Catalyzes the oxidation of primary alcohols including methanol. a primary alcohol + 2 Fe(III)-[cytochrome cL] = an aldehyde + 2 Fe(II)-[cytochrome cL] + 2 H(+) Binds 1 PQQ group per subunit. PQQ is inserted between disulfide Cys-135-Cys-136 and the indole ring of Trp-275. Binds 1 Ca(2+) ion per subunit. Heterotetramer composed of 2 alpha and 2 beta subunits. MDH is the major protein in the cell during growth on methanol (in P.denitrificans MDH constitutes up to 15% of the total cell protein). Belongs to the bacterial PQQ dehydrogenase family.