Transcript Development of Software Package for Determining Protein

Development of Software Package for
Determining Protein Titration
Properties
Final Presentation
Spring 2010
By
Kaila Bennett, Amitoj Chopra,
Jesse Johnson, Enrico Sagullo
Background
Proteins participate in many
biological processes via charge
characteristics
Biological processes include:
Binding
Enzymatic catalysis
Conformational transitions
Stability
Ionizable amino acids
Electrostatic interactions
Salt Bridges
Dipole-Dipole
Coulombic
Facilitate interactions with aqueous
environments
Mediate polar contributions for
Depicts electrostatic potential for human CR2 (PDB
biological processes
code,1LY2; isopotential contour) red negative, and
blue positive
Functions of proteins are dependent on
protonation states of ionizable amino
acid residues
Amino acid ioniziability can be
quantified by as the –log(Ka) where Ka
is ionization constant
pKa for a single amino acid is the point
at which there is a 50% probability of
ionized state
pKa values are highly dependant on the
environment and the interaction
between other ionizable residues
pKa in essence quantifies a proteins
overall charged characteristics
Our software package will take into
consideration three types of pKa
Model pKa
Intrinsic pKa
Apparent pKa
Partial charge
Background
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
VCP E108
VCP E120
SPICE K108
SPICE K120
0
2
4
6
pH
8
10
Zang and Morikis BioPhysw J. 2006
12
14
Catalysis
Asp102 of Chymotrypsin – hydrogen bond with His57 – increases pKa
His57 can accepts proton from Ser195 – activates serine protease for cleavage of
substrate
pKa shift important for each chemical reaction in catalytic mechanism
Necessary to donate and abstract protons from neighboring groups
Without pKa shift of His57, catalysis would not be possible!

Background
Linearized Poisson-Boltzmann
Equation (LPBE) solved by
Adaptive Poisson Boltzmann
Solver
ε high
F
4e2
 (r)(r)  0(r) (r)(r) 
 z (r  ri )
0k BT i1 i
ε low
2
2 (r) 
ε:
κ:
I:
q:
φ:
2
4e I
0k BT
M
I
1
z2i n 0i

2 i1
Dielectric coefficient
Ion accessibility function

Ionic strength
Charge
Electrostatic potential
1
  iq i
2
κ surface
q,, ,
Electrostatic Free Energies
G electro 
ε surface

κ=0
κ≠0
Solvent Charges
Partial Charges (Electric dipoles)
Background Charges
Courtesy of C. Kieslich
Background
Change in free energies can
quantified by the Thermodynamic
Cycle
Thermodynamic cycle has four
proposed states:
G nBc
Polymer

Bound deprotonated
Free deprotonated
Bound protonated
Free protonated
Free energy values allow us to
calculate intrinsic pKa’s
Intrinsic pKa is a theoretical value 
that defines the pKa for a single
amino acid when all others titratable
amino acids are neutralized
Intrinsic pKa allow us to quantify
apparent pKa
But first Interaction energy matrix
must be calculated
Polymer
AH
Intrinsic pKa
F
G B
n
GcB F
G nF c
AH

intr
a
pK

A-
Model pKa
 pK
model
a
ZGenv

2.303k BT
A-
Background
Interaction energy matrix are
quantified by calculating the
Coulombic electrostatic potential
between two ionizable residues
To account for all possible
ionization states the use of
statistical analysis methods mainly
clustering can be applied
Clustering is accomplished by
separating ionizable groups into
intra-cluster, which are treated
exactly and inter-cluster treated
approximately to alleviate
combinatorial challenge
This allow for the the quantification
of apparent pKa
Figure: Test case protein 1LY2 (CR2)
Coloring scheme:
Basic Blue, Acidic Red, Cystine Cyan, Tyrosine
green
Background
Apparent pKa’s can be elucidated
by intrinsic pKa and interaction
energy matrix
This relationship reflects the
pH-dependent interactions
between ionizable groups with all
other ionizable groups in there
charged state within the protein
From apparent pKa generation of
Titration Curves
Overall titration Curve for protein
Individual Titration Curves for single
amino acids
Stability Curves
Shows the most stable point of protein
i.e global minimum
Zang et al. JMB. 2007
Background
Equation equating intrinsic pKa to change in free energy and model pKa
intr
a
pK
 pK
model
a
Z
kB
T
= Ion Valence (-1, +1)
= Boltzmann constant
= Temperature
model
pKa = Model pKa
pKintr
a = Intrinsic pKa
ZGenv

2.303k BT
Genv = Gc
Self Energy
BF
 Gn
BF

Equation to determine apparent pKa by relating interaction energy and
intrinsic pKa
G inter
Interaction energy
app
intr
pKa = pKa 
matrix
2.303kBT


