Cohesion index

[sacdallago]

• Come up with a metric to represent a complex' cohesion
• Calculate it on the fly for selected curves and compare to average of given experiment and given complexes in that experiment

--> Initially something like:

For complex: Sum of euclidian distances between every pair of nodes in the network / number of nodes in the network

For experiment: Sum over all average distances (above) / number of complexes represented by experiment

Then refine:

--> Well characterized complexes in experiment (i.e. which have all participants in experiment) have a better weight then not well characterized

[sacdallago]

Cohesion indexes for PPIs

DROP VIEW IF EXISTS protein_vectors;
CREATE OR REPLACE VIEW protein_vectors AS
  SELECT "uniprotId", "experiment", array_agg(ratio) as "vector"
  FROM mecu.public."temperatureReads"
  GROUP BY "uniprotId", "experiment";

DROP VIEW IF EXISTS ppi_distances;
CREATE OR REPLACE VIEW ppi_distances AS
  SELECT inter1.interactor1, inter1.vector as "vector1", inter2.interactor2, inter2.vector as "vector2", inter1.experiment, euclidian(inter1.vector, inter2.vector) as "distance"
  FROM (
       SELECT protein_proteins.interactor1, protein_proteins.interactor2, protein_vectors.experiment, protein_vectors.vector
       FROM protein_proteins, protein_vectors
       WHERE
           protein_proteins.interactor1 != protein_proteins.interactor2 AND
           protein_proteins.interactor1 = protein_vectors."uniprotId"
       ) as inter1,
       (
       SELECT protein_proteins.interactor1, protein_proteins.interactor2, protein_vectors.experiment, protein_vectors.vector
       FROM protein_proteins, protein_vectors
       WHERE
           protein_proteins.interactor1 != protein_proteins.interactor2 AND
           protein_proteins.interactor2 = protein_vectors."uniprotId"
       ) AS inter2
  WHERE
      inter1.interactor1 = inter2.interactor1 AND
      inter1.interactor2 = inter2.interactor2 AND
      inter1.experiment = inter2.experiment;

DROP VIEW IF EXISTS average_ppi_distance_per_experiment;
CREATE MATERIALIZED VIEW average_ppi_distance_per_experiment AS
SELECT experiment, SUM(distance)/COUNT(*) as "average_distance"
FROM ppi_distances
GROUP BY experiment;

-- REFRESH MATERIALIZED VIEW average_ppi_distance_per_experiment;

DROP VIEW IF EXISTS average_ppi_distance_per_ppi;
CREATE MATERIALIZED VIEW average_ppi_distance_per_ppi AS
SELECT interactor1, interactor2, SUM(distance)/COUNT(*) as "average_distance", array_agg(experiment) as "experiments"
FROM ppi_distances
GROUP BY interactor1, interactor2;

-- REFRESH MATERIALIZED VIEW average_ppi_distance_per_ppi;

NB: Views are materialized, thus need to be refreshed every now and then. Average per experiment could be an indicator of how good an experiment is. Average of interaction across experiments could be an indicator of how likely an interaction is.

--> SUPER INTERESTING: compare average for interaction with HIPPIE score!

UPDATE: with join instead of where clause (potentially faster)

DROP VIEW IF EXISTS ppi_distances;
CREATE OR REPLACE VIEW ppi_distances AS
  SELECT inter1.interactor1, inter1.vector as "vector1", inter2.interactor2, inter2.vector as "vector2", inter1.experiment, euclidian(inter1.vector, inter2.vector) as "distance"
  FROM (
       SELECT protein_proteins.interactor1, protein_proteins.interactor2, protein_vectors.experiment, protein_vectors.vector
       FROM protein_proteins, protein_vectors
       WHERE
           protein_proteins.interactor1 != protein_proteins.interactor2 AND
           protein_proteins.interactor1 = protein_vectors."uniprotId"
       ) as inter1
         INNER JOIN
           (
           SELECT protein_proteins.interactor1, protein_proteins.interactor2, protein_vectors.experiment, protein_vectors.vector
           FROM protein_proteins, protein_vectors
           WHERE
               protein_proteins.interactor1 != protein_proteins.interactor2 AND
               protein_proteins.interactor2 = protein_vectors."uniprotId"
           ) AS inter2
           ON
               inter1.interactor1 = inter2.interactor1 AND
               inter1.interactor2 = inter2.interactor2 AND
               inter1.experiment = inter2.experiment;

