Question

Mannose has the same molecular formula as glucose and the same geometry except at carbon-2, where the \(\mathrm{H}\) and \(\mathrm{OH}\) groups are interchanged. Draw the structures of \(\alpha\) - and \(\beta\) -mannose.

Short answer

Question: Draw the structures of α-mannose and β-mannose and explain the differences between them. Answer: α-mannose and β-mannose are isomers that have the same molecular formula (\(\mathrm{C_6H_{12}O_6}\)) but differ in the orientation of the hydroxyl group at the anomeric carbon (carbon-1). In α-mannose, the hydroxyl group at carbon-1 is axial (downwards) while in β-mannose, the hydroxyl group is equatorial (upwards). Besides this difference at the anomeric carbon, mannose also differs from glucose at carbon-2, where the \(\mathrm{H}\) and \(\mathrm{OH}\) groups are interchanged. The remaining functional group placements on carbons 3, 4, 5, and 6 are the same for both α-mannose and β-mannose.

Step-by-step solution

Understanding α and β notation

In carbohydrates, the α and β notation refers to the orientation of the hydroxyl group attached to the anomeric carbon (carbon-1). α refers to when the hydroxyl group is axial (downwards or below the plane), while β refers to when the hydroxyl group is equatorial (upwards or above the plane).

Identifying the molecular formula of mannose

The molecular formula of mannose is the same as that of glucose: \(\mathrm{C_6H_{12}O_6}\). The difference between mannose and glucose lies in the geometry around carbon-2, where the \(\mathrm{H}\) and \(\mathrm{OH}\) groups are interchanged.

Drawing the structure of α-mannose

To draw α-mannose, follow these steps: 1. Draw the skeleton structure, with six carbons forming a straight chain. 2. Assign the functional groups to each carbon: - Carbon-1: α-mannose has an axial (downwards) OH group. - Carbon-2: mannose differs from glucose at carbon-2, so place the OH group axial (downwards) instead of axial (upwards) as in glucose. - Carbon-3: OH group axial (upwards). - Carbon-4: OH group axial (downwards). - Carbon-5: OH group axial (upwards). - Carbon-6: CH2OH (above the plane). After placing the functional groups in the correct positions, the structure of α-mannose is complete.

Drawing the structure of β-mannose

To draw β-mannose, follow these steps: 1. Draw the skeleton structure, with six carbons forming a straight chain. 2. Assign the functional groups to each carbon: - Carbon-1: β-mannose has an equatorial (upwards) OH group. - Carbon-2: mannose differs from glucose at carbon-2, so place the OH group axial (downwards) instead of axial (upwards) as in glucose. - Carbon-3: OH group axial (upwards). - Carbon-4: OH group axial (downwards). - Carbon-5: OH group axial (upwards). - Carbon-6: CH2OH (above the plane). After placing the functional groups in the correct positions, the structure of β-mannose is complete.

Key concepts

Mannose Structure

Mannose is a simple sugar or monosaccharide that shares the same molecular formula as glucose but differs in the arrangement of atoms at carbon-2. This makes mannose a stereoisomer of glucose. Mannose sugars are part of the aldohexose group, meaning they biologically function as six-carbon sugars with an aldehyde group.
Mannose predominantly exists in two cyclic forms: α-mannose and β-mannose.
These two forms consistently interconvert in aqueous solutions, a phenomenon known as mutarotation. Visualizing these structures helps remind us that in its cyclic form, the molecule creates a ring that includes an oxygen atom.

• The ring closure results from an aldehyde interacting with an alcohol group in the same sugar molecule.
• This intramolecular reaction forms a hemiacetal linkage.

Understanding mannose’s structure is crucial for recognizing its role in biology, particularly in human metabolism and cell interactions.

Anomeric Carbon

The concept of the anomeric carbon is central to understanding sugars like mannose. The anomeric carbon is the carbon derived from the carbonyl carbon (the aldehyde carbon) when a sugar cyclizes to form a ring.
When mannose cyclizes, this anomeric carbon becomes asymmetric, enabling the formation of two different configurations of the hydroxyl group attached to it.

• In α-mannose, the hydroxyl group at the anomeric carbon (carbon-1) points downwards or axial in the chair conformation.
• In β-mannose, this same hydroxyl group points upwards or equatorial.

The anomeric carbon is significant because its configuration can influence the function and properties of the sugar. For mannose, the ability of enzymes to recognize and act on molecules may depend on whether the sugar is in the α or β form.
This knowledge impacts various biochemical processes including fermentation and glycosylation.

Molecular Formula C6H12O6

Mannose shares the molecular formula \( \mathrm{C_6H_{12}O_6} \) with other sugars like glucose. This formula represents a hexose, which is any six-carbon sugar with twelve hydrogens and six oxygens.
What’s pivotal about mannose is that despite having the same chemical formula as glucose, mannose differs due to the configuration around its stereocenters, specifically at carbon-2.
Such sugars that have the same molecular formula but differ structurally as stereoisomers are known as hexoses. Their identical formulas but distinct characteristics highlight the complexity and variety found within carbohydrate chemistry.

• These differences have real-world implications since they lead to different physical and reactivity properties.
• Even slight variances in structure can determine a sugar's interaction with enzymes and its biological roles in organisms.

Stereoisomers

Stereoisomers are molecules that share the same molecular formula and sequence of bonded atoms, but differ in the three-dimensional orientation of atoms in space. Mannose and glucose are excellent examples of this concept, differing at one stereocenter: carbon-2.

• At carbon-2, mannose and glucose have inverted configurations of the hydroxyl (OH) group and the hydrogen.

This rotation does not change the chemical composition but drastically impacts molecular behavior and interactions.
Interestingly, stereoisomers are further divided into two groups: enantiomers (non-superimposable mirror images) and diastereomers (not mirror images). Mannose and glucose are diastereomers.
Understanding stereochemistry is crucial in carbohydrate chemistry because molecules may exhibit vastly different properties and biological activities based on their three-dimensional structures.
Pharmaceutical design often utilizes stereochemistry to create drugs that specifically interact with biological targets, illustrating the importance of stereochemistry in real-world applications.

α and β Anomers

The terms α and β anomers describe the two configurations that occur at the anomeric carbon of cyclic monosaccharides like mannose. In the cyclic form, the sugar’s carbonyl group reacts internally, forming a ring structure and creating an asymmetric center at the former carbonyl carbon, known as the anomeric carbon.
The classification into α or β depends on the direction of the -OH group at this anomeric position:

• In α-anomers, the hydroxyl group on the anomeric carbon is positioned axially or below the plane in a Haworth projection.
• In β-anomers, the hydroxyl group is positioned equatorially or above the plane.

This distinction critically influences the sugar’s properties and how it participates biochemically.
For example, the formation of glycosidic bonds—connections between sugar molecules in polysaccharides—can be affected by whether a sugar is in an α or β anomeric form.
Knowledge of these structures is important not only for understanding basic carbohydrate chemistry but also for their applications in biochemistry, such as enzyme specificity and the digestion of sugars.