David M. SmithDiv. Org. Chem. and Biochem., Institut Ruđer Bošković, Zagreb

Specific Interactions Between Sense and Complementary Peptides:

What Can Molecular Dynamics Tell Us?

Complementary Peptides: What are they ?

3’ ← AUA-CCC-CCG-AAG-UAC ← 5’Complementary mRNA (-)

5’ → TAT-GGG-GGC-TTC-ATG → 3’Sense DNA

3’ ← ATA-CCC-CCG-AAG-TAC ← 5’Complementary DNA

C ← Ile-Pro-Ala-Glu-His ← NComplementary Peptide

5’ → UAU-CCC-GGC-UUC-AUG → 3’Sense mRNA (+) Transcription

N → Tyr-Gly-Gly-Phe-Met → CSense PeptideTranslation

ChemBioChem. 2002, 3, 136

Some Mekler-Idlis Pairs

CysArgGlySer

Ala

TrpGlyArgArg

Pro

SerAlaThrPro

Gly

CysAgrGlySer

Thr

Sense Complementary Sense Complementary

Biophyzika. 1969, 14, 581

Hydropathicity and the Molecular Recognition Theory

NH2CHC

CH2

O

N

HN

HNCHC

CH2

O

CH2

C

OH

O

HNCHC

CH3

O

NC

NHCHC

CH

HO

O

H3C

CH2

CH3

O

Hydrophobic HydrophobicHydrophilic

Hydrophilic

H2N CH C

CH2

O

OH

NH CH C

H

OHN CH C

H

OHN CH C

CH2

OHN CH C

CH2

OH

O

CH2

S

CH3 HydrophobicHydrophobic

Hydrophilic

Hydrophilic

Biochem. Biophys. Res. Commun. 1984, 121, 203

An Alternative Definition of Complementary Peptides:

3’ → AUA-CCC-CCG-AAG-UAC → 5’Complementary mRNA (-)

N → Ile-Pro-Pro-Lys-Tyr → CComplementary Peptide

5’ → TAT-GGG-GGC-TTC-ATG → 3’Sense DNA

3’ ← ATA-CCC-CCG-AAG-TAC ← 5’Complementary DNA

5’ → UAU-CCC-GGC-UUC-AUG → 3’Sense mRNA (+)

N → Tyr-Gly-Gly-Phe-Met → CSense Peptide

Pro. Nat. Acad. Sci. 1985, 82, 1372

Some Root-Bernstein Pairs

ArgArgArgArg

Ala

GlyGlyGlyGly

Pro

ProProProPro

Gly

CysCysTrpstop

Thr

Sense Complementary Sense Complementary

J. Theor. Biol. 1983, 100, 99

The SystemNH CH C

CH2

O

OH

NH CH C

H

OHN CH C

H

OHN CH C

CH2

OHN CH C

CH2

HN

O

CH2

S

CH3

CH3C

O

H3C

HN CH C

CH

O

CH2

CH3

NC

O

N

C

O

HN CH C

CH2

O

CH2

CH2

CH2

NH2

NH CH C

CH2

NH

O

OH

CH3

H3C

C

O

H3C

Ace-Tyr-Gly-Gly-Phe-Met-NmeAce-Ile-Pro-Pro-Lys-Tyr-Nme

Croat. Chem. Acta. 1998, 71, 591

Molecular Dynamics: The Force Field

U(R) = bonds

Kr (r - req)2 angles

K ( - eq)2+

Bonds Angles

Dihedrals

Van der Waals Electrostatic

Vn

2dihedrals

(1 + cos[n - +

i<j

Aij

rij12

-atoms

Bij

rij6

+qi qj

riji<j

atoms

+

+

+

Implicit Solvation (Elec.)

qi qj

f gb(rij,Ri,Rj)

i<j

atoms

+ + A+

Implicit Solvation (Non Elec.)