[sacdallago]

Functions to calculate euclidian distance

create function vec_sub(arr1 double precision[], arr2 double precision[]) returns double precision[]
immutable
strict
language sql
as $$
SELECT array_agg(result)
    FROM (SELECT (tuple.val1 - tuple.val2)*(tuple.val1 - tuple.val2) 
        AS result
        FROM (SELECT UNNEST($1) AS val1
               ,UNNEST($2) AS val2
               ,generate_subscripts($1, 1) AS ix) tuple
    ORDER BY ix) inn;
$$
;

create function euclidian(arr1 double precision[], arr2 double precision[]) returns double precision
immutable
strict
language sql
as $$
select sqrt(SUM(tab.v)) as euclidian from (SELECT 
     UNNEST(vec_sub(arr1,arr2)) as v) as tab;
$$
;

[sacdallago]

Cohesion index for complexes (assumes all of the above exists)

DROP VIEW IF EXISTS pairwaise_complex_interactions;
CREATE OR REPLACE VIEW pairwaise_complex_interactions AS
SELECT protein_proteins.interactor1, protein_proteins.interactor2, complex_protein_pairs."complexId"
FROM protein_proteins
       JOIN (
            SELECT A."uniprotId" AS interactor1, B."uniprotId" AS interactor2, A."complexId"
            FROM protein_complexes as A
                   LEFT JOIN protein_complexes as B
                     ON A."complexId" = B."complexId" AND A."uniprotId" != B."uniprotId"
            ) AS complex_protein_pairs
         ON protein_proteins.interactor1 = complex_protein_pairs.interactor1 AND
            protein_proteins.interactor2 = complex_protein_pairs.interactor2;

DROP VIEW IF EXISTS average_complex_distance_per_experiment;
CREATE MATERIALIZED VIEW average_complex_distance_per_experiment AS
SELECT experiment, "complexId", AVG(distance)
FROM ppi_distances
JOIN pairwaise_complex_interactions
    ON ppi_distances.interactor1 = pairwaise_complex_interactions.interactor1 AND
       ppi_distances.interactor2 = pairwaise_complex_interactions.interactor2
GROUP BY experiment, "complexId";

A few things:

• the innermost nested joint produces duplicates (AB and BA) for every interaction. I use The second join to filter unique interactions. This assumes that I never register duplicate interactions to begin with
• I could implement counting, aka. how many interactions do I conserve per complex per experiment. This would actually be /2, since I duplicate every interaction
• I could further condense in cross-experiment averages, but it's subject to the overall quality of all experiments

[sacdallago]

The full .sql

distance.zip

[sacdallago]

Correlation and covariance between euclidian distances of temperature reads for interacting proteins (according to HIPPIE) per experiment VS hippie score at different strengths (0 (all), 0.25, 0.5, 0.75, 0.8, 0.9).

1. Correlation:

   create view ppi_scores_distnaces_correlations as
   SELECT bins.bins, ppi_distances.experiment, corr(ppi_distances.distance, ppi_distances.correlation) AS corr
   FROM ppi_distances,
      unnest (ARRAY[(0)::numeric, 0.25, 0.5, 0.75, 0.8, 0.9]) bins(bins)
   WHERE (ppi_distances.correlation > (bins.bins)::double precision)
   GROUP BY bins.bins, ppi_distances.experiment
   ;

2. Sample covariance

   create view ppi_scores_distnaces_covariance as
   SELECT bins.bins, ppi_distances.experiment, covar_samp(ppi_distances.distance, ppi_distances.correlation) AS corr
   FROM ppi_distances,
      unnest (ARRAY[(0)::numeric, 0.25, 0.5, 0.75, 0.8, 0.9]) bins(bins)
   WHERE (ppi_distances.correlation > (bins.bins)::double precision)
   GROUP BY bins.bins, ppi_distances.experiment;

[sacdallago]

Next up: how to compare these measures on the fly with analyzed complexes.

1. Calculate euclidian distance between every (unique) pair in query
2. Average distances
3. Create "scale" for specific experiment's known PPI distances (sort them)
4. Find where current distance fits and assign a score (e.g.: below 50% of data = good fit,..)

[sacdallago]

I think much of this has been done. The rest I'll investigate when I get back to this > Feb