1. Systematic calculation and characterization of local motions in allosteric proteins Michael D. Daily 1 and Jeffrey J. Gray 1,2 1 Program in Molecular & Computational Biophysics and 2 Chemical & Biomolecular Engineering, Johns Hopkins University Abstract Introduction Dataset of 51 Allosteric Proteins Precise, diverse motion calculations Statistics of allosteric transitions Theoretical implications We have exploited the large number of known allosteric crystal structures to systematically characterize local conformational changes in allosteric proteins toward the goal of increasing the theoretical understanding of the structural basis of protein allostery on the atomic scale. We have compiled a set of 51 pairs of known inactive and active allosteric protein structures from the Protein Data Bank. We have measured changes in dihedral angles and Cartesian displacements for backbones and side chains and rearrangements in residue-residue contacts for each protein. Several examples show that these automated calculations reveal functionally interesting pictures of local motions which corroborate many features previously observed manually by crystallographers. In addition, statistical analysis of the calculated motions shows that on average, 20 percent of residues differ significantly between the two crystal structures of an allosteric protein in addition to possible changes in dynamics. Allosteric motion is more probable in weakly constrained local structural environments like loops and solvent-exposed regions than in strongly constrained environments like helices, strands, and buried regions. Backbone and contact motions are correlated at separations of up to 20 residues in sequence space and up to 20 Å in Cartesian space. Together, these observations suggest structural rules for designing allosteric protein systems. Signaling proteinsDNA-binding proteinsEnzymes G protein ran (1IBR.pdb) PurR (1WET.pdb) phosphofructokinase (4PFK.pdb) Domain and subunit motion Allosteric transitions comprise 10-20% of protein residues Local structural environment influences allosteric motion 10-20% of an allosteric protein changes backbone conformation, moves relative to the core, or changes interactions with other residues Side-chain motion is significant in controls (10-15%) but more common in allosteric proteins (25-30%) Extents of motion have high σ → significant variability in allosteric mechanisms Proteins in three classes change conformation to similar extents apolar: A, C, F, I, L, M, P, V, W, Y; polar: D, E, G, H, K, N, Q, R, S, T secondary structure (helix, strand, loop) assigned by DSSP buried, exposed – all-atom ASA ≤ 30% or > 30%, respectively (naccess) Polar residues (especially side-chains) more likely to move than apolar residues Secondary structure (backbone H- bonds) constrains backbone but not side-chain Burial constrains all motions (contact constraints) Polar vs. apolar effect is a proxy for exposed vs. buried (data not shown) Summary: Motion most likely in weakly constrained environments An important part of allostery in many oligomers Future Directions Tetramer interface 7° rotation substrate loop 1 loop 2 effector substrate loop 1 loop 2 effector L L L L LLL L L L T (inactive) state R (active) state Previous work in allostery Low-resolution structural models KNF “sequential transition” model MWC “pre-existing equilibrium” model L Choe et al. (2000), fig. 1 Manually compare I and A states → qualitative mechanistic models Importance and applications Major mechanism of control and regulation in biology Improved high-resolution understanding of allostery will aid in −understanding / treating diseases caused by malfunctioning allosteric proteins −Designing novel allosteric proteins as biological control devices substrate Design allosteric response into a non- allosteric protein *obtained directly from authors; not in PDB Funding/ Acknowledgements Calculate motions in three types of degrees of freedom important to protein structure Calculated motions do not in themselves constitute comprehensive mechanistic models Statistical analyses reveal basic insights into structural basis of protein allostery: −Significant changes in average structure (~20%) are common in allosteric proteins → not just a dynamic phenomenon −Protein