Biophysical and Bioengineering Methods for the Study of the Complement System at Atomic Resolution

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1 Biophysical and Bioengineering Methods for the Study of the Complement System at Atomic Resolution DIMITRIOS MORIKIS Department of Bioengineering University of California, Riverside USA BUDDHADEB MALLIK Department of Bioengineering University of California, Riverside USA LI ZHANG Department of Chemistry University of California, Riverside USA Abstract: - We present examples from our research in the fields of immunophysics, structural bioinformatics, design of proteins with tailored activities, and rational drug design. Our aim is to understand the function of the complement system, which is part of innate immunity, and to design regulators and inhibitors against illregulated activation of the complement system. We use atomic resolution computational and spectroscopic methods, such as molecular dynamics simulations, electrostatic calculations, and nuclear magnetic resonance. Specifically, we discuss the role of structure, dynamics, and electrostatics in (i) protein-protein association, (ii) classification of bioactivities, (iii) protein design, and (iv) drug design and optimization. Key-Words: Immunophysics, Biocomputation, Molecular Dynamics, Electrostatics, Poisson-Boltzmann, Electrostatic Similarity Index, NMR, Complement System, Complement Control Protein 1 Introduction The complement system [1] is the first line of innate immune response against invading foreign pathogens and a link between innate and adaptive immunities. It also acts as a disposer of waste, such as circulating immune complexes and products of inflammatory injury. The complement system is a collection of more than 30 proteins in serum and cell surfaces, which during activation are cleaved to functional fragments and/or combine with other proteins to form functional supramolecular assemblies. The complement system is activated through three different, complex, and interconnected pathways, the alternative, the classical, and the lectin pathways. Activation of the complement system is regulated by the so-called regulators of complement activation. Fine regulation of the complement system contributes to the recognition of self from non-self by the immune system. However, in certain autoimmune diseases and other pathological situations this recognition breaks down accompanied by excessive activation of ill-regulated complement system. In addition, certain viruses mimic regulators of complement activation, both structurally and functionally, to evade the immune system. Here, we call collectively complement receptors, regulators, and viral inhibitors as complement control proteins (CCP), which interact with complement proteins, protein fragments, or protein assemblies. There are complex networks of multitudes of interactions for complement components with other complement and noncomplement proteins. Our research focuses on the study of the immune system. The goals of our research are (i) to understand the physical basis of complement system function (immunophysics), (ii) to determine the role of structure, dynamics, and underlying physicochemical properties in the formation of active complement fragments, complexes, or assemblies (structural bioinformatics), (iii) to design CCP proteins with tailored activities, based on immunophysics and structural bioinformatics

2 classifications (bioengineering of CCPs), and (iv) the design of low-molecular mass complement inhibitors, based on immunophysics and structuredynamics-interactions-thermodynamics-activity correlations (rational drug design). The starting point of our research is the availability of threedimensional structures. Structure determination of complement proteins, fragments, complexes, assemblies, CCPs, and drug inhibitors is a highly active field of research and has been recently reviewed [1]. Also, the use of quantitative physical methods in the study of the complement system, and immune system in general [], becomes increasingly widespread in complementing traditional methods using immunological assays, immune cell biology, and animal models. In this mini-review, we present an overview of our currently active research projects. We briefly summarize our methods, followed by specific paradigms from the study of the activation, function, regulation, and inhibition of the complement system. Methods Our methods are both computational and experimental []. Our computational methods include classical molecular dynamics (MD) simulations and electrostatic calculations. Our experimental methods include mainly nuclear magnetic resonance (NMR) methods and other spectroscopic methods. Also, we use protein structures deposited at the Protein Data Bank, which are determined by X-ray diffraction and other crystallographic methods..1 Molecular dynamics (MD) simulations Typically, high-resolution protein structures determined by X-ray crystallography or NMR spectroscopy are used for computational modeling of proteins and protein complexes []. Crystallographic structures correspond to single static conformations, which are most favorable for the crystallization conditions. Also, NMR structures are conformationally averaged because of averaging of the NMR parameters used for structure determination. NMR structures converge to a particular structural motif, despite the fact that they are presented as