Introduction to MD simulations of DNA systems. Aleksei Aksimentiev

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1 Introduction to MD simulations of DNA systems Aleksei Aksimentiev

2 Biological Modeling at Different Scales spanning orders of magnitude in space and time

The computational microscope Massive parallel computer

3 Time resolution: 2 fs Spacial resolution: 0.

3 The computational microscope Massive parallel computer Blue Waters (UIUC): ~200,000 CPUs 2.5 nm Time scale: ~ µs Length scale: 10K - 1,000M atoms or (< 70 nm) 3 Time resolution: 2 fs Spacial resolution: 0.1 A Atoms move according to classical mechanics (F= ma) Interactions between atoms are defined by the molecular force field

4 What is Molecular Dynamics? Energy function has two parts: - chemical bond interactions - non-bonded interactions

5 Chemical Structure Bonds: Every pair of covalently bonded atoms. Angles: Two bonds that share a common atom form an angle. Dihedrals: Two angles that share a common bond form a dihedral. Impropers: Any planar group of four atoms forms an improper.

6 The MD method models atoms with point par3cles interac3ng through classical poten3als angle bond dihedral Lennard-Jones (van der Waals) electrostatic

7 MD force field: a approach - Parametrize parts of the structure - Assemble the parts Example: a protein is a collection of 20 amino acids Bonding cannot change(!)

8 To run MD you ll need Computer (multi-core/gpu or cluster) MD code (NAMD, Gromacs, Charmm, ) Input coordinates (typically.pdb): specifies initial state of the system Protein structure file (typically.psf): specifies chemical bond information Parameter file: provides atom-type specific values to interacting potentials Configuration file (.namd or similar): run-type parameter, temperature, etc Constraints or other simulation-specific files (typically.pdb) Output: MD trajectory (.dcd file): describes how coordinates change in time Analysis tools (VMD, python, etc. "8

9 What is MD good for? Minimum requirements: - Well-defined ques3on - Atomic-detail structure (or disordered state) - Minimum chemistry - Volume of 60 x 60 x 60 nm 3 or less - Processes taking less than 100 microseconds Typical ques3ons: - What is the equilibrium structure in physiological environment? - What is the free-energy cost of going from A to B? - What is the path from A and B? - How does the structure respond to external force or field? - What is going on in my experiment?

wall of radius R Apply a half-harmonic wall potential only to DNA Solve the

10 All-Atom Molecular Dynamics Simulation of DNA Condensates Add 64 DNA helices Add polyamine cations (+4) Add 150 mm NaCl Add explicit water DNA-confining wall of radius R Apply a half-harmonic wall potential only to DNA Solve the equation of motion (F= ma) under periodic boundary condition in all directions

CUFIX Improves Simulations of DNA Condensates http://bionano.physics.illinois.

(bar) 10 6 4 2 6 4 2 1 22 24 AMBER99 + CUFIX (MD included 200 mm Na) CHARMM27 26 AMBER99 28 30 DNA-DNA distance (Å) 32 Pressure (bar) 10 1 4 2 4 2 4 2 22 AMBER99 +

11 CUFIX Improves Simulations of DNA Condensates Pressure (bar) CHARMM27 25 [Na] = 250 mm [Mg] = 20 mm [spermine] = 2 mm AMBER99 + CUFIX AMBER99 30 DNA-DNA distance (Å) Pressure (bar) AMBER99 + CUFIX (MD included 200 mm Na) CHARMM27 26 AMBER DNA-DNA distance (Å) 32 Pressure (bar) AMBER99 + CUFIX AMBER99 CHARMM DNA-DNA distance (Å) y (Å) 0 y (Å) 0 y (Å) x (Å) x (Å) x (Å) Yoo & Aksimentiev, NAR 2016

12 From cadnano to all-atom Cadnano design A i ii iii i ii iii i ii iii i Ideal Solvated structure structure cadnano2pdb Jejoong Yoo SM. Douglas,, WM. Shih, Nucleic Acids Res., 2009 CHARMM36 force field Explicit water [MgCl2] ~ 10 mm NAMD 1 to 3M atoms 500 to 1,000 CPUs 12

