Trehalose is a disaccharide that can be obtained from yeasts, fungi, sea urchins, algae, and insects. Deduce the structure of trehalose from the following information:
1. Acid hydrolysis of trehalose yields only b-glucose.
2. Trehalose is hydrolyzed by $\alpha$ -glucosidase but not by $\beta$ -glucosidase enzymes.
3. Trehalose is a nonreducing sugar; it does not mutarotate, form a phenylosazone, or react with bromine water.
4. Methylation of trehalose followed by hydrolysis yields two molar equivalents of 2,3,4,6 -terra- $Q$ -methyl-p-glucose.