Transcript Optimization of C3 Inactivation with Compstatin Analogs

Bioengineering
Binding Free Energy Calculations
for Complex Formation between
C3c and Compstatin Analogs
Ioannis Mountziaris
Chris A. Kieslich, Dimitrios Morikis
Department of Bioengineering
University of California, Riverside
August 21, 2008
Overview
Introduction: Compstatin and the Complement
System
 Methodology:




Results:



Poisson-Boltzmann Calculations
Force-field Calculations
Experimental Data Set
Theoretical Data Set
Conclusions and Future Work
C3 and the Complement System
Cascade of biochemical
reactions that trigger an
immune response to an
antigen

C3
C3d
C3c
C3c+C3d
C3a
C3a
C3d
Alberts et al. MBOC. New York: Garland Science, 2002.
PDB: 2A73 from Gros et al. Nature 2005; 437: 505-511.
Structural Image by I. Mountziaris, 2008.
Complement Activation Pathways & Inhibition Targets
Alternative pathway
Classical pathway
Factor B
Ag-Ab
complexes
C1qsrrs
Ba
C3(H2O)Bb
C2b
C1qsrrs
C2
C2a
Tick-over
activation
C3(H2O)
C3
Factor D
C3
C3a
MBL-MASP
MBL-MASP
Pathogen
cell surface
carbohydrates
C4
C4b
C3b
C4a
Fluid
phase
C4b
Lectin pathway
Common
pathway
Fluid
phase
C3b
Surface
bound
C4b
Surface
bound
C3b
Factor B
Ba
Factor D
C3
C4b2a
C3a
C3bBb
C3b
C5
C4b2a3b
C5a
C3bBb3b
C5b
C6
C7
C5b67
C8
(C9)n
C5b678(9)n (MAC)
Morikis & Lambris (2005) Structural biology of the complement system, CRC Press
Amplification
loop
Green arrows
denote protein
complexes
responsible for
inflammation and
cell/ parasite
death
Red arrows
denote inhibition
targets
Complement involvement in disease
Acute disorders
Chronic disorders
• Asthma
• Alzheimer’s disease
• Adult respiratory distress syndrome
• Age-related macular degeneration
• Autoimmune diseases
Burns, wound healing
• Ancylosing spondylitis
Hyperacute rejection (organ transplant)
• Angiodema
Guillain-Barré syndrome
• Crohn’s disease
Ischemia-reperfusion injury
• Glomerulonephritis
• Heart attack
• Hemolytic-uremic syndrome
• Skeletal muscle
• Rheumatoid arthritis
• Stroke
• Multiple sclerosis
• Lung inflammation
• Myasthenia gravis
• Multiple organ dysfunction syndrome
• Neisserial infection
• Septic shock
• Paroxysmal nocturnal hemoglobinuria
• Trauma, hemorrhagic shock
• Psoriasis
• Xenotransplantation
• Pyogenic bacterial infections
Reaction to Biomaterials /
• Systemic lupus erythematosus
Implants
• Ulcerative colitis
• Hemolysis
• Angioplasty
• Infertility
• Cardiopulmonary bypass
• Obesity
• Hemodialysis
• Organ rejection (transplantation)
• Platelet storage
• Thrombosis
• Type I diabetes Mellitus
•
•
•
•
Introduction to Compstatin



13-amino acid peptide chain
Found in 1996 via phagedisplayed random peptide
library by Lambris group at
the University of
Pennsylvania
Binds to C3, and inhibits
cleavage of C3 into C3a and
C3b
Compstatin in complex with C3c
Compstatin
Structural images by I. Mountziaris, 2008.
PDB: 2QKI from Gros et al. J. Biol. Chem 2007; 282: 29241-29247.
Electrostatic Free Energy Calculations using
Poisson-Boltzmann Equation



ε High
Create theoretical grid in three-space
around the protein
provides a set amount of points for the
calculation to focus on
ε Low
Using the data known about the 20
ε surface
amino acids such as their electrostatic
κ surface
properties, order and orientation
within the protein complex, as well as
predetermined parameters, the
program calculates the interactions
between the protein and the statistical q,  ,  ,  
inclusion of solution ions
∆G (Coulombic)
In vacuum
∆∆G (Solvation)
ε: Dielectric coefficient
κ: Ion accessibility function
q: Charge
φ: Electrostatic potential
Coulomb’s Law:
V( r ) 
In solution
4e2
    (r ) (r )   0 (r ) (r ) (r ) 
 0 k BT
2
Compstatin
q
4 0 r
Linearized Poisson-Boltzmann Equation:
∆G (Solution)
C3c
1
Final
Complex
F
 z  (r  r )
i 1
i
i
Apolar Calculations via SASA/SAV

