Flexweb and First/Froda Kirill Speranskiy
Flexweb and First/Froda http://flexweb.asu.edu Kirill Speranskiy Outline 1. Rigidity analysis, rigid units, flexibility 2. FRODA model, protein mobility http://flexweb.asu.edu Rigidity analysis Proteins and rigidity Rigidity analysis of proteins, based on the distribution of constraints (covalent bonds, hydrogen bonds, hydrophobic interactions …), shows that proteins can be divided up into rigid regions of different sizes. These vary from a “rigid core” which may comprise most of the atoms in the protein, through mobile rigid clusters (e.g. sections of alpha-helix containing some tens of atoms) to single atoms (in flexible side chains). These rigid clusters can form the basis of a geometric simulation, as the SiO4 tetrahedra did for the silicate minerals. While tetrahedra have a geometrically ideal form, the clusters in proteins are defined empirically from an X-ray crystal structure. Protein structure • You need a structure to start with in PDB format. • Preferably high-resolution (<2A if possible) X-ray structure, with good steric quality. • You need to add hydrogens. • REDUCE adds all hydrogens, flips sidechains etc. Rigidity analysis • Done in FIRST using pebble game http://flexweb.asu.edu/software/pebble_game/2D_interactive/ http://linkage.cs.umass.edu/pg/ Rigidity analysis • You must choose which constraints (hydrogen bonds, hydrophobic tethers) to include in the analysis and which to leave out, e.g. by picking an energy scale for hbonds: “first -E -1.5” Rigid cluster decomposition of barnase Mobile rigid cluster (mobile in simulations). Rigid core (immobile in simulations). Flexible region (mobile in simulations). Hydrogen bond dilution plot “FRODA” The exploration of conformational space is carried out by FRODA (Framework Rigidity Optimised Dynamic Algorithm). The rigid core of the protein is kept frozen while all mobile atoms undergo random motion (Monte Carlo step) followed by geometric simulation to produce a new conformer. No distinction is made between main and side chain, nor between members of closed ring† structures and other atoms. †(In Tolkein’s story, the hobbit Frodo- or Froda in the original hobbitish- undertakes a quest to free Middle-Earth from the dominion of the Rings of Power). FRODA and mobility • Mobility depends on both instantaneous flexibility and other (e.g. steric) constraints. • Has to be explored; there’s generally no analytic way to obtain mobility. • FRODA (Framework Rigidity Optimised Dynamic Algorithm) aims to explore the mobility of a flexible protein structure by perturbing the atomic positions and then re-imposing the constraints. The original FRODA procedure The original FRODA procedure The original FRODA procedure Applications Application 1: random walks for mobility. Application 2: direct targeting. Application 3: expansion/contraction. Application 1: random walks for mobility • Random motion based on intrinsic flexibility. • From a single input crystal structure, generate a flexible ensemble. • Bridge between crystal and NMR data. • A crystal structure is a structure, not the structure. Comparison to NMR • Comparing globally-aligned RMSD by residue for the FRODA ensemble and the barnase protein (1BNR) NMR ensemble. Barnase mobility from NMR and FRODA 3 NMR FRODA_long RMSD (global ensemble) 2.5 2 1.5 1 0.5 0 0 20 40 60 Residue (barnase) 80 100 120 Barnase motion: the NMR ensemble. Initial state of Adenylate Kinase The protein closes and opens repeatedly. Flexibility analysis of the bovine mitochondrial ADP-ATP carrier Flexibility analysis of the bovine mitochondrial ADP-ATP carrier Total number of FRODA conformation is 10000 per run RMSD 1.2 Ǻ The root mean square deviation between initial structure and structure of last snapshot from FRODA run is ~3.0 Ǻ which shows that structure without ligand have significantly larger mobility. Standalone version of First/Froda Application 2: getting from A to B • Pathway between two known conformers. • Direct targeting: we bias the perturbation towards the target positions. ADK morph • The conformational change is more than 7 A RMS-D. • Came within 0.5 Angstroms of target after 1556 conformers (176 seconds runtime). Application 3: using the centrifuge • If you don’t have a specific target in mind, one simple operation is to increase or decrease the radius of gyration of the protein and see if any interesting domain motions happen. • FRODA has a centrifuge function which biases the perturbations radially. • A positive directed step moves out; a negative one moves in. ADK collapse Comparison of collapsed and closed forms Conclusions Geometric simulation is a rapid and concise method for handling collective motions. Geometric simulation based on rigidity analysis of proteins allows very rapid exploration of conformation space. This means that conformer exploration, for e.g. drug design, may now be faster than interpretation and analysis; for example, it took longer to produce the graphics for this presentation than it did to produce the data. Simulation time and CPU resources need not be the ratelimiting step in protein simulation.