SIMULATIONS OF PEPTIDEFOLDING and DYNAMICS

Krzysztof Kuczera

Departments of Chemistry and Molecular BiosciencesUniversity of Kansas

IMAWorkshop Jan14-18, 2008

Replica-exchange molecular dynamics

T1

T2

T3

T4

Propagate independenttrajectories at temperaturesT1 > T2 > T3 …Stop and compare energiesExchange between neighbors

ii

jiij

kT

EE

ejiw

jiw

1

))((

)(

1)(

Advantages:+ accelerated sampling @ low T+ Boltzmann distributions @ all T+ Minimal process communication

21-residue helix-forming peptide

Blocked peptide: Ac-WAAAH+-(AAARA)3-A-NH2

21 residues

Simulation 1: equilibrium distribution start: helix trajectory: 30 ns

Simulation 2: folding start: extended trajectory: 15 ns

Method: CHARMM with CMAP electrostatics: GBMV nonpolar: Gnp=- A with = 4 cal/(mol Å2)

REMD at 8 temperatures, 280-450 K

MMTSB tool kit (C.L. Brooks, Scripps)

Sm

kcal/mol cal/(mol K) K

-12 -40 296G.S. Jas & K. Kuczera, Biophys. J., 87:3786 (2004)

Experiments:Gouri S. JasBaylor University

Sm

kcal/mol cal/(mol K) K

REMD -10 -30 330-350Experiment -12 -40 296

Hydrogen bonds:HB: Oi…Ni+4 < 4.0 Å f = <NHB>/17

Backbone conformations:population of residues within 30o of () = (-62o,-41o)

Data points with error bars: from 15-30 ns of REMD simulationSolid lines: from fit to van’t Hoff equation

Zimm-Bragg ParametersStatistical weights partition function coil : 1 helix with h-bond: w = s helix without h-bond: v = 1/2

REMD results at 300 K: helix fraction = 0.78 number of helix fragments = 1.08

w = 1.86 v = 0.11

Previous Ala-based peptide simulations: w = 1.12 – 2.12 v = 0.06 – 0.30

Equilibrium distribution 300 K 450 K

helix

PPII

strand

Folding: transition state

w(n) = -kTln[P(n)]w(n) = -kTln[P(n)/C(n)]

C(n) = 17!/n!(17-n)!

Equilibrium REMD: conclusions

• We have calculated an equilibrium melting curve for a helix-forming peptide with GB/SA model

• Thermodynamics qualitatively correct Melting temperature exaggerated

•Global free energy minimum = -helixat low T = coil at high T

• Microscopic information about helix unfolding - unfolding initiated at termini

transition state ½ helix - formation of compact structures at low T - and PPII structures at high T

REMD simulation of helix folding

Ideal -helix appears after 2.8 ns

Folding REMD: conclusions

• -helix structure found after ca. 3 ns simulation time

• confirm that helix is global FE minimum, not a memory effect

• folding in room T replica is sequential

• structures and properties sampled are similar to trajectory starting from helix • conformational sampling acceleration of REX-MD over direct MD is ca. 100 overall (ca. 12per CPU) [3 ns folding in REMD vs. 300 ns exp time scale]

Acknowledgments

• Gerald Lushington, University of Kansas Molecular Modeling and Graphics Laboratory – Athlon cluster • Michael Feig, John Caranicolas and Charles L. Brooks III MMTSB Tool Set (2001), The Scripps Research Institute • Gouri S. Jas, Baylor University - experiments

• ACS PRF $$$

w(n) = -kT ln P(n)

Sm

kcal/mol cal/(mol K) K

REMD -10 -30 330-350Experiment -12 -40 296

T1

T2

T3

T4

Replica-exchange MD:Propagate independenttrajectories at temperaturesT1 > T2 > T3 …Stop and compare energiesExchange between neighbors

REMD simulation of helix-coil equilibrium

Sm

kcal/mol cal/(mol K) K

Exp -12 -40 296

REMD -7 -20 354

REMD hbonds -10 -27 354

w(n) = -kT ln P(n)