From Dynamics to Thermodynamics using Molecular Simulation

Transcription

1 From Dynamics to Thermodynamics using Molecular Simulation David van der Spoel

2 Computational Chemistry Physical models to describe molecules Software to evaluate models and do predictions - GROMACS Model validation and development Applications in Chemistry - Water & other liquids (Applications in Biology - PitGP, Virus, Malaria)

3 Computational Chemistry Ab-initio methods Density functional theory Semi-empirical Atomistic Force field Coarse grained FF / QSAR / Continuum descriptions

4 Computational Chemistry Ab Initio DFT Accuracy Force Field Semi- Empirical Coarse graining Cost

5 Computational Chemistry Accuracy per $ Ab Initio DFT Accuracy Force Field Semi- Empirical Coarse graining Log(Cost)

6 Computational Chemistry Ab Initio Accuracy Force Field Semi- Empirical DFT 0 Coarse graining Log(Cost) Depends on the problem!

7 What is Molecular Dynamics Coordinates of atoms/particles as a function of time Time correlation functions Experimental: Nuclear Magnetic Resonance spectroscopy Computer simulations at different levels of spatial and temporal accuracy Sampling the conformational space - partition function

8 M.Levitt, Nat. Struct. Biol. 8 (2001), p

9 How Many Lennard-Jones Parameters for a Protein? Two parameters per interaction One atom type per element (C,H,N,O,S) : 10 with combination rules, 40 without With four atom types per element: 40 with combination rules, 760 without

10 The Physical Model What determines the quality? How can we test it?

11 Our Gr8t Software

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13 Liquid FF Benchmark Test available force field for how good they reproduce properties for ~ 150 organic liquids 1000 molecules/box 10 ns production sims OPLS/AA, GAFF + CGenFF from literature

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15 Simple props 2500 GAFF OPLS/AA CGenFF 100 GAFF OPLS/AA CGenFF Calc. (g/l) H vap,calc. (kj/mol) Exper. (g/l) H vap,exper. (kj/mol) Density Enthalpy of Vaporization

16 Not so simple props Due to cut-off of Van der Waals forces? Polarization? GAFF OPLS/AA 100 GAFF OPLS/AA Calc. (10-3 N/cm) ,Calc Exper. (10-3 N/cm) ,Exper. Surface Tension Dielectric Constant

17 2 Phase Thermodynamics method! Complex props GAFF OPLS/AA GAFF OPLS/AA 1.5 c V,Calc. (J/mol K) T,Calc. (10-3 /K) c V,Exper. (J/mol K) T,Exper. (10-3 /K) Heat capacity Compressibility

18 Yihzak Marcus: The Properties of Solvents

19 Handbook of Chemistry & Physics

20 Science in the 21 st century...

21 70 ethanamide ,1-dichloroethane Fit Data used in fit 10.5 Fit Data used in fit Data not used in fit 60 ε(0) 55 ε(0) T (K) methanol T (K) bromomethane Fit Data used in fit 18 Fit Data used in fit Data not used in fit ε(0) 40 ε(0) T (K) T (K)

22 Force field N a b RMSD % Dev. R 2 ρ (g/l) GAFF % OPLS/AA % CGenFF % OPLS/AA % ΔH vap (kj/mol) GAFF % OPLS/AA % CGenFF % γ (10 3 N/m) GAFF % OPLS/AA % ε(0) GAFF % OPLS/AA % α P (10 3 /K) GAFF % OPLS/AA % OPLS/AA % κ T (1/GPa) GAFF % OPLS/AA % OPLS/AA % c (J/mol K) Statistics Quantitative evaluation per property.

23 Benchmark is Foundation for Future FF > 100,000 experimental data points gathered in a SQL database Allows rational FF derivation... at last No more of this

24 Can Quantum Chemistry Help? Compute properties for which there is no experimental data Electric properties (multipole moments) polarizabilities are reproduced well Energies?

25 Enthalpy of Formation Calc. - Exper G2 G3 G4 CBS-QB Exper. (kj/mol)

26 Polarizability (A 3 ) Aldehydes Esters-Methyl-AlkanoatesBenzene derivatives Cyclic mono ethers Cycloalkanes Difluoroalkanes Esters-Alkyl-Methanoates Alkanes Ethers-Methoxy-Alkanes Ketones Perfluoroalkanes Primary Alcohols Primary Thiols NH Primary Amines Primary Carboxylic AcidsPrimary Nitroalkanes O 2 Secondary Amines # Carbon H 2 O Tertiary Amines Fear not Nature is linear...

