An introduction to QM and QM/MM models Prof. Dr. Ville R. I. Kaila - PowerPoint PPT Presentation

An introduction to QM and QM/MM models Prof. Dr. Ville R. I. Kaila Department of Chemistry Prof. Ville R. I. Kaila Technical University of Munich (TU München) CSC Spring School 16.3.2018

Outline of the lecture Introduction to QM and QM/MM calculations Quantum mechanical models of (bio)chemical systems (QM, QM/MM, QM/QM methods) Some words about what "QM" can refer to in the QM/MM simulations How to construct quantum (bio)chemical models? QM cluster models QM/MM models What do I get out from QM/MM simulations? 1 & 2) Structures, energetics, and dynamics from QM and QM/MM 3) Reaction pathways and free energies at QM/MM level PES scans, QM/MM-FEP, LRA, QM/MM-US/WHAM and string simulations 4) Characterizing the QM models by molecular property calculations Characterizing protein conformations by calculation of optical properties

Outline of hand-on lecture 2 & 3 Setup of a protein QM/MM MD simulation Ubiquitin in water Exploring chemical reactions with QM/MM free energies Modeling a S N 2 reaction in water

Learning goals of today’s lectures Understand how QM and QM/MM models work Become familiar with what type of information is obtained from biomolecular QM or QM/MM calculations Know strategies to obtain potential energy surface scans from QM/MM Know methods to compute free energy from QM/MM simulations Become familiar with ways to characterize spectroscopic properties from QM/MM Become familiar with how to setup a QM/MM simulations for (bio)chemical systems How to compute free energies using QM/MM methods

Who am I/who are we? Spectral Tuning in Rhodopsin and Cone Pigments The Kaila team at TU Munich

Our Research Interests in a Nutshell Enzyme Catalysis Bio-inspired catalysts Photobiology Energy converting enzymes Designing new proteins Structure/Function/Dynamics How is light-energy captured? What is special about the How to mimic nature? biological environment? Differences in chem. vs. bio.? Di Luca e t al . PNAS (2017) Mader et al . Nature Comm. (2018) Suomivuori et al. PNAS (2017) Gamiz et al. JACS (2017) Gamiz-Hernandez et al. JCPB (2014) Zhou et al. JACS (2014) Supekar et al . Angew Chemie (2016) Kaila & Hummer JACS 133 (2011) Kaila et al . Nature Chemistry (2014) Sharma et al . PNAS (2015) Kaila & Hummer PCCP 13 (2011) Gamiz et al . Angew. Chemie (2015) Kaila et al . PNAS (2014)

Motivation for Quantum (Bio)chemical Calculations

QM models of (bio)chemical systems To accurately describe (bio)chemical reactions one needs to rely on quantum chemical models Example of applications: enzyme catalysis; photobiological systems; systems where biomolecular force fields fail ( e.g. accurate differences in conformation of ligands, protein side chains)

Overview of Quantum (Bio)chemical Models

QM models of Biochemical Systems Types of quantum chemical models used for (bio)chemical systems I) QM Cluster Models Cut out a central part of the protein active site, Fix terminal atoms to account for protein framework model the surroundings as a polarizable medium

QM models of Biochemical Systems Types of quantum chemical models used for (bio)chemical systems I) QM Cluster Models Cut out a central part of the protein active site, Fix terminal atoms to account for protein framework model the surroundings as a polarizable medium II) QM/MM Models Cut out a central part of the protein active site, model the surroundings explicitly using force fields, couple QM and MM regions together

QM models of Biochemical Systems Types of quantum chemical models used for (bio)chemical systems I) QM Cluster Models Cut out a central part of the protein active site, Fix terminal atoms to account for protein framework model the surroundings as a polarizable medium II) QM/MM Models Cut out a central part of the protein active site, model the surroundings explicitly using force fields, couple QM and MM regions together III) QM/QM Models (embedding models) Cut out a central part of the protein active site, model the surroundings explicitly using approximate QM Account for the interaction between QM and QM regions

QM models of Biochemical Systems What does the QM refer to? I) QM Cluster Models Cut out a central part of the protein active site, Fix terminal atoms to account for protein framework model the surroundings as a polarizable medium II) QM/MM Models Cut out a central part of the protein active site, model the surroundings explicitly using force fields, couple QM and MM regions together III) QM/QM Models (embedding models) Cut out a central part of the protein active site, model the surroundings explicitly using approximate QM Account for the interaction between QM and QM regions

