MATTHEWS_COEF (CCP4: Supported Program)

NAME

   matthews_coef  -  Misha  Isupov's Jiffy to calculate Matthews
   coefficient.

SYNOPSIS

   matthews_coef
   [Keyworded input]

DESCRIPTION

   The Matthews Coefficient and solvent content are calculated from
   the unit cell and the molecular weight of the molecules in the unit
   cell. A description of the Matthews coefficient Vm and how it
   relates to solvent content is given below.

   The  probabilities  from  the  Matthews  coefficient paper of
   Kantardjieff and Rupp are also printed, P(reso) for the probability
   using  the  input  high  resolution  limit and P(tot) for the
   probability  across  all  resolution  ranges.  This gives the
   probability of a particular Matthews coefficient based upon the
   high resolution limit.

  Input:

   The program requires the information below which is input via
   keywords. No input files are required.
     * cell parameters
     * the spacegroup i.e. number of symmetry operations
     * the number of molecules in the asymmetric unit
     * the molecular weight of 1 molecule ( ~ number of residues *
       110), or the number of residues in 1 molecule
     * the high resolution limit (optional)

  Output:

   No output files are generated; below is a sample of the log output.
  THE MATTHEWS COEF. IS :  1.74
  SOL % IS : 28.96

   or, if used with the AUTO keyword:
or given protein molecular weight,  or estimated from number of residu
es 110
Nmol/asym  Matthews Coeff  %solvent       P(tot)

  1         3.98            69.14         0.09
  2         1.99            38.28         0.90
  3         1.33             7.42         0.01

   Using  both  the  AUTO keyword and the RESO limit (example at
   resolution 5.0):
For given protein molecular weight,  or estimated from number of resid
ues 110
Nmol/asym  Matthews Coeff  %solvent       P(5.00)     P(tot)

  1         3.98            69.14         0.19         0.09
  2         1.99            38.28         0.80         0.90
  3         1.33             7.42         0.01         0.01

   The highest P(tot) is a strong indicator of the preferred solution.

KEYWORDED INPUT

   Available keywords are:

     AUTO,  CELL,  MODE, MOLWEIGHT, NMOL, NRES, RESO, SYMMETRY,
     XMLOUTPUT

Compulsory keywords

  CELL a b c [alpha beta gamma]

   You must give the unit cell parameters. The angles default to 90.0
   if omitted.

  SYMMETRY

   Either the spacegroup number or name can be given. Alternatively,
   the symmetry operators can be input explicitly, each separated with
   a '*'. However, the program only requires the total number of
   operators.

Extra keywords

  NRES <number_of_residues>

   This is used to estimate the molecular weight of one molecule in
   Daltons.  It  is assumed that on average each protein residue
   contains 5 carbons, 1.35 nitrogens, 1.5 oxygen, 8 hydrogen and 0.05
   sulphur atoms, and thus has a molecular weight of 112.5 Da. It is
   assumed that each DNA residue has an average weight of 325.96 Da.
   The average weight for a DNA/protein complex is calculated assuming
   a ratio of 0.25/0.75.

   Obviously, these estimates are very approximate, and it is better
   to input the real molecular weight.

  MOLWEIGHT <molecular_weight>

   The molecular weight of a molecule in Daltons. What is important is
   the total molecular weight of the molecules in the asymmetric unit.
   This keyword is used in conjunction with NMOL. If this is not
   given, the program calculates a tentative molecular weight of the
   molecule, assuming the unit cell is 47% solvent in the case of
   protein, 64% for dna and 60% for a protein/dna complex.

  NMOL <number>

   This keyword is not compulsory but is used in conjunction with
   MOLWEIGHT. The <number> of molecules per asymmetric unit. Default
   1.

  AUTO

   This keyword is not compulsory and can be used in conjunction with
   NMOL and MOLWEIGHT. It produces a list of incrementing number of
   molecules, from NMOL (default 1), in the asymmetric unit whilst the
   %solvent is >0.0.

  RESO <high_resolution_limit>

   This keyword is not compulsory. The high resolution limit is used
   in the probability scoring.

  MODE <Dna/Comp/other>

   Non-compulsory keyword. Mode C indicates that a dna/protein complex
   is to be modelled, and mode D indicates that dna is to be modelled.
   Other input leads to the calculation with protein only. The default
   is protein only.

  XMLOUTPUT

   This  keyword is of little use for the 'user'. When specified
   matthews_coef will output a small XML file of the results. The name
   and location of the XML file can be specified on the command line
   with XMLFILE, otherwise the file will be called MATTHEWS_COEF.xml.

