Special Topics in Computational Biology: Formal Methods in Systems Biology

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Special Topics in Computational BiologyFormal
Methods in Systems Biology
Spring, 2008

• Chris Langmead
• Department of Computer Science
• Carnegie Mellon University
• James Faeder
• Department of Computational Biology
• University of Pittsburgh School of Medicine

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General Info

• Course Numbers
• CMU 15-872(A)
• CMU 02-730
• Pitt CMPBIO 2045(Arts Sciences)
• Pitt MSCBIO 2045 (School of Medicine)
• Location Newell-Simon Hall (NSH) 3002 - OK?
• Time Tu, Th 130-250 PM
• Instructors
• Chris Langmead (cjl_at_cs.cmu.edu)
• Jim Faeder (faeder_at_pitt.edu)
• Office Hours By appointment (please email)
• Course Wiki http//bionetgen.org/index.php/Formal
  _Methods_in_Systems_Biology (email Jim for
  account)

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Course Format An Informal Course about Formal
Methods

• Introductory lectures (two weeks)
• Students will read and present research papers
• Sign up for open dates on the wiki (25 -
  projects)
• Students will design and complete a course
  project on a subject of special interest
• Grading is based on completion of work
• Flexibility depending on course enrollment
• Journal club
• Focused project
• Review article

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Encouragement

• Opportunity to learn about new areas and methods
  that will be of direct interest in your research.
• (True for the instructors as well)
• We will operate as a multi-disciplinary team
• Computer Scientists, Physicists, Chemists,
  Engineers, Mathematicians, , Biologists
• Good communication essential

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Products of the Course

• Comprehensive bibliography in wiki format
• Research projects leading to publishable results
  in the field
• Review article (?)
• Improved organization and presentation skills
• Participation on a multi-disciplinary team

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Introductions

• Your name
• Your university, department, research area(s) and
  research advisor
• Your educational background
• Computer Science, Math, Physics, etc.
• Goals taking the course

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Outline of Todays Lecture

• Definition of terms
• Goals
• Examples of Successful Abstractions
• Flux Balance Analysis
• Mass Action Kinetics
• Brief survey of topics

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Importance of Symbols

• Invention of symbol for zero and decimal system
  for writing numbers among the greatest human
  inventions.
• 3 known independent inventions
• In each case, development took centuries
• Major impact on trade, culture, and philosophy.
• Celebration of zero dot in Sanskrit poetry
• The dot on her forehead / Increases her beauty
  tenfold,/ Just as a zero dot sunya-bindu
  /Increases a number tenfold. -Biharilal

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Key Definitions - Formal Methods

• In computer science and software engineering,
  formal methods are mathematically-based
  techniques for the specification, development and
  verification of software and hardware systems.
• The use of formal methods for software and
  hardware design is motivated by the expectation
  that, as in other engineering disciplines,
  performing appropriate mathematical analyses can
  contribute to the reliability and robustness of a
  design.
• However, the high cost of using formal methods
  means that they are usually only used in the
  development of high-integrity systems, where
  safety or security is important.

- WIKIPEDIA
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Expanded View of Formal Methods

• Formal abstractions that may be used to model
  system of interest
• In addition to sytems that can be formally
  analyzed, we will consider representations that
  can only be fully explored by simulations.

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Key Definitions - Systems Biology

• Systems biology is a relatively new biological
  study field that focuses on the systematic study
  of complex interactions in biological systems,
  thus using a new perspective (integration instead
  of reduction) to study them.
• Particularly from 2000 onwards, the term is used
  widely in the biosciences, and in a variety of
  contexts.
• Because the scientific method has been used
  primarily toward reductionism, one of the goals
  of systems biology is to discover new emergent
  properties that may arise from the systemic view
  used by this discipline in order to understand
  better the entirety of processes that happen in a
  biological system.

- WIKIPEDIA
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Origin of Systems Biology

• Completion of genome projects is major
  inspiration
• Provided parts list for the cell
• Next obvious step is to ask how parts work
  together to carry out function?

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Vision for Role of Computer Science in Systems
Biology

• Computer science could provide the
  abstractions needed for consolidating knowledge
  of biomolecular systems
• ...the abstractions, tools and methods used to
  specify and study computer systems should
  illuminate our accumulated knowledge about
  biomolecular systems.

