Digitally Pulling Proteins: Molecular Dynamics Simulations

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ACS Fellows Program Series Lessons Learned from Molecular Dynamics Simulations

Dr. Rigoberto Hernandez Georgia Institute of Technology and ACS Board of Directors

Dr. Stephen Quirk Kimberly-Clark Corporation



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June 12, 2014

Digitally Pulling Proteins: Molecular Dynamics Simulations Rigoberto Hernandez

Georgia Tech Chemistry & Biochemistry

Adaptive Steered Molecular Dynamics Preliminaries: SMD, Jarzynski’s Inequality, NAMD

Stretching Decaalanine

G. Ozer, S. Quirk and R. Hernandez, (in vacuum), J. Chem. Phys. 116, 1328 (2012). G. Ozer, S. Quirk and R. Hernandez, (in solvent), J. Chem.Theory. Comput, 8, 4837 (2012).

Dr. Ozer

Unfolding of NPY

G. Ozer, E.Valeev, S. Quirk and R. Hernandez, J. Chem.Theory Comput., 6, 3026 (2010). (doi:10.1021/ct100320g) R. Hernandez @ Georgia Tech

ASMD of the long-distance unfolding of neuropeptide Y (NPY)

• •

Gungor Ozer

Stephen Quirk

Questions:

-

Does NPY bind in folded/unfolded form? How does NPY unfold?

Approach:

-

P1: Use accelerated dynamics to map the unfolding trajectory

-

P2: Adaptive SMD (Jarzynski’s Theorem) to calculate PMF for long paths

-

P3: Use TST to calculate rates

G. Ozer, E.Valeev, S. Quirk and R. Hernandez, J. Chem.Theory Comput., 6, 3026-3038 (2010)

R. Hernandez @ Georgia Tech

Neuropeptide Y (NPY) !

!

!

Background: "

36 residue peptide tail

"

Abundant in mammalian CNS

TWO CONFORMATIONS "

α-helix & polyproline tail folded onto helix

"

Free tail fluctuates away from helix

STRUCTURE CONTROVERSY "

Adopts pp-fold as a monomer (active form) Nordmann, Blommers, Fretz, Arvinte, and Drake, Eur. J. Biochem., (1999) (Dobson 1992, Reeve 2000, Blundell 1981, Darbon 1992, Boulanger 1995)

"

NMR studies suggest no pp-fold in dimer or when bound to dodecylphosphocho-line (DPC) micelles (membrane mimic) Cowley, Hoflar, Pelton,, and Saudek,, Eur. J. Biochem., (1992)

"

But, at low concentrations, monomeric NPY favors a less ordered structure in which the α-turn of NPY is more destabilized Bettio, Dinger, and Beck-Sickinger, Protein Sci., (2002)

"

QUESTION: Before binding, is NPY open or in the pp-fold? R. Hernandez @ Georgia Tech

P1 Accelerated Dynamics of NPY Tail – Turn – Helix (ANGLE)

Free MD with 49 trajectories Full unfolding was not allowed

Tail – Helix (DISTANCE)

Tail travels away from the helix as a whole

⇒ The tail appears to unfold as a hinged motion R. Hernandez @ Georgia Tech

Summary: Tail unhinges away from the α-helix in the apparent unfolding path !

The unfolding of NPY follows a hinging mechanism rather than a random opening of tail. PRO5

Angle: PRO5-ALA12-LEU24 Distance: PRO5-ALA12

LEU24 Initial angle: ~24.4 o; Initial distance: ~16.1 A Final angle: ~144.4 o; Final distance: ~14.3 A

ALA12

!

Residues from ALA12 to PRO5 fluctuates considerably less than the residues from TYR1 to LYS4.


P2: Steered MD simulations at 500K & 310K !

Steered Molecular Dynamics (SMD) simulations "

Harmonically attached to a dummy particle that moves on that curved path

"

The potential between this “dummy” and the atom(s) that is being pulled:

1 U(r1,r 2 ,...,t) = k vt − R(t) − R 0 .n 2

[ (

!