   Example of input
CELL 73.58 38.73 23.19
SYMM 19
MOLW 6600.0
AUTO
XMLO

   Example of output file
<?xml version="1.0"?>
 <matthews_run>>
  <MATTHEWS_COEF
    ccp4_version="4.1"
    date=" 1/25/02"
   />
  <keyword
  >

  </keyword>
  <cell
    volume="   66085.78"
   />
  <result
    nmol_in_asu="           1"
    matth_coef="   2.503249"
    percent_solvent="   50.89439"
    prob_matth="  0.9962950"
   />
  <result
    nmol_in_asu="           2"
    matth_coef="   1.251625"
    percent_solvent="   1.788778"
    prob_matth="   3.564707E-03"
   />
 </matthews_run>

PROGRAM FUNCTION

  Matthews Number

Vm =   cell volume ( cubic As)      V
       -----------------------   = ---
           M*nasymu*nmols_asu      M*Z

         M         =   molecular weight of protein in daltons
         V         =   volume of unit cell.
         Z         =   no. of molecules in unit cell. = nasymu*nmols_a
su
         nasymu    =   number of asymm. units
         nmols_asu =   number of molecules in asym unit.


Molecular weight

          = number of protein residues in molecule * 110
                                              - very roughly!!!
          = number of non hydrogen protein atoms in molecule *14
                                              - roughly!!!!

   Use RWCONTENTS to read your PDB file if you have one; it will count
   number of atoms of each type. Alternatively, GET_PROT can be used
   to calculate the Molecular Weight from a sequence. Note that while
   the Matthews coefficient is not very sensitive to the Molecular
   Weight, the probabilities from the Matthews coefficient paper of
   Kantardjieff and Rupp can be, especially if there are several
   molecules in the asymmetric unit.

   Matthews found Vm somewhere between 1.66+ and 4.0+ corresponding to
   protein contents of 75% to 30% but proteins with higher solvent
   contents will give higher values of Vm. E.g. for a solvent content
   of 90%, the Vm would be 12+.

   Using this you can calculate Vm assuming nmols_asu = 1/4,1/2,1,2,3
   etc  etc..  You  MAY  be  able  to  narrow down the number of
   possibilities for nmols_asu. If Vm falls outside the range above
   then the number of molecules per asymmetric unit assumed, is likely
   to be incorrect.

  Protein fraction

   Turning this into fraction of protein in asymmetric unit:
            Total mass of Protein in unit cell
Vp  =    ---------------------------------------
          Protein density   *  Unit cell volume


Vp  = M*Z*u/(V*Dp)    = 1/(N*Dp*Vm)

where   Vp = fraction of protein volume in asymmetric unit.
        Vm = Matthews Number        (A**3/Daltons)
        Dp = density of protein = 1.35  (g/cc)   (ref 1)
        N  = Avogadro constant  = 6.023*10**23  gmole**(-1)
        u  = Mass of Hydrogen   = 1.66*10**-24  g

( It is sufficient to approximate the mass of a Hydrogen atom as
(1/N) because the mass of 1 mole of Hydrogen approximates to 1g.)

==>From this it is easy to obtain the formula derived in Matthews i.e.

                       Vp = 1.66*v / Vm
                          = 1.23 / Vm
                            1/Dp is Matthew's v = 0.74 cc/g )

   Alternatively:

Vp  = Np* AV/V

where   Np  = number of protein atoms in unit cell
             (including hydrogens)
        AV  = average atomic volume in A**3 - = 10 approximately.

             (There are about the same number of hydrogens
              as C N O etc.)


If Vp equals fraction of protein volume  in asymmetric
unit

Density  =    Dp *Vp  +   Ds* (1-Vp)
         =   1.35*Vp  + 1.0 * (1-Vp)
         =   0.35*Vp  + 1.0

Ds = density of solvent.  = 1.0 for H[2]O

therefore    Vp  =   (density -1.0)/0.35

   If you know the density you can work backwards and find the number
   of molecules in the asymmetric unit exactly.

EXAMPLES

    1.
matthews_coef << eof
CELL 73.58 38.73 23.19
symm 19
molweight 6600.0
nmol 1
eof
    2. With keyword 'AUTO'
matthews_coef << eof
CELL 73.58 38.73 23.19
SYMM 19
MOLW 6600.0
AUTO
eof

AUTHORS

   Originator: Misha Isupov
   Additions  by:  Charles  Ballard  ccb@dl.ac.uk,  Alun  Ashton
   a.w.ashton@ccp4.ac.uk, Eleanor Dodson ccp4@ysbl.york.ac.uk

REFERENCES

    1. Matthews, J.Mol.Biol 33, 491-497 (1968).
    2. Kantardjieff and Rupp, Protein Science 12, 1865-1871 (2003).

SEE ALSO

   GET_PROT
   RWCONTENTS