27 Summary Force Field Intermolecular energies within ~ 5-7 kj/mol in force fields - for supported atom types A lot of work going on in force field tuning and development Many properties can be computed based on long classical simulations

28 References Carl Caleman, Paul van Maaren, Minyan Hong, Jochen Hub, Luciano Costa, David van der Spoel, J. Chem. Theor. Comput. 8 (2012) David van der Spoel, Paul van Maaren, Carl Caleman, Bioinformatics (2012) doi: / bioinformatics/bts020 Oliver Lange, David van der Spoel, Bert L. de Groot - Biophysical Journal 99 (2010)

29 The Two Phase Thermodynamics Method David van der Spoel, Uppsala University

30 What s the problem? For ideal gases theories exist from which one can derive thermodynamics properties For solids another kind of theory exists For liquids there is no such thing

31 1 st Ansatz Treat Liquid just like a Solid - system of harmonic oscillators

32 Berens et al. JCP 79 (1983) pp2375

33 Berens et al. JCP 79 (1983) pp2375

34 The trick S(v) can be derived from the velocity autocorrelation function Assume the frequencies in the classical simulation are correct (and the amplitudes) Reweigh the S(v) to get a corresponding Quantum S(v)

35 8000 Example - C2H6SO Bonds 6000 Angles & Dihedrals S(ν) Collective modes ν (1/ps)

36 Now we will try to comprehend the solid component of the density of states, DoS solid (ν). Here, each mode is considered to be harmonic and we use the partition function for a quantum harmonic oscillator as given by McQuarrie [8]: q q HO (ν) = e βhν/2 1 e βhν (S9) where h is Planck s constant, β = 1/k B T. Since the canonical partion function Q of a system is given by the product of the components (Equations , reference [6]): and therefore Q = ln Q = N i=1 N i=1 q i ln q i (S10) (S11) Caleman et al. JCTC 8 (2012) 61-74

37 Final Result 1 Berens et al. JCP 79 (1983) pp2375

38 2 nd Ansatz Treat a liquid as a combination of solid and ideal gas - 2 phase thermodynamics Gas can be treated as a hard-sphere gas for which analytical thermodynamical results exist Lin et al. JCP 2003, JPCB 2012, Pascal PCCP 2011

39 Final Result 2 Determine fluidicity - how fluid is the simulation between 0 and 1 Modified weighting function - same as Berens for the solid part + another for the gas part Lin et al. JCP 2003, JPCB 2012, Pascal PCCP 2011

40 How does it work? Do MD simulation with flexible bonds, ps (time step 0.2 fs) Save velocities every 4-5 fs Compute mass-weighted velocity ACF and compute properties S, E, A, Cv by weighting the S(v) and integrating!

41 Heat Capacity Cv 300 GAFF OPLS/AA c V,Calc. (J/mol K) c V,Exper. (J/mol K) Caleman et al. JCTC 8 (2012) 61-74

42 Hydrophobic Segregation, Phase Transitions and the Anomalous Thermodynamics of Water/Methanol Mixtures Tod A. Pascal and William A Goddard, III J. Phys. Chem. B

43 Summary 2PT Promising new method Lowest frequencies contribute most - may also work with constraints Very recently also for mixtures More development and testing needed

44 References Carl Caleman, Paul J. van Maaren, Minyan Hong, Jochen S. Hub, Luciano T. Costa, David van der Spoel: Force Field Benchmark of Organic Liquids: Density, Enthalpy of Vaporization, Heat Capacities, Surface Tension, Compressibility, Expansion Coefficient and Dielectric Constant J. Chem. Theor. Comput. 8 pp (2012) Lin, S. T.; Blanco, M.; Goddard, III, W. A. J. Chem. Phys. 2003, 119, Lin, S.-T.; Maiti, P. K.; Goddard, III, W. A. J. Phys. Chem. B 2010, 114, Pascal, T. A.; Lin, S.-T.; Goddard, III, W. A. Phys. Chem. Chem. Phys. 2011, 13, Huang, S.-N.; Pascal, T. A.; Goddard, III, W. A.; Maiti, P. K.; Lin, S.-T. J. Chem. Theory Comput. 2011, 7, Berens, P. H.; Mackay, D. H. J.; White, G. M.; Wilson, K. R. J. Chem. Phys. 1983, 79,