Networks and Pathways II

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Networks and Pathways II

CBW Bioinformatics Workshop February 23th 2006,
Toronto Christopher Hogue The Blueprint
Initiative
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About this talk

• The Future and Requirements for Cell Simulation
• Systems Biology and Modeling

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The Old Future
Jules Verne Machines and adventures
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Artists Concept Adventures in faraway places
and the machines that get us there
Galileo Probe Concept Instrument Design
Reality
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The New FutureAdventures Inside Cellular Life
Forms
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David Goodsells painting at the molecular level
Zoom in to the bacterium a simple cell
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Propellor
Protein Motor
Assembly Line for Proteins
DNA
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How did this image come about?

• Information integration by the artist
• High level view taken from light microscope
• Filled in with parts drawn to scale
• Parts from Life Science Databases
• Over 25,000 protein structures in PDB database
• Complete E. coli, Human Genome in GenBank
• 12 Million PubMED articles

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Software, not hardware, does the last
magnification

• The Artist the human brain
• Memory, knowledge, semantics, inference
• Bioinformatics Software
• Ultimately has to be rule based
• Integrate a disparate variety of information
  sources
• Creating a computer simulation of the living
  cellular system

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RequirementsTowardsCellularSimulation
Whole Cell Visualization
Modular Cell Simulation Software Layer
Data Access Layer
PARTS Molecules SeqHound
InteractionsReactionsKinetics, PTMs
Initial Conditions
Machine Readable Data
Expression, Concentration, Localization/distributi
ons
microscopy
GENBANK PDB
BIND KEGG
The PRINT Literature (PubMed)
Human Readable Data
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Classification of Simulation Methods

• Deterministic get same results with same input
  (large scale input)
• Stochastic get different results with same
  input (small scale input)
• Spatial movement (diffusion) of entities in
  space accounted for
• Non-spatial assumes homogeneous mixture in
  unlimited volume

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Modeling Techniques

• Quantum Mechanics
• Molecular Dynamics
• Brownian Dynamics
• Monte Carlo Molecular
• Cellular Automata
• Petri Networks
• Partial Differential Equations
• Stochastic Differential Equations
• Ordinary Differential Equations
• Flux and Energy Balance
• Boolean Networks
• Static Models

Increasing scope and efficiency Decreasing
resolution and complexity
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Static Model

• Static implies no analysis of temporal effects
• An example of how protein interaction networks
  recapitulate cellular structure
• Nucleolar network derived from core analysis of
  high-throughput yeast interactions

• F Fibrillar Center
• transcription of rDNA into rRNA
• D Dense Fibrillar Center
• finishing of rRNA with various enzymes snoRNP
• migrates to cytoplasm during chromatin
  condensation in cell cycle
• G Granular Component
• Ribosome assembly
• Stays in the nucleus

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9-core from 15,000 yeast interactions
Dense Fibrillar Center
Fibrillar Center
Granular Component
Surprisingly, a simple dense interconnected
network of F, D, and G proteins recapitulates the
Nucleolar image, ignoring spatial and temporal
information
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Flux Balance Analysis

• Simulates Flux or Flow thorugh Metabolic Pathways
• Kinetics of each step not required
• Predicts effects of gene knockouts

B. Palsson UCSD Engineering
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Ordinary Differential Equations - Nonlinear ODE

• Assumes a homogeneous solution with unlimited
  volume
• v1
• 2x ? y
• dx/dt -2v1
• dy/dt v1

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A simple ODE model of yeast glycolysis
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ODE Based Systems

• Gepasi (Mendes, 1997 Mendes Kell, 2001)

http//dbk.ch.umist.ac.uk/softw/gepasi.html

• SBML http//www.sbml.org
• A data exchange format for network models
• JWS Online http//jjj.biochem.sun.ac.za/

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JWS online
http//jjj.biochem.sun.ac.za/
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JWS OnlineDatabase of ODE based Models
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Oscillation a common behavior
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Control Theory Fourier Transform of Oscillatory
Data
Can we reduce the ODE model even further to
Amplitude and Frequency?
Biophys J, January 2002, p. 99-108, Vol. 82, No.
1 Control Analysis for Autonomously Oscillating
Biochemical Networks Karin A. Reijenga, Hans V.
Westerhoff, Boris N. Kholodenko,   and Jacky L.
Snoep 
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Some Problems with DE approaches

