A COMPLEX NETWORK APPROACH TO FOLLOWING THE PATH OF ENERGY IN PROTEIN CONFORMATIONAL CHANGES Del Jackson CS 790G Complex Networks

Outline  Background  Related Work  Methods

Hypothesis  Utilize existing techniques to characterize a protein network  Explore for different motifs based upon all aspects of molecular modeling

Proteins  Biopolymer  From 20 amino acids  Diverse range of functions  Sequence  Structure  Function

Protein Structure  Primary  Sequence of amino acids  Secondary  Motifs

Protein Structure  Tertiary  Domains  Quaternary  “Hinges” exist between domains

Fundamental Questions

Motivation  Misfolded proteins lead to age onset degenerative diseases  Pharmaceutical chaperones  Fold mutated proteins to make functional

Simulation Methods/Techniques  Energy Minimization  Molecular Dynamics (MD)  Simulation Langevin Dynamics (LD)  Simulation Monte Carlo (MC) Simulation  Normal Mode (Harmonic) Analysis  Simulated Annealing

Molecular Dynamics  Computer simulation using numerical methods  Based on math, physics, chemistry  Initial value problem

Molecular Dynamics Limitations  Long simulations inaccurate  Cumulative errors in numerical integration  Huge CPU cost  500 µ s simulation ran in 200,000 CPUs  Without shared memory and continuous communication  Coarse-graining  Empirical method but successful

Elastic Network Model  Representing proteins mass and spring network  Nodes: Mass α- carbons  Edges: Springs Interactions

Complicated and the Complex  Emergent phenomenon  “Spontaneous outcome of the interactions among the many constituent units”  Forest for the trees effect  “Decomposing the system and studying each subpart in isolation does not allow an understanding of the whole system and its dynamics”  Fractal-ish  “…in the presence of structures whose fluctuations and heterogeneities extend and are repeated at all scales of the system.”

Network Metrics  Betweenness  Closeness  Graph density  Clustering coefficient  Neighborhoods  Regular network in a 3D lattice  Small world  Mostly structured with a few random connections  Follows power law

PDB

Converting PDB to network file  VDM  Babel

Test Approach

Flexweb

Flexweb - FIRST  Floppy Inclusions and Rigid Substructure Topography  Identifies rigidity and flexibility in network graphs  3D graphs  Generic body bar (no distance, only topology)  Full atom description of protein (PDB)

FIRST  Based on body-bar graphs  Each vertex has degrees of freedom (DOF)  Isolated: 3 DOF x-, y-, z-plane translations  One edge: 5 DOF 3 translations (x, y, z) 2 rotations  Two+ edges: 6 DOF 3 translations 3 rotations

FIRST – body bar  Bar represents each degree of freedom  5 bars more rigid than node with 2 bars  6 bars (5 bars per site with only 1 atom)

Pebble game algorithm  Determines how bars affect degrees of freedom in system  Each DOF is represented by a pebble

Pebble game algorithm  Small set of rules for moving pebbles on and off bars  One per bar  Game ends when no more valid moves exist  Determines if possible to rotate around edge (flexible) or if it is locked (rigid)

Pebble Game results Flexible hinges Hyperstatic

Other tools to incorporate  FRODA  Framework Rigidity Optimized Dynamics Algorithm  Maintains a given set of constraints, Covalent bonds, hydrogen bonds and hydrophobic tethers  Bonding- or contact-based, with no long-range interactions in the system  TIMME  FlexServ

Other tools to incorporate  FRODA  TIMME  Tool for Identifying Mobility in Macromolecular Ensembles  Identifies rigidity and flexibility in snapshots of networks  Agglomerative hierarchy based on standard deviation of distances between pairs of sites from mean value over 2 or more snapshots  FlexServ

Other tools to incorporate  FRODA  TIMME  FlexServ  Coarse grained determination of protein dynamics using NMA, Brownian Dynamics, Discrete Dynamics  User can also provide trajectories  Complete analysis of flexibility Geometrical, B-factors, stiffness, collectivity, etc.

Experimental Data  Cardiac myopathies

Experimental Data  Access to 15 mutations in skeletal myosin  Affects on function are characterized

Combine all approaches

Derived Topology  Nodes  Alpha carbons  Edges  Weight determined by results of other algorithms  Topological view of molecular dynamics/simulations

First Step  Create one-all networks  Try different weights on edges  Start removing edges  Apply network statistics  Betweenness, closeness, graph density, clustering coefficient, etc  See if reflect changes in function (from experimental data)

Questions?