇡✏0rij

�

✓b

Bonded parameters from quantum mechanics

} LJ parameters from

experiments

U(r) =X

bonds

kb(b� b0)2 +

X

angles

k✓(✓ � ✓0)2 +

X

dihedrals

k�(1 + cos(n�� 0))

U(r) =X

bonds

kb(b� b0)2 +

X

angles

k✓(✓ � ✓0)2 +

X

dihedrals

k�(1 + cos(n�� 0))

+X


4✏ij

"✓�ij

rij

◆12

�✓�ij

rij

◆6#

+X


qiqj4⇡✏0rij

�

✓b

U(r) =X

bonds

kb(b� b0)2 +

X

angles

k✓(✓ � ✓0)2 +

X

dihedrals

k�(1 + cos(n�� 0))

U(r) =X

bonds

kb(b� b0)2 +

X

angles

k✓(✓ � ✓0)2 +

X

dihedrals

k�(1 + cos(n�� 0))

+X


4✏ij

"✓�ij

rij

◆12

�✓�ij

rij

◆6#

+X


qiqj4⇡✏0rij

�

✓b

}Partial charges from quantum

mechanics

Add 64 DNA helices

Add polyamine cations (+4)

Add 150 mM NaCl

Add explicit water

Solve the equation of motion (F= ma) under periodic

boundary condition in all directions

DNA-confining wall of radius RApply a half-harmonic wall

potential only to DNA

y (n

m)

15-ns MDCross-sectional view of MD using CHARMM27 Na

Standard CHARMM & AMBER Force Fields Are Not Perfect for the Simulation of DNA Condensates

x (nm)

1

2

46

10

2

46

100

Pres

sure

(ba

r)

3025DNA-DNA distance (Å)

Rau et al. AMBER99 CHARMM

1

2

46

10

2

46

100Pr

essu

re (

bar)


Rau et al. AMBER99 CHARMM

[Na] = 250 mM [Mg] = 20 mM

Rau et al.Rau et al.

CHARMM27

AMBER99

CHARMM27

AMBER99

Long-lasting contact ion pairs (CIP) between Na+ and phosphate stabilize contact DNA pairs.

2

4

12

4

102

4

100

Pres

sure

(ba

r)


Todd et al. AMBER99 CHARMM

[spermine] = 2 mM

Todd et al.

CHARMM27

AMBER99

Due to excessive CIP formation, the simulations

underestimate both inter-DNA distance and pressure in DNA

array systems.

[Na] = 250 mM outside

Yoo & Aksimentiev, JPCL 2012

Harmonic wall

Rau et al, PNAS 1984 Todd et al, BJ 2008

Champaign-Urbana Non-Bonded FIX (CUFIX): Improved Lennard-Jones Parameters for CHARMM & AMBER

• “Much of what is known about association and dissociation of solutes and ions comes from measurements of colligative properties” — Molecular driving forces by Dill & Bromberg.

-4 -2 0 2 41.21.00.80.60.40.20.0

Density (g/cm3)

Na Acetate Water Total

Na ≈

Dimethylphosphate Acetate

Yoo & Aksimentiev, JPCL 2012 Yoo & Aksimentiev, JCTC 2016

Yoo, Wilson & Aksimentiev, Biopolymers 2016

200

150

100

50

0

OSM

pre

ssur

e (b

ar)

43210molal conc (m)

200

150

100

50

0

OSM

pre

ssur

e (b

ar)

43210molal conc (m)

Murad & Powles, JCP 1993 Luo & Roux, JPCL 2010

0.20

0.15

0.10

0.05

0.00

-0.05

-0.10

U LJ (

kcal

/mol

)

4.03.63.22.8

Na–O distance (Å)

0.20

0.15

0.10

0.05

0.00

-0.05

-0.10

U LJ (

kcal

/mol

)

4.03.63.22.8

d (Å)

Standard rmin = 3.11 Å

rmin = 3.20 Å

Standard

NBFIX

CUFIX for CHARMM36 & AMBER99

Effectively infinite slab under PBC

Exp. from Robinson 1959

http://bionano.physics.illinois.edu/CUFIX

Yoo & Aksimentiev, JPCL 2012

http://bionano.physics.illinois.edu/CUFIX

1

2

46

10

2

46

100

Pres

sure

(ba

r)323028262422

DNA-DNA distance (Å)

Rau et al. AMBER99+CUFIX AMBER99 CHARMM

1

2

46

10

2

46

100

Pres

sure

(ba

r)


Rau et al. AMBER99+CUFIX AMBER99 CHARMM

CUFIX Improves Simulations of DNA Condensates

-120

-80

-40

0

40

80

120

y (Å

)

-120 -80 -40 0 40 80 120x (Å)

