BioExcel Webinar Series #5: QM/MM approaches in CPMD

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QM/MM approaches in CPMD

Presenters: Emiliano IppolitiHost: Adam Carter

BioExcel Educational Webinar Series #5

30 June, 2016

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This webinar is being recorded

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BioExcel Overview• Excellence in Biomolecular Software

- Improve the performance, efficiency and scalability of key codes

• Excellence in Usability- Devise efficient workflow environments

with associated data integration

• Excellence in Consultancy and Training- Promote best practices and train end users

DMI Monitor

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Data Source

Monitoring flow

Data flow

Service Invocation

DMI Optimiser

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DMI Gateway

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Portal / Workbench

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Registry

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Interest Groups

• Integrative Modeling IG• Free Energy Calculations IG• Best practices for performance tuning IG• Hybrid methods for biomolecular systems IG• Biomolecular simulations entry level users IG• Practical applications for industry IG

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Today’s Presenter

Emiliano Ippoliti is a research associate in the Institute of Computational Biomedicine of ForschungszentrumJülich (Germany). He took his PhD in Theoretical Physics at the University of Trieste in 2005 with a thesis about the theoretical foundations of quantum mechanics. From 2006 to 2009 he was a postdoctoral fellow at the International School for Advanced Studies in Trieste where he became expert on predicting optical properties for biologically relevant systems. Then, he moved to the German Research School for Simulation Sciences in Aachen/Jülichas a research associate until 2014 where he applied diverse enhanced sampling techniques to biological systems. His current interests focus on HPC approaches and methodologies for systems of biological relevance, in particular classical and ab initio molecular dynamics.

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QM/MM approaches in CPMD

[email protected]

BioExcel webinar 30/06/2016

Emiliano IppolitiForschungszentrum Jülich (Germany)

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Quantum DescriptionThere are cases where the dynamical behavior of the electrons of your systems cannot be neglected and a quantum mechanical description is required:

1. Chemical reactions (e.g. enzymatic reactions): electron transfer, bond breaking and bond formation

2. Systems with metal atoms (e.g. metallo proteins): no universal parametrization for metal atoms

3. Proton transport (e.g. aerobic generation of ATP and oxygen):Grotthuss mechanism (charge/topological diffusion vs mass diffusion)

4. Spectroscopic analysis and prediction (e.g. absorption and fluorescence spectra)

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CPMD

CPMD is an highly efficient parallel ab initioelectronic structure and molecular dynamics

program

Plane wave/pseudopotential implementation of

Density Functional Theory (DFT)

• Car-‐Parrinello MD• Born-‐Oppenheimer MD• EhrenfestMD

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www.cpmd.org

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Additional Features

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• Works with norm conserving or ultrasoft pseudopotentials• LDA, LSD and the most popular gradient correction schemes; free

energy density functional implementation• Isolated systems and system with periodic boundary conditions• Molecular and crystal symmetry• Wavefunction optimization: direct minimization and diagonalization• Geometry optimization: local optimization and simulated annealing• Molecular dynamics ensembles: NVE, NVT, NPT• Response functions• Excited states• Many electronic properties• Time-‐dependent DFT (excitations, molecular dynamics in excited states)• Coarse-‐grained non-‐Markovianmetadynamics• Path integral MD

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Scalability

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CPMD is an highly efficient parallel code. In particular, the MD algorithm is based on:

• A coarse-‐grained MPI-‐based algorithm, optimally parallelized for a distributed-‐memory architecture.

• A second fine-‐grain OpenMP-‐based parallelism, to exploit the multicores processors with shared memory.

The two parallelization strategies are indeed independenton each other.

CPMD runs efficiently on several different architecture. The best scaling is achieved on special parallel hardware with lightweight kernels like IBM BlueGene class:

IBM BlueGene/P Jülich Supercomputing Center

20102013

IBM BlueGene/Q Jülich Supercomputing Center

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QM/MM Approach

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The system is separated into two parts:

A small QM part comprises the chemically/photophysically active region treated by computationally demanding electronic structure methods.

The remainder MM part is described efficiently at a lower level of theory by classical force fields.

