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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
non-bonded pairs i,j
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
non-bonded pairs i,j
4✏ij
"✓�ij
rij
◆12
�✓�ij
rij
◆6#
+X
non-bonded pairs i,j
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
non-bonded pairs i,j
4✏ij
"✓�ij
rij
◆12
�✓�ij
rij
◆6#
+X
non-bonded pairs i,j
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)
323028262422DNA-DNA distance (Å)
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)
3028262422DNA-DNA distance (Å)
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
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)
3025DNA-DNA distance (Å)
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)
3028262422DNA-DNA distance (Å)
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
Strategy: change resolution for speed and detail
Strategy: change resolution for speed and detail
Strategy: change resolution for speed and detail
Strategy: change resolution for speed and detail
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
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
Interactions in a simple coarse-grained DNA model
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
Interactions in a simple coarse-grained DNA model
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
Interactions in a simple coarse-grained DNA model
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
Interactions in a simple coarse-grained DNA model
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
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