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Developing Molecular Dynamics Simulations using a Go-like Model to study folding of Cro protein families Max Shokhirev BMB Senior Honors Thesis Fall 07- Spring 08 Background Image from 1rzs1.pdb courtesy of PDB

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Overview Background Evolution of Cro Proteins and what they are Ideas behind Molecular Dynamics (MD) Simulation Project Overview of function Simulations of Cro proteins Conclusions/Future Study

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

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

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P22 vs λ Cro P22 Croλ Cro

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P22 vs λ Cro P22 Croλ Cro

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Two approaches… The Cro protein family has been studied with Alanine-Scanning Mutagenesis and Hybrid-Scanning Mutagenesis 1 Computational approach Molecular Dynamics Data-mining 4 Etc.

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My Project… Phase I Create a program for flexible MD simulations using a Go-like potential Its working! Phase II Use the program to study the P22 and λ Cro protein systems. Work in progress!

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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

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Velocity-Verlet Integrator Scheme for calculating new position, velocity, and acceleration at each time step: Position 1. Compute New Position Half Velocity 2. Compute Half Velocity Force 3. Compute Force Velocity 4. Compute Velocity Position Velocity Acceleration Time step -1 -.5 0.5 1

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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

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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: V i = (Normalized Gaussian Random number) * sqrt((Kb*Na*T)/M i )

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Temperature Control… System is coupled to a virtual heat bath: V new =V old *sqrt(1-(ts/tau)*(1- T target /T current )) ts = time step length tau = coupling coefficient

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

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Bond Interactions V = ½k(X i -X 0 ) 2 F i = k*(X i -X 0 )/X i

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Angle Interactions

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Dihedral Interactions

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Lennard-Jones Interactions Non-specific By atom type Specific 6-12 10-12

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Simulating Cro Proteins… Temp = 350 Temp = 800 Temp = 350 Temp = 800 P22 Cro λ Cro

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Calculating Melting Temp 1. Run simulation(s) at different temps 2. Calculate q values for each temp 3. At Tm q values fluctuate around 0.5 1. Can plot histogram of q values 2. Free energy profile for each temp 1. E = -Kb*T*log(P(q)) 4. Need to scale the simulation to real- world values

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Q values for P22 Cro 2000

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Histogram Free Energy P22 Cro 730 750 795 Temp

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Q values for λ Cro 2000 NaN occurred!

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Histogram Free Energy λ Cro 650 700 780 Temp

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Real Melting Temperatures λ Cro 334 K 1 Oligomer with T m <= 313 K 1 λ Cro A33W/F58D pure monomer P22 Cro 327 K 1

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Melting Temperatures Contradict Real Data! λ Cro should have a slightly HIGHER T m when compared to P22 Cro! Simulation predicted LOWER: λ CroP22 Cro TmTm ~700~750

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Energy Profile Differences P22 Cro shows 2 free energy minima at the melting temperature λ Cro has only 1 free energy minima at the melting temperature P22 λ Cro

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Q values at T=755

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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 folding 2

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LJ10-12 Results T=750

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More Results P22 Cro’s Folding temperature decreased!

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More Results… λ Cro’s folding temperature decreased as well (700->650)

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More Results…

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Hardships along the way… Stopping rotation throughout the simulation Increase delay between submission to thira NaN errors due to dihedral angle near 0 Signs on dihedral angles need to be assigned

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Conclusions A MD Simulation program was written to study Cro proteins Folding temperatures observed Contradicts known values λ Cro has only one free energy minimum at its folding temperature, while 2 minima are observed for P22 Cro. Effect of LJ 10-12 potential on simulations

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Future Research Make sense of melting temperature discrepancy Simulations on Alanine mutants of λ Cro and P22 Cro Residue stability studies Submit thesis!

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Acknowledgements… 1. "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). 2. “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 Dr. Osamu Miyashita Dr. Florence Tama M-T Group

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