In (bio)chemical applications the QM treatment can refer to... Ab initio or density functional theory (DFT) treatment: N 3 - N 6 (see lectures by Dr. Johansson) Semi-empirical QM methods ( e.g. AM1, MNDO, PM6/PM7, (SCC)-DFTB); linear scaling – N 2 Reactive force fields ( e.g. EVB methods); linear scaling Applicable for large biochemical It is challenging to apply any method with a Basis sets systems formal computational scaling of higher than N 4 Not-that-applicable for large in molecular simulations of chemical problems biochemical systems N N 2 N 3 N 4 N 5 N 6 N 7 N! QM Method HF MP2 CCSD CCSD(T) FCI Semi- empirical DFT

QM/MM discussion in these lectures will focus on DFT/MM but..... some words about modeling the QM part with semi-empirical or reactive force fields

Tight–binding DFT (DFTB) and self-consistent charge approx. (SCC-DFTB) Minimizing the energy of DFT eqn., but only with respect to the shape of the KS orbitals, not by changing the density Self Consistent Charge-DFTB model: (SCC-DFTB) Use point charges to describe the density sampling of 100-1000 ps range is possible with SCC-DFTB + accuracy well benchmarked for standard parametrizations SCC-DFTB developers: - Qiang Cui, Wisconsin Madison - not available parameters - Marcus Elstner, KIT for all elements (Fe, S, etc.)

and sometimes also Reactive Force Fields are called QM/MM... Classical force fields have a defined topology – energy steeply rises if bonds are stretched

Reactive Force Fields X Y H Empirical Valence Bonds (EVB) (Warshel and Weiss, 1981) b 1 b 2 r 3 2

Reactive Force Fields Empirical Valence Bonds (EVB) methods have been to many biological proton transfer reactions

My philosophy to Computational (Bio)chemistry

Requirements of Computational Methodology II A multi-scale approach for multi-scale problems Quantum chemical techniques Continuum and coarse- System size grained Explore local MM method Accelerated chemistries sampling QM Classical Explore conformational Molecular phase-space Dynamics QM/MM QM/QM DFT/MM Classical molecular Gamiz et al. JACS (2017) Quantum Supekar et al. Angew. Chemie (2017) simulation techniques Correlated Chemical Di Luca et al . PNAS (2017) Suomivuori et al. PNAS (2017) quantum DFT models Supekar et al . Angew. Chemie (2016) chemistry Sharma et al . PNAS (2015) Gamiz et al . Angew. Chemie (2015) Kaila et al . PNAS (2014) Applicable timescale Time scale Zhou et al . JACS (2014) Kaila et al . Nature Chem. (2014)

Requirements of Computational Methodology II Multi-scale molecular simulations Classical molecular dynamics simulations input : experimental structure output: µ s-timescale dynamics in different conformational/catalytic/non- equilibrium states

Requirements of Computational Methodology II Multi-scale molecular simulations Classical molecular dynamics simulations molecular structures Quantum Classical

Requirements of Computational Methodology II Multi-scale molecular simulations Classical molecular dynamics Hybrid quantum/classical simulations simulations (QM/MM) molecular structures Quantum coupling between Classical local & non-local effects site-directed mutagenesis Free-energies/barriers for catalysis, mechanisms biophysical experiments structural studies

How to build a QM cluster model of a biochemical system?

Where should I cut the residues? Proteins are polymers

Where should I cut the residues? Where should I cut the residues? Model residue size: 33 è 16 atoms Cut at C b atom minimal model where protein strain can easily be included

Where should I cut the residues? Where should I cut the residues? Model residue size: 33 è 16 atoms Cut at C b atom minimal model where protein strain can easily be included Model with 10 residues: * 10 x 16 atoms = 160 atoms 10 x 33 atoms = 330 atoms * *

Philosophy of Quantum Biochemical Modelling System of interest: enzyme active site/biochromophore Cluster models: Include first protein solvation sphere, charged, hydrogen- bonding, stacking residues Bioinformatical sequence comparisons can be highly informative in deciding, which residues to include in the QM model

Philosophy of Quantum Biochemical Modelling Simplest environmental effect: Model the protein environment as a homogenous low-dielectric polarizable medium ( e =4) Conductor-like Screening MOdel (COSMO) Polarizable Continuum Model (PCM) * * Restrain or fix terminal carbons atoms in model to simulate the rigidity of the protein framework * * * * *