• Almost all simulation systems are ultimately
  based on solving either ordinary differential
  equations (ODEs), partial differential equations
  (PDEs) or stochastic differential equations
  (SDEs)
• Differential equations are hard to work with
  when simulating
• spatial phenomena,
• discrete events (binding, switching)
• non continuous variables (low copy number)
• when key parameters are unknown or unknowable

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More Problems

• DEs are notorious for instabilities or situations
  where small rounding errors lead to singularities
  or chaotic behavior
• DE methods are not conducive to visualization or
  interactive movies
• DE methods require considerable mathematical
  skill and understanding (not common among
  biologists)
• DE methods dont easily capture stochasticity or
  noise (common in biology)
• Issue of realism cells dont do calculus

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Do we need the calculus?

• Sidney Brenner calls it biological arithmetic
  not calculus
• Needs to accommodate the discrete (binding,
  signaling) and continuous (substrate
  concentration) nature of many cellular phenomena
• Approaches which avoid DEs
• Petri Nets (stochastic and hybrid)
• Cellular Automata
• Monte Carlo simulations

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Petri Nets from network control analysis
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Petri Nets

• A directed, bipartite graph in which nodes are
  either "places" (circles) or "transitions"
  (rectangles)
• A Petri net is marked by placing "tokens" on
  linked or connected places
• When all the places have a token, the transition
  "fires", removing a token from each input place
  and adding a token to each place pointed to by
  the transition (its output places)
• Petri nets are used to model concurrent systems,
  particularly network protocols w/o differential
  eqs.
• Hybrid petri nets allow modeling of continuous
  and discrete phenomena

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Hybrid Petri Nets Phage Assembly
Matsuno H, Tanaka Y, Aoshima H, Doi A, Matsui M,
Miyano S. Biopathways representation and
simulation on hybrid functional Petri net.In
Silico Biol. 20033(3)389-404.
Predicted protein expression
l phage control circuit
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Petri Nets - Limitations

• Not designed to handle spatial events or spatial
  processes easily
• Stochasticity is imposed, it does not arise
  from underlying rules or interactions
• Does not reproduce physical events (brownian
  motion, collisions, transport, binding, etc.)
  that might be seen in a cell Petri Nets are
  more like a plumbing and valving control system

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Cellular Automata

• Computer modeling method that uses lattices and
  discrete state rules to model time dependent
  processes a way to animate things
• No differential equations to solve, easy to
  calculate, more phenomenological
• Simple unit behavior -gt complex group behavior
• Used to model fluid flow, percolation, reaction
  diffusion, traffic flow, pheromone tracking,
  predator-prey models, ecology, social nets
• Scales from 10-12 to 1012

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CA Methods in Games
SimCity 2000
The SIMS
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Cellular Automata
Can be extended to 3D lattice
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Dynamic Cellular Automata

• A novel method to apply Brownian motion to
  objects in the Cellular Automata lattice (mimics
  collisions)
• Brownian motion is scale-free in heterogeneous
  mixtures
• Allows simulations to span many orders of time
  (nanosec to hours) and space (nanometers to
  meters)

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SimCell http//wishart.biology.ualberta.ca/SimCel
l/
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SimCell

• CA or Agent-based simulation system
• Designed to permit easy set-up (4-step set-up
  Wizard)
• Allows for general dynamic, stochastic modeling
  of almost all cellular processes (enzyme
  kinetics, diffusion, metabolism, operon activity)
• Allows real time monitoring (graphing) and
  animation of the system

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SimCell Interactions

• User defines interaction rules between molecular
  objects using a simple GUI according to
  biological observations and measurements
• Interaction rules framed internally as logical
  boolean operations (if-then-else and do
  while) that respect boundaries and cellular
  barriers

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SimCell Interactions

• Five different types of objects allowed in
  SimCell
• small molecules
• soluble proteins
• membrane proteins
• DNA molecules
• membranes
• Interactions reduced to relatively small number
  of possibilities
• Touch and Go (TG)
• Bind and Stick (BS)
• Transport (TRA)

