RnaCancerClassifier

This project is about converting miRNA expression profiles of healthy and cancerous tissue samples into an Answer Set Program (ASP) that constructs an optimal Boolean classifier for distinguishing between these tissue types in terms of their miRNA fingerprint.

• The code is written in Python 2
• The computation of the classifiers requires clasp and gringo from Potassco
• Send questions / remarks to hannes.klarner@fu-berlin.de or leave an issue

What is a classifier?

Mathematically, a classifier is a Boolean expression where a variable represents high or low presence of a particular miRNA. The structure of the Boolean expression should be constrained by the types of biochemical circuits that may be synthesized in a laboratory.

First, it must be given in conjunctive normal form (CNF). In this context, each (disjunctive) term of a CNF is called gate. If the expression evaluates to 1, i.e., iff all gates evaluate to 1, then the classifier predicts cancerous tissue. An example of a classifier with three gates and six inputs is:

 (g7 + g12 + !g13) * (g2 + g5) * (!g8)

where g7 represents the expression of miRNA number seven, + means disjunction, * means conjunction and ! means negation.

types of constraints

Currently we have implemented the following constraints:

• upper bound for number of total inputs
• upper bound of number of gates
• specification of admissible gate types in terms of
  • bounds on the numbers of negated and non-negated inputs and
  • bound on occurences of a gate type in the classifier

In practice it is desirable to compute classifiers with a minimal number of gates or inputs or both. We have implemented the following optimization strategies:

• first minimize number of gates, then minimize total number of inputs
• first minimize total number of inputs, then minimize number of gates
• only minimize total number of inputs
• only minimize number of gates

Example

input data

A data file is a 0-1 matrix that contains miRNA expression profiles and whether the tissue is healthy or cancerous. An example is toy.csv:

ID, Annots, g1, g2, g3
1,  0,      1,  1,  0
2,  0,      0,  0,  1
3,  1,      0,  1,  0

• ID is the row index
• Annots specifies whether a tissue is healthy with 0 or cancerous with 1
• g1, g2, ... specifies whether the expression of a miRNA in a tissue is low with 0 or high with 1

generate the ASP file

An ASP file is created by a call of the function classifier.csv2asp. Its parameters specify all the classifier constraints. An example is given in the file toy.py. The parameters are specified at the top of the file.

FnameCSV = "toy.csv"
FnameASP = "toy.asp"
UpperBoundInputs = 3
UpperBoundGates  = 2
GateTypes = [{"LowerBoundPos":0,"UpperBoundPos":1,
              "LowerBoundNeg":0,"UpperBoundNeg":0,
              "UpperBoundOcc":1},
             {"LowerBoundPos":0,"UpperBoundPos":0,
              "LowerBoundNeg":0,"UpperBoundNeg":1,
              "UpperBoundOcc":2}]
EfficiencyConstraint = True
OptimizationStrategy = 1

The meaning of the parameters is explained below:

• FnameCSV the data file

• FnameASP the ASP file to be generated

• UpperBoundInputs upper bound on total number of inputs

• UpperBoundGates upper bound on number of gates

• GateTypes a dictionary with keys

  • LowerBoundPos = lower bound of positive inputs to gate
  • UpperBoundPos = upper bound of positive inputs to gate
  • LowerBoundNeg = lower bound of negative inputs to gate
  • UpperBoundNeg = upper bound of negative inputs to gate
  • UpperBoundOcc = upper bound of occurences of gate in classifier

  of tuples (x,y) where x is the upper bound of non-negated inputs and y the upper bound of negated inputs of a gate of that type

• EfficiencyConstraint should be kept at True

• OptimizationStrategy a number between one and four where

  • 1 = minimize number of gates, then minimize number of inputs
  • 2 = minimize number of inputs, then minimize number of gates
  • 3 = minimize number of inputs
  • 4 = minimize number of gates

To generate the ASP file with the given constraints, call the function classifier.csv2asp:

    classifier.csv2asp(FnameCSV, FnameASP, UpperBoundInputs, UpperBoundGates,
                       GateTypes, EfficiencyConstraint, OptimizationStrategy)

