Molecular Dynamics Simulations of Cro Proteins: Mutation!

1. Molecular Dynamics Simulations of Cro Proteins:Mutation! Max Shokhirev Miyashita-Tama Group 5-14-08 Background Image from 1rzs1.pdb courtesy of PDB

2. Overview • Background • Evolution of Cro Proteins and what they are • Ideas behind Molecular Dynamics (MD) • Alanine Scanning Simulations • Conclusions

3. Evolution of Protein Structure Neutral Sequence Networks1 1= ancestor 2= same fold descendant 3= different fold via unstable mutations (relaxed) 4= frameshift descendant 5= different fold via stable mutations

4. Cro Proteins? • DNA-binding proteins • Initiate lytic pathway in bacteria3 • Ancestral forms have 5 α-helices, with the 2nd and 3rd forming a helix-turn-helix DNA-binding motif (P22 Cro is an example) • Bacteriophage λ Cro consists of 3 α-helices and the 4th and 5th helices are replaced by a β-hairpin.

5. P22 vs λ Cro P22 Croλ Cro

6. P22 vs λ Cro

7. Two approaches… • The Cro protein family has been studied with Alanine-Scanning Mutagenesis and Hybrid-Scanning Mutagenesis1 • Computational approach • Molecular Dynamics • Data-mining 4 • Etc.

8. Molecular Dynamics (MD) • Deterministic • Given initial conditions and parameters it is possible to calculate the conditions at any other point in time. • Iterative (Discrete) • Repeat force calculations at each time step and move particles accordingly. • Need to pick Δt such that the particles move continuously

9. Velocity-Verlet Integrator • Scheme for calculating new position, velocity, and acceleration at each time step: • Compute New Position • Compute Half Velocity • Compute Force • Compute Velocity Time step -1 -.5 0 .5 1 Position Velocity Acceleration

10. Initial Conditions… • Initial Positions • Extracted from PDB file • Bonding Interactions • Bonding information from PDB • Direct bonds, allowed angles, allowed dihedrals • Velocity? • Generated using genVel based on equipartition theory at a specified temperature. • Other parameters • Masses, LJ types, Specific LJs, general simulation parameters

11. Initial Temperature… • The temperature is proportional to the average speed of particles in a system. We can assign temperatures based on the Maxwell-Boltzman velocity distribution function: • Vi = (Normalized Gaussian Random number) * sqrt((Kb*Na*T)/Mi)

12. Temperature Control… • System is coupled to a virtual heat bath: • Vnew=Vold*sqrt(1-(ts/tau)*(1- Ttarget/Tcurrent)) • ts = time step length • tau = coupling coefficient

13. Force Field • Force on each particle calculated from components • Direct bond • Angle • Dihedral • Specific LJ • Non-specific LJ

14. Bond Interactions • V = ½k(Xi-X0)2 • Fi = k*(Xi-X0)/Xi

15. Angle Interactions

16. Dihedral Interactions

17. Lennard-Jones Interactions 10 • Non-specific LJ • By atom type (6-12) • Specific(native) LJ • 6-12 • 10-12

18. Thus far… • Phase I • Create a program for flexible MD simulations using a Go-like potential • Simulator seems to be working for bond, angle, dihedral, LJ (10-12 and 6-12). Cro proteins are folding/unfolding! • Phase II • Results from honors thesis • Phase III • Mutational studies of Cro proteins

19. Phase II – Honors Thesis • Cro folding and unfolding • Melting temperature simulations • Comparison of 6-12 and 10-12 LJ interactions • Alanine Scanning for P22 and Lambda Cro

20. Cro Folding and Unfolding Temp = 350 Temp = 800 P22 Cro λ Cro

21. Cro Folding and Unfolding T = 300 T = 300 T = 1000

22. Calculating Melting Temp • Run simulation(s) at different temps • Calculate Q values for each temp • At Tm Q values fluctuate around 0.5 • Can plot histogram of Q values • Free energy profile for each temp • E = -Kb*T*log(P(q)) • Calculate Specific Heat • Derivative of total energy plot at each temp. • Values are not scaled to real-world values

