Transcript Developing Molecular Dynamics Simulations using a Go

Molecular Dynamics
Simulations of Cro Proteins:
Mutation!
Max Shokhirev
Miyashita-Tama Group
5-14-08
Background Image from 1rzs1.pdb courtesy of PDB
Overview
 Background
 Evolution
of Cro Proteins and what they
are
 Ideas behind Molecular Dynamics (MD)
 Alanine
Scanning Simulations
 Conclusions
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
Cro Proteins?
 DNA-binding
proteins
lytic pathway in bacteria3
 Ancestral forms have 5 α-helices, with the
2nd and 3rd forming a helix-turn-helix DNAbinding motif (P22 Cro is an example)
 Bacteriophage λ Cro consists of 3 αhelices and the 4th and 5th helices are
replaced by a β-hairpin.
 Initiate
P22 vs λ Cro
P22 Cro
λ Cro
P22
vs
λ Cro
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)
 Deterministic
 Given
initial conditions and parameters it is
possible to calculate the conditions at any
other point in time.
 Iterative
 Repeat
(Discrete)
force calculations at each time step
and move particles accordingly.
 Need to pick Δt such that the particles
move continuously
Velocity-Verlet Integrator

1.
2.
3.
4.
Scheme for calculating new position,
velocity, and acceleration at each time
step:
Compute New Position
Compute Half Velocity
Compute Force
Time step
Compute Velocity
-1 -.5 0 .5 1
Position
Velocity
Acceleration
Initial Conditions…

Initial Positions


Extracted from PDB file
Bonding Interactions

Bonding information from PDB


Velocity?


Direct bonds, allowed angles, allowed dihedrals
Generated using genVel based on equipartition
theory at a specified temperature.
Other parameters

Masses, LJ types, Specific LJs, general simulation
parameters
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…
 System
is coupled to a virtual heat bath:
 Vnew=Vold*sqrt(1-(ts/tau)*(1-
ts = time step length
 tau = coupling coefficient

Ttarget/Tcurrent))
Force Field
 Force
on each particle calculated from
components
 Direct
bond
 Angle
 Dihedral
 Specific
LJ
 Non-specific LJ
Bond Interactions
= ½k(Xi-X0)2
 Fi = k*(Xi-X0)/Xi
V
Angle Interactions
Dihedral Interactions
Lennard-Jones Interactions
10
•Non-specific LJ
•By atom type (6-12)
•Specific(native) LJ
•6-12
•10-12
Thus far…

Phase I



Phase II


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!
Results from honors thesis
Phase III

Mutational studies of Cro proteins
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
Cro Folding and Unfolding
Temp = 350
P22 Cro
λ Cro
Temp = 800
Cro Folding and Unfolding
T = 300
T = 1000
T = 300
Calculating Melting Temp
1.
2.
Run simulation(s) at different temps
Calculate Q values for each temp
1.
2.
3.
At Tm Q values fluctuate around 0.5
Can plot histogram of Q values
Free energy profile for each temp
1.
3.
Calculate Specific Heat
1.
4.
E = -Kb*T*log(P(q))
Derivative of total energy plot at each temp.
Values are not scaled to real-world values
Q values for P22 Cro
P22 Melting Temperature
Q values for λ Cro
λ Cro Melting Temperatures
Purple = 10-12 LJ
Orange = 6-12 LJ
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
Specific Heats
6-12
P22 Cro ~ T=750
λ Cro ~ T= 685
Real Melting Temperatures

λ Cro

334 K1



Oligomer with
Tm <= 313 K1
λ Cro
A33W/F58D
pure monomer
P22 Cro

327 K1
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
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
LJ10-12 Results
6-12 LJ Potential
P22
λCro
10-12 LJ Potential
LJ Observations…
1.
2.
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)
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
P22 Alanine Scanning
P22 Cro (LJ 6-12 and 10-12) Alanine mutations
0.6
0.55
<Q>
0.5
0.45
0.4
0.35
0.3
3334 353637 3839 404142 434445 464748 495051 5253 545556 5758
Resiude Mutated
Lambda Alanine Scanning
Lamda Cro <Q> at Tf vs Alanine Mutant
0.52
Average Q value
0.5
0.48
0.46
0.44
0.42
0.4
0.38
34353637383940414243444546474849505152535455565758
Residue
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.
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)
Removing native + dihedrals
1rzs:
mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a
5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta
Removing Native/Mixing Dihedrals
1rzs:
mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a
5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta
Removed Inter-domain native cont.
Purple Lambda 6-12 LJ
Gray Lambda 10-12 LJ
Red P22 10-12 LJ
Black P22 6-12 LJ
1rzs:
mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a
5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta
Removing Dihedral Angles Only
1rzs:
mykkdvidhf gtqravakal gisdaavsqw kevipekday rleivtagal kyqenayrqa a
5cro: meqritlkdyamrf gqtktakdlg vyqsainka- --ihagrkif ltinadgsvy aeevkpfpsn kktta
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
Acknowledgements…
Dr. Osamu Miyashita
Dr. Florence Tama
M-T Group
1.
2.
3.
4.
"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 offlattice 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