Pathway Logic

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Pathway Logic

• Symbolic Analysis of Biological Signaling

Presented by Geoffrey
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Introduction

• Tremendous growth of genomic sequence information
  combined with technological advances in the
  analysis of gene expression has revolutionized
  research in biology and biomedicine
• Investigation of signaling and metabolic pathways
  would benefit greatly from the use of predictive
  models
• Although these pathways are complex, fundamental
  concepts that stemmed from contemporary research
  indicates that they are also amenable to analysis
  via computational methods. E.g. most signaling
  pathways involved hierarchical assembly in space
  and time of multi-protein complexes that regulate
  the flow of information via stimulation or
  inhibition

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Introduction

• Various models have been proposed that
  incorporates quantitative information such as
  rate and/or concentration information
• However they are limited due to the difficulty in
  obtaining the relevant parameters e.g. Michaelis
  constant etc. as well as stochastic features of
  signaling molecules
• Hence another way to look at such pathways is by
  the logic of signal, e.g. use of p-calculus to
  represent and forward simulate signaling pathway
• In this paper, we will look at the development of
  logical models based on the application of formal
  methods tools to mammalian signaling pathways

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Levels of Abstraction

• Continuous Abstraction
• Involves continuous mathematics such as
  differential equations and are analyzed using
  sophisticated numerical computational packages
• However the complexity of biological processes
  limits its accuracy and effective description
• Discrete Abstraction
• Natural processes are described by purely
  symbolic expressions
• Applicable to less predictable phenomena such as
  biological signaling processes (as we shall see
  later on)

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Pathway Logic

• Pathway Logic an algebraic structure enabling
  the symbolic analysis of biological signaling
  pathways
• It uses rewriting theories to formalize the
  informal models that biologists use to describe
  processes
• Advantages of using Pathway Logic
• Can include both facts and principles relating
  and categorizing data elements and processes
• Allows data to be interpreted, combined and
  queried in the context of biological knowledge
• Allows models with various levels of details
• Dynamically generate pathways using search and
  model-checking
• Transformation to Petri nets for analysis and
  visualization
• Roadmap views of dynamically generated pathways
• Pathway logic algebra can be written in the Maude
  executable specification language

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Pathway Logic Example

• As an example, we will consider a major
  receptor-mediated pathway in mammalian cells,
  focusing on the Epidermal Growth Factor Receptor

Fragment of the mammalian EGFR system
illustrating the activation of a downstream
mitogenic signaling pathway involving the gene
for the autocrine EGRF ligand TGFa
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Biological Sorts and Elements

• The basic declaration of types in Pathway Logic
  (or Maude) is by using the keyword sorts and
  subsorts
• Constants and operators are defined using the
  keyword ops

sorts Protein Chemical Thing . subsorts Protein
Chemical lt Thing . ops EGFR EGF PIP3 Pdk1 PKCe
-gt Protein . ops Ca -gt Chemical
Thing is a sort that encompasses Protein and
Chemical, something like a super class
EGRF, EGF, PIP3, Pdk1, PKCe are operations that
maps from empty to the Protein sort, indicating
that they are constants of Protein
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Protein Modification

• Pathway Logic allows a comprehensive algebra of
  protein modification. The example below shows a
  small part of its declaration and specification
  in Maude

sorts Modification ModSet . subsort Modification
lt ModSet . ops GDP GTP act deact -gt
Modification . op none -gt ModSet . op _ _
ModSet ModSet -gt ModSet assoc comm id none
. op _-_ Protein ModSet -gt Protein right id
none .

• Sets of modifications are applied to proteins
  using the operator _-_ for example EGRF
  act represents the activated form of EGRF

This line denotes a list of modification sets
that has elements that are associative,
commutative and has none as its identity element
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Protein Association

• Signaling proteins commonly associate to form
  functional complexes. This is represented using
  Maude by the following specification code

sort Complex . subsort Complex lt Thing . op __
Thing Thing -gt Complex comm

• Hence multi-protein complexes can be specified
  from proteins and other things by using the
  operator
• And example would be the inhibitory complex
• (IqGap1 (Ecadherin bCatenin))

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Protein Compartmentalization

• In eukaryotic cells (i.e. cells with nucleus)
  proteins and other molecules exist in complex
  mixtures that are compartmentalized.
• They are represented algebraically by the
  following declarations

Sorts Soup Enclosure MemType . Subsort Thing lt
Soup . Op empty -gt Soup . Op _ _ Soup Soup -gt
Soup assoc comm id empty . Ops CM NM -gt
MemType . Op ___ MemType Soup Soup -gt
Enclosure .
Contents of the membrane
Contents of the membrane
The type of membrane
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Protein Compartmentalization

• An enclosure has its own membrane part and
  internal, each with its own constituent soup
• For example

CM cmSoup PIP3 Pdk1 - act cytoSoup PKCe

• This represents a cell containing the chemical
  PIP3 and the activated form of Pdk1 in the cell
  membrane and PKCe in the interior (or cytoplasm)
• cmSoup and cytoSoup are variables that are
  declared on the fly of sort Soup