The output is

--- csv2asp
 input file: toy.csv
 upper bound on inputs: 3
 upper bound on gates: 1
 gate types (upper bound positive / negative inputs): [(3, 3)]
 efficiency constraints: True
 optimization strategy: 2 (minimize inputs then minimize gates)
 miRNAs:  3
 samples: 3
 created: toy.asp
 now run: gringo toy.asp | clasp --opt-mode=optN

Now use the ASP solver Potassco to compute the optimal classifiers:

$ gringo toy.asp | clasp --opt-mode=optN --quiet=1
Solving...
Answer: 1
gate_input(1,negative,g3) gate_input(2,negative,g1)
Optimization: 2 2
Answer: 2
gate_input(1,positive,g2) gate_input(2,negative,g1)
Optimization: 2 2
Answer: 3
gate_input(2,negative,g3) gate_input(1,negative,g1)
Optimization: 2 2
Answer: 4
gate_input(2,positive,g2) gate_input(1,negative,g1)
Optimization: 2 2
OPTIMUM FOUND

Models       : 5     
  Optimum    : yes
  Optimal    : 4

which tells us that there are four optimal classifiers:

gate_input(1,negative,g3) gate_input(2,negative,g1)
gate_input(1,positive,g2) gate_input(2,negative,g1)
gate_input(2,negative,g3) gate_input(1,negative,g1)
gate_input(2,positive,g2) gate_input(1,negative,g1)

A classifier is defined in terms of the inputs to each of its gates. The three arguments of each gate_input are: the ID of the gate, whether the input is positive or negated and the name of the miRNA. Converted into Boolean expressions the classifiers above are

!g3 * !g1
 g2 * !g1
!g1 * !g3
!g1 *  g2

visualize a classifier

To create a drawing of a classifier call the function classifier.gateinputs2pdf:

   GateInputs = "gate_input(2,positive,g2) gate_input(1,negative,g1)"
   FnamePDF = "toy.pdf"
   classifier.gateinputs2pdf(FnamePDF, GateInputs)

The function requires the program dot. The result is the file toy.pdf:

--- gateinputs2pdf
 found 2 inputs: ['gate_input(2,positive,g2)', 'gate_input(1,negative,g1)']
 created toy.pdf

check consistency

All classifiers obtained from the ASP solver are by definition consistent with the data. Sometimes it may be necessary to check whether a classifier that is not obtained from the ASP solver is consistent with a given data file. In that case you have to convert the classifier into a gate_input string (by hand) and call the function classifier.check_classifier:

    GateInputs = "gate_input(1,negative,g1)"
    classifier.check_classifier(FnameCSV, GateInputs)

The output informs you of all encountered inconsistencies (malfunctions):

--- check_classifier
 miRNAs:  3
 samples: 3
 found 1 input(s) for function generation: ['gate_input(1,negative,g1)']
 testing each sample against the function..
 ** found malfunction:
    gate_id = 1
    gate_inputs = set([('g1', 'negative')])
    miRNA_expressions = g1=0
    tissue = healthy
    tissue_id = 2
 classifier = gate_input(1,negative,g1)
 data = toy.csv
 result = 1 inconsistencies set(['2'])

check csv data

To check whether there are inconsistencies or constants in the data call the function classifier.check_csv. It lists all miRNAs that are constant across all samples, i.e., always high or always low, and checks if there are profiles that are identical in terms of the miRNA profile but differ w.r.t. to the annotation. If there are inconsistencies then there is no classifier.

Files

• classifier.py contains the main functions:

  • csv2asp converts a csv data file into a Potassco ASP file for the construction of a classifier
  • gateinputs2pdf generates a graph-based drawing of a classifier
  • gateinputs2function used internally by check_classifier
  • check_classifier checks whether a given classifier is consistent with a given data file
  • mat2csv converts a mat file into a csv file in the required format

• toy.csv an example of input data

• toy.py an example of parameters settings