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Extends the range of applicability to the

much larger biologically relevant systems

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QM/MM interfaces in/for CPMD developed during the years

2005: Gromacs 3.3/CPMD interface

M. Eichinger, P. Tavan, J. Hutter, and M. Parrinello, J. Chem. Phys. 110, 10452 (1999)

2002: CPMD/Gromos96 interface

2013: IPHIGENIE/CPMD interface

2002: CPMD/Gromos96 interface

1999: EGO/CPMD interface

A. Laio, J. VandeVondele, and U. Röthlisberger J. Chem. Phys. 116, 6941 (2002)

P. K. Biswas, V. Gogonea, J. Chem. Phys. 123,164114 (2005)

M. Schwörer, B. Breitenfeld, P. Tröster, S. Bauer, K. Lorenzen, P. Tavan, and G.Mathias, J. Chem. Phys., 138, 244103 (2013)

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QM/MM Coupling

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MM

QMHybrid QM/MM scheme:

• Small part of the system at quantum (QM) level

• Rest of the system at force field (MM) level

The hybrid QM/MM potential energy contains three types of interactions:

• Interactions between atoms in the QM region (straightforward description)

• Interactions between atoms in the MM region (straightforward description)

• Interactions between QM and MM atoms Subtractive vs AdditiveCoupling Schemes

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Subtractive Scheme

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= + −MM

QM QMMM

MM

In the subtractive scheme, the QM/MM potential energy of the system is obtained in three steps:

Pros: Cons:• No communication between the

QM and MM routines needed

Straightforward implementation

• Force field for QM part required• Force field has to be “flexible” to

describe changes when chemical reactions occur

• Absence of QM polarization due to the MM part

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CPMD/Gromos96 Coupling

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In the more advanced additive scheme, the QM/MM potential energy of the whole system is a sum of the MM energy terms, QM energy terms and QM/MM coupling terms:

EQM / MM = EQM Rα{ }( )+ E MM RI{ }( )+ EQM−MM Rα{ }, RI{ }( )

From the DFT Kohn-‐Sham Hamiltonian

H eKS From a Gromos96 or

an Amber-‐like force field

EQM−MM = Ebonded

QM−MM + Enon−bondedQM−MM !=

EQM−MM = Ebonded

QM−MM + Enon−bondedQM−MM

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Bonded interactions

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Introduced when covalent bonds connecting theQM and the MM regions are cut:

MM

QM

In addition, in this case care has to be taken when evaluating the QM wave function. In CPMD the following methods are available:

QM• Monovalent capping atoms: usually hydrogen atoms at an appropriate position along the bond vector

• Link atom pseudopotentials: linking atom with scaled down pseudopotential and the required valence charge, which requires to constrain the bond distance appropriately

• Optimized effective core potentials: optimized link atom pseudopotential that takes care of the need of the constraint, avoiding to impose constraints

O. A. v. Lilienfeld, D. Sebastiani, I. Tavernelli, and U. Rothlisberger, Phys. Rev. Lett. 93, 153004 (2004)

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EQM−MM = Ebonded


=

Enon−bondedQM−MM = Esteric

QM−MM + EelectrostaticQM−MM ! !=

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EQM−MM = Ebonded


=

Enon−bondedQM−MM = Esteric

QM−MM + EelectrostaticQM−MM ! !=

Electrostatic interaction between MM charges and QM charge density EelectrostaticQM−MM =

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Electrostatic Coupling Schemes

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• Mechanical embedding: no influence of MM charges on the QM part, i.e QM calculation is gas-‐phase-‐like without additional potential due to the MM atoms.

• Electrostatic embedding: QM polarization due to the MM part included.

• Polarized embedding: MM polarization due to the QM part included as well(non-‐self consistently or fully self-‐consistently).

EelectrostaticQM−MM

EelectrostaticQM−MM

• Neglected• Established by assigning a fixed set of effective charges to the

QM region (for example, those given by the force field) • QM partial charges re-‐compued at every integration step of the

simulation (least-‐squares fitting procedure to reproduce

Estimated through an additional term to the QM Hamiltonian, where it is taken into account in terms of an external charge distribution.

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Electrostatic Embedding

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• Electrostatic interactions between QM and MM subsystems are handled during the computation of the electronic wave function

• The charged MM atoms enter the QM Hamiltonian as one-‐electron operators:

Eelectrostatic

QM−MM = −qIe

ri − R II∈MM∑

i∈QM∑ ⎯→⎯ qI

ρ(r)r − R I

d∫I∈MM∑ r

• Thus, the electrons “see” the MM atoms as special nuclei with non-‐integer and possibly negative charge

Is the polarization induced by qI realistic?

Electron spill-‐out problem at the bondaries

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Is the polarization induced by qI realistic?

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• qI have been parametrized to provide a realistic description of an MM systemrather than of a physically correct charge distribution.

• In principle, one would need to re-‐derive the charges for use in QM/MM frameworks

• In practice, most researchers use default force field parameters.

