A COMPLEX NETWORK
APPROACH TO FOLLOWING
THE PATH OF ENERGY IN
PROTEIN CONFORMATIONAL
CHANGES
Del Jackson
CS 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

Secondary
 Motifs
of amino acids
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 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


Forest for the trees effect


“Spontaneous outcome of the interactions among the many
constituent units”
“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


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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:
 x-,
 One
3 DOF
y-, z-plane translations
edge: 5 DOF
3
translations (x, y, z)
 2 rotations
 Two+
3
edges: 6 DOF
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
 Bonding-
bonds, hydrogen bonds and hydrophobic tethers
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?