3

2

1

0

Charge conc. (M)

3210M

-120

-80

-40

0

40

80

120

y (Å

)

-120 -80 -40 0 40 80 120x (Å)

3

2

1

0

M

3210M

-120

-80

-40

0

40

80

120

y (Å

)-120 -80 -40 0 40 80 120

x (Å)

3

2

1

0

M

[Na] = 250 mM [Mg] = 20 mM [spermine] = 2 mM

AMBER99 AMBER99

2

4

12

4

102

4

100

Pres

sure

(ba

r)


Todd et al. AMBER99+CUFIX AMBER99 CHARMM

AMBER99

AMBER99 + CUFIX

AMBER99 + CUFIX

Yoo & Aksimentiev, NAR 2016

AMBER99 + CUFIX (MD included 200 mM Na)

CHARMM27

CHARMM27

CHARMM27

DNAispackagedbyamotor

At higher forces, DNA will deformPackaging process is slow (~min), all-atom simulation at physiological forces is not possible

Can one simulate the process?

Takes about 3 minutes to pack DNA 130 times longer than the capsid !

Max Force: 100pN

Movie: Carlos Bustamante Lab

Strategy: change resolution for speed and detail

500 bp dsDNA fragment modeled at different resolutions

24 bp/2 beads 12 bp/2 beads 6 bp/2 beads 3 bp/2 beads 1 bp/2 beads All-atom, ~100 bp

Interactions in a simple coarse-grained DNA model


Bond potentialr0 = nbp ⇥ 3.4 A

f0 = 1000pN

kspring = f0/r0

Elastic constant

r0 Force

Exte

nsio

n

http://www.phys.ens.fr/~cocco/Art/24physworld.pdf


Angle potentialPersistence length

s

Lp = 50 nm

e−s/Lp = ⟨cos θ⟩ =∫

𝕏d𝕏 cos θ δ(θ′�[𝕏] − θ)e−βU[𝕏]

∫𝕏

d𝕏 e−βU[𝕏]=

∫ π0

sin θ dθ cos θe−β 12 kspringθ2

∫ π0

sin θ dθ e−β 12 kspringθ2


90°

�

Dihedral angle potential

Twist persistence lengthLtw = 90 nm

hcos�i = e�s/Ltw

Z ⇡

0d� cos� e�

kdihed(��0)2

2kBT = e�s/Ltw

�0 = s⇥ 10.14�/A


4 nmcutoff

DNA-DNA distance (Å)

Pres

sure

(bar

)

a) c)

Atomistic capsidAtomistic DNA

Grid-based capsidAtomistic DNA

z z zGrid-based capsid

coarse-grained DNA

F

F

F

z

Periodic in axial axis

Pr

b)

6.8

nm

~28 nm

'1$�FRQÀQLQJ�ZDOO�RI�UDGLXV�5

,RQV

F

F

F

F

F

F


4 nmcutoff

80 80

4 bp/

Optimized to reproduce Rau & Parsegian pressureHalf-harmonic

wall to preventstrand crossing

Mapping between coarse-grained resolutions

For each helix, fit a 3D spline through bead coordinates

at end of simulation

coordinate1D spline

Fit a spline between quaternion representation of

rotations

Packaging viruses with ARBD

ARBD: Atomic Resolution Brownian Dynamics (multi-resolution)

Package DNA (CG) with ARBD, into CryoEM reconstruction of a HK97 bacteriophage capsid. A cryoEM map of the portal is fitted into the original capsid reconstruction, and DNA is

packaged through the portal.

Smooth, purely repulsive grid-based potential obtained by blurring cryoEM density and adding the portal

MulB-resoluBonpackagingdsDNAviruses

Internalpressureduringpackaging

�27Pressure (atm)

Perc

ent o

f DN

A

outs

ide

caps

id, % Evilevitch et

al, PNAS

Comparisontostructuraldata

�28

Simulation ExperimentJ. Mol. Biol. (2009) 391, 471-483, Hendrix et al

Cryo-electron microscopy

q [Å−1]

experiment simulation

I(q)

[a.u

.]

Small Angle X-ray Scattering

Experiment: Journal of molecular biology, 408: 541 (2011)

Simulation SAXS data were generated from CRYSOL, using an atomistic PDB of the protein coat and packaged DNA

Conclusionsandoutlook

�29

Obtained first atomic-resolution structure of packaged viral particle

Developed accurate multi-resolution representation of DNA—DNA and DNA—protein interactions

To do: Extend the model to ssRNA and ssDNA viruses

Acknowledgements

• Funding through CPLC

• Computations

Jejoong Yoo David Winogradoff

Chris Maffeo Kush Coshic

resolving the structure of viral genomes with atomic

Documents