structural ensembles. However, Proteins are dynamic systems undergoing a variety of motions at a very wide range of time scales. MD simulations are used to study local or global motions of protein structural elements or building blocks and conformational transitions []. In that sense, MD studies are natural extensions of protein structure determination. Initial structures for MD simulations are derived experimentally by X-ray or NMR methods or computationally by structural homology modeling based on experimental structures. Traditionally, restrained MD or MD-based simulated annealing calculations have been used for structure refinement using experimental restraints. Molecular dynamics simulations [] are based on the numerical solution of Newton s equations of motion for the biomolecular system d ri F t) = mi = U ( r, r,..., r ) i ( i 1 dt where F i (t) is the force exerted on atom i, m i is the mass and r i is the vector of the atomic coordinates of atom i. U(r) is the potential energy of the system from a molecular mechanics force field covalent non bonded U( r ) = U ( r ) + U ( r ) where the covalent geometry (bonded interactions) includes terms for bonds, angles, torsions, and improper angles (the latter determine chirality and planarity) and the non-bonded term includes van der Waals and electrostatic interactions. The kinetic energy of the system is given by N 3 1 K = Nk BT = mi vi i= 1 where k B is the Boltzmann constant, T the temperature, m i and v i are the mass and velocity of atom i, respectively. Solvent molecules can be considered either implicitly or explicitly. In the case of implicit solvation models an additional potential energy term is used. When the solvent is considered explicitly, the biomolecule and solvent molecules are placed in a virtual box and the MD simulation is performed using periodic boundary conditions. MD simulations using explicit solvation are more realistic but slower than MD simulations using implicit solvation, which on the other hand offer a quick span of the conformational space of the biomolecule. MD simulations offer thermodynamic information for accessible states by the system and their free energies, and kinetic information on the interconversion of states with the related time scales. Typical information we get from MD simulations is root-mean square deviations (RMSD) for backbone or all-heavy atoms, root-mean square fluctuations (RMSF), probability maps for atomic contacts or hydrogen bonds, motional amplitudes, RMSD maps, conformational transitions and their time scales, correlated motions using principal component analysis, potential energies (and contributions from various potential energy terms), pairwise interaction N

3 energies, kinetic energies, and other analyses specific to the biological system.. Electrostatic calculations The role of charge is essential in all biological processes []. Several chemical groups carry electric dipole moments and ionizable amino acids carry unit or partial charges, depending on their ph. Charges are responsible for hydrogen bond, salt bridge formation, and long-range electrostatic interactions within the biomolecule, and for interaction with the solvent and with counter ions in the solvent. Nonbonded van der Waals and electrostatic interactions are based on charge. Electrostatic interactions are essential contributors in structure specificity, protein stability, protein-protein or protein-ligand association, and enzymatic catalysis. Electrostatic calculations [3] are based on the solution of the Poisson-Boltzmann equation. Typically for the study of biomolecules at atomic resolution, the popular linearized Poisson- Boltzmann equation is used 4πze k T f [ ε ( r) ϕ( r) ] κ ( r) ε ( r) ϕ( r) = ρ ( r) where ϕ(r) is the electrostatic potential in units of ±k B T/e, ε(r) the distance-dependent dielectric coefficient, ρ f (r) the fixed charge density in the biomolecule, e the electron charge, z the valence, k B the Boltzmann constant, and T the temperature. The dielectric properties of the biomolecular interior are separated from the aqueous solvent by the biomolecular surface, which is typically defined by the centers of probe spheres with 1.4 Å radii, representing water molecules in contact with the van der Waals surface of solvent-exposed atoms. The dielectric coefficient is typically -0 in a protein and about 80 in the aqueous solvent. The solvent ions are represented by the Debye-Hückel screening parameter 8πe I κ ( r) = ε ( r) k BT where I is the ionic strength of the solution. The ion accessibility area is defined in a similar manner as the biomolecular surface but with probe spheres of (typically).0 Å radii, representing ion molecules in contact with the van der Waals surface of solventexposed atoms of the biomolecule. Electrostatic potentials can be converted to free energies using appropriate hypothetical thermodynamic cycles, which decompose various contributions to the free energies for computational purposes [3]. Electrostatic potentials are used to predict solvation, ionization, and electrostatic B (solvation + ionization) free energies, intrinsic and apparent pk a values, ph dependence of protein stability (unfolding-folding transition) and association, etc. Electrostatic potentials in the form of projections on protein surfaces have become an integral part of the presentation of newly determined protein structures by X-ray diffraction or NMR methods. In