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Analysis Techniques

• Given a formal symbolic model of the networks,
  several kinds of analyses can be carried out
• Static Analysis
• Forward and Backward Search
• Explicit State Model Checking
• Meta-analysis
• Static analysis allows one to examine the
  structure of the model and to understand how the
  elements are related and organized by just
  looking at the model itself
• It also provides a means to check for
  inconsistencies or ill-formed declaration and
  also to look for missing information

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The Dynamics of Pathway Logic Biochemical Events

• To model biochemical events such as signaling
  processes, we use the dynamic part of a rewrite
  theory, or rewrite rules, to express such
  reactions
• To express the following rule Activated Erk1
  is rapidly translocated to the nucleus where it
  is functionally sequestered and can regulate the
  activity of nuclear proteins including
  transcription factors, we have the following
  rule in Maude

rl410.Erk1/2.to.nuc CM cmSoup
cytoSoup Erk1-act NM nmSoup
nucSoup gt CM cmSoup cytoSoup
NM nmSoup nucSoup Erk1-act
. rl438.Erk.act.Elk ?Erk1/2-act Elk1 gt
?Erk1/2-act Elk1-act .
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The Dynamics of Pathway Logic Biochemical Events

• As another example, In the presence of PIP3,
  activated Pdk1 recruits PKCe from the cytoplasm
  to the cell membrane and activates it

Rl757.PIP3.Pdk1.act.PKCe CM cmSoup PIP3
Pdk1-act cytoSoup PKCe gt CM
cmSoup PIP3 Pdk1-act PKCe-act cytoSoup
metadata cite 21961415 .

• The metadata is just an optional tag that cites
  the justification of the rule using the MedLine
  database Unique Identifier

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Dynamic Analysis

• Hence given the cell declarations and the
  rewriting rules, we can analyze networks by
  executing the rewriting rules to obtain cell
  states
• In Maude there are two rewriting strategies the
  normal top down strategy by means of the command
  rewrite and the command frewrite which means
  fair rewrite. The second one is better as it
  ensures that no laws are left out in the
  execution
• We can also find all the possible outcomes using
  the command search

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Dynamic Analysis

• Hence considering the PKC network

op q14 -gt Dish . eq q14 PD(Ca CM PIP2
PI3Ka-act PLCb1-act Pten-act
Erk1 Pdk1 PKCa PKCe) .

• Using the rewrite and frewrite commands will give

rewrite q14 . result Dish PD(CM Ca DAG
IP3 PI3Ka-act PLCb1-act Pten-act
Erk1 Pdk1 PKCa-act PKCe-act NM empty
empty ) frewrite q14 . Result Dish
PD(CM Ca DAG IP3 PI3Ka-act PLCb1-act
Pten-act Pdk1-act Erk1 PKCa-act
PKCe-act NM empty empty)
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Dynamic Analysis

• Using the search command..

search q14 gt! DDish . ... Solution 3 (state
23) DDish --gt PD(CM Ca DAG IP3
PI3Ka-act PLCb1-act Pten-act Pdk1-act
PKCe-act PKCa-act NM
empty Erk1-act)
Search till termination
Path Graph of the PKCe network
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Model Checking

• One of the capabilities of using Pathway Logic
  and Maude system is Model Checking
• LTL (Linear Temporal Logic) formulas can be used
  to assert whether or not a state is reachable
  (This has uses in biomedicine to find out whether
  or not, targeting a specific enzyme will produce
  side effects)

subsort Dish lt State . op prop1 -gt Prop . eq
PD(outSoup CM cmSoup
cytoSoup NM nmSoup
NM nmSoup cJun-act cFos-act)
prop1 true . red q1 ltgt prop1
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Meta Analysis

• There is a variety of metadata associated with
  the executable model of a signaling network. This
  includes information justifying or qualifying a
  rule and also ordering information, i.e. allows
  us to reason about the models themselves
• These form of analyses can be used to answer
  simples questions such as What are the rule
  labels? or What constants of the sort Protein
  have been declared?
• These questions are used to query about the model
  structure and content

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Graphical Representation

• Ultimately, Maude is still a text based tool
  which may not be suitable for biologists to study
  and analyze
• One way to view Pathway Logic is to use BioNet
  viewer, which is an applet written by the authors
  to view the pathways
• In the model, ovals represent the components
  (proteins, chemicals) with blue ovals
  representing the initial states while white ovals
  represent reachable states
• The rectangles represent the rewriting rules and
  the edges connect reactants and products to rules
• Other than viewing the pathways, some analyses
  can also be performed using the BioNet viewer
• Demo click

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Conclusion

• A formal framework and the application of modern
  model checking and symbolic techniques has been
  proposed for the modeling of biological processes
  such as signaling networks
• Allows biologists to ask questions that are of
  different nature than simple forward simulation,
  such as If I use a drug to target a certain
  protein, will it also affect other proteins and
  chemicals and how will they be affected?
• Performs mainly qualitative analysis of networks
  that are not only restricted to gene level (such
  as the Gene regulatory networks shown previously)
• However it does have its limitations for certain
  cases where proteins and enzyme concentration
  plays an important part of analyzing the network
  such as the oscillation of Mitogen Activated
  Protein Kinase (MAPK) pathways

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Thank you