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
Slide 2
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
Slide 3
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
Slide 4
Cro Proteins? DNA-binding proteins Initiate lytic pathway in
bacteria 3 Ancestral forms have 5 -helices, with the 2 nd and 3 rd
forming a helix-turn-helix DNA- binding motif (P22 Cro is an
example) Bacteriophage Cro consists of 3 - helices and the 4 th and
5 th helices are replaced by a -hairpin.
Slide 5
P22 vs Cro P22 Cro Cro
Slide 6
P22 vs Cro P22 Cro Cro
Slide 7
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.
Slide 8
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 Cro protein systems. Work in progress!
Slide 9
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 t
such that the particles move continuously
Slide 10
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
Slide 11
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
Slide 12
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 )
Slide 13
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
Slide 14
Force Field Force on each particle calculated from components
Direct bond Angle Dihedral Specific LJ Non-specific LJ
Slide 15
Bond Interactions V = k(X i -X 0 ) 2 F i = k*(X i -X 0 )/X
i
Slide 16
Angle Interactions
Slide 17
Dihedral Interactions
Slide 18
Lennard-Jones Interactions Non-specific By atom type Specific
6-12 10-12
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
Slide 21
Q values for P22 Cro 2000
Slide 22
Histogram Free Energy P22 Cro 730 750 795 Temp
Slide 23
Q values for Cro 2000 NaN occurred!
Slide 24
Histogram Free Energy Cro 650 700 780 Temp
Slide 25
Real Melting Temperatures Cro 334 K 1 Oligomer with T m
More Results Cros folding temperature decreased as well
(700->650)
Slide 33
More Results
Slide 34
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
Slide 35
Conclusions A MD Simulation program was written to study Cro
proteins Folding temperatures observed Contradicts known values 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
Slide 36
Future Research Make sense of melting temperature discrepancy
Simulations on Alanine mutants of Cro and P22 Cro Residue stability
studies Submit thesis!
Slide 37
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, 1054210553 (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 259267 (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):
17831787 (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, 800809 (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
