the following diagram shows the "lock & key" model for enzymes and their substrates. Explain how this works, and why it is an important system within living cells.

The "lock & key" model is an analogy used to explain the mechanism of enzyme-substrate interaction. Enzymes are biological catalysts that enhance the rate of chemical reactions in living organisms. The model suggests that enzymes and their substrates have a complementary shape, similar to how a key fits into a lock. Here is an explanation of how this model works:

1. Enzyme: Enzymes are protein molecules synthesized by living cells, which have a specific three-dimensional structure. Enzymes have a region called the active site, which is the site where the substrate binds and the chemical reaction occurs.

2. Substrate: Substrates are molecules on which enzymes act to catalyze a specific reaction. Substrates have a complementary shape to the active site of the enzyme, like a key fitting into a lock.

3. Enzyme-Substrate Interaction: When the substrate enters the active site of the enzyme, it forms temporary bonds with the amino acid residues present in the active site. This interaction leads to the formation of an enzyme-substrate complex.

4. Reaction Catalysis: The enzymes facilitate the conversion of substrates into products by lowering the activation energy required for the reaction to occur. This occurs due to the precise arrangement of amino acids in the active site, which compensates for the energy required to initiate the reaction.

5. Product Formation: After the enzyme facilitates the reaction, the products are released from the active site. The enzyme remains unchanged and is free to catalyze other similar reactions.

The "lock & key" model is crucial within living cells for several reasons:

1. Specificity: Enzymes exhibit high specificity, meaning they recognize and bind to specific substrates. This allows cells to control and regulate biochemical reactions as each enzyme catalyzes a specific reaction. Without specificity, reactions would be disorganized and inefficient.

2. Efficiency: Enzymes increase the rate of chemical reactions, allowing cellular processes to occur rapidly. Since enzymes lower the activation energy required for reactions, they speed up processes that would otherwise be too slow for cells to survive.

3. Conservation of Energy: Enzymes allow chemical reactions to occur under mild conditions (lower temperatures and pressures) compared to non-enzymatic reactions. This conservation of energy is crucial for metabolic pathways, where multiple reactions occur, as it prevents the wasteful expenditure of energy.

4. Control: Enzymes enable cells to regulate metabolic pathways. They can be activated or inhibited by various factors such as temperature, pH, and regulatory molecules, allowing cells to respond to changing environmental conditions and maintain homeostasis.

Overall, the "lock & key" model of enzymes and substrates is an essential system within living cells as it enables the efficient and precise control of biochemical reactions, contributing to the overall functionality and survival of organisms.