Initial Velocity - Online Tutor, Practice Problems & Exam Prep

Initial reaction velocities (v₀) of enzyme-catalyzed reactions are crucial for understanding enzyme kinetics. These velocities are measured at the beginning of reactions when substrate concentrations are highest, allowing for maximum reaction rates (v_max). Enzyme kinetics plots graph v₀ against substrate concentration, highlighting that as substrate concentration increases, the reaction rate approaches saturation. This saturation indicates that the enzyme is fully occupied, preventing further increases in reaction velocity. Accurate comparisons of reaction rates require constant conditions for other variables like temperature and pH.

Initial Velocity

In this video, we're going to talk a lot more about the initial velocities of enzyme catalyzed reactions. As we already know from our previous lesson videos, when biochemists study enzyme catalyzed reactions in a lab, they mainly focus on the initial rates of the enzyme catalyzed reactions. A lot of this has to do with the fact that enzyme catalyzed reaction rates naturally decrease over time. The reason these enzyme catalyzed reactions proceed over time has to do with the fact that the substrate concentration is also decreasing over time. Remember, higher substrate concentration is correlated with a higher reaction rate, and so a lower substrate concentration is correlated with a lower reaction rate. The reason that the substrate concentration is decreasing over time is because the substrate is literally being converted into products over time. Additionally, the reverse reaction from the product backwards to reform the substrate becomes more significant as a concentration accumulates over time. If this reverse reaction becomes more of a factor over time, it's going to make it more difficult for a biochemist to measure the forward reaction rate if the reverse reaction is occurring at a significant rate.

The initial velocity, abbreviated as \( v_0 \), is the reaction velocity at the very beginning of a reaction when the substrate concentration is at its highest and the reverse reaction from product back into substrate is essentially negligible since there is really zero or no product at the very beginning of a reaction. Essentially, what we're saying here is that the initial velocity, \( v_0 \), is really the best chance that a reaction has at approaching its maximum velocity, \( v_{\text{max}} \), which we're going to talk a lot more about in another video later in our course. We will be able to talk about this idea of approaching its maximum velocity in more detail in that video. But just to give you a quick preview, enzymes are not able to attain their maximum velocities; they are only able to approach their maximum velocities. We'll talk more about that idea in a different topic when we talk about maximum reaction velocity.

But for now, let's take a look at this example down below and in this example we actually have two different graphs. We have this graph over here on the left and then we have this graph over here on the right. Now, looking at the graph on the left first, notice that we have the product concentration on the y-axis and the time as the reaction progresses on the x-axis, and we've seen this graph plenty of times in our previous lesson videos. We know that the curve looks just like this, and ultimately we know that the product concentration stops increasing over time, and that's because at the equilibrium, we know that the product concentration has gotten to a point where equilibrium has been reached. At equilibrium, we know that the rate of the forward reaction is exactly equal to the rate of the reverse reaction. However, if we look at the very beginning of the reaction, where the time is really close to zero, and we know that if we take the slope of a line that's tangent to any point on this curve, we can get the reaction rate. If we take the slope of the line early on in this curve, we can get the initial reaction rate because we have the initial slope. This initial slope of our curve is going to give us the initial reaction rate, and the reaction rate is always going to be the change in product concentration over the change in time.

Looking at this graph over here on the right, notice the instructions are telling us to draw in the curve for the second graph below. So there is no curve and we need to draw the curve in. Notice that the y-axis is actually changing. It's very important for us to note what these y-axes actually are. In this y-axis what we have is the reaction rates, and on this one, we have the product concentration. Over time, as we already discussed above, we know that reaction rates naturally decrease over time. So we expect the reaction rate here is actually going to decrease over time. It's going to start really high but then ultimately, it's going to decrease as time progresses. This curve should look like a decreasing slope over time.

What this means is that the initial reaction rate, \( v_0 \), is the fastest possible rate. The initial reaction rate occurs where we have the initial time, and the initial time is where the time is approximately equal to zero, really early on. This is where we can expect to find our initial reaction rate really early on in the reaction. So this is our \( v_0 \) and that’s why we expect the initial reaction rate to be the fastest rate. It's important to note that all of the enzyme kinetics calculations we're going to see in our course moving forward from this point are going to assume that the reaction velocity measured is the initial velocity, \( v_0 \). Essentially, because the initial velocity allows us to approach the maximum velocity, it makes it easier to compare reaction velocities across different enzyme catalyzed reactions when we’re specifically focusing on the initial velocity. If we weren't comparing the initial velocities, it would be very difficult to compare reaction velocities across different enzyme catalyzed reactions.

This concludes our lesson on initial reaction velocity, and we’ll be able to apply all of these concepts that we’ve learned here as we move along in our course. I'll see you guys in our next lesson video where we'll be able to talk about the enzyme kinetics plots.

Initial Velocity

Alright. So from our previous lesson video, we know that biochemists mainly focus on the initial reaction velocities of enzyme-catalyzed reactions. In this video, we're going to talk about a plot that biochemists commonly use to measure those initial reaction velocities, known as an enzyme kinetics plot. An enzyme kinetics plot graphs the initial reaction velocity of an enzyme-catalyzed reaction, or \( v_0 \), on the y-axis, and plots the substrate concentration on the x-axis. If we take a look at our image on the left hand side, you'll see an enzyme kinetics plot. Notice we have the initial reaction velocity plotted against the substrate concentration. If we follow it and make a curve, it makes a curve that looks really similar to the previous curves that we saw. However, we need to take into account what's actually on the x-axis, as simple as it might sound. You'll notice is that the x-axis shows the initial substrate concentration. In contrast to our previous graph which showed time in seconds on the x-axis. This means that in the previous graph, we monitored the progress of the reaction over time, but here, we are monitoring different reactions that have different substrate concentrations. It's essential to understand that the initial reaction velocity, or \( v_0 \), can only occur at a very specific period and very early on at the beginning of the reaction. This means we cannot monitor the initial reaction velocity over time because it would no longer be the initial velocity.