13 Structural dynamics

Chicken wire frame represents center line of helices & junction Yoo and Aksimentiev, PNAS 110:20099 (2013) 28 26

14 Structural fluctuations reveal local mechanical properties Structural fluctuation of DNA origami nanorod Persistence length (µm) µm HC0 pers l p SQ0 30 Cross-section - Inter-DNA distance in color map - Chicken wire frame represents center line of helices & junction Yoo and Aksimentiev, PNAS 110:20099 (2013) DNA-DNA distance (Å) Persistence length of DNA origami Simulations predict higher rigidity for honeycomb-lattice design

15 A Practical Guide to DNA Origami Simulations Using NAMD Walk through the protocol for all-atom simulations of DNA origami using the NAMD package Cadnano design All-atom structure in a MgCl2 solution Perform MD simulation and analysis cadnano2pdb web server All-atom model After optimization

16 Chen-Yu Li

17 Tiled DNA nanostructures DNA Origami DNA bricks Identical nucleotide sequence in both structures Ke et al. Science 338:1177 (2012) Origami Bricks All-atom MD 165 ns each Slone et al., New J. Phys. 18: (2016) nanohub.org/resources/legogen

18 ENRG MD tool kit : a universal all-atom structure converter CaDNAnano CanDo oxdna Nanoengineer vhelix DAEDALUS NAB enrgmd tool-kit #enrgmd hextube.json Tiamat NAMD all-atom MD Simulation Files hextube.psf hextube.pdb hextube.namd hexube.exb CHARMM parameters

19 Cryo-EM reconstruction versus all-atom simulation High-resolution cryoelectron microscop Petascale computer system

20 Cryo-EM reconstruction versus all-atom simulation Bai et al, PNAS 109:20012 (2012)

21 Cryo-EM reconstruction versus all-atom simulation Bai et al, PNAS 109:20012 (2012)

22 Cryo-EM reconstruction versus all-atom simulation Bai et al, PNAS 109:20012 (2012) Pseudo-atomic model

23 MD simulation of the cryo-em object starting from a cadnano design Bai et al, PNAS 109:20012 (2012) 7M atom solvated model ~200 ns MD trajectory

24 MD simulation of the cryo-em object starting from a cadnano design Bai et al, PNAS 109:20012 (2012) 7M atom solvated model ~200 ns MD trajectory

25 MD simulation of the cryo-em object starting from a cadnano design Bai et al, PNAS 109:20012 (2012) 7M atom solvated model ~200 ns MD trajectory

26 Electron density maps Cryo-EM reconstruction All-atom MD simulation

27 Comparison with experiment Maffeo, Yoo & Aksimentiev, NAR 44: 3013 (2016) EM density psuedo-atomic model simulation

28 Making images and animations of DNA nanostructures with VMD Images from a single structure Image with multiple representations Animation based on a trajectory Animation including transitions

29 Elastic network of restraints guided MD (ENRG MD) ~10,000 times more efficient Solvent replaced with elastic network Maffeo, Yoo & Aksimentiev, NAR 44: 3013 (2016)

End-end angle ( ) 100 90 80 70 60 0 5 10 15 20 25 30 19 18 17 Programmed 16 15 ˆt 3 bend 14 13 12 11 10 9 14 8

31 Curved DNA origami systems Experiment Dietz, H. et al, Science, s = L ˆt ˆt ˆt End-end angle ( ) Programmed ˆt 3 bend ˆt s = Bend per 7-bp array cell ( ) Time (ns) Programmed bend Array cell index Yoo and Aksimentiev, PNAS 110:20099 (2013)

32 Multi-resolution simulations of self-assembled DNA nanostructures

33 DNA membrane channels Dr. Ulrich F. Keyser Cambridge, UK

34 DNA Ion Channels Langecker, M. et al., Science: 338, Nano Letters, 13: 2351 ~1 ns conductance Angewandte Chemie /anie

35 MD simulation of DNA channel conductivity cadnano or NanoEngineer-1 A all-atom coordinates Nanocapillary Göpfrich, Kerstin et al., Nano Lett., 2015, 15(5), (Right) design from Burns, Jonathan R. et al., Nat. Nanotechnol., 2016, 11,

