## Thursday, January 29, 2015

### Finding mass spectra with PostgreSQL: Tanimoto similarity in SQL

Now that we can store mass spectra in PostgreSQL, the next question is how to find them?

There is more than one solution to this problem. One is the Tanimoto coefficient or Jaccard index of the peaks.

The Tanimoto coefficient T can be calculated as T = c / (a+b-c) with c the number of peaks both spectra have in common and a and b the number of peaks in each spectrum.

Similarity is then expressed as a number between 0 and 1, with 0 meaning no and 1 maximum similarity. Likewise the Tanimoto distance 1-T expresses the distance between two spectra.

On a table like

CREATE TABLE <spectra_table>
(
id integer NOT NULL,
"m/z" numeric NOT NULL,
intensity numeric NOT NULL

)

this can easily be done in SQL with a common table expression:

WITH SQ AS (select "m/z" from <spectra_table> where id=1),
ST AS (select "m/z" from <spectra_table> where id=2),
SC AS (select count(1)::float as common from SQ, ST where sq."m/z" = st."m/z")
select (select common FROM SC) / ((select count(1) from sq) + (select count(1) from st) - (SELECT common FROM SC))
as spectral_tanimoto;

If desired, further properties like the peak intensity can be used to narrow the match:

WITH SQ AS (select "m/z", intensity from <spectra_table> where id=1),
ST AS (select "m/z", intensity from <spectra_table> where id=2),
SC AS (select count(1)::float as common from SQ, ST where sq."m/z" = st."m/z" and sq.intensity = st.intensity)
select (select common FROM SC) / ((select count(1) from sq) + (select count(1) from st) - (SELECT common FROM SC))
as spectral_tanimoto;

The problem here is, that the join between the peaks relies on exact matching properties. 'Fuzzy' joins can relax this to some extent. The simple variant is to cast the m/z values to integers:

WITH SQ AS (select "m/z"::int from <spectra_table> where id=1),
ST AS (select "m/z"::int from <spectra_table> where id=2),
SC AS (select count(1)::float as common from SQ, ST where sq."m/z" = st."m/z")
select (select common FROM SC) / ((select count(1) from sq) + (select count(1) from st) - (SELECT common FROM SC))
as spectral_tanimoto;

PostgreSQL's range types allow finer grained control:

WITH SQ AS (select "m/z" from <spectra_table> where id=1),
ST AS (select "m/z" from
<spectra_table> where id=2),
SC AS (select count(1)::float as common from SQ, ST where numrange(sq."m/z"-0.25, sq."m/z"+0.25,'[]') && numrange(st."m/z"-0.25, st."m/z"+0.25,'[]'))
select (select common FROM SC) / ((select count(1) from sq) + (select count(1) from st) - (SELECT common FROM SC))
as spectral_tanimoto;

Neat. But this comes with a serious caveat, since 'fuzzy' joins may produce excess tuples by their very nature. Given a table with two entries 1.1 and 0.9, joining with 1.1 and a range of +/- 0.2, now both tuples will match, generating two result tuples!

In the context of the Tanimoto coefficient, this can lead to the anomaly that the numerator c becomes larger than the denominator. If this happens, T > 1 or T < 0 may occur, which are strictly undefined. So handle with care.

The nicer properties of the calculation are, that you can easily transform spectra measured with different ionization levels and that it can be made run very fast, if you know the target T you like to filter with beforehand.

1.) Since an m/z of 50 measured at an ionization of +1 means a mass of 50 u but a m/z of 50 measured at ionization +2 means a mass of 100 u (m/z is the ratio between mass and charge of the Ion measured), the statements above would give false results if the ionization was different and not taken into account. This can be done at the join level:

...where sq."m/z"*2 = st."m/z"...

Usually the MS software does that for you so you have normalized spectra, but anyway...

2.) If you know the number of peaks in each spectrum and the target T you want to filter with, similarity searches can be made very fast. Here is the paper on how to do it.

That's it for today. Spectral contrast in SQL next.

## Tuesday, January 27, 2015

### oracle_fdw: 'cannot use LDAP' means 'don't even touch'

The README for the oracle_fdw clearly says: "You cannot use LDAP functionality both in PostgreSQL and in Oracle, period."

Actually this means: "DO NOT EVEN TOUCH!"

I found this out yesterday when tracking down frequent sigsevs in one of our PostgreSQL servers.

The Oracle instant client was set up with NAMES.DIRECTORY_PATH=(TNSNAMES, LDAP) in sqlnet.ora.

Even when the connect string used in the FDW is in the //<server>:<port>/<service> form, i.e. no Oracle name resolution is required, just allowing LDAP in sqlnet.ora will kill your server.

## Thursday, January 22, 2015

### Calculating theoretical isotope patterns for mass spectrometry with PostgreSQL and pgchem::tigress

New year, new challenge: mass spectra.

