1. Molecular Dynamics Arjan van der Vaart vandervaart@asu.edu PSF346 Center for Biological Physics Department of Chemistry and Biochemistry Arizona State University

2. 1. Atoms are classical point-masses that move in a physical potential 2.The potential is fitted to experiments and quantum mechanical calculations 3.The potential is transferable 4.Atoms are propagated by classical (Newtonian) dynamics Molecular Dynamics (MD): – + BondsAnglesDihedrals Improper Dihedrals Electrostatics van der Waals Bonded termsNon-bonded terms k b (r–r 0 ) 2 ka(–0)2ka(–0)2 (q 1 q 2 )/(  r) E[(r m /r) 12 –(r m /r) 6 ] ki(–0)2ki(–0)2 k d [1+cos(n  –  0 )]

3. What can you do with MD?

4. a.thermodynamic data (by using statistical mechanics) b.kinetic data (by using statistical mechanics) 1.Obtain data that is normally measured by experiments 2.Obtain data that cannot be measured by experiments a.very high spatial and time resolution data b.certain energies, correlation functions, etc. c.decomposition of energies

5. Example Let’s look at a MD simulation of salt in liquid water http://www.public.asu.edu/~avanderv/nacl.tar.gz Questions 1.Do you see order, chaos, or something in between? 2.What kind of motions do you see? 3.Are there any differences in the time scales of the motions (what type of motions occur frequently/rarely, how long do the motions last) 4.Are there differences in the structure of water around the positively and negatively charged ions? 5.What kind of interactions forms the water with itself? How stable (long lasting) are these? 6. Could such detailed information be obtained from experiments?

6. Computer simulations can: 1.provide quantitative data 2.provide qualitative data 3.provide experimentally verifiable data 4. help predict properties

7. Thus: Computer simulations can complement experiments by providing data that is hard to obtain experimentally

8. The question my research addresses is: How do conformational changes work?

9. The question my research addresses is: How do conformational changes work? Conformational change = The change in shape of a biomolecule upon binding other molecules

10. Maltose-binding protein Proc. Natl. Acad. Sci. USA 100 12700 (2003)

11. Oxygen transport by hemoglobin Protein Data Bank www.rcsb.org

12. Membrane fusion by hemagglutinin of influenza virus Nature Struct. Biol. 8 653 (2001)

13. ATP hydrolysis by F 1 -ATPase Nature 386 299 (1997)

14. Conformational changes are crucial for the functioning of many proteins 2. kinases e.g. Src tyrosine kinase 1. transport proteins e.g. maltose-binding protein 3. molecular motors e.g. F O F 1 -ATPase 4. etc. etc.

15. The question my research addresses is: How do conformational changes work? -) How are they triggered/induced -) How are they propagated -) What are their pathways -) What is their function

16. protein domain motion unwinding of DNA helix protein folding molecular dynamics small system molecular dynamics large system 10 -6 10 -3 110 3 s Need to “speed up” simulations: apply biases 10 -15 10 -12 10 -9 Timescales of Conformational Motion

17. grey black

18. Alanine dipeptide C 7ax LL RR 0.0 3.0 6.0 9.0 12.0 0120-120 0 120 -120   C 7eq CH 3 –C–N—C  —C–N–CH 3 O –– – H O –– – H – CH 3 

19. ∆  =0.0005Å ∆  =0.00001Å

20. P F =0.0005Å P F =0.0003Å P F =0.0002Å P F =0.0004Å

21. P F =0.001Å P B =0.001Å P F =0.001Å P B =0.000Å

22. Artifacts Energy Rmsd Trajectories

23. GroEL:  Helps proteins fold  2 rings stacked back to back; each with a central cavity “trans” cavity (closed state): volume = 85,000 Å 3, hydrophobic cavity lining “cis” cavity (open state): volume = 175,000 Å 3, hydrophilic cavity lining Rings switch between closed and open state; this is driven by ATP binding/hydrolysis

24. GroEL: helps proteins fold Sigler et. al. Nature 371 578 (1994), Nature 388 741 (1997) open H I closed H I

25. GroEL Cycle GroES 7 ATP 7 ADP Folded Unfolded trans cis = Closed (t) Intermediate (r’) Open (r’’)

26. How does this help protein folding? Key notion: Protein folding in vivo is complicated, due to molecular crowding 1.provides a water-like, shielded environment, preventing aggregation 2.might there be a second effect?

27. http://www.public.asu.edu/~avanderv/groel.tar.gz MD trajectory of opening motion of GroEL in presence of unfolded protein (rhodanese) 1.What is GroEL, what the protein? 2.Is the entire GroEL present, or only a part (and which)? 3.Describe what happens to GroEL 4.Describe what happens to rhodanese More difficult: 1.Characterize the binding of the part of rhodanese that is tightly bound. What type of contacts are important? 2.Compare this binding to experimental studies (pdb databank entry 1DKD). What is similar, what is different? (e.g. type of contacts, orientation, type of interactions)