pKapp
a = Apparent pKa
G inter = Interaction energy



Interaction energy cannot be determined directly so statistical mechanical
method is used
Rationale: Flow Chart
Experimental Procedure
Table of Code
Call APBS
Our Sequence
Call APBS 2
Intrinsic pKa
Call APBS 3
Intrinsic/pKa 2
Call APBS 4
Interaction Energy
Cat 2PQR
Interaction Energy 2
Neutral to Charge
Calculation Coulomb Function
APBS template
Self Energy function
APBS template new
Interaction Coulomb
pKa
Plot Titration
Mean
Cat PDB
Hybrid
Titration Output
Our Sequence
Runs through
entire PDB
sequence
Identifies
ionizable
residue
Assigns Residue number
Assigns one
letter code
to first
column
Assigns model pKa
Assigns
location of
charged atom
Intrinsic pKa 2
Runs only through
ionizable groups
Creates
four
states
of TC
Writes the newly
created states to file
Calls APBS to
calculate free
energies
Interaction Coulomb
Opens file to
write
Writes to file in specific format
Outputs interaction energies
Calculates
Coulombic
Electrostatic
potentials
between
ionizable
residues
Hybrid
Model pKa
SelfEnergy
Unit
Charge
Interaction
Energies
Group
Number
GUI
Individual Titration
curves
Primary
console
User can click to view
individual titratable residues
Overall titration
curve
Stability Curves
Table of pKa for each
titratable residues
Results (Intrinsic pKa)
Protein 1LY2
Residue
Intrinsic pKa (ours)
Arginine
12.62
Aspartic Acid
4.29
Cystine
N/A
Glutamic Acid
4.06
Histidine
7.93
Lysine
10.52
Tyrosine
7.82
Intrinsic pKa due in fact modify model pKa (model
pKa for Arginine = 12.00)
Results (Apparent pKa)
Results( Titration Curves)
Isoelectric
point at pH=10
Isoelectric point, where the charge is zero (i.e where positive charge cancels out negative
charge)
Results (Stability Curves)
Global Minimum
GStab (pH)
 2.303k BT( QF  QU )
pH
Analysis of Results
Strong interactions
One of the biggest changes in pKa was E-40, if we use molecular graphics we can
discern its binding partner is K-57, meaning very favorable association distance
was 4.98 Å
Weak Interaction
Coloring scheme:
Basic Blue, Acidic
Red, Cystine Cyan,
Tyrosine green
Analysis of Program
APBS (Ours)
Termini
No
UHBD (Dr. Morikis)
C-terminus
Histidines
Single tautomers
All tautomers
Charge Distribution
Distribution of Charge
Localized unit charge
Solver
LPBE from APBS
Different LPBE solver
used by UHBD more fine
Grid
Single grid
Focusing grids
Dielectric Constant
ε = 40
ε = 80
Force field
Implementation of free
energy
Ours
H++
PARSE
AMBER
Ours
pKa tool
APBS
Delphi
Discussion
We completed our initial goal for this
project
Have a working prototype
Our apparent pKa values for 1LY2
have a good degree of correlations
with other software
Are in agreement with structural
details
We ran our program for lysozyme and
although our software generated
similar trends in pKa (meaning
favorable associations, acidic was
downshifted and basic was upshifted),
Absolute values were not reproduced
Figure: Lysozyme or 2LZT PDB
Future Work
Expand program to be compatible for all platforms
Include termini in calculations
Include protein complexes, or multiple chains
Calculation of binding energies
Minimize calculation run times
Use Monte Carlo simulations for clustering instead of Hybrid
Fine tuning performance testing
Conclusion
Successfully took a PDB and generated
titration and stability curves
Implemented different thermodynamic cycles
and optimized them to fit our protocol
Incorporated APBS, PDB2PQR, and Hybrid in
order to calculate free energies and apparent
pKa’s
Apparent pKa for 1LY2 had a high degree of
correlation
Combined all scripts into an easy-to-use GUI
Acknowledgments
Dr. Dimitrios Morikis
Chris Kieslich
Ronald Gorham
Dr. Jerome Schultz
Gokul Upadhyayula
Hong Xu
Dr. Thomas Girke
References
1) Nielsen, J.E., McCammon and A. J. Calculating pKa values in enzyme active site. Protein Science.12.
1894-1901. 2007.
2) Antosiewicz, M.J. Protonation free energy levels in complex molecular systems. Biopolymers.89. 262269. 2007.
3) Wu, J., and Morikis, D. Molecular thermodynamics for charged biomacromolecules. Fluid Phase
Equilibria. 241. 317-333. 2006.
4) Gilson M. K. Multiple site titration and molecular modeling: two rapid methods for computing
energies and forces for ionizable groups of protein. Proteins. 15. 266-282. 1993.
5) Baker, N.A., Sept, D., Joseph, S., Holst, M.J., and Mccammon, J.A. Electrostatic nanosystems:
Application to microtubules and the ribosome. Proceedings of the National Academy of Science. 98.
10037-10041. 2001.
6) Nielsen J.E., and Vreind G. Optimizing the hydrogen – bond network in Poisson-Boltzmann equationbased pK(a) calculations. Proteins. 43. 403-412. 2001.
7) Prota A.E., Sage D.R, Stehel, T., and Fingeroth, J.D. The crystal of human CD21: Implication of
Epstein- Barr virus and C3d binding. The Proceedings of the National Academy of Science. 99. 1064110646. 2002.
Questions?
Our group would like to mention that no
computers were injured in the making of the
software package
Conformation Change
Another important biological process that is dependent on pKa of the
environment is transition states of proteins
Conformational switch
-5
-3
-1
1
3
5
7
9
11 13 15 17 19 21 23 25
0
h: helix
-0.1
c: coil
Tyr67
Tyr100
Tyr115
Tyr177
Asp68
Asp76
Asp144
Asp160
Glu162
Glu173
-0.2
Partial charge
Gh-c(neutral)
neutral
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
-1
pH
G
h,ion
(pH)
ionized
G
c,ion
(pH)
+
–+ –
– +–+–
++–
++
–
––
–
+ Gh-c(pH) +
His121
His119
Catalytic site
His108
His132
His137
Figure: Morikis et al, Protein Sci 2001
Binding
Salt Bridge
pKa shifts also effect intermolecular salt bridges
Salt bridges are short range, Columbic interactions that occur between two
ionizable amino acid residues
From S.Fischer et al, Proteins 2009
Rationale
Developing a software package that not only incorporates APBS to
calculate free energies but also calculate protein titration characteristics,
will help ultimately aid to elucidate proteins stability, catalysis, salt bridges,
binding
Figure: Test case protein 1LY2 (CR2)