structures use constraints to control location of motion, possibly to direct signal propagation between allosteric and functional sites −Local motions are correlated up to 20Å distance, enough to bridge two spatially distinct sites over several residues −Mechanical communication is an important, general phenomenon in protein allostery Possible test resource for flexibility prediction algorithms such as COREX (Hilser & Freire 1996), elastic network models (Bahar et al. 1997), FIRST (Jacobs et al. 2001), and statistical coupling analysis (Suel et al. 2003) ARCS fellowship (M. Daily) JHU Program in Molecular and Computational Biophysics NIH training grant (M. Daily) NIH award K01-HG02316 (J. Gray) Pymol and R (figures and calculations) Discriminating true motions from crystallographic noise Allosteric motions in protein space Sequence space Three-dimensional space Coupling among local allosteric motions Motion value histograms for five non-allosteric protein pairs (control 1, black), nine allosteric protein pairs in same state (control 2), and allosteric benchmark. Threshold. Set thresholds to exclude ~99% of background motion in controls Thresholds are intuitively reasonable cutoffs for large motions Smaller motions may be functionally significant in some allosteric proteins Motions for ras G protein (4Q21.pdb vs. 6Q21.pdb) Switch I and II previously identified by Milburn et al. Most of protein is rigid Motions tend to occur in contiguous segments (especially backbone and contacts) Strong consensus between measures in most flexible regions displacementsdihedral changescontact changes ras G protein purine repressor phosphofructokinase ΔSC ≥ 2.0 Å ΔC α ≥ 1.2 Å ΔC α ≥ 3.0 Å max(|Δχ 1 |,|Δχ 2 |) ≥ 46° max(|Δφ|,|Δψ°|) ≥ 30° max(|Δφ|,|Δψ°|) ≥ 65° max(f I, f A ) ≥ 0.2 0.3 0.4 0.5 Most of protein is structurally conserved Contact changes, backbone motions cluster strongly in space Backbone displacements, dihedral changes, and contact motions localize to similar regions of structures PFK: motions localize between catalytic and allosteric sites (esp. contact changes) → possible allosteric pathway Average fraction of residues moving (mean ± s.d) by six measures in six sets of proteins: two control datasets, three classes of allosteric proteins, and all allosteric proteins. Correlation functions statistically measure strength and significance of local cooperative effects and distance ranges over which they occur Backbone and contact motions strongly correlated at short separations (< 20 res. or < 20Å) → local clustering of motions Apparent long-range correlations for backbone and side-chain motions present only in a small minority of allosteric proteins (data not shown) Summary: distinctly non-random organization of backbone and contact motions in allosteric proteins Allosteric mechanisms Quantify organization of moving parts, connectivity between sites max(|Δφ|, |Δψ|)θ αβ max(|Δχ 1 |, |Δχ 2 |)max(f I, f A ) ΔCαΔCα ΔSC ΔφΔφΔψΔψ local backbone conformation backbone position relative to protein core side-chain orientation local side-chain conformation atomic interactions with other residues Sequence correlation function C m (Δi)Cartesian correlation function C m (r) Correlations are normalized against reference correlation (correlation expected if moving residues are distributed randomly) Control signaling pathways Control transcription by binding DNA Regulate reactions and biochemical pathways Three functional classes A wide variety of targets Signaling proteins DNA-binding proteins Enzymes novel effector X Goals and new contributions Precisely identify local motions in known allosteric protein structures Statistically investigate amount and structural distribution of motions A C X X X X X X X X X X X X X X X X X X X XX X max(|Δφ|, |Δψ|)ΔC α θ αβ max(|Δχ 1 |, |Δχ 2 |)ΔSCmax(f I, f A ) control 10.03 ± 0.030.02 ± 0.030.01 ± 0.020.13 ± 0.090.11 ± 0.080.03 ± 0.02 control 20.03 ± 0.020.01 ± 0.01 0.16 ± 0.080.10 ± 0.050.02 ± 0.02 signaling0.16 ± 0.060.22 ± 0.090.13 ± 0.050.33 ± 0.070.26 ± 0.060.24 ± 0.09 transcription0.20 ± 0.080.12 ± 0.080.07 ± 0.030.35 ± 0.120.24 ± 0.090.18 ± 0.07 enzymes0.12 ± 0.070.21 ± 0.110.06 ± 0.030.30 ± 0.090.21 ± 0.070.16 ± 0.06 all allosteric0.15 ± 0.070.20 ± 0.100.09 ± 0.050.32 ± 0.090.24 ± 0.070.20 ± 0.09