On an enzyme kinetics plot, time cannot be on the x-axis when including the initial reaction velocity. Instead of seeing this graph as a solid line, notice that we have individual data points instead. While textbooks might show a solid line, in reality, these data points come from completely separate experiments. Imagine there's one experiment in a test tube where a biochemist chooses a low initial substrate concentration, measures the initial reaction, and plots that data point. In a different test tube, the biochemist might increase the substrate concentration slightly, measure the reaction rate, and plot that data point. After collecting many data points, a curve of best fit is drawn, which you typically see in textbooks. However, drawing a solid line can be misleading as it suggests monitoring the initial reaction rate over time, which is not the case since time is not on the x-axis.

Also, note that the y-axis is different. In this graph, we have the initial reaction rate, unlike the product concentration seen in other charts. This discrepancy in axes leads to different interpretations when the graph levels out. The leveling out below signifies enzyme saturation, quite distinct from reaching equilibrium as might be interpreted in other settings where the product concentration levels out.

We also observe graphs comparing the initial reaction rate with the reaction rate after 30 seconds. The data shows that the reaction rate after 30 seconds is less than the initial reaction rate at corresponding substrate concentrations. Biochemists focus on initial reaction velocities rather than velocities at later times, like 30 seconds in, to ensure accurate representation of maximum velocity.

It's crucial that the initial reaction velocity varies with substrate concentration when other variables influencing the reaction rate, like temperature, pH, and enzyme concentration, are constant. Ensuring consistency across separate experiments allows for accurate comparisons between data points. This lesson has emphasized the importance of understanding the axes on enzyme kinetics plots, which dictate interpretation and will be revisited throughout our course in practice sessions. I'll see you guys there.

Why is the initial velocity (V₀) the best chance a reaction has at approaching its maximum velocity (V_max)?

• A. [Substrate] decreases over time.
• B. Reverse reaction from Reactant ← Product becomes more significant over time.
• C. Reaction rates increase over time.
• D. a and b.
• E. All the above.

Calculate the initial reaction rate for A → B, given that [A] _i = 9.6 M, [B] _i = 0 & [A] _f after 0.01 μsec = 9.14 mM.

• A. 46 M/s.
• B. 959 M/s.
• C. 9.59 x 10⁸ M/s.
• D. 4.6 x 10⁷ M/s.

In the graph below, why does the curve have a steep incline at first that gradually declines to a horizontal line?

• A. Because the substrate becomes an inhibitor at high concentrations.
• B. Because the substrate is able to stimulate the enzyme at low concentration.
• C. Because the transition state complex is more unstable at low substrate concentrations.
• D. Because the available enzyme is saturated with substrate at high enough concentrations.
• E. Because the Gibbs free energy approaches zero at high substrate concentrations.

Here’s what students ask on this topic:

What is the significance of initial velocity (v0) in enzyme kinetics?

Initial velocity (v0) is crucial in enzyme kinetics because it represents the reaction rate at the very beginning of the reaction when substrate concentration is highest. This allows for the measurement of the maximum potential reaction rate (vmax) before the substrate concentration decreases and the reverse reaction becomes significant. By focusing on v0, biochemists can more accurately compare the catalytic efficiencies of different enzymes under consistent conditions, such as constant temperature and pH.

How do enzyme kinetics plots help in understanding enzyme activity?

Enzyme kinetics plots graph the initial reaction velocity (v0) against substrate concentration. These plots help in understanding how the reaction rate changes with varying substrate concentrations. As substrate concentration increases, the reaction rate also increases until it approaches a maximum velocity (vmax), indicating enzyme saturation. This helps in determining key kinetic parameters like Km (Michaelis constant) and vmax, which are essential for characterizing enzyme activity and efficiency.

Why do biochemists focus on initial reaction velocities instead of reaction rates at later times?

Biochemists focus on initial reaction velocities because they provide the most accurate measure of an enzyme's catalytic potential. At the beginning of the reaction, substrate concentration is highest, and the reverse reaction is negligible. This allows for a clearer understanding of the enzyme's maximum reaction rate (vmax). Measuring reaction rates at later times can be misleading due to decreasing substrate concentrations and increasing product concentrations, which can affect the reaction rate and complicate comparisons between different enzyme-catalyzed reactions.

What factors must be kept constant when measuring initial reaction velocities in enzyme kinetics experiments?

When measuring initial reaction velocities (v0) in enzyme kinetics experiments, it is crucial to keep several factors constant to ensure accurate and comparable results. These factors include temperature, pH, and enzyme concentration. Any variation in these conditions can affect the reaction rate, making it difficult to compare the initial velocities of different reactions. By maintaining constant conditions, biochemists can reliably assess the catalytic efficiency and kinetic parameters of enzymes.

How does substrate concentration affect the initial reaction velocity in enzyme-catalyzed reactions?

Substrate concentration significantly affects the initial reaction velocity (v0) in enzyme-catalyzed reactions. At low substrate concentrations, the reaction rate increases linearly with increasing substrate concentration. However, as substrate concentration continues to rise, the reaction rate approaches a maximum velocity (vmax) and levels off. This plateau occurs because the enzyme becomes saturated with substrate, meaning all active sites are occupied, and adding more substrate does not increase the reaction rate further. This relationship is described by the Michaelis-Menten equation.