Rate Calculations

The change must be identified clearly. It might be the mass of substrate used, the volume of product formed or a change in concentration. It is not normally a change in the amount of enzyme: an enzyme acts as a catalyst and is not used up by the reaction.

When product is being formed:

When substrate is disappearing, calculate the amount used as:

This makes the reported rate of substrate use positive. Dividing by the elapsed time gives the average rate over that interval.

Carrying out a rate calculation

Suppose a protease uses up $5\text{ g}$ of protein in $30$ minutes. If the rate is required in grams per hour, convert the time first:

Now substitute the values:

This means that the enzyme-catalysed reaction used protein at an average rate of $10\text{ g}$ per hour during the measured period. It does not mean that $10\text{ g}$ of enzyme was used.

The same data could be expressed per minute:

These values describe the same rate in different units. Always convert the time before dividing if a particular unit is requested.

Units carry biological meaning

A rate unit combines the unit for the measured change with the time unit. A mass measured in grams over minutes gives $\text{g/min}$; a volume measured in cubic centimetres over seconds gives $\text{cm}^3\text{/s}$.

A number without an appropriate rate unit does not fully describe the result. The unit also helps to reveal errors: dividing a mass by a time should produce a mass-per-time unit, not simply grams.

Using completion time as a measure of activity

Some enzyme investigations record only the time needed to reach a fixed end point. For example, a starch-and-amylase mixture can be sampled into iodine until the iodine remains orange, indicating that starch is no longer detected. If each trial begins with the same amount of substrate and uses the same end point, each trial represents the same overall change.

In this situation, the completion time itself is not the rate. A shorter time means a faster reaction, so time and rate have an inverse relationship. A useful relative measure is:

For example, if an end point is reached in $20\text{ s}$:

If another trial takes $40\text{ s}$, its relative rate is $0.025\text{ s}^{-1}$. The first trial has the larger relative rate and therefore the greater enzyme activity.

A value in $\text{s}^{-1}$ does not state the amount of substrate converted each second unless that amount is known. It is a relative rate used to compare trials that represent the same fixed change.

Finding rate from a graph

When measurements are taken throughout a reaction, plot time on the horizontal axis and the measured quantity on the vertical axis. The average rate between two points is the graph's gradient over that interval:

A steeper rising line means product is forming more rapidly. If substrate amount is plotted, the line falls as substrate is used. Its gradient is negative because the measured amount is decreasing, but a steeper downward line still represents faster substrate use; compare the magnitude of the gradients when comparing speed.

Enzyme-reaction graphs often become less steep with time. This means the rate is decreasing, perhaps because less substrate remains available. A calculated rate must therefore be linked to a stated time interval rather than assumed to remain constant throughout the reaction.

Comparing experimental conditions

Rate calculations allow results from different temperatures, pH values or substrate concentrations to be compared. The condition producing the greatest calculated rate is the one under which the enzyme worked fastest in that investigation.

A fair comparison requires the same method, starting quantities and end point, with other relevant variables controlled. End-point measurements also have limited precision: if a mixture is tested only at set intervals, the true end point lies between the last positive test and the first negative test. The calculated rate should not therefore be presented with unjustified precision.