36 MD simulation of DNA channel conductivity DNA Optimize Cholesterol Lipid A Mg(H2O)6 2+ H2O Nanocapillary K + Cl - Göpfrich, Kerstin et al., Nano Lett., 2015, 15(5),

37 MD simulation of DNA channel conductivity DNA Optimize Cholesterol E Lipid A Mg(H2O)6 2+ Nanocapillary Instantaneous current: H2O K + Cl - Göpfrich, Kerstin et al., Nano Lett., 2015, 15(5),

38 MD simulation of DNA channel conductivity A E Nanocapillary Göpfrich, Kerstin et al., Nano Lett., 2015, 15(5),

39 Chemistry matters RMSF > 6 Å = K + = Cl E Nano Letters, 13: 2351 RMSF < 3 Å Angewandte Chemie /anie ns ns ns Cholesterol Density of lipid head groups

1 ns Gramicidin ion channels Experiment:

40 Small conductance DNA channel 1 helix 140,000 atoms Conductance < 0.1 ns Y Current / na Count Experiment Conductance: ~ 0.1 ns Gramicidin ion channels Experiment: Ulrich Keyser (Cambridge) Eugen Stulz (Southampton) Mathias Winterhalter (Jacobs U) 1 M KCl Current / na Probability Simulation Goepfrich, et al., Nano Lett 16: 4665 (2016)

Lipid molecules can translocate to the other leaflet through

41 All-atom MD simulation of lipid-dna interface Chen Yu Li No applied electric field Z Distance from pore Distance from pore Lipid molecules can translocate to the other leaflet through the toroidal pore made by DNA Nature Communications 9: 2426 (2018)

42 Lipid translocation through toroidal pores is very common and very fast

Lipid translocation in cells is catalyzed by enzyme Extracellular space F(t)/F(0) 1 0.

Deficiency in lipid scrambling could result in autoimmune response or Scott syndrome.

43 Lipid translocation in cells is catalyzed by enzyme Extracellular space F(t)/F(0) Image credit: Kelly Yang Cytoplasm PC Sph PE PS Lipid molecules are asymmetrically distributed in the cell membrane. apoptosis or thrombin formation: F(t)/F(0) Time (t) Time (t) scramblase Deficiency in lipid scrambling could result in autoimmune response or Scott syndrome. xin: ratio of labeled lipid in the inner leaflet k q and ks: rate constant for quenching and scrambling Brunner et al, Nature 516, ,

44 Experimental verification Alex Ohmann Ohmann, Li, Ulrich F. Keyser, Aksimentiev, Nature Communications 9: 2426 (2018)

45 Experimental verification Scale bars are 10 µm Alex Ohmann Ohmann, Li, Ulrich F. Keyser, Aksimentiev, Nature Communications 9: 2426 (2018)

Works in human cells Human cells contain PS lipids at the inner membrane Annexin V binds specifically to PS lipids Scale bar is 20 µm Breast cancer cells from the

46 Works in human cells Human cells contain PS lipids at the inner membrane Annexin V binds specifically to PS lipids Scale bar is 20 µm Breast cancer cells from the cell line MDA-MB-231 Positive control: apoptosis-inducing microbial alkaloid staurosporine Negative control: DNA folding buffer Nature Communications 9: 2426 (2018)

47 Tutorials overview Design Cadnano (today) Simulations All-atom with NAMD (today) Images and movies with VMD Cadnano toolkit (tomorrow) Coarse-grained with ARBD (tomorrow)

48 Acknowledgements Jejoong Yoo Chen-Yu Li Jejoong Yoo Chen-Yu Li

Why Proteins Fold? (Parts of this presentation are based on work of Ashok Kolaskar) CS490B: Introduction to Bioinformatics Mar.

Why Proteins Fold? (Parts of this presentation are based on work of Ashok Kolaskar) CS490B: Introduction to Bioinformatics Mar. 25, 2002 Molecular Dynamics: Introduction At physiological conditions, the