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Transformational Grammars and PROSITE Patterns. Roland Miezianko CIS 595 - Bioinformatics Prof. Vucetic. Agenda. Transformational Grammars Definition The Chomsky Hierarchy Finite State Automata FMR-1 Triplet Repeat Region Regular Grammar Example PROSITE Patterns in Regular Grammar Form.

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transformational grammars and prosite patterns

Transformational Grammarsand PROSITE Patterns

Roland Miezianko

CIS 595 - Bioinformatics

Prof. Vucetic

agenda
Agenda
  • Transformational Grammars
    • Definition
    • The Chomsky Hierarchy
  • Finite State Automata
    • FMR-1 Triplet Repeat Region
    • Regular Grammar Example
  • PROSITE
    • Patterns in Regular Grammar Form
assumptions
Assumptions
  • Treated biological sequences as one-dimensional strings of independent and uncorrelated symbols.
  • Need to address interaction among base pairs to understand secondary structures.
secondary structures
Secondary Structures
  • The 3-D folding of proteins and nucleic acids involves extensive physical interactions between residues that are not adjacent in primary sequence. [1]
  • Require a model for secondary structure that reflect the interaction among base pairs.
modeling strings
Modeling Strings
  • General theories for modeling strings of symbols has been developed by computational linguists
    • Chomsky in 1956, 1959
    • Interested in how a brain or computer program could algorithmically determine whether a sentence was grammatical or not
transformational grammars
Transformational Grammars
  • Transformational Grammars consist of:
    • Symbols
      • Abstract Nonterminal Symbols
      • Terminal Symbols
    • Rewriting Rules (Productions)
      • A --> B
transformational grammars example
Transformational Grammars, Example

Example Grammar

Two-letter terminal alphabet: {a, b}

Single nonterminal letter: S

Three Productions:

S->aS

S->bS

S->e (e=special blank terminal symbol)

Example derivation of our simple grammar:

S->aS->abS->abbS->abb

chomsky hierarchy
Chomsky Hierarchy
  • Four types of restrictions on grammar’s productions resulted on four classes of grammars.
    • Regular Grammars
    • Context-Free Grammars
    • Context-Sensitive Grammars
    • Unrestricted Grammars
chomsky hierarchy9
Chomsky Hierarchy

unrestricted

context-sensitive

context-free

regular

automata
Automata
  • Each grammar has a corresponding abstract computational device called: automaton

GrammarParsing Automaton

Regular Finite State

Context-Free Push-Down

Context-Sensitive Linear Bounded

Unrestricted Turing Machine

frm 1 triplet repeat region
FRM-1 TripletRepeat Region
  • FRM-1 gene sequence contains CGG which is repeated number of times
  • Number of triplets is highly variable between individuals
  • Increased copy number is associated with a genetic disease
frm 1 triplet repeat region12
FRM-1 TripletRepeat Region
  • FSA will match any string from the “language” that contains the strings:

GCG CTG

GCG CGG CTG

GCG CGG CGG CTG

GCG CGG CGG CGG CGG … CTG

frm 1 triplet repeat region14
FRM-1 TripletRepeat Region

Regular Grammar for our Finite State Automaton finds any number of copies of CGG

prosite patterns
PROSITE Patterns
  • PROSITE database is an example of a biological application of regular grammars
    • Unlike methods which assign scores to alignments, PROSITE patterns either match a sequence or do not.
prosite patterns16
PROSITE Patterns
  • Consists of a string of pattern elements separated by dashes and terminated by a period
    • Pattern Element – single letter
    • [ ] - any one letter
    • { } – anything but enclosed letters
    • X – any residue can occur
    • X(y) – any letter of length y
prosite patterns17
PROSITE Patterns

RNP-1 Motif

[RK]-G-{EDRKHPCG}-[AGSCI]-[FY]-[LIVA]-x-[FYM].

conclusion
Conclusion
  • Transformational grammars are useful in developing acceptors of different length sequences and for matching specific multi-sequence regions.
  • Higher order grammars in the Chomsky hierarchy are more difficult to program and apply
references
References

[1] Durbin, R. Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. University of Cambridge Press, 1998.

[2] Gibson, G. A Primer of Genome Science. Sinauer Associates, Inc. Publishers, 2002.

[3] Mount, D. Bioinformatics: Sequence and Genome Analysis. Cold Spring Harbor Laboratory Press, 2001.

[4] PROSITE Database http://us.expasy.org/prosite/