Question

Draw Haworth projection formulas for dimers of glucose with the following types of glycosidic linkages: (a) \(A \beta(1 \rightarrow 4)\) linkage (both molecules of glucose in the \(\beta\) form) (b) \(\operatorname{An} \alpha, \alpha(1 \rightarrow 1)\) linkage (c) \(\mathrm{A} \beta(1 \rightarrow 6)\) linkage (both molecules of glucose in the \(\beta\) form)

Short answer

Draw β(1→4) linkage between C1 and C4, α,α(1→1) linkage between both C1s, and β(1→6) linkage between C1 and C6.

Step-by-step solution

Understand Glycosidic Linkages

Glycosidic linkages describe how two sugar molecules (monosaccharides) are connected through an oxygen atom. Each linkage's notation includes the positions of carbon atoms involved and the anomeric form (α or β) of the sugar molecules.

Draw the \beta(1 → 4) Linkage

For this linkage, two glucose molecules in their β-form connect using a glycosidic bond between the 1st carbon of the first glucose and the 4th carbon of the second glucose. Draw the Haworth projection with the linkage clearly between C1 of the first glucose and C4 of the second.

Draw the α, α(1 → 1) Linkage

For this linkage, two glucose molecules in their α-form connect using a glycosidic bond between the 1st carbon of both glucose molecules. Draw both glucose in their α-form and show the bond between C1 of the first glucose and C1 of the second.

Draw the \beta(1 → 6) Linkage

For this linkage, two glucose molecules in their β-form connect using a glycosidic bond between the 1st carbon of the first glucose and the 6th carbon of the second glucose. Draw both glucose molecules in their β-form, ensuring the linkage is shown from C1 of the first glucose to C6 of the second.

Key concepts

Haworth projection

The Haworth projection is a common way to represent the cyclic structure of monosaccharides. It simplifies complex 3D structures into a 2D format, making it easier to visualize the molecule's layout and the positions of the atoms.
In the Haworth projection:

• The ring is usually drawn with the oxygen atom positioned at the top right.
• Carbon atoms are numbered clockwise from the anomeric carbon, which is the carbon linked to the oxygen in the ring.
• For glucose, if the hydroxyl group (-OH) on the anomeric carbon is pointing down, it’s the α-form; if it's pointing up, it's the β-form.

This representation helps in studying glycosidic linkages, as you can clearly see the atoms involved in the bonding.

β(1→4) linkage

In a β(1→4) linkage, two glucose molecules in the β-form connect through a bond between the 1st carbon (C1) of one glucose and the 4th carbon (C4) of the other.
This type of linkage is common in cellulose, a major component of plant cell walls.
Here’s how you can draw it in Haworth projection:

• Draw the first glucose in the β-form, ensuring the -OH on C1 is up.
• Connect the C1 of the first glucose to the C4 of the second glucose, also in the β-form.
• The bond formation results in the release of a water molecule (condensation reaction).

This linkage creates a straight, linear chain of glucose molecules, contributing to the rigidity and strength of cellulose.

α,α(1→1) linkage

The α,α(1→1) linkage is a unique bond where two glucose molecules in the α-form connect via their anomeric carbons (C1). This results in a disaccharide known as trehalose.
To illustrate this in the Haworth projection:

• Both glucose molecules will have their -OH on C1 pointing down (α-form).
• Link the C1 of the first glucose to the C1 of the second glucose directly.
• This linkage does not involve the formation of a linear chain but forms a structure more akin to a closed loop.

The α,α(1→1) linkage plays a crucial role in certain biological functions, such as energy storage and protection against environmental stress in some organisms.

β(1→6) linkage

A β(1→6) linkage is where two glucose molecules in the β-form connect through a bond between the 1st carbon (C1) of one glucose and the 6th carbon (C6) of the other.
This type of linkage is common in glycogen and amylopectin, which are branches in the polysaccharide chains.
Drawing this in the Haworth projection involves:

• Placing the first glucose in the β-form with the -OH on C1 pointing up.
• Connecting the C1 of the first glucose to the C6 (typically part of the CH2OH group) of the second glucose, also in β-form.

This β(1→6) linkage introduces branching points in polysaccharides, making the structure more complex and compact; it's essential for the rapid release of glucose units during metabolism.