To answer this question, it is essential to have an understanding of the Michaelis-Menten kinetics of enzymes.

When plotting a graph of initial reaction rate as a function of substrate concentration, the resulting plot shows a hyperbolic relationship. At first, the rate increases linearly with a fairly steep slope. But as substrate concentration rises, the graph begins to level off.

The question, however, is to determine the order of the reaction with respect to substrate (the effect substrate has on reaction rate). One helpful way to determine this is to make use of the Michaelis-Menten equation.

With this equation in mind, we can make predictions on how substrate concentration will affect the reaction order.

Low Substrate Concentrations:

When substrate concentration is very low, we can assume that . As a result of this, we can essentially say that . Thus, at low concentrations of , the equation can change as follows.

As we can see above, under conditions of low substrate concentration, the reaction is first-order with respect to enzyme and first-order with respect to substrate. This means that any slight change in the concentration of substrate will proportionately affect the reaction rate (for instance, if the substrate concentration increases by , then the reaction rate will also increase by , assuming that enzyme concentration is held constant).

*** As a side note, it's also worth noting that the above expression also includes a new reaction rate constant, one that is a ratio of two other constants, . This term is actually what is used to assess an enzyme's efficiency, since it states the reaction rate under conditions of very low substrate concentration.

High Substrate Concentrations:

Now, let's see what happens when substrate concentration is high. When this happens, we can say that . Just as we made an estimation before, we can do so once again by stating that  under such conditions. Next, we can take a look at how this changes the original equation.

As we can see, under high substrate concentrations (saturating conditions), the reaction is at its maximum value. Furthermore, notice that the  term cancels out of the expression. This means that, under saturating conditions, the reaction is zero-order with respect to substrate and first-order with respect to enzyme. The consequence of this is that a change in substrate concentration is unable to change the reaction rate; only a change in enzyme concentration (or temperature) can affect the rate at saturating substrate concentrations.

With Michaelis-Menten Kinetics, The Vmax is the maximum rate of the enzyme mediated reaction. When a system has a concentration of substrate well above Km (which is the concentration of substrate at which the reaction is proceeding at one-half Vmax), then it is said that the system is saturated. In this state, the reaction is occurring basically at Vmax, since there is plenty of substrate to react with the enzyme, and adding more substrate would not increase the reaction rate. Rather, the concentration of enzyme is the limiting factor of how much reaction product will be produced per unit time.