To calculate the theoretical isotope pattern for a given molecule in PostgreSQL you need two things:
1. a cheminformatics toolkit to determine the element composition of the molecule and it's exact mass
2. a usably fast and accurate algorithm to infer the isotope pattern from the composition
For 1. I take OpenBabel, for 2. the Mercury7 algorithm as implemented in libmercury++.
Then, the two have to be made working together. Like so:

typedef struct
{
size_t num_entries;
double *mz;
double *intensity;
double *intensity_normalized;
unsigned int *md;
} _ISOTOPE_PATTERN;

extern "C" _ISOTOPE_PATTERN *
ob_molfile_to_isotope_pattern(char *molfile, int charge, double normal)
{
_ISOTOPE_PATTERN *retval;
vector msa_mz;
vector msa_abundance;
vector composition;
vector m;
const double limit = 10e-30;
OBMol mol;
OBConversion conv;
string tmpStr (molfile);
istringstream molstream (tmpStr);
double mass_diff, monoisotopic_mass, scale = 1.0, delta = numeric_limits::max();
int i=0;

//Initialize composition vector to all zeroes
for(unsigned int i=0; i         composition.push_back(0);

conv.SetInAndOutFormats("MDL",NULL);

if (mol.Empty ())
return NULL;

// Add missing hydrogens, if any
mol.AddHydrogens(false, false); // All Hs, no PH correction

//Iterate over atoms and update the composition vector accordingly
FOR_ATOMS_OF_MOL(atom, mol)
{
switch (atom->GetAtomicNum())
{
case 1: // H
composition++;
break;
case 6: // C
composition++;
break;
case 7: // N
composition++;
break;
case 8: // O
composition++;
break;
case 16: // S
composition++;
break;
case 35: // Br
composition++;
break;
case 17: // Cl
composition++;
break;
case 53: // I
composition++;
break;
case 15: // P
composition++;
break;
case 9: // F
composition++;
break;
default: // Others ignored
break;
}
}

// Calculate isotope patterns with MERCURY7
if(0 != mercury::mercury(msa_mz, msa_abundance, composition, charge, limit))
{
return NULL;
}

monoisotopic_mass = mol.GetExactMass();

// Allocate return value and copy values
retval = (_ISOTOPE_PATTERN*) calloc(1,sizeof(_ISOTOPE_PATTERN));

retval->num_entries = msa_mz.size();
retval->mz=(double*) calloc(msa_mz.size(), sizeof(double));
retval->intensity=(double*) calloc(msa_abundance.size(), sizeof(double));
retval->intensity_normalized=(double*) calloc(msa_abundance.size(), sizeof(double));
retval->md=(unsigned int*) calloc(msa_abundance.size(), sizeof(unsigned int));

copy(msa_mz.begin(), msa_mz.end(), retval->mz);
copy(msa_abundance.begin(), msa_abundance.end(), retval->intensity);
copy(msa_abundance.begin(), msa_abundance.end(), retval->intensity_normalized);

for(std::vector::iterator it = msa_mz.begin(); it != msa_mz.end(); it++)
{
mass_diff = *it-monoisotopic_mass;

m.push_back(mass_diff);

if(abs(mass_diff) < delta)
{
delta = abs(mass_diff);
scale = msa_abundance[i];
}
i++;
}

scale = normal / scale;

for(i=0; retval->num_entries; i++)
{
retval->intensity_normalized[i] *= scale;
}

copy(m.begin(), m.end(), retval->md);

return retval;
}

This parses a V2000 or V3000 molfile into a molecule object, iterates over the atoms and generates the elemental composition for Mercury7, calculates the exact mass and the theoretical isotope pattern. It then stores the m/z vector, the peak vector and the derived peak vector normalized to some value, e.g. 100%, and the mass distance relative to the base peak m/z value. All of this is stored in the C structure _ISOTOPE_PATTERN in order to transfer it from C++ to the C code of PostgreSQL.

Over to the PostgreSQL side of things :-)

PG_FUNCTION_INFO_V1 (pgchem_isotope_pattern);

Datum
pgchem_isotope_pattern (PG_FUNCTION_ARGS)
{
_ISOTOPE_PATTERN *isotope_pattern = NULL;
_ISOTOPE_PATTERN *pattern_copy = NULL;
FuncCallContext *ctx=NULL;
MemoryContext original_ctx=NULL;
DECOMPRESSED_DATA *original_data=NULL;
char *tmpMolfile=NULL;

if(SRF_IS_FIRSTCALL())
{
MOLECULE *arg_molecule = PG_GETARG_MOLECULE_P (0);
int32 arg_charge = PG_GETARG_INT32 (1);
float8 arg_normal = PG_GETARG_FLOAT8 (2);
ctx = SRF_FIRSTCALL_INIT();

original_ctx = MemoryContextSwitchTo(ctx->multi_call_memory_ctx);