• In force fields, only the combination of atomic charges and Lennard-‐Jones parametersprovides a reasonable description of all the relevant effects (including polarization, dispersion, Pauli repulsion, etc) taken together: part of the interaction due to polarization of the QM region is thus already accounted for by the Lennard-‐Jones potential.

Ideally not only qI, but also the Lennard-‐Jones parameters would need to be reparametrized for usage in electrostatic

embedding QM/MM simulations

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Electron Spill-out

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A further problem that may arise when using standard MM atomic chargesto describe the charge distribution in the MM system, is the risk of over-‐polarization near the boundary:

The point charges on the MM side of the interface may attract (or repel) the electrons too strongly

Electron density spilling out into the MM region

QMMM

QM/MM boundary

+

Such artefacts can become serious if large flexible basis set (e.g., withpolarization and diffuse functions), or as in our case plane waves are usedin theQM calculations

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Electron Spill-out

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Eelectrostatic

QM−MM = qI

ρ(r)υ Ismear r − R I( )r − R I

d∫I∈MM∑ r

The electron spill-‐out can be avoided by using smeared-‐out charges insteadof the traditional point charges:

where the smearing function can be a Gaussian distribution or anothersuitable function centered at the MM atom. In the CPMD/Gromos96scheme:

υ I

smear r( ) = rc,I4 − r 4

rc,I5 − r5 r rc,I = covalent radius of the atom I

In contrast to the point charge model, the Coulomb interaction between theQM electrons and the smeared charge distributions does not diverge if theelectrons approach theMM atoms.

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Flavors of QM/MM Schemes

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QM/MM methods

Subtractive schemeAdditive scheme

Mechanicalembedding

Electrostatic embedding

Polarizedembedding

Fixed partial charges

Non self consistent

Full selfconsistent

Recalculated partial charges

EelectrostaticQM−MM = 0

CPMD/Gromos96

Point charge model

Smeared-‐outcharge model

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Electrostatic Embedding in theCPMD/Gromos96 Interface

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• Hierarchical approach to deal with electrostatic interactions in combination with an empirical modification of the short-‐range terms that does not require a refit of the MM force field used and that overcomes the computational bottleneck in computing the integral term of the interacting Hamiltonian within a plane-‐wave scheme.

• Electrostatic embedding tailored to study dynamics of complex biomolecular systems and chemical reactions

• “Fully” Hamiltonian formulation from which the additional external electrostatic potential to be included in the Kohn-‐Sham Hamiltonian and the one acting onto the MM atoms as results of the QM charge distribution can be obtained consistently.

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Hierarchical Electrostatic Embedding

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Electrostatic part of the interacting Hamiltonian is split into short-‐range medium-‐range and long-‐range contributions:

EelectrostaticQM−MM == Ees−sr

QM−MM

+ Ees−mr

QM−MM

+ Ees−lr

QM−MM

Explicit electrostatic interaction(NN atoms)

RCUT_NN RCUT_MIX RCUT_ESP

a. Charge > 0.1eExplicit electrostatic interaction(NN atoms)

b. Charge < 0.1e(R)ESP coupling Hamiltonian(EC atoms)

(R)ESP coupling Hamiltonian(EC atoms)

If LONG-‐RANGE:Interaction with a multipole expansion for the QM system up to quadrupolar order

If not:QM system coupled to force-‐field charges

QM region in VDW representation

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Short-range term

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Ees−sr

QM−MM

== qI ρ(r)υ Ieff r − RI( )dr∫

I∈NN∑

υ I

eff r( ) = rc,I4 − r 4

rc,I5 − r5

• Only involving the „nearest-‐neighbour’’ (NN) atoms:

1. MM atoms within a certain cutoff range (RCUT_NN) around QM atoms

2. MM atoms with a charge larger than 0.1e and at a distance r between RCUT_NN and RCUT_MIX from any QM atom

• Evaluated exactly by summing all grid points/MM atom contributions in the NN class explicitly:

Modified Coulomb interaction

(smeared charges)RCUT_NN RCUT_MIX

Charge > 0.1e

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Medium-range term

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RCUT_NN RCUT_MIX

Charge < 0.1e

RCUT_ESP

• Only involving the „ESP Coupling’’ (EC) atoms:

1. MM atoms with a charge smaller than 0.1e and at a distance r between RCUT_NN and RCUT_MIX from any QM atom

2. MM atoms with a distance r between RCUT_MIX and RCUT_ESP from any QM atom

• Charge density approximatelyrepresented by ElectroStaticPotential-‐based D-‐(R)ESP chargescentered on the QM atoms as obtained from a dynamical fitting procedure.