Solvent Accessible
Surface Area (SASA) and
Solvent Accessible
Volume (SAV) methods
calculate the nonpolar
free energies by taking
the difference in the
surface area or volume
when the components are
in solution or in complex.
Peak
No Peak
Force-field Calculations with CHARMM

Force-field calculations
are made based on
pre-determined
parameters for the
force field potential
energy and chemically
favorable topologies of
the amino acids and
the constituent
chemical groups in the
CHARMM force-field.
Eempirical = Ebonds + Eangles + Etorsions
+ EvdW + Eelectro
Methodology
Experimental Data Set
Theoretical Data Set
Obtain Parent PDB from Protein
Data Bank
Obtain Parent PDBs
Create mutants using WHATIF,
and optimize structure
Clean Files
Clean Files and make PSF file
using VMD
Perform Energy
Minimization using NAMD
Perform Molecular
Dynamics simulation using
NAMD
Calculate CHARMM Force-field
Energies
Convert PDB files to PQR
format for APBS calculation
using PDB2PQR
APBS is called
Convert PDB files to PQR format
for APBS calculation using
PDB2PQR
Calculate Electrostatic Free
Energies with APBS
Calculate
Electrostatic
Free Energies
Calculate
Nonpolar SASA
Free Energies
Calculate
Nonpolar SAV
Free Energies
Experimental Data Study



Contained 45
experimentally tested
analogs of compstatin
Measured electrostatic
interactions via APBS
and the electrostatic
and van der Waals
binding contributions
using force-field
calculations
Performed Molecular
Dynamics Simulations
Parent Compstatin in
Complex with C3c for 1ns in
vacuum
Energy minimization (local)
E(x)
Molecular dynamics (global)
E(x)
x
x
Weak Exponential Correlation Between
Free Energy Calculations and RIA
Comparison
∆∆Gvan
Solvation
Calculations
Force-field
Calculated
der Waals
Correlation
ofof∆∆G
Solvation
vs.Energy
RIA
between
Energy
Minimization
and Molecular
from
5000
step
Energy
Minimization
vs.
after 5000 step
Energy
Minimization
Dynamics Simulations
Relative Inhibitory Activity
(kJ/mol)
Energy
Free
(kcal/mol)
Energy
Free
(kJ/mol)
Energy
Free
1000
900
-35
850
10
20
30
40
50
800 0
-40
800
R² = 0.0422
600
750
-45
700
400
-50
650
R² = 0.1005
600
200
-55
Energy
550
Minimization
-60
0
500
0M5 M4 M3
10M2 M1 A2
20 A5 A1 A4
30 A3 I1 40
50I5
I2
I3
I4
-65
RelativeCompstatin
Inhibitory Activity
Activity
(RIA)
Relative
Inhibitory
Variant(RIA)
Theoretical Data Study


Contained 100 theoretical SQ059 SQ086 SQ098 SQ055 SQ088
analogs of compstatin
Measured both the
electrostatic interactions via
APBS as well as the apolar
interactions
Solvent-accessible surface
area (SASA)
 Solvent-accessible volume
(SAV)
Theoretical data set showed a
variety of possible compstatin
confirmations by trying to
optimize binding coefficients
between C3c and compstatin
mutants


SQ040 SQ087 SQ072 SQ024 SQ077
Floudas, Morikis et al. 2008 Submitted
Correlation Between Calculated Free
Energy and Normalized Binding Coefficients
900
800
700
600
500
400
300
200
100
0
Correlation ∆∆G (Solvation)
∆∆G Solvation (kJ/mol)
Free Energy in Solution
(kJ/mol)
Correlation ∆G Solution
R² = 0.0017
0
50
100
150
200
900
800
700
600
500
400
300
200
100
0
R² = 0.0007
0
50
100
150
200
Normalized Binding Coefficient (natural log)
Normalized Binding Coefficient (natural log)
Correlation ∆G near Vacuum
Correlation Apolar ∆G (SASA)
Free Energy near
vacuum(kJ/mol)
100
0
-100
0
50
100
150
200
-200
-300
-400
-500
R² = 0.0055
Normalized Binding Coefficient (natural log)
Free Energy SASA (kJ/mol)
200
60
50
40
30
20
10
R² = 0.0007
0
0
50
100
150
200
Normalized Binding Coefficient (natural log)
Conclusions

