Veracity through variety (of methods):Simulating dipeptides with little volume

Tanja van Mourik

Overview

• Why study peptides with computational methods?

• What is computational quantum chemistry?

1. Background

2. Application

• The shape of a small peptide

little “volume”

1. Background theory

Why study peptides with computational methods?

• the shape of biomolecules is important for their function

• it is difficult to deduce the shape unambiguously from experiments

• computational data can help experimental assignment

function

shape

?

What is computational quantum chemistry?

Quantum chemistry is based on quantum mechanics

Particles are completely characterised by their wavefunction

Wavefunction can be obtained from the Schrödinger equation:

H =E

H =E

However, the Schrödinger equation cannot be solved exactly

Need to use approximate methods

in general:

more precise methods == higher computational demand

larger basis sets => more precise results => higher computational demand

more precise methods == higher computational demand

Level of theory depends on method and basis set

Method: approximate way to solve the Schrödinger equation

Basis set: representation of the wavefunction

H =E

2. Application

The shape of the Tyr-Gly dipeptide

N

O

O

O-H

H H

C CCC

C

C = carbonO = oxygen

N = nitrogenH = hydrogen

N

H-OC

CC

CC

C

H

H

H

H

H-O

2 x 2 x 2 x 3 x 6 x 6 x 12 x 12 = 124416 conformers

single-pointcalculationsHF/3-21G*

33433

geometryoptimisationsHF/3-21G*

300

single-pointMP2/6-31+G*

20

Hierarchical Selection Scheme

geometry optimisationsMP2/6-31+G*

selected conformers:

create structures ofall possible conformers

sort according to their numberof H-bond interactions

124416

geometryoptimisations

B3LYP/6-31+G*20

0.0 3.4 3.6 3.9 4.2

4.5 5.6 5.6 5.7 5.8

6.5 6.5 7.0 7.1 7.1

7.4 10.5 10.5 10.6 11.0

conf 1 conf 2 conf 3

conf 4 conf 5 conf 6

Geometries from B3LYP/6-31+G(d)

Structures were computed with two different levels of theory:

• B3LYP/6-31+G*

• MP2/6-31+G*

method basis set

MP2 and B3LYP generally assumed to be of similar accuracy.However, the MP2 and B3LYP structures differ considerably!

fGly

B3LYP structure MP2 structure

missing dispersion?

BSSE?

Dispersion: physical attraction between atoms

BSSE: artificial attraction between atoms

B3LYP, MP2: two different quantum-chemical methods

rotationaround fGly

MP2/6-31+G*

B3LYP/6-31+G*

fGly

DE

[k

J/m

ol]

MP2 B3LYP

B3LYPminimum MP2

minimum

MP2minimum

Possible reasons for the different geometries obtainedwith B3LYP and MP2:

• MP2 results may be affected by BSSE (unphysical attraction)

• B3LYP results may be affected by missing dispersion (physical attraction)

We can reduce the BSSE in the MP2 calculationsby using larger basis sets

rotationaround fGly

MP2 B3LYP

B3LYPminimum MP2

minimum MP2

minimum

MP2/6-31+G*

B3LYP/6-31+G*MP2/6-31+G*MP2/avdzMP2/avtzMP2/avqz

fGly

DE

[k

J/m

ol]

veracity through variety

MP2/avdz

MP2/avtz

MP2/avqz

BSSE (kJ/mol)

BSSE not the same over the fGly range

Summary

Using computational quantum chemistry one canpredict almost any molecular property, withoutprior knowledge of the molecular system

But: to obtain reliable results, high levels of theoryneed to be used, requiring large computational resources

Results obtained with high-level methods can beused to verify/calibrate more approximate methods

Here: shape of a small peptide

“little volume”

=> “veracity through variety”

Static structures => no velocity

Problem

Hierarchical selection scheme is not guaranteedto select the most stable conformers

(Even high-level methods may miss conformers)

Can data science help to selectmost relevant conformers?

Acknowledgements

Engineering and Physical Sciences Research Council(EPSRC)

The Royal Society

EaStCHEM

Leo Holroyd (UCL and St Andrews)

Ashley Shields (St Andrews)

EaStCHEM Research Computing Facility

Dimitrios Toroz (UCL)

Jie Cao (St Andrews)

“Tyrosine-glycine revisited: Resolving the discrepancy between theory and experiment”Leo F. Holroyd and Tanja van Mourik, Phys. Chem. Lett. 621, 124-129 (2015).

“Performance of the M06-L density functional for a folded Tyr-Gly conformer”J. Cao and T. van Mourik, Chem. Phys. Lett. 485, 40-44 (2010).

“Insufficient description of dispersion in B3LYP and large basis set superposition errors in MP2 calculations can hide peptide conformers”L. F. Holroyd and T. van Mourik, Chem. Phys. Lett. 442, 42-46 (2007).

“The structure of the gas-phase tyrosine-glycine dipeptide”D. Toroz and T. van Mourik, Mol. Phys. 104, 559-570 (2006).

“Comparison of ab initio and DFT electronic structure methods for peptides containing an aromatic ring: The effect of dispersion and BSSE”A. E. Shields and T. van Mourik, J. Phys. Chem. A 111, 13272 – 13277 (2007).

“Conformational structure of tyrosine, tyrosyl-glycine and tyrosyl-glycyl-glycine by double resonance spectroscopy”A. Abo-Riziq, L. Grace, B. Crews, M.P. Callahan, T. van Mourik and M.S. de Vries, J. Phys. Chem. A 115, 6077-6087 (2011).

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