) ]

2

PMF Calculation "

Calculate work€at each step

"

Use Jarzynski’s equality to relate non-equilibrium W to equilibrium ΔF

or Jarzynski, C., Phys Rev Lett., 78 (14), 2690-2693 (1997) Park S. & Schulten K., JCP., 120 (13), 5946-5961 (2004)


P2 SMD Unfolding of NPY at 300K and 500K Work & PMF @ 500 K

SMD with 144 trajectories k = 7.2 kcal/mol (500 pN/mol)

Work & PMF @ 310 K

PMF dominated by the lowest trajectory The accuracy is suspicious

⇒ Lowest-Energy Trajectory Dominates PMF


P2 Second-Order Cumulant (SOC) of SMD unfolding of NPY EA vs. SOC @ 500 K


EA vs. SOC @ 310 K

Exponential average : ΔG =

1 ln e − βW β

Cumulant expansion : ΔGB ← A

A

β2 β3 2 2 = −β W + W − W − (...) + ... 2 !####"####$ !6#"#$

(

SECOND ORDER

)

HIGHER TERMS

Work distribution is not Gaussian

⇒ SOC does Not Converge to Exponential Average (EA)


Think-Pair-Share Query •

SMD does not appear to work for NPY pulls beyond 5 Angstroms of pulling. What should we do?

A

A) Pull more slowly👆

B

B) Pull more often C) Pull differently D) Give up

C D


P2 Slower pulls of SMD unfolding Work & PMF @ 500 K


Work & PMF @ 310 K

⇒ Differences between SOC and EA remain and convergence is not improved


P2 Adaptive Steered MD ALGORITHM

A:

p

q

x:

p

q

B:

p

q

λ •

Pull the first (1/n)λ step (many times!)

Compare trajectories Pick the configuration that requires the amount of work closest to JA (a heuristic proof provided in the article listed below.) •

•

Assign the chosen configuration to be input for the next (1/n) λ step

•

Loop until λ completed

One can generalize this to divide the RC into many steps

G. Ozer, E.Valeev, S. Quirk and R. Hernandez, J. Chem.Theory Comput., 6, 3026-3038 (2010)


P2 Adaptive SMD Unfolding of NPY Work & PMF @ 500 K


Work & PMF @ 310 K

NOTE: PMF at low T has a higher barrier as expected (because its unfolding rates is much slower)

⇒ PMF no longer dominated by a single trajectory, and R. Hernandez hence convergence can be achieved. @ Georgia Tech

P3 Second-Order Cumulant (SOC) of adaptive SMD unfolding of NPY Work & PMF @ 500 K


Work & PMF @ 310 K

Work distribution is Gaussian along RC ESTIMATED RATES: @ 500K: 5.5x105 s-1 (unfolding in 1.8 µs) @ 310K: 5.1x10-5 s-1 (unfolding in >5 hours)

⇒ SOC and EA agree suggesting that the adaptive SMD R. Hernandez allows the system to remain “harmonic” @ Georgia Tech

P3 Monomeric NPY adopts pp-fold UNFOLDING RATES @ 500K: 5.5x105 s-1 (unfolding in 1.8 µs) @ 310K: 5.1x10-5 s-1 (unfolding in >5 hours) !

Recall: STRUCTURE CONTROVERSY "

Adopts pp-fold as a monomer (active form) Nordmann, Blommers, Fretz, Arvinte, and Drake, Eur. J. Biochem., (1999) (Dobson 1992, Reeve 2000, Blundell 1981, Darbon 1992, Boulanger 1995)

"

NMR studies suggest no pp-fold in dimer or when bound to dodecylphosphocho-line (DPC) micelles (membrane mimic) Cowley, Hoflar, Pelton,, and Saudek,, Eur. J. Biochem., (1992)

"

But, at low concentrations, monomeric NPY favors a less ordered structure in which the α-turn of NPY is more destabilized Bettio, Dinger, and Beck-Sickinger, Protein Sci., (2002)

⇒ Our results are consistent with: •NPY adoption of PP-fold in solution •there exists a timescale after which it can unfold (which could have led Bettio et al observation.)



