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The rate of respiration increases with increasing temperature until an optimum temperature is reached, after which, it decreases. This is due to enzyme (i.e. any of numerous complex proteins that are produced by living cells) kinetics.
Respiration is the enzyme-mediated process through which cells produce energy.
Enzymes are proteins that catalyze reactions. They are temperature sensitive.
Energy of Activation
A certain amount of energy is required for a reaction to occur when an enzyme encounters its substrate. This is called the energy of activation. Molecules have more energy at higher temperatures, therefore reactions are more likely to occur. The molecules also move around more and so are more likely to collide and potentially react.
High temperatures can damage the structure of a protein. If the shape of an enzyme's active site (where it makes contact with its substrates) is lost, then it cannot function properly. High temperatures reduce the rate of respiration because they damage the enzymes that are involved in respiration.
The temperature at which an enzyme works best is called the optimum temperature. Above this, the protein begins to be damaged by the heat.