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A Tool for Automated Inference of Executable Rule- Based Biological Models Chelsea Voss, Jean Yang, Walter Fontana Static Analysis in Systems Biology, 2017 The need for biological models executable models for in silico experimentation

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A Tool for Automated Inference of Executable Rule- Based Biological Models

Chelsea Voss, Jean Yang, Walter Fontana Static Analysis in Systems Biology, 2017

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The need for biological models

executable models for “in silico” experimentation

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programming is hard

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The need for computer-generated models

NLP

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Some NLP output requires logical inference

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules NLP produces:

Mechanistic rules

§

Non-mechanistic rules

§ §

Domain knowledge

§ § §

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules NLP produces:

Mechanistic rules

§

Non-mechanistic rules

§ §

Domain knowledge

§ § §

???

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules NLP produces:

Mechanistic rules

§ MEK phosphorylates ERK1

Non-mechanistic rules

§ §

Domain knowledge

§ § §

???

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules NLP produces:

Mechanistic rules

§ MEK phosphorylates ERK1

Non-mechanistic rules

§ MEK phosphorylates the ERK protein

family

§ Active ERK phosphorylates RSK

Domain knowledge

§ § §

???

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules NLP produces:

Mechanistic rules

§ MEK phosphorylates ERK1

Non-mechanistic rules

§ MEK phosphorylates the ERK protein

family

§ Active ERK phosphorylates RSK

Domain knowledge

§ When ERK1 is phosphorylated, it is

active

§ S151D-mutated ERK1 behaves as if

always phosphorylated

§ ERK1 and ERK2 are in the ERK protein

family

???

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Some NLP output requires logical inference

Executable model needs: Mechanistic rules

  • MEK phosphorylates ERK1
  • MEK phosphorylates ERK2
  • Phosphorylated ERK1

phosphorylates RSK

  • Phosphorylated ERK2

phosphorylates RSK

  • S151D-mutated ERK1

phosphorylates RSK

NLP produces:

Mechanistic rules

§ MEK phosphorylates ERK1

Non-mechanistic rules

§ MEK phosphorylates the ERK protein

family

§ Active ERK phosphorylates RSK

Domain knowledge

§ When ERK1 is phosphorylated, it is

active

§ S151D-mutated ERK1 behaves as if

always phosphorylated

§ ERK1 and ERK2 are in the ERK protein

family

???

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Mechanistic rules Non-mechanistic rules Domain knowledge

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Mechanistic rules Non-mechanistic rules Domain knowledge Models

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Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models

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Our contribution

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models

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Our contribution: how it works

1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models

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Our contribution: how it works

1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models 2: Implement interpretation

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Our contribution: how it works

1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models 2: Implement interpretation 3: Create predicates

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1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models 2: Implement interpretation 3: Create predicates

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1: Predicates over models, in a logic

First, choose a modeling language.

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1: Predicates over models, in a logic

First, choose a modeling language: Kappa.

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1: Predicates over models, in a logic

First, choose a modeling language: Kappa.

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1: Predicates over models, in a logic

First, choose a modeling language: Kappa. Why Kappa?

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1: Predicates over models, in a logic

First, choose a modeling language: Kappa.

[Figure due to Danos et al. 2009: Abstracting the ODE Semantics

  • f Rule-Based Models: Exact and Automatic Model Reduction.]

Why Kappa? Well-defined operational semantics allow us to reason precisely.

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1: Predicates over models, in a logic

First, choose a modeling language: Kappa. Second, devise a logic for quantifying over models.

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1: Predicates over models, in a logic

[Conversations with Husson & Krivine, 2015-2016]

First, choose a modeling language: Kappa. Second, devise a logic for quantifying over models. Datatypes:

  • Graphs represent the state of a Kappa system
  • Rules are sets of <graph, action> pairs
  • action rewrites graph, creates new graph
  • Models are sets of rules
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1: Predicates over models, in a logic

[Conversations with Husson & Krivine, 2015-2016]

First, choose a modeling language: Kappa. Second, devise a logic for quantifying over models. Datatypes:

  • Graphs represent the state of a Kappa system
  • Rules are sets of <graph, action> pairs
  • action rewrites graph, creates new graph
  • Models are sets of rules

Predicates:

  • Atomic predicates specify a set of rules
  • Predicates specify a set of models
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Atomic predicates class AtomicPredicate:

Top Bottom Equal PreLabeled, PostLabeled PreUnlabeled, PostUnlabeled PreParent, PostParent PreLink, PostLink PreHas, PostHas Add, Rem DoLink, DoUnlink DoParent, DoUnparent Named

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Atomic predicates class AtomicPredicate:

Top Bottom Equal PreLabeled, PostLabeled PreUnlabeled, PostUnlabeled PreParent, PostParent PreLink, PostLink PreHas, PostHas Add, Rem DoLink, DoUnlink DoParent, DoUnparent Named

Predicates class Predicate:

And Not Or Implies ModelHasRule ForAllRules Top Bottom

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Example predicate syntax tree

a = Agent(‘a’) b = Agent(‘b’) p = And( ModelHasRule(lambda r: PregraphHas(r, a.bound(b))), ModelHasRule(lambda r: PostgraphHas(r, a.unbound(b))))