Which of the following characteristics would be least useful in choosing a protein with which to verify ASMD:

A

A) A protein whose reaction/unfolding path is easy to identify

B

B) A protein that plays a role in human health

C

C) A protein whose PMF is well-known D) A protein whose PMF can be converged using ASMD on current HPC resources

D


Decaalanine • 10 alanine residues • 104 atoms • Helical secondary structure

• Pulling C

(in yellow) at sites, 1 and 10 α

• Note H-bonds (in courtesy of Hailey Bureau

blue)


ASMD: stretching decaalanine

•

•

Questions:

-

Does Adaptive SMD really work? What is the role of water in the stretching of helix to a coil?

Approach:

-

Compare adaptive SMD to previous work by Park and Schulten in vaccum

-

Use adaptive SMD to obtain PMF and Hbonding profiles in solvent

G. Ozer, S. Quirk and R. Hernandez, (in vacuum), J. Chem. Phys. 116, 1328 (2012). G. Ozer, S. Quirk and R. Hernandez, (in solvent), J. Chem.Theory. Comput, 8, 4837 (2012).


ASMD of Decaalanine • Use Schulten structure

(Aminated not acetylated N-terminus)

• Hold N-terminus • Pull C-terminus w/t auxiliary spring

courtesy of Hailey Bureau

• CHARMM force field ?! • Vaccum ?! R. Hernandez @ Georgia Tech

Stretching decaalanine in vacuum: SMD vs. Adaptive SMD ν = 100Å/ns ν = 100Å/ns

ν = 10Å/ns

ν = 10Å/ns

S. Park and K. Schulten, J. Chem.Phys. 120, 5946 (2004) G. Ozer, S. Quirk and R. Hernandez, (in vacuum), J. Chem. Phys. 116, 1328 (2012).

In Vacuum!


ASMD vs. Steps+Equilibration • ν = 100Å/ns

ν = 10Å/ns

• G. Ozer, S. Quirk and R. Hernandez, (in vacuum), J. Chem. Phys. 116, 1328 (2012).

At the end of each step, we can do one of two things:

•

Equilibrate all trajectories under 0 force & then restart (FR-ASMD)

•

Pick a structure from the ensemble of trajectories & use that for the next step (ASMD)

ASMD with JA choice gives rise to converged Eq’ed PMF! In Vacuum!


ASMD vs. SMD: RMS Error •

•

G. Ozer, S. Quirk and R. Hernandez, (in vacuum), J. Chem. Phys. 116, 1328 (2012).

RMS Error:

•

measured as a function of initial and final energy difference (relative to reversible.)

•

sampled from the total number of trajectories.

ASMD is particularly good at the faster time step, but still good at slow time step. In Vacuum!


Convergence of H-Bond counts ν = 100Å/ns

ν = 10Å/ns


•

We can also monitor other observables weighted according to the work function.

•

We look at internalhydrogen bonds as defined by relative OO distance.

•

We see similar results for ASMD and SMD w/t equilibration for τ

•

Also find convergence w.r.t. pulling speed. In Vacuum!


Stretching decaalanine in water: Potential of Mean Force (PMF) • Decaalanine is stretched in TIP3P water from 13Å to 33Å:

Configurations

• Three different

pulling rates: 100Å/ns, 33Å/ns, and 10Å/ns

• Several sets of

trajectories per step (tps)

• Convergence is

achieved at 10Å/ ns and 400 tps

G. Ozer, S. Quirk and R. Hernandez, (in solvent), J. Chem.Theory. Comput, 8, 4837 (2012).

In Tip3P


Stretching decaalanine in water: Potential of Mean Force (PMF)

• The free energy cost to stretch the chain is much lower in solvent than in vaccum • The coil region is flatter, and appears to be more structured G. Ozer, S. Quirk and R. Hernandez, (in solvent), J. Chem.Theory. Comput, 8, 4837 (2012).

In Tip3P


Stretching decaalanine in water: H-Bonds along path intra vacuum

•The initial H-bonding (up to the minimum) is relatively flat as this involves an internal rearragement

•The loss of intra-peptide H-bonds is more dramatic in solvent.

• The solvent replaces the hydrogen bonds as the peptide is stretched.

intra solvent

• The first-half of the inter-peptide H-bonds is slower

than the second-half—possibly reflected in the PMF.

solvent inter


inter


Puzzle: In vacuum, the total number of Hbonds are nearly constant for the first 10 Angstroms, but they break in solvent. Why?