Molecular Dynamics in Practise

Fi = mi ai

-dUdri

= mid2ri

dt2

In practise we must numerically integrate these equations with a finite time step

(typically 1-2 fs)

In principle, doing MDs is simply a matter of solving Newton’s equations of motion

Molecular Dynamics in Action

50 ps of MD at 300 K with implicit solvation

Analysis: Structural Deviations

Root Mean Square Deviation from a reference structure vs time

Analysis: Clustering

BackboneOverlay

Cluster 1, Pop. = 28%<E> = -57.5 kcal/mol

Cluster 2, Pop. = 45%<E> = -58.6 kcal/mol

Cluster 3, Pop. = 27%<E> = -58.5 kcal/mol Minimum Energy Structure

E= -16.7 kcal/mol

Analysis: Clustering

28%

27%

45%

Implicit solvent, 150 ns

Principle Component Analysis

Projections onto the eigenvectors of the covariance matrix

Principle Component Analysis

28%

27%

45%

What about the force field?FF94, Implict solvent, 150 ns

Differences in the Force Field

12%

58%

27%

FF99, Implict solvent, 150 ns4%

Differences in the Force Field

51%

16%

33%

FF03, Implict solvent, 150 ns

What Does Experiment SayNMR experiments in water show an essentially random distribution of conformers

Biophys. J. 2004, 86, 1587

NMR, experiments in binary bilayered mixed micelles(bicelles) show a well-defined structure:

Explicit Solvation

50 ps of MD at 300 K with explicit solvation (NVT)

Explicit Solvation: Analysis

54 %

19%

27%

40 ns of MD at 300 K with explicit solvation (FF03)

Replica Exchange DynamicsSingle simulations, especially in explicit solvent, are prone to become trapped in potential energy minima

Increasing the temperature can facilitate barrier crossingsbut can lead to irrelevant results

P(exchange) = exp -kBTi

1

kBTj

1Ei - Ej

A modern solution is to construct several replica simulationswith different temperatures and allow them to exchange according to:

Replica Exchange Dynamics

16 replicas simulated for 2.5 ns each, implying 40ns in total.The temperatures range between 275K and 420K such that P≈0.2.

Replica Exchange Dynamics

27%

33%

40%

40 ns (16 x 2.5) of MD at 275-420 K with explicit solvation (FF03)

Non-Exchanging Replicas

Replica exchange MD is an inherently parallel method

An alternative approach is to construct several non-interacting replicas (distributed computing)

An efficient way to implement this is to first run one simulation at high temperature and to cluster the results

The structure closest to the centroid of each cluster canthen be used as a starting point for each replica

Non-Exchanging Replicas

30%

33%

37%

40 ns (8 x 5) of MD at 300 K with explicit solvation (FF03)

Sense and Complementary Peptides

1 ns of MD at 300 K with explicit solvation

Sense and Complementary Peptides

40 ns (8 x 5) of MD at 300 K with explicit solvation

19%

30%

23% 13%

16%

A Closer Look at the Clusters

Cluster 1: Population 30 %

A Closer Look at the Clusters

Cluster 2: Population 19 %

A Closer Look at the Clusters

Cluster 3: Population 23 %

A Closer Look at the Clusters

Cluster 4: Population 13 % Cluster 5: Population 16 %

Analysis: Structural Properties

Separation of the centres of mass of the two peptides

Analysis: Structural Properties

Separation of the centres of mass of the complementary residues

Conclusions• The force field can have a strong influence on the structural properties. FF03 can probably be trusted.

• Met-enkephalin does not have a well-defined native structure in aqueous solution at 300 K.

• Met-enkephalin does exhibit some affinity for its complementary counterpart but this is apparently not based on the specific interactions predicted by the Molecular Recognition Theory.

• Non-interacting replicas constitute a good approximation to the replica exchange method and a good alternative to a single long simulation, at least for small peptides.

BackboneOverlay

Analysis: Clustering (ff03)

Cluster 1, Pop. = 51%<E> = 0.4 kcal/mol

Cluster 2, Pop. = 33%<E> = -0.5 kcal/mol

Cluster 3, Pop. = 16%<E> = 0.4 kcal/mol Minimum Energy Structure

E= -16.7 kcal/mol

Analysis: Clustering (ff03)

51%

16%

33%

Principle Component Analysis (ff03)

51%

16%

33%