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1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models 3: Create predicates 2: Implement interpretation

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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
  • High-performance satisfiability solver
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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
  • High-performance satisfiability solver
  • Wide variety of datatypes supported: arithmetic, fixed-size bit-vectors,

extensional arrays, datatypes, uninterpreted functions, and quantifiers

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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
  • High-performance satisfiability solver
  • Wide variety of datatypes supported: arithmetic, fixed-size bit-vectors,

extensional arrays, datatypes, uninterpreted functions, and quantifiers

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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
  • High-performance satisfiability solver
  • Wide variety of datatypes supported: arithmetic, fixed-size bit-vectors,

extensional arrays, datatypes, uninterpreted functions, and quantifiers

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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
  • High-performance satisfiability solver
  • Wide variety of datatypes supported: arithmetic, fixed-size bit-vectors,

extensional arrays, datatypes, uninterpreted functions, and quantifiers

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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Demo at http://rise4fun.com/z3
  • High-performance satisfiability solver
  • Wide variety of datatypes supported: arithmetic, fixed-size bit-vectors,

extensional arrays, datatypes, uninterpreted functions, and quantifiers

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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Using Z3 to interpret our predicates
  • Declare Z3 datatypes to represent
  • Recursively build Z3 predicates from our predicate classes
  • Use (check-sat) and (get-model)
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2: Implement interpretation of predicates

  • Solving predicates in this logic is reducible to first-order logic
  • Workhorse: Z3 Theorem Prover
  • Using Z3 to interpret our predicates
  • Value added:
  • Extract models
  • Detect inconsistencies (if P is our facts so far and Q is a new predicate, and P/\Q

is unsatisfiable, then Q is inconsistent with the existing facts)

  • Detect redundancy (if Q is a new fact, and P => Q, then Q is redundant)
  • Detect ambiguity (if model M satisfies predicate P, and P/\¬(model=M) is

satisfiable, then P has multiple solutions)

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>>> from syndra.engine import macros, predicate

Usage example: Inconsistency checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK")

Usage example: Inconsistency checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = predicate.Not(x)

Usage example: Inconsistency checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = predicate.Not(x) >>> x_and_y = predicate.And(x, y)

Usage example: Inconsistency checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = predicate.Not(x) >>> x_and_y = predicate.And(x, y) >>> print x_and_y.check_sat()

Usage example: Inconsistency checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = predicate.Not(x) >>> x_and_y = predicate.And(x, y) >>> print x_and_y.check_sat() False

Usage example: Inconsistency checking

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>>> from syndra.engine import macros, predicate

Usage example: Redundancy checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK")

Usage example: Redundancy checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = macros.phosphorylated_is_active("ERK")

Usage example: Redundancy checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = macros.phosphorylated_is_active("ERK") >>> z = macros.directly_activates("MEK", "ERK")

Usage example: Redundancy checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = macros.phosphorylated_is_active("ERK") >>> z = macros.directly_activates("MEK", "ERK") >>> x_and_y_imply_z = predicate.Implies(predicate.And(x, y), z)

Usage example: Redundancy checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = macros.phosphorylated_is_active("ERK") >>> z = macros.directly_activates("MEK", "ERK") >>> x_and_y_imply_z = predicate.Implies(predicate.And(x, y), z) >>> print x_and_y_imply_z.check_sat()

Usage example: Redundancy checking

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>>> from syndra.engine import macros, predicate >>> x = macros.directly_phosphorylates("MEK", "ERK") >>> y = macros.phosphorylated_is_active("ERK") >>> z = macros.directly_activates("MEK", "ERK") >>> x_and_y_imply_z = predicate.Implies(predicate.And(x, y), z) >>> print x_and_y_imply_z.check_sat() True

Usage example: Redundancy checking

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1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models 2: Implement interpretation 3: Create predicates

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3: Tools for creating predicates

  • Macros
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3: Tools for creating predicates

  • Macros

PreLabeled(A, phosphorylated) ∧ PreUnbound(A, B) ∧ PostLabeled(A, phosphorylated) ∧ PostBound(A, B)

A phosphorylates B

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3: Tools for creating predicates

  • Macros

PreLabeled(A, phosphorylated) ∧ PreUnbound(A, B) ∧ PostLabeled(A, phosphorylated) ∧ PostBound(A, B)

A phosphorylates B

  • directly_phosphorylates
  • phosphorylated_is_active
  • directly_activates
  • negative_residue_behaves_as_if_phosphorylated
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3: Tools for creating predicates

  • Macros
  • Interface with INDRA

[INDRA: Gyori et al. From word models to executable models of signaling networks using automated assembly. 2017]

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3: Tools for creating predicates

  • Macros
  • Interface with INDRA
  • indra.statements.Phosphorylation
  • indra.statements.Activation
  • indra.statements.ActiveForm

[INDRA: Gyori et al. From word models to executable models of signaling networks using automated assembly. 2017]

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1: Predicates

  • ver models

Mechanistic rules Non-mechanistic rules Domain knowledge Space of possible models 2: Implement interpretation 3: Create predicates

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NLP

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NLP

Syndra

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NLP

https://github.com/csvoss/syndra

Syndra