A

A) There must be something wrong in the model

B

B) Not all hydrogen bonds are created equal

C

C) Intra-protein hydrogen bonds are less stable in water

D

D) Intra-protein hydrogen bonds are more stable in water


Stretching decaalanine in vacuum: Which H-Bonds? ν = 100Å/ns •In vacuum: •Initially all i→i+4 (α-helix) •Then i→i+3 (310-helix) ν = 10Å/ns

•No i→i+5 (π-helix) •Finally all broken


inter

In Vacuum!


Stretching decaalanine in water: Which H-Bonds? ν = 100Å/ns •In vacuum: (lighter lines) •Initially all i→i+4 (α-helix) ν = 33Å/ns

•Then i→i+3 (310-helix) •No i→i+5 (π-helix) •Finally all broken •In solvent:

ν = 10Å/ns

•Initially all i→i+4 (α-helix) •Very little i→i+3 (310-helix) — circa 20Å •Very little i→i+5 (π-helix) crushed early •Finally all broken

G. Ozer, S. Quirk and R. Hernandez, (in solvent), J. Chem.Theory. Comput, 8, 4837 (2012).

inter

In Tip3P


Digitally Pulling Proteins: Molecular Dynamics Simulations

CONCLUSIONS and FUTURE DIRECTIONS

• SMD (with Jarzynski NonEq PMF) vs. ASMD • • •

SMD for a complex reaction doesn’t alway converge. Strong dominance of the lowest energy traj. on PMF. ASMD achieved converged work distribution –thus more accurate free energy profile– along the chosen (reaction) path.

• Suggests/Confirms: •

Monomeric NPY adopts biologically active PP-fold; it does not unfold upon binding. • Nordmann, Blommers, Fretz, Arvinte, and Drake, Eur. J. Biochem., 261, p216 (1999) • [Dobson 1992, Reeve 2000, Blundell 1981, Darbon 1992, Boulanger 1995 &1998]

• Decaalanine Stretching/Pulling: • Recovers PMF in vacuum • Traverses very different paths in vacuum vs. Solvent G. Ozer, E.Valeev, S. Quirk and R. Hernandez, J. Chem.Theory Comput., 6, 3026 (2010). G. Ozer, S. Quirk and R. Hernandez, (in vacuum), J. Chem. Phys. 116, 1328 (2012). G. Ozer, S. Quirk and R. Hernandez, (in solvent), J. Chem.Theory. Comput, 8, 4837 (2012).


Acknowledgments

• • • • • • • • • •

Collaborators

Turgay Uzer, Georgia Tech Charles Eckert, Georgia Tech Charles Liotta, Georgia Tech Rosa Benito, Politécnica de Madrid Tino Borondo, Autónoma de Madrid Thomas Bartsch, U. Loughborough, UK John Stanton, U. Texas (Austin) Iain Boyd, U. Michigan Ronald Hanson, Stanford Stephen Quirk, Kimberly-Clark

My Group

Dr. Alex Popov Dr. Eliezer Hershkovits Dr. Inga Ulusoy Dr. Svetlana Khokhlova

Funding & Partners

Dr. Caley Allen Galen Craven Ben Mahala Hailey Bureau Ryan Bucher R. Hernandez @ Georgia Tech

Acknowledgments

• • • • • • • • • •

Collaborators

My Group

Turgay Uzer, Georgia Tech Charles Eckert, Georgia Tech Charles Liotta, Georgia Tech Rosa Benito, Politécnica de Madrid Tino Borondo, Autónoma de Madrid Gungor Ozer Thomas Bartsch, U. Loughborough, UK John Stanton, U. Texas (Austin) Iain Boyd, U. Michigan Ronald Hanson, Stanford Stephen Quirk, Kimberly-Clark Stephen Quirk

Funding & Partners

en Gal

Dr . Al

ex

Pop ov

s

vit o hk s r

Hailey Bureau ven a r C

ze

r.

D

e Eli

Ben Mahala

Rhylova k ho an K a Bu lan t e ch v S . er r D

y All e l a C Dr.

e H r

en

Dr. I

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Ulus oy







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Digitally Pulling Proteins: Molecular Dynamics Simulations

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