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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 Ag-Ab complexes C1qsrrs Ba C3(H2O)Bb C2b C1qsrrs C2 C2a Factor B 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 4e 2 (r ) (r ) 0 (r ) (r ) (r ) 0 k BT 2 Compstatin q 40 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.