Why does Alcohol-Dehydrogenase prefer ethanol over methanol?

Question

So I've had this experiment at university, where we tried using (yeast) ADH on different alcohols and measuring which one gets turned over the fastest. We also learned that ADH prefers shorter alcohols over longer ones. Now, that would mean the methanol to methanal reaction should've been the fastest, but it didn't react whatsoever. Our lab supervisor reassured me that that's okay, but forgot to tell me the reason why it's the case.

Answer 1

The alcohol dehydrogenases are dimeric proteins, with catalytically active $\ce{Zn^2+ }$ ions. These catalytic $\ce{Zn^2+ }$ ions have distorted tetrahedral geometry, coordinated to one histidine (His-67) and two cysteine residues (Cys-46 and Cys-174) of the enzyme (Ref.1). The catalytic site of alcohol dehydrogenase is shown in left hand site of following image (part $\bf{a}$) and its mechanism of oxidation of primary ord secondary alcohols to corresponding aldehyde or ketones, respectively are shown in part $\bf{b}$ (Ref.1 & 2):

Accordingly, the role of zinc in the dehydrogenation reaction is to promote deprotonation of the alcohol, thereby enhancing hydride transfer from the zinc alkoxide intermediate. Keep in mind that alcohol dehydrogenases are exquisitely stereo specific; and by binding their substrate via a three-point attachment site, which can enables the enzyme to distinguish between prochiral methylene protons in ethanol (Ref. 1 & 3):

All three hydrogens are equal thus enzyme cannot distinguish them for specific sites for pro-S- and/or methyl (of ethanol) or R-group of other alcohols. It is clear that the shapes of the binding sites are distinguish for pro-S- and methyl (of ethanol) or R-group of other alcohols. The binding site for methyl and R-group of other alcohols may be stereoselective for methyl group, but large enough to bind other R-groups as well according to values given in Table 7 of your reference. Yet, it may be too large to bind the hydrogen of methanol because the hydrogen would be too small for necessary tight binding.

References:

1. Robert R. Crichton, "Chapter 12: Zinc: Lewis Acid and Gene Regulator," In Biological Inorganic Chemistry: A New Introduction to Molecular Structure and Function; Second Edition, Elsevier B.V.: Amsterdam, The Netherlands, 2012, pp. 229-246 (ISBN: 978-0-444-53782-9).
2. Gerard Parkin, "Synthetic Analogues Relevant to the Structure and Function of Zinc Enzymes," Chem. Rev. 2004, 104(2), 699–768 (DOI: https://doi.org/10.1021/cr0206263).
3. Donald Voet and Judith G. Voet, In Biochemistry; 3rd edition, John Wiley & Sons: Chichester, NY, 2004, p. 1360 (ISBN-10: 978-0-471-19350-0).