Experimental Dataset:



Force-field calculations show hydrophobic/nonpolar effects are
significant as predicted in previous studies
Need to include solvent when modeling C3c-compstatin binding
Theoretical Dataset:


SASA/SAV method is too coarse for modeling this binding
Numerous confirmations and orientations (compstatin variant)
exhibit excellent C3c binding.
Conclusions

Experimental Dataset:



Theoretical Dataset:



Force-field calculations show hydrophobic/nonpolar effects are
significant as predicted in previous studies
Need to include solvent when modeling C3c-compstatin binding
SASA/SAV method is too coarse for modeling this binding
Numerous confirmations and orientations (compstatin variant)
exhibit excellent C3c binding.
The crystal structure shows a shallow recess instead of a wellformed binding site. This makes binding weak and possibly nonBinding It site
onthatC3
shallow, thus
numerous
specific.
is likely
the is
forcevery
field calculations
represent
trapping
inCompstatin
a ragged and
shallow (various
potential energy
surface
with several
local
mutants
shapes)
can bind
with nearminima
and low energy barriers. This allows for several favorable
equal efficiency
rearrangements of side chains, and disfavors the energetic
discrimination of the various compstatin analogs
Conclusions

Experimental Dataset:



Force-field calculations show hydrophobic/nonpolar effects are
significant as predicted in previous studies
Need to include solvent when modeling C3c-compstatin binding
Theoretical Dataset:


SASA/SAV method is too coarse for modeling this binding
Numerous confirmations and orientations (compstatin variant)
exhibit excellent C3c binding.

Binding site on C3 is very shallow, thus numerous Compstatin
mutants (various shapes) can bind with near-equal efficiency

Differences between our models and "wet lab" findings 
Energetics of Compstatin-C3c binding may differ from CompstatinC3 binding.
Future Work

Increase the size of our datasets

more compstatin variants

Run Molecular Dynamics simulations at longer time
scales (e.g., 100 ns)

Incorporate solvation effects in Molecular Dynamics
simulations

Include entropic effects at binding interface

Explicitly calculate of Hydrogen Bond contributions
Acknowledgements
•
•
•
•
•
Chris Kieslich
Aliana López de Victoria
Dr. Morikis
Jun Wang and the BRITE program
National Science Foundation
References

Baker N.A., Sept D, Joseph S, Holst M.J., McCammon J.A. Electrostatics of nanosystems: application to
microtubules and the ribosome. Proc. Natl. Acad. Sci. A 98, 10037-10041 2001. (APBS)

Bellows, M., Fung, H., Taylor, M., Floudas, C. and Morikis, D. New Compstatin Variants Through Novel De Novo
Protein Design Frameworks Applied to a Complex with Complement Component C3c, Submitted.

Dolinsky T.J., Nielsen J.E., McCammon J.A., Baker N.A. PDB2PQR: an automated pipeline for the setup,
execution, and analysis of Poisson-Boltzmann electrostatics calculations. Nucleic Acids Research 32 W665-W667
(2004).

Humphrey, W., Dalke, A. and Schulten, K., "VMD - Visual Molecular Dynamics", J. Molec. Graphics, 1996, vol. 14,
pp. 33-38.

Morikis, D. and Lambris J. (2005) Structural Biology of the Complement System, Boca Raton: CRC Press.

James C. Phillips, Rosemary Braun, Wei Wang, James Gumbart, Emad Tajkhorshid, Elizabeth Villa, Christophe
Chipot, Robert D. Skeel, Laxmikant Kale, and Klaus Schulten. Scalable molecular dynamics with NAMD. Journal
of Computational Chemistry, 26:1781-1802, 2005.

Sahu, A., Soulika, A., Morikis, D. , Spruce, L., Moore, W. T., and Lambris, J. D. (2000) Binding kinetics, structureactivity relationship, and biotransformation of the complement inhibitor Compstatin, Journal of Immunology 165 ,
2491-2499.

Yang, J., Kieslich, C., Gunopulos, D., and Morikis, D. (2008) Insights into protein-protein interactions using a highthroughput computational protocol for alanine scans and clustering analyses of the spatial distributions of
electrostatic potentials, In Preparation.
Questions?
Compstatin
Compstatin in complex with C3c
Structural images by I. Mountziaris, 2008.
PDB: 2QKI from Gros et al. J. Biol. Chem 2007; 282: 29241-29247.