Lys-Trp-Lys: Structure and Solvation by Molecular Dynamics Simulations

Ali Hassanali

Protein Dynamics Atomic Fluctuations,

Side-Chain Motion

Loop Motion, Rigid-bodyMotion of helices

Domain and Subunitmotion

Folding/unfolding,Helix-Coil transitions

10-15 – 10-12 s

10-9 – 10-6 s

10-6 – 10-3 s

10-3 – 104 s

Ligand docking flexibility

Active site conformation adaptation, Binding

Hinge-bending, catalysis

Hormone activation, catalysis

Water Dynamics – Protein Dynamics – Biological Functioning

Indole-Water/Indole-Protein Debate

• MRD: Magnetic Resonance Dispersion (Halle. et. al.)

• Dielectric Relaxation (Steinhauser et.al. , Weingartner et.al. )

• NMR

• Fast water• Long time scale is dominated

by fluctuation of side-chains.

• QENS (quasi electron neutron scattering) (Head-Gordon et.al)

• TDFSS (Zewail et.al., Zhong et.al., Bagchi et.al.)

• Slow water• Long time scale is

attributed to dynamic exchange between bulk and hydration shell

• Agreement on two time-scales existing – disagreement on what causes the long time-scales.• Fundamentally: Experimental techniques characterize degree of perturbed water differently

protein

biological?? water

Theoretical Model

• La state Mulliken charges obtained from CASSCF calculations by Sobolewski and Domcke Chem. Phys. Lett. 315 (3-4): 293, 1999.• S0 state dipole ~ 2.41 D and La state dipole ~ 4.96 D• “Excitation” achieved by instantaneously changing ground-state charges to excited state charges• No QM integrated into this technique. (Callis. et al) • No adjustment to ground-state charges to avoid force-field clashing.

KWK Isomers

KN N KC

• Isomeric structures driven by interactions and potentially hydrophobic interactions.

cation-

Ground State: KN < N < KC

Excited State: N < KN < KC

Free-Energy Calculations

ddA

A()A H1

1

0

1

0

)0(

molkJKK

molkJKN

NC

N

/11.5)()(

/15.3)()(

• Free energy difference between each isomer and reference structure determined• Thermodynamic Integration techniques used• MD simulations yield free-energy differences and free-energy derivatives

Ground State: Excited State:

molkJNK

molkJNK

C

N

/2.3)()(

/85.)()(

KN :71%, N: 20%, KC: 9% KN :35.8%, N: 50.2%, KC: 13.9%

Ground-state free energy calculations with GROMOS96 yield same ordering

cationπ • Importance of these interactions in chemistry and biology: stabilizing protein structure during/after protein folding, protein-ligand recognition. Dougherty. Science, 271(5246): 163, 1996.• Chipot et. al. JACS 118 (12): 2998 1996, show that forcefields underestimate binding energy between toluene and ammonium in gas phase by ~ 6 kcal mol-1

• They also demonstrate that this binding energy is reduced in solvent between the range 3 - 4.7 kcal mol-1

• Aliste et. al. Biochemistry, 42(30):8976,2003 conduct their analysis without making any changes to the GROMOS96 forcefield.

LJ well-depths ~ 10 kcal mol-1

A realistic model will account for unequal polarization effects and one lysine should be farther away from the indole (Minoux and Chipot, J.Am. Chem. Soc., 121(44):10366, 1999)

Fluorescence Anisotropy

• Data fit with a double exponential for both MD and experimental data• Short time component attributed to local wobbling motion of tryptophan• Long time component represents tumbling of peptide with pi-cation complex.• Pi-cation complex doesn’t mean lysine is rigid! (Qiu et. al. J.Phys. Chem.,B 109(35): 16901,2005)• Note first 100 fs of experimental data represents internal conversion between 1La and 1Lb states

)0()0()0()(

52

2)( tPtr

Karplus et al. Biochemistry, 22(12):2884, 1983

Stokes Shifts• Double energy difference between absorbed and emitted photons

)0()()( indoleindolestokes EtEtE

• Depends on the electronic excitation energy. Gas phase excitation energy of indole chromophore is ignored in our calculations due to cancel out

)()()( ,, tEtEtE SoindoleLaindoleindole

Explicit time dependence on La excited state potential

surface

)()()( ,,, tEtEtE SwaterindoleSproteinindoleSindole

• No modeling of Lb La conversionGround

Excited

t

Competitive Solvation

• Inverse correlation between indole-protein and indole-water solvation energies• Indole-protein/water fluctuate over a very large range but total solvation energy does not!• Competition independent of water model. SPC demonstrates same phenomena• Range of ground-state fluctuations is less but still exists.• Relationship to rugged landscape of proteins/peptides where gains/loss in enthalpy and entropy pave the free energy landscape?

Long equilibrium excited

and ground

state runs

Stokes Shifts Results

• Stokes shifts data for three isomers shown with error-bars• Three important time scales• Inset shows inertial regime• Inertial regime dominated by indole-water solvation

Ground

Excited

t

N-Complex Fits

SececectS

ttg

t

g 2211

2

SecececectS

tttg

t

g 332211

2

molkJS

psmolkJc

psmolkJc

fsmolkJc gg

/32.33

5.52,/98.4

79.0,/49.9

47,/85.18

22

11

MD

Experiment

molkJS

psmolkJc

psmolkJc

psmolkJc

fsmolkJc gg

/22.31

3.23,/96.1

3.3,/87.7

613.0,/24.12

590,/15.9

33

22

11

• Total Stokes shift show remarkable agreement• Experimental inertial decay is slower than MD: experimental or MD (forcefield) artifact?• No isomerization detected in experiment• Small errors in barrier size can affect rates of activated processes in MD• Were Stokes shifts observed long enough to witness isomerization?

N-Complex Solvation

• Steady lowering of solvation energy drives overall process• Initial drop over 1 ps is dominated by indole-water contribution• 0.79 ps and 54 ps solvation process involves compensation between protein and water to solvate indole• For KN and KC , isomerization

makes similar analysis difficult

N-Complex Peptide Readjustment

• Clear motion of lysine NT ammonium toward indole by ~ 0.08 nm• C-terminus lysine side-chain moves by same distance but farther away• N-terminus lysine side-chain also shows minor adjustment

KN & KC Peptide Readjustment

• KC shows clear response by moving toward indole and then relaxing• KN shows a less discernible process perhaps due to faster isomerization rates• Remote lysines for both isomers show clear response by moving away from

the indole ring• Other coordinates for KN might reveal similar behavior as KC

Peptide Dynamics, Isomerization

• Chain-extension breaks pi-cation and perhaps hydrophobic interactions• Isomerization rates for KN is faster than KC

• KC isomerization is driven by kinetics, even though it is at a higher free energy

than KN

KN N KC N

NH3 +

NH3 +

Peptide-Motions

Acknowledgements

• Sherwin Singer

• Dongping Zhong

• Tanping Li

• Members of Singer and Zhong groups

Thank you for listening!

Funding Sources:

• LIGDP and NSEC