addition, isopotential contour surfaces in the spaces surrounding proteins are useful to identify ligand entry points into the proteins or for recognition of protein-protein or protein-ligand complexes. Finally, electrostatic similarity indices (ESI) are a useful method to quantify electrostatic potentials and to cluster structurally and functionally homologous proteins according to electrostatics..3 NMR spectroscopy Multidimensional and multinuclear NMR spectroscopy [] is used to study the structure and dynamics of proteins and peptides. Standard NMR structural studies typically include resonance assignments, linewidth and chemical shift analysis, NOE connectivity patterns, NOE volumes, NOEderived distances, scalar coupling constants and derived torsion angles. Perturbations of NMR parameters upon complex formation are popular for binding studies. Standard dynamics studies by NMR include derivation of T 1 and T relaxation times, chemical exchange, heteronuclear NOEs, order parameters, hydrogen exchange rates, and protection factors. For our research we use NMR for structural studies aimed to structure-based drug design. Also, we use NMR-derived or deduced restraints and distance geometry and MD-based simulated annealing methods for complete structure determination of peptides. Typically, we collect D TOCSY, DQF-COSY, NOESY, and ROESY NMR spectra, which are sufficient for structural studies or structure determination of small peptides up to kd molecular masses. 3 Applications We briefly present the breadth of our studies in immunophysics, structural bioinformatics, protein design, and rational drug design using the methods described above. We discuss a specific example from our research in each of the above four directions. 3.1 Immunophysics of the complement system: C3d-CR association

4 Immunophysics is the study of the physical basis of immune system function. The term physical basis refers to the underlying physico-chemical properties, such as dynamics, solvation, electrostatics, and thermodynamics, which are responsible for the formation of structure, interactions, and function. We have shown that electrostatics plays significant role in the association of complement protein C3 with complement receptor CR [5]-[7]. C3d is predominantly negatively charged protein and CR is excessively positively charged. We have proposed a -step model for the process of C3d-CR association, which separates recognition from binding. Recognition refers to the acceleration in the formation of an encounter complex, which is owed to long-range electrostatic interactions by the macrodipoles of the two proteins. Binding refers to the actual docking of the two proteins after local structure rearrangements and solvent exclusion from the binding interface, which is owed to formation of short range interactions, such as hydrogen bonds, salt bridges, van der Waals and hydrophobic contacts, as well as long-range range electrostatic interactions of macrodipoles. We have decomposed electrostatic interactions in the form of macroscopic electrostatic potentials and residue-residue interactions in the form of titration curves for the whole proteins and individual ionizable residues, apparent pk a values, solvent accessible surface areas (SASA), and interaction free energies [8]. We have demonstrated the role of dynamics on the modulation of the spatial distribution of electrostatic potentials using MD simulations, but also on local charge-charge interactions using pairwise electrostatic energies and shifts in apparent pk a values from model pk a values for ionizable residues [5],[8]. Finally, we have predicted the ionization and association free energies for the C3d-CR complex as a function of ph and ionic strength and we have shown that they are in good agreement with experimental data [8]. Similar studies are underway for other protein complexes within the complement system. 3. Structural bioinformatics classification of complement proteins, regulators, and inhibitors: CR1, CR, VCP, and SPICE Structural bioinformatics is the use of computational methods for the classification, mining, and prediction of biomolecular structures and the physico-chemical properties that either contribute to structure formation or results from the presence of specific structure. Examples are protein structural architecture, dynamic motions of protein domains, electrostatic and other physico-chemical property characterization, enzymatic property analysis, etc. In our research, we use MD simulations to determine local, segmental, and global motions for complement proteins such as C3d, C3a, and C5a, complement control proteins such as CR1, CR, VCP, and SPICE, complement complexes such as C3d-CR and numerous theoretical mutants of the above with variable activities [6]-[8]. The basic structures are available from experimental crystallographic or NMR data and the structures with mutations are modeled using structural homology methods. Of particular challenge have been the dynamics of the complement control proteins, which resemble linear chains of sausagelike CCP modules connected with short and flexible loops. Each CCP module consists of residues and each intermodular loop consists of about 4 and sometimes up to 8 residues. Of particular interest is the intermodular mobility, which we distinguish and separate in our analysis from intramodular flexibility. This type of research aids in answering long-standing questions