if(arg_molecule->original_format==FORMAT_V2000 || arg_molecule->original_format==FORMAT_V3000)
{
original_data = decompress_data(CIPTR(arg_molecule),arg_molecule->compressed_sizeo, arg_molecule->sizeo);
tmpMolfile = strdup(original_data->decompressed_data);
}
else
{
tmpMolfile = ob_smiles_to_V2000 (SMIPTR(arg_molecule));
}

isotope_pattern = ob_molfile_to_isotope_pattern(tmpMolfile, arg_charge, arg_normal);

if(NULL!=tmpMolfile)
{
free(tmpMolfile);
}

if(NULL == isotope_pattern)
{
elog (ERROR, "Could not generate isotope pattern!");
PG_RETURN_NULL();
}

pattern_copy = (_ISOTOPE_PATTERN*) palloc0(sizeof(_ISOTOPE_PATTERN));
pattern_copy->mz = (double*) palloc0(isotope_pattern->num_entries*sizeof(double));
pattern_copy->intensity = (double*) palloc0(isotope_pattern->num_entries*sizeof(double));
pattern_copy->intensity_normalized = (double*) palloc0(isotope_pattern->num_entries*sizeof(double));
pattern_copy->md = (unsigned int*) palloc0(isotope_pattern->num_entries*sizeof(unsigned int));

pattern_copy->num_entries = isotope_pattern->num_entries;

memcpy(pattern_copy->mz, isotope_pattern->mz, isotope_pattern->num_entries*sizeof(double));
memcpy(pattern_copy->intensity, isotope_pattern->intensity, isotope_pattern->num_entries*sizeof(double));
memcpy(pattern_copy->intensity_normalized, isotope_pattern->intensity_normalized, isotope_pattern->num_entries*sizeof(double));
memcpy(pattern_copy->md, isotope_pattern->md, isotope_pattern->num_entries*sizeof(unsigned int));

if(NULL != isotope_pattern->md)
free(isotope_pattern->md);

if(NULL != isotope_pattern->mz)
free(isotope_pattern->mz);

if(NULL != isotope_pattern->intensity)
free(isotope_pattern->intensity);

if(NULL != isotope_pattern->intensity_normalized)
free(isotope_pattern->intensity_normalized);

if(NULL != isotope_pattern)
free(isotope_pattern);

isotope_pattern = NULL;

ctx->max_calls = pattern_copy->num_entries;
ctx->user_fctx = pattern_copy;

if(get_call_result_type(fcinfo, NULL, &ctx->tuple_desc) != TYPEFUNC_COMPOSITE)
{
elog (ERROR, "Calling the isotope pattern SRF in a context that does not expect tuples in return is not supported!");
}

BlessTupleDesc(ctx->tuple_desc);

MemoryContextSwitchTo(original_ctx);
}

ctx = SRF_PERCALL_SETUP();

isotope_pattern = ctx->user_fctx;

if(ctx->call_cntr < ctx->max_calls)
{
HeapTuple rettuple = NULL;
Datum *retvals;
bool *retnulls;

retvals = (Datum*) palloc0(4*sizeof(Datum));
retnulls = (bool*) palloc0(4*sizeof(bool));

retvals = Float8GetDatum(isotope_pattern->mz[ctx->call_cntr]);
retvals = Float8GetDatum(isotope_pattern->intensity[ctx->call_cntr]);
retvals = Float8GetDatum(isotope_pattern->intensity_normalized[ctx->call_cntr]);
retvals = UInt8GetDatum(isotope_pattern->md[ctx->call_cntr]);

retnulls = false;
retnulls = false;
retnulls = false;
retnulls = false;

rettuple = heap_form_tuple(ctx->tuple_desc, retvals, retnulls);

pfree(retvals);
pfree(retnulls);

SRF_RETURN_NEXT(ctx, HeapTupleGetDatum(rettuple));
}
else
{
SRF_RETURN_DONE(ctx);
}
}

This is a set returning function, meaning that it can return multiple rows in one call, i.e. it returns a complete table. Basically it retrieves the molecule argument from PostgreSQL, calls ob_molfile_to_isotope_pattern(), constructs a set of tuples and returns them to PostgreSQL. The basics of set returning functions can be found here and here.

Now we can declare the function to PostgreSQL:

CREATE OR REPLACE FUNCTION isotope_pattern(IN molecule, IN integer DEFAULT 0, IN double precision DEFAULT 100.0)
RETURNS TABLE("m/z" double precision, intensity double precision, intensity_normalized double precision, mdtbp integer) AS
'libpgchem', 'pgchem_isotope_pattern'
LANGUAGE c IMMUTABLE STRICT;

and use it:
select * from isotope_pattern('c1ccccc1I'::molecule) where intensity >= 0.01;

 m/z intensity intensity_normalized mdtbp 203.9436 0.934689933304048 100 0 204.946987674881 0.0634781699018538 6.79136124612619 1

Visualized it looks like this:

Nice. And everything (except the GUI) in the database.