Regev and Shapiro, Cells as Computation, Nature
(2002).
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Abstract Representations in Biology

• DNA sequence represented by strings with 4 letter
  alphabet (ATGC)
• Protein sequence and structure
• Strings with 20 letter alphabet
• Set of 3D atomic coordinates (PDB file)

The KaiC hexamer, a Circadian clock protein. From
pdb.org.
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(Some) Desirable Properties of an Abstract
Representation

• Relevant / accurate
• Computable
• Understandable
• Extensible
• Scalable
• Modular
• Hierarchical

1-4 from Regev and Shapiro, Cells as
Computation, Nature (2002).
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An Irony

• CS community aims to provide powerful abstract
  representations to improve understanding of
  systems.
• Manner of reporting results - technical reports
  in conference proceedings - presents major
  barrier to wider adoption by science and
  engineering communities.
• There is a need for better communication among
  disciplines!

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Sometimes formalism creates a barrier
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(No Transcript)
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Example Red blood cell model
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Agenda

• We are looking for useful abstractions that can
  improve our understanding of how biological
  systems behave

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Goals

• Language(s) for constructing whole-cell models
  (comprehensive, system-wide)
• Formal analysis (reasoning) of such models
• Simulation of models on distributed systems
• Combination of analysis and simulation to predict
  behavior of models
• genotype ? phenotype

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Challenges

• Accuracy
• Missing interactions
• Computability
• Requirement to perform simulations for many
  properties of interest
• Poor scaling of simulations
• Understanding
• Problem of network visualization
• Extensibility
• Missing biophysics
• Scalability
• Need to compute behavior on multiple scales, e.g.
  tissue?cell?cytoplasm?nucleus

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Mathematical vs. Computational Models
Consider an elementary chemical reaction
r1 A B -gt C

• Computational

• Mathematical

module A 0..N init N r1 (A gt 0) -gt kAB
(A A - 1) endmodule
How important is this distinction?
Fisher Henzinger, Nat. Biotechnol. (2007).
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Tension between Accuracy and Computability

• Application of formal methods requires that
  elements of representation be relatively simple.
• For example, a representation that includes all
  analytical functions in mathematics might not be
  useful - impossible to make predictions.
• In general, increasing the complexity of the
  representation limits ability for analysis.
• Representations are sometimes chosen for
  amenability to analysis rather than realism -
  e.g. boolean networks.
• Computational (executable) models tend to make
  restrictions explicit.

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Some successful abstractions in systems biology

• Flux Balance Analysis
• Genome-wide models of metabolism
• Mass Action Kinetics
• Cell-cycle model
• Growth factor signaling model

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Network Reconstruction (2D Annotation)
B. O. Palsson, Nature Biotechnology 22, 1218 -
1219 (2004)
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Network Reconstruction (cont.)

• Wiring diagram for the components in a cell
• Elements are
• Molecular Components (Species)
• Interactions (Reactions)
• Additional detail can be added.
• Genome-wide reconstructions for metabolism are
  available for many model organisms (including
  Homo Sapiens!)
• All such interactions are ultimately represented
  by a genome-scale stoichiometric matrixa
  two-dimensional genome annotation.

B. O. Palsson, Nature Biotechnology 22, 1218 -
1219 (2004)
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Overview of Flux Balance Analysis

• Genome-wide reconstruction of metabolic network
• Assume steady state
• Assume optimal growth (biomass production)

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Genome-Wide Reconstruction of Haemophilus
influenzae
Edwards, J. S. et al. J. Biol. Chem.
199927417410-17416
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Single and double deletion in the central
metabolic pathways of H. Influenzae
Edwards, J. S. et al. J. Biol. Chem.
199927417410-17416
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What Accounts for Success?