regarding the intermodular angle and how it affects binding or how neighboring modules communicate directly or through alosteric interactions, e.g. for CR [8]. We have shown that individual CCP modules carry distinct electrostatic properties, which are directly related to binding and activity. We have also shown that modular mobility contributes to the spatial arrangement (including enhancement or cancellation) of the electrostatic potentials, which in turn variably affect association. This is the case for all CR1, CR, VCP, SPICE, and their mutants. We have used covariance analysis to determine correlated modular motions during the MD trajectories for VCP, SPICE, and selected mutants and how these motions relate to the distinct electrostatic properties of each module [6]. Finally, we have used electrostatic similarity indices (ESI) to classify electrostatic properties of CR1, CR, VCP, SPICE, and their mutants and we have found excellent correlations between ESI classification and association abilities with their target proteins and/or activities [6]. Similar studies are underway for other complement components. 3.3 Design of complement regulators with tailored activities: VCP and SPICE Protein design using homology or ab initio computational methods, or combination of both, is a highly active field of research. Validation of protein design is typically performed using X-ray diffraction or NMR spectroscopy methods, or function/activity experiments. The aim of such studies is to

5 bioengineer proteins with tailored and improved properties. Our work is based on the observation that dynamics and electrostatics play a critical role in the function of complement control proteins [5]-[9]. Our design is based on our basic research using immunophysics and structural bioinformatics, described in Sections 3.1 and 3.. Our long-term goal is to design protein agonists and antagonists of complement interactions. Specifically, we are working with complement receptors CR1 and CR, and viral proteins secreted from pox viruses, VCP and SPICE. We have shown that the up to 100-fold difference in potency between VCP and SPICE is owed to differences in their macroscopic electrostatic potentials [6],[9]. VCP and SPICE are made of four CCP modules and differ by only 11 mutations. Based on electrostatic potential and ESI analyses we have designed a mutant VCP with only two critical mutations, which we predicted to have similar binding and activity properties with SPICE. This was later confirmed experimentally [9]. We have also designed several other theoretical mutants with variable activities, most of which were subsequently experimentally tested [6],[9]. These studies have yielded an extraordinary correlation between macroscopic electrostatic properties with binding and activities. Subtle differences have also been investigated using site-specific electrostatic properties, such as titration curves, stabilities, and apparent pk a values [6]. Structural snapshots from molecular dynamics trajectories have also been used to quantify how intermodular dynamics influence the spatial distribution of electrostatic potentials, how dynamics can be incorporated in our design [6]. Similar studies are underway for other complement control proteins. 3.4 Rational drug design of low molecular mass inhibitors of complement activation: the cyclic peptide compstatin Rational drug design is based on the use of threedimensional structures and structure-activity relations (SAR). For optimal studies, the structure of the ligand and the active site of the target are necessary. However, in the absence of target structure, ligand-based design is possible. The construction of pharmacophore models from basic physico-chemical properties, which contribute to ligand-target binding, is a popular method in rational drug design. Our lead complement inhibitor is compstatin and several of its active derivatives [4]. Compstatin is a 13-residue cyclic peptide, cyclized with a disulfide bridge. We have solved the structure of compstatin using NMR spectroscopy and we have performed structural studies for several derivatives of compstatin using NMR, which revealed structural subtleties and dynamic elements [10]-[1]. The derivatives of compstatin were designed to introduce perturbations in the structure of compstatin with the aim to determine which structural elements were important for structural stability and for activity, measured in parallel experimental studies. Based on these NMR and activity studies, we were able to construct sequence and structural templates, which formed the basis for experimental [1] and computational [13] combinatorial optimization and further rational optimization, including incorporation of non-natural amino acids [14]. Another area of our research activity is the incorporation of dynamics in ligand-based drug design [15],[16]. Small peptides in solution are very flexible spanning a large conformational space in the form of ensembles of interconverting conformers. In the case of compstatin, the NMR data identified a major structural conformer but also suggested the presence of other conformers with smaller populations. This was evident by the averaging of the measured NMR parameters and the observation of subtle structural variability in the various active derivatives of compstatin [10]- [1],[14]. MD simulations based on the complete NMR ensemble of structures identified conformers, which were