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Touch Go
No interaction
Interaction/catalysis
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Bind Stick
Preserve ID
Interaction/catalysis
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Transport
1-way in 1-way out
both ways
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SimCell Molecules and Interaction Rules
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Enzyme-Substrate Progress Curves CA is more
realistic - sensitive to number of molecules
Lactate Lo (1 e-kt)
Lactate Lo (1 e-kt)
pyruvate NADH ? lactate NAD
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Drawing Interaction Rules with SimCell
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The TCA Cycle SimCell
Acetate
Acetyl-CoA
Glycerol
Pyruvate
Oxaloacetate
Citrate
Isocitrate
L-Malate
?-Ketoglutarate
Fumarate
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Succinate dehydrogenase
Succinate
Succinyl-CoA
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Metabolic Profiling with NMR
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Succinate Production
Observed Predicted (SimCell)
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Glycerol Consumption
Observed Predicted (SimCell)
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Repressilator
Nature, 403 335-338 (2000)
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Repressilator
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Repressilator ODE predicted behavior
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Repressilator observed in growing culturecells
blinking
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SimCell Repressilator Oscillations
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SimCell vs. ODE
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Monte Carlo Simulation Method

• Monte Carlo Simulation Method random binding
  and displacement of molecules based on given rate
  and diffusion constants
• Attempt to model instances of molecules, their
  physics, motion and binding
• More detailed than CA approach, but similar

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Modeling receptor motion on a cell surface

• Assuming the cell is a sphere
• The surface area of the cell is vast compared to
  those of molecules
• Local interactions between molecules on the cell
  surface can be considered to be planar
• Spherical 3D surface can be mapped on to a 2D
  planar surface by uniform area mapping

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Example EGFR

• A 3D structure is transformed and viewed at the
  axis perpendicular to the cell membrane
• Binding sites are determined from the positions
  of alpha carbons of the two farthest residues
  that constitute the site
• Radius of the molecule is the average distance
  from the center of mass to the surface binding
  sites (circle enclosed by blue circle)

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Representation of a protein

• Each molecule is represented as a solid circle
  with a radius on a planar grid.
• The area of the circle is used for collision
  detection.
• The radius is the approximate distance from the
  center of mass to the edge of the molecule
  (determined by the average positions of all
  surface binding sites)
• Binding sites are represented as arcs on the
  circle, with the arc lengths representing the
  sizes of the binding sites
• The distance of the binding sites to the center
  of mass must be at least that of the radius
  (surface) but can be greater (distal)

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Collision and Diffusion

• Rotational diffusion is random (fast in this time
  scale)
• Unidirectional displacement of molecules follows
  a Gaussian-like distribution
• Time step decided by the maximum possible
  displacement traveled by a molecule that is less
  than the diameter of the smallest molecule.
• This is to ensure that molecules dont skip
  over each other.

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Modeling motion on a Membrane2D Probabilistic
model of Molecular MotionHow far does a molecule
travel? Sample a move distance using
probability density function.
Sampling over 30 intervals of displacement
?0Inf f(s)ds 1
Derived from Ficks Second Law for 2 Dimensions
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Binding

• Two types of binding reactions
• 1. Diffusion limited kgtgt D
• 2. Not diffusion limited Dgtgtk
• Binding is said to occur based on the following
  criteria
• Two interaction sites are compatible
• The sites are within line of sight of each
  other and within interaction distance
• The probabilistic threshold of binding (dependent
  on the kinetics of the binding sites) is met
• More detailed than CA approach but requires
  microscopic binding parameters.

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Modeling Techniques - Redux

• Quantum Mechanics
• Molecular Dynamics
• Brownian Dynamics
• Monte Carlo Molecular
• Cellular Automata
• Petri Networks
• Partial Differential Equations
• Stochastic Differential Equations
• Ordinary Differential Equations
• Flux and Energy Balance
• Boolean Networks
• Static Models

Decreasing scope and efficiency Increasing
resolution and complexity
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How to Choose a Modeling Method?

• With unlimited time and computation resources
  choose the modeling method of the lowest level
  (i.e. Quantum Mechanics)
• It may account for largest amount of data
• Its solutions may converge to higher level
  solutions if the extra detail is not needed
• It does not scale
• Occams Razor the simplest explanation is the
  one to choose!
• Choose the highest level-of-detail method that
  can satisfactorily depict the given phenomenon.
• Biology and evolution do not always take the
  simple route.
• Sensitivity Analysis is the answer you get from
  modeling robust to different parameter values
  taking into account possible error or differences
  in biochemical measurements?

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Cyber Cell DBhttp//redpoll.pharmacy.ualberta.ca/
CCDB/
A unique compilation of parameters required for
modeling an entire E. coli cell. Useful
resource for systems biology.