• Knowledge Base
• Metabolic chemistry known from gt50 years
  biochemistry and genome sequence
• Simple Abstraction
• Biochemistry reduced to list of reaction
  stoiochimetries
• Powerful Computation Method
• Highly optimized solvers for Linear Programming
  problem
• Extensibility
• Non-optimal growth in mutants
• Constraints arising from molecular crowding

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Cellular Signal Transduction
signaling complex
plasma membrane
adaptor
SH3 domain
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Mass Action Kinetics
Differential Equations
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Reaction Network Model of Signaling
Kholodenko et al., J. Biol. Chem. 274, 30169
(1999)
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Comparing Model and Experiment
Experimental Data
Simulation Results
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Benefits of Mass Action Kinetic Modeling

• Large knowledge base of signaling biochemistry
• Models dynamical behavior
• Computational Methods Well Established
• ODE solvers for continuous systems
• Nonlinear Dynamics Theory
• Extensibility
• Stochastic Simulation Algorithm for discrete
  systems
• Spatially-resolved models can be built on same
  mass action equations

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Limitations of Mass Action Kinetic Modeling

• Rapidly expanding knowledge base
• Many components and interactions unknown
• Lack of precision
• ad hoc assumptions to limit combinatorial
  explosion (next lecture)
• Large sets of nonlinear ODEs are difficult to
  simulate or analyze
• No comprehensive models yet

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Map of Signaling Initiated by a Single Family of
Receptors
Oda and Kitano (2006) Mol. Syst. Biol.
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Map of Signaling Initiated by a Single Family of
Receptors
Analysis is limited to simple graph theoretic
measures and qualitative discussions of
architecture.
Oda and Kitano (2006) Mol. Syst. Biol.
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(Partial) List of Topics

• Boolean Networks
• Petri Nets
• Statecharts
• Process Algebras
• Agent-Based Modeling
• Hybrid Systems
• Model Checking
• Simulation Algorithms

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Brief Overview of Two Useful Abstractions

• Boolean Networks
• Petri Nets
• Statecharts
• Process Algebras
• Agent-Based Modeling
• Hybrid Systems
• Model Checking
• Simulation Algorithms

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Boolean Networks
BN model of cell cycle in budding yeast
G1
Li, F., et al. PNAS 101, 47814786 (2004).
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Boolean Networks
BN model of cell cycle in budding yeast
G1
Update
Li, F., et al. PNAS 101, 47814786 (2004).
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Boolean Networks
BN model of cell cycle in budding yeast
G1
Update
Blue arrows form stable basin of attraction
Li, F., et al. PNAS 101, 47814786 (2004).
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Balance Sheet for BNs

• Pro
• Models may be constructed on basis of scant data
• Fast computation
• Strong analysis tools (?)
• Good for reasoning about stability and robustness

• Con
• Two levels may not be enough
• Lack of compositionality
• Not hierarchical, but may be embedded in more
  complex models.

Li S, Assmann SM, Albert R (2006) Predicting
Essential Components of Signal Transduction
Networks A Dynamic Model of Guard Cell Abscisic
Acid Signaling. PLoS Biol 4(10) e312
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Petri Nets
Chaouiya, C. Petri net modelling of biological
networks. Brief. Bioinform. 8, 210219 (2007).
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Petri Nets
Time Evolution
Chaouiya, C. Petri net modelling of biological
networks. Brief. Bioinform. 8, 210219 (2007).
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Petri Nets Generalize Network Reconstruction
p3
t2
p4
C corresponds to S
Chaouiya, C. Brief. Bioinform. 8, 210219 (2007).
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Some useful formal properties of PNs

• P-invariants ( ) Mass Conservation
• T-invariants ( ) Loops / Ele. Modes
• Reachability - whether a state can be reached
• Liveness - whether a transition can be fired

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Overview of PNs

• PNs are graphs, and provide tight connection
  between visualization and modeling
• PN formalism is isomorphic to network
  reconstruction formalism (reaction networks)
• Many extensions are possible to overcome
  limitations
• Colored Petri Nets, Hierarchical CPNs,
  Multi-level PN, Stochastic PNs, etc.
• Extensions provide further modeling capabilities
  at the expense of analysis.

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Concluding Remarks

• Goal of course is to explore various
  representations from CS literature that can be
  used to model biomolecular systems.
• What opportunities do these representations offer
  in terms of analysis, simulation, understanding,
  and scalability?

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Simulation Algorithms

• Requirements
• Asynchronous
• Stochastic
• (Modular)
• (Hierarchical)
• Methods
• ODEs
• Model reduction
• Kinetic Monte Carlo (aka Gillespies method)

For distributed computation
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Comparison of two models of vulval development in
C. elegans
Giurumescu, et al. PNAS 103, 13311336 (2006).
Fisher, et al. PNAS 102, 19511956 (2005).