A COMPLEX NETWORK APPROACH TO FOLLOWING THE PATH OF ENERGY IN PROTEIN CONFORMATIONAL CHANGES Del JacksonCS 790G Complex Networks - 20091019

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

How did this fold?

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 µs 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

How to characterize connections?

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 resultsFlexible 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

Timme

FRODA

Flexserv

FIRST

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?