not accessible by the NMR data, and quantified their populations [15]. We have extended our MD studies to design quasi-dynamic pharmacophore models, by examining the relative topologies of selected pharmacophore points during MD trajectories [16]. The selection of the number and type of pharmacophore points was dictated by our SAR studies. We have demonstrated that using D probability distributions for certain pairs of distanceangle or distance-dihedral angle of pharmacophore points, a distinction of active from inactive compstatin analogs is possible. The rationale for the use of this method is that the backbone structure and side chain orientations of active analogs should be similar and different for those of inactive analogs, while taking into account the variability of the structural elements because of the dynamic character (flexibility) of peptides. We have also discussed the caveats for the application of the quasi-dynamic pharmacophore method related to the inherent internal flexibility of peptides (backbone torsions and rotameric states), the selection of pharmacophore points and active/inactive peptide

6 training set, and the specifics of the MD protocols [16]. The most active analogs include non-natural amino acids with specific π π and π-cation capabilities, which direct our research towards the design of peptidomimetics. Similar studies are underway for other low-molecular mass peptidic and non-peptidic complement inhibitors, targeting different points of the complement activation pathways. 4 Conclusion The purpose of this mini-review is to demonstrate the power of atomic resolution computational methods, such as MD simulations and electrostatic calculations, in combination with atomic resolution crystallography and solution spectroscopic methods, such as X-ray diffraction and NMR spectroscopy for the study of the immune system. We have presented specific paradigms for hypothesis-driven basic research (immunophysics), database-driven basic research (structural bioinformatics), biotechnology research (protein design), and biopharmaceutical research (drug design). The examples we have presented aim to understand the function, regulation, and inhibition of the complement system and to develop anti-complement therapeutics against autoimmune disease and other pathological conditions which involve ill-regulated activation of the complement system. References: [1] D. Morikis, J. D. Lambris (Eds.), Structural Biology of the Complement System, CRC Press, 005. [] D. Morikis, J. D. Lambris, Physical methods for structure, dynamics and binding in immunological research, Trends in Immunology, Vol.5, 004, p.p [3] J. Wu, D. Morikis, Molecular thermodynamics for charged biomacromolecules, Fluid Phase Equilibria, Vol.41, 006, p.p [4] D. Morikis, J. D. Lambris Structure, dynamics, activity, and function of compstatin and design of more potent analogs, in Structural Biology of the Complement System, p.p , D. Morikis and J. D. Lambris (Eds.), CRC Press, 005. [5] D. Morikis, J. D. Lambris, The electrostatic nature of C3d-CR association, Journal of Immunology Vol.17, 004, p.p [6] L. Zhang, D. Morikis, Immunophysical Properties and Prediction of Activities for Vaccinia Virus Complement Control Protein and Smallpox Inhibitor of Complement Enzymes Using Molecular Dynamics and Electrostatics, Biophysical Journal Vol.90, 006, pp [7] D. Morikis, L. Zhang, An immunophysical study of the complement system: examples for the ph dependence of protein binding and stability, Journal of non-crystalline solids, 006, In Press. [8] L. Zhang, B. Mallik, D. Morikis, Immunophysical exploration of C3d-CR(CCP1-) association using molecular dynamics and electrostatics, 006, Submitted. [9] G. Sfyroera, M. Katragadda, D. Morikis, S. N. Isaacs, J. D. Lambris, Electrostatic modeling predicts the activities of orthopoxvirus complement control proteins, Journal of Immunology Vol.174, 005, p.p [10] D. Morikis, N. Assa-Munt, A. Sahu, J. D. Lambris, Solution structure of compstatin, a potent complement inhibitor, Protein Science Vol.7, 1998, p.p [11] D. Morikis, M. Roy, A. Sahu, A. Troganis, P. A. Jennings, G. C. Tsokos, J. D. Lambris, The structural basis of compstatin activity examined by structure-function-based design of peptide analogs and NMR, Journal of Biological Chemistry Vol.77, 00, p.p [1] A. M. Soulika, D. Morikis, M.-R. Sarrias, M. Roy, L. A. Spruce, A., Sahu, J. D. Lambris, Studies of Structure-Activity Relations of Complement Inhibitor Compstatin, Journal of Immunology Vol.170, 003, p.p [13] J. L. Klepeis, C. A. Floudas, D. Morikis, C. G. Tsokos, E. Argyropoulos, L. Spruce, J. D. Lambris, Integrated computational and experimental approach for lead optimization and design of compstatin variants with improved activity, Journal of the American Chemical Society Vol.15, 003, p.p [14] B. Mallik, M. Katragadda, L. A. Spruce, C. Carafides, C. G. Tsokos, D. Morikis, J. D. Lambris, Design and NMR characterization of active analogs of compstatin containing non-natural amino acids, Journal of Medicinal Chemistry Vol.48, 005, p.p [15] B. Mallik, J. D. Lambris, D. Morikis, Conformational inter-conversion of compstatin probed with molecular dynamics simulations, Proteins: Structure, Function, and Bioinformatics Vol.53, 003, p.p [16] B. Mallik, D. Morikis, Development of a quasidynamic pharmacophore model for anticomplement peptide analogs, Journal of the American Chemical Society Vol.17, 005, p.p