MATTPROB is an updated, parameter free estimator calulating normalized probabilities for the occurrence of multimerization states. Originally the parameterized estimator was based on a 2003 survey of Vm (Matthews coefficient) and solvent content (Vs) distribution of about 11,000 non-redundant crystallographic PDB entries (Kantardjieff and Rupp, Protein Science 12:1865-1871, 2003). The parameter-free kernel estimator works for any given resolution range and has been updated with V(s) vs. resolution data current to 2026. The absence of binning and the 150k kernel data deliver more accurate results than the older, parameterized version. For implementation of mattprob in other programs use the 2026 kernel data sets. For those who care, we used Scott's rule (h = std·n^-0.2) and applied a modest constant inflation (1.3) generating the resolution-limited KDE plots.The calulator can also be used in legacy paramaterized mode with the 2013 or 2003 data. For nucleic acids and nucleic acid-protein complexes, data for resolution extremes are sparse in all modes, and the resolution discrimination not really meaningful.

Higher packing density and thus lower solvent content correlate with increasing resolution and can be used to provide a more refined probability for the occurrence of a certain oligomerization state. The program thus accepts resolution as additional information to select the proper probability distribution. The assumption is that observed resolution represents an estimate for the lower limit for crystal quality, i.e., crystals obviously diffract to at least this value (but could also diffract better). It must be understood that the answers are always relative probabilities based on our current state of knowledge and that no clear answer may result in certain cases.

One can also enter the molecular data for one monomer and select its known multimerization state, in case you know what basic multimer unit you are looking for. For example, if your known molecular unit is a trimer, you may want to look for 3-mer, 6-mer, 9-mer etc. Note that crystallographic axes coinciding with multimer axes can result in improbably low Vm for a single multimer unit. Whenever possible, use the correct molecular weight based on the sequnce and not the estimated value based on residue number.

The results are represented in tabular form at the top of the output followed by two graphs showing the normalized probability distributions (resolution corrected and all PDB data) against Vm and Vs, respectively.    

We would appreciate citation of the two following references when using this program in published work:

• Matthews BW. 1968. Solvent content of protein crystals. J Mol Biol 33:491-497.

• Kantardjieff KA, Rupp B. Matthews coefficient probabilities: Improved estimates for unit cell contents of proteins, DNA, and protein-nucleic acid complex crystals. Protein Science 12:1865-1871 (2003). Citation link: https://onlinelibrary.wiley.com/documentcitationdownload?publicationDoi=10.1002/%28ISSN%291469-896X&doi=10.1110/ps.0350503&type=journal

• Weichenberger CX and Rupp B. Ten years of probabilitic estimates of biocrystal solven content: New insights via nonparamatric kernel density estimate. Acta Crystallogr D70(6) 1579-1588 (2014). Citation link:https://scripts.iucr.org/cgi-bin/paper?S1399004714005550

The old parameterized fit function and parameter files from 2003 and 2013 are also available for download.

For developers, the implemenation and the link to the data filed for the kernel estimator can be found in the Computational Crystallography Newsletter 15, January 2015.