A. Laio, J. VandeVondele, and U. Rothlisberger, J. Phys. Chem. B 106, 7300 (2002)

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Long-range term

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• Computed approximately by expanding the charge density of the QM system in terms of multipoles up to quadrupolar order:

Ees−lrQM−MM

= qIC

R I −R+ Di

R I −R3 RIi − Ri( )

i∑

⎧⎨⎪

⎩⎪I∉NN∑

+ 12

Qij

R I −R5 RIi − Ri( ) RIj − Rj( )

i, j∑

⎫⎬⎪

⎭⎪

• Coefficients C, Di, Qij are the usual multipole moments computed from the charge density ρ(r) of the QM part with respect to the geometric center of the QM system, , where i=1,2,3 are the cartesiancomponents.

R = (R1,R2,R3)

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Cu(II) binding to α-synuclein

Asp2

Met1

Cu

?HighestaffinityCu(II) binding site on α-synuclein

• NMR experiments did not allow resolvingunumbiguosly the fourth coordinating residue

• Two hypotheses compatible with energeticarguments:

His50H2O

ΔG = -15.10227 Kcal/mol ΔG = -15.73982 Kcal/mol

A. Binolfi et al., Inorg. Chem. 49(22), 10668 (2010)

Method CPMD/MM + TDDFT

Functional PBE

Energy cutoff 70 Ryd

Pseudopotentials DCACP MT

Temperature 300 K

Fictitioismass 600 a.u.

Absorption spectra

Wavelength (nm)

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Platination of ATP7A transporter

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V. Calandrini et al., Dalton Trans. 43, 12085 (2014)

ATP7A coppertransporter (apo)

CYS19

CYS22

Complex with the Pt-adductExperimental compatible bindingmode

1 2 3Alternative chemically plausible

binding modes

CD spectrum ✓δ13Cβ(Cys22) ✕Δδ13Cβ (apo) ✓

CD spectrum ✓δ13Cβ(Cys22) ✓Δδ13Cβ (apo) ✓

CD spectrum ✕δ13Cβ(Cys22) ✓Δδ13Cβ (apo) ✓

CD spectrum ✓δ13Cβ(Cys22) ✓Δδ13Cβ (apo) ✕

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CPMD/Gromos96

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Cons:• Bad scaling performance in comparison with “full-QM” CPMD• Non-free Gromos96 license required to use this interface

Pros:• Full Hamiltonian QM/MM coupling• Support of both Gromos96 and Amber force fileds• Extensively validated for biologically relevant systems• Most popular among CPMD community

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The New QM/MM Interface

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in collaboration with:

U. Rothlisberger’s group (EPFL Lausanne)(developer of the CPMD/Gromos96 interface)

Zürich(owner of CPMD)

J. M. Haugaard Olsen (University of Southern Denmark)S. Meloni (University La Sapienza, Rome)

V. Bolnykh (RWTH Aachen and Cyprus Institute)

is developing a new QM/MM interface

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The New QM/MM Interface

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• Implementation: Interface built in the CPMD code

• Physics: Full Hamiltonian coupling based on the well-validated CPMD/Gromos96 interface

• Abstraction: interfacing any classical MD code with minimal code intervention (Gromacs 5 will be first used as proof of concept)

• Flexible: managing two (QM and MM) or even more layers at the same time

• Running model: separate pools of processes running CPMD+Interface and the partner MD code(s)

Propagation of the equation of motion done by CPMD

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Advantages

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The new QM/MM interface of CPMD will allow one to:

1. Improve the poor HPC scaling performance of the current most used QM/MM interface in CPMD (CPMD/Gromos96).

1. Provide a QM/MM interface with the same coupling of the CPMD/Gromos96 one but completely free (for academic users) as CPMD is.

1. Have additional features, including the possibility to work with: • different MD codes interfacing CPMD• more resolution layers at the same time• different (polarizable) force fields• more general simulation boxes (triclinic ones)

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Audience Q&A session

Please use the Questions function in GoToWebinar application

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NEXT BIOEXCEL WEBINAR

Mid July – To Be Confirmed

Find out more at www.bioexcel.eu/webinars

Also coming up:

BDE Webinar: The Open PHACTS pilotIncluding a talk by Stian Soiland-‐Reyes (BioExcel)6th July, 14:00 BST / 15:00 CESThttps://www.big-‐data-‐europe.eu/event/webinar-‐pilot/