molecular dynamics simulations of cro proteins: mutation! max shokhirev miyashita-tama group 5-14-08...

Molecular Dynamics Molecular Dynamics Simulations of Cro Proteins:Simulations of Cro Proteins:Mutation! Mutation!

Max Shokhirev

Miyashita-Tama Group

5-14-08

Background Image from 1rzs1.pdb courtesy of PDB

OverviewOverviewBackground

Evolution of Cro Proteins and what they are

Ideas behind Molecular Dynamics (MD)Alanine Scanning SimulationsConclusions

Evolution of Protein StructureEvolution of Protein StructureNeutral Sequence Networks1

1= ancestor

2= same fold descendant

3= different fold via unstable mutations (relaxed)

4= frameshift descendant

5= different fold via stable mutations

Cro Proteins?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.

P22P22 vs λ Cro vs λ Cro

P22 Cro λ Cro

P22P22 vs λ Cro vs λ Cro

Two approaches…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.

Molecular Dynamics (MD)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

Velocity-Verlet IntegratorVelocity-Verlet Integrator Scheme for calculating new position,

velocity, and acceleration at each time step:

1. Compute New PositionPosition

2. Compute Half VelocityHalf Velocity

3. Compute ForceForce

4. Compute VelocityVelocity

PositionVelocityAcceleration

Time step-1 -.5 0 .5 1

Initial Conditions…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

Initial Temperature…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)

Temperature Control…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

Force FieldForce FieldForce on each particle calculated from

components Direct bond Angle Dihedral Specific LJ Non-specific LJ

Bond InteractionsBond Interactions

V = ½k(Xi-X0)2

Fi = k*(Xi-X0)/Xi

Angle InteractionsAngle Interactions

Dihedral InteractionsDihedral Interactions

Lennard-Jones InteractionsLennard-Jones Interactions

•Non-specific LJ

•By atom type (6-12)

•Specific(native) LJ

•6-12

•10-12

10

Thus far…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

Phase II – Honors ThesisPhase II – Honors ThesisCro folding and unfoldingMelting temperature simulationsComparison of 6-12 and 10-12 LJ

interactionsAlanine Scanning for P22 and Lambda

Cro

Cro Folding and UnfoldingCro Folding and Unfolding Temp = Temp = 350 350 Temp = Temp = 800800

P22 CroP22 Cro

λ Croλ Cro

Cro Folding and UnfoldingCro Folding and Unfolding

T = 1000 T = 300T = 300

Calculating Melting TempCalculating Melting Temp

1.1. Run simulation(s) at different tempsRun simulation(s) at different temps

2.2. Calculate Q values for each tempCalculate Q values for each temp1.1. At Tm Q values fluctuate around At Tm Q values fluctuate around 0.50.5

2.2. Can plot histogram of Q valuesCan plot histogram of Q values

3.3. Free energy profile for each tempFree energy profile for each temp1.1. E = -Kb*T*log(P(q))E = -Kb*T*log(P(q))

3.3. Calculate Specific Heat Calculate Specific Heat 1.1. Derivative of total energy plot at each temp.Derivative of total energy plot at each temp.

4.4. Values are not scaled to real-world valuesValues are not scaled to real-world values

Q values for P22 CroQ values for P22 Cro

P22 Melting TemperatureP22 Melting Temperature

Q values for Q values for λ Croλ Cro

λ Cro Melting Temperaturesλ Cro Melting Temperatures

Purple = 10-12 LJ

Orange = 6-12 LJ

Melting Temperature from Melting Temperature from Specific HeatSpecific HeatWe 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

Specific Heats Specific Heats

P22 Cro ~ T=750

λ Cro ~ T= 685

6-12

Real Melting TemperaturesReal Melting Temperatures λ Cro

334 K1

Oligomer with Tm <= 313 K1

λ Cro A33W/F58D pure monomer

P22 Cro 327 K1

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

P22 λ Cro

Test Effect of LJ10-12 pot.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 6-126-12 pot to a 10-1210-12 potential. This should theoretically increase

“cooperativity” of folding2

LJ10-12 ResultsLJ10-12 Results

P22

λCro

6-12 LJ Potential 10-12 LJ Potential

LJ Observations…LJ Observations…

1. The melting temperatures decreased when using a 10-12 LJ potential.

2. The 10-12 LJ Potential shows a higher degree of cooperativity (esp for P22)

Alanine ScanningAlanine ScanningMutate 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

P22 Alanine ScanningP22 Alanine ScanningP22 Cro (LJ 6-12 and 10-12) Alanine mutations

0.3

0.35

0.4

0.45

0.5

0.55

0.6

3334353637383940414243444546474849505152535455565758

Resiude Mutated

<Q

>

Lambda Alanine ScanningLambda Alanine ScanningLamda Cro <Q> at Tf vs Alanine Mutant

0.38

0.4

0.42

0.44

0.46

0.48

0.5

0.52

34353637383940414243444546474849505152535455565758

Residue

Avera

ge Q

valu

e

Alanine Scanning ResultsAlanine Scanning ResultsAlanine Scanning simulations match

melting temperature dataAlanine Scanning simulations show

regions that decrease stability, which does not match the real data.

Phase III – Cro Mutation StudiesPhase III – Cro Mutation StudiesWhat drives structural stability?

Native interactions Native interactions (between divergent and

not divergent domains) Dihedral Interactions Angle Interactions (the future)

Removing native + dihedralsRemoving native + dihedrals

1rzs: mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a

5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta

Removing Native/Mixing DihedralsRemoving Native/Mixing Dihedrals



Removed Inter-domain native cont.Removed Inter-domain native cont.



Purple Lambda 6-12 LJ

Gray Lambda 10-12 LJRed P22 10-12 LJ

Black P22 6-12 LJ

Removing Dihedral Angles OnlyRemoving Dihedral Angles Only



ConclusionsConclusions An MD Simulation program was An MD Simulation program was writtenwritten to study Cro to study Cro

proteinsproteins P22 has been shown to P22 has been shown to unfold and refoldunfold and refold as a function as a function

of temperature.of temperature. Folding Folding temperaturestemperatures observed from free energy profile observed from free energy profile

and specific heat data.and specific heat data. λ Cro has only λ Cro has only one free energy minimumone free energy minimum at its folding at its folding

temperature, while temperature, while 2 minima2 minima are observed for P22 Cro. are observed for P22 Cro. The 10-12 LJ interaction allows for The 10-12 LJ interaction allows for higher cooperativityhigher cooperativity.. Alanine scanning simulations Alanine scanning simulations qualitativelyqualitatively match real match real

data. data. Dihedral angle interactionsDihedral angle interactions are essential to stability of are essential to stability of

mutantsmutants

Acknowledgements…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).

3. “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).

4. "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



http://www.geocities.com/drpaulng/UC-AquariumFilter.JPG

http://upload.wikimedia.org/wikipedia/commons/4/42/Bond_dihedral_angle.png

molecular dynamics simulations of cro proteins: mutation! max shokhirev miyashita-tama group 5-14-08...

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