23. Q values for P22 Cro

24. P22 Melting Temperature

25. Q values for λ Cro

26. λ Cro Melting Temperatures Purple = 10-12 LJ Orange = 6-12 LJ

27. Melting Temperature from Specific Heat • We can obtain the melting temperature by plotting the specific heat as a function of simulation temperature • The specific heat is the derivative of the total energy function with respect to temperature

28. Specific Heats 6-12 P22 Cro ~ T=750 λ Cro ~ T= 685

29. Real Melting Temperatures • λ Cro • 334 K1 • Oligomer with Tm <= 313 K1 • λ Cro A33W/F58D pure monomer • P22 Cro • 327 K1

30. Melting Temperature Conc. • P22 Cro ~ 745/750 • λ Cro ~ 690/685 • P22 Cro is a 2-state folder, λ Cro is not! P22 λ Cro

31. Test Effect of LJ10-12 pot. • Simulations performed on P22 Cro and λ Cro under nearly identical conditions • Change the Lennard-Jones potential from a 6-12 pot to a 10-12 potential. • This should theoretically increase “cooperativity” of folding2

32. LJ10-12 Results 6-12 LJ Potential 10-12 LJ Potential P22 λCro

33. LJ Observations… • The melting temperatures decreased when using a 10-12 LJ potential. • The 10-12 LJ Potential shows a higher degree of cooperativity (esp for P22)

34. Alanine Scanning • Mutate the structurally divergent residues to alanine. • Remove the native contacts for each residue. • Simulations at the folding temperature of each Cro protein. • Average Q values for each residue

35. P22 Alanine Scanning

36. Lambda Alanine Scanning

37. Alanine Scanning Results • Alanine Scanning simulations match melting temperature data • Alanine Scanning simulations show regions that decrease stability, which does not match the real data.

38. Phase III – Cro Mutation Studies • What drives structural stability? • Native interactions • Native interactions (between divergent and not divergent domains) • Dihedral Interactions • Angle Interactions (the future)

39. Removing native + dihedrals 1rzs: mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a 5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta

40. Removing Native/Mixing Dihedrals 1rzs: mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a 5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta

41. Removed Inter-domain native cont. 1rzs: mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a 5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta Purple Lambda 6-12 LJ Gray Lambda 10-12 LJ Red P22 10-12 LJ Black P22 6-12 LJ

42. Removing Dihedral Angles Only 1rzs: mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a 5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta

43. Conclusions • An MD Simulation program was written to study Cro proteins • P22 has been shown to unfold and refold as a function of temperature. • Folding temperatures observed from free energy profile and specific heat data. • λ Cro has only one free energy minimum at its folding temperature, while 2 minima are observed for P22 Cro. • The 10-12 LJ interaction allows for higher cooperativity. • Alanine scanning simulations qualitatively match real data. • Dihedral angle interactions are essential to stability of mutants

44. Acknowledgements… Dr. Osamu Miyashita Dr. Florence Tama M-T Group • "Relationship between sequence determinants of stability for two natural homologous proteins with different folds", L.O. Van Dorn, T. Newlove, S. Chang, W.M. Ingram, and M.H.J. Cordes. Biochemistry.45, 10542–10553 (2006). • “Scrutinizing the squeezed exponential kinetics observed in the folding simulation of an off-lattice Go-like protein model”, H. K. Nakamura, M.Sasai, M Takano. Chemical Physics.307 259–267 (2004). • “Mechanism of action of the cro protein of bacteriophage lambda.” A Johnson, B J Meyer, and M Ptashne. Proc Natl Acad Sci U S A. 75(4): 1783–1787 (1978). • "High polar content of long buried blocks of sequence in protein domains suggests selection against amyloidogenic nonpolar sequences", A.U. Patki, A.C. Hausrath, and M.H.J. Cordes. Journal of Molecular Biology. 362, 800–809 (2006). Images Used: http://upload.wikimedia.org/math/8/1/d/81db614753d616c395a65928ac27686c.png http://www.geocities.com/drpaulng/UC-AquariumFilter.JPG http://upload.wikimedia.org/wikipedia/commons/4/42/Bond_dihedral_angle.png