Why do polysaccharides consisting of alpha-glucose have helical structures?

Why do the polysaccharides consisting of alpha-glucose such as starch and glycogen have helical structure, while the one such as cellulose consisting of beta glucose don't display such structures?

The textbook said that is because of the angle of 1-4 linkage,what kind of the angle is it that makes helical structure?

1 Answer

Note: This is an off the top of my head answer (I might be horribly wrong), but it has prompted me to do some research. I will add more details, and/or make corrections once I am done. In the meantime, I would love to hear what others have to say on this.

Pictured below is the 2D structure of amylose

This primarily composed of $\alpha$-(1-to-4)-D-glucose units. Although the $\alpha$-(1-to-4) links are capable of relatively free rotation about their torsional angles, hydrogen bonding between the $\ce{O}$3 and $\ce{O}$2 encourages helicogenesis.

Single helical amylose has hydrogen-bonding between $\ce{O}$2 and $\ce{O}$6 atoms on outside surface of the helix and the ring oxygen pointing inwards.

Contrat this with cellulose which is a linear polymer of $\beta$-(1-to-4)-D-glucopyranose units.

The fully equatorial conformation of $\beta$-linked glucopyranose residues stabilises the chair structure, minimising its flexibility.

Pictured below, the 2D structure of cellulose and displaying the intrastrand hydrogen bonding

Interactive 3D visualisation for amylose and cellulose.