## Peristaltic Pump

A propelling unit moves the carrier stream through the flow injection analyzer. Although several different propelling units have been used, the most common is a peristaltic pump. As illustrated here, a peristaltic pump consists of a set of rollers attached to the outside of a rotating drum. Tubing from the reagent reservoirs fits between the rollers and a fixed plate. As the drum rotates the rollers squeeze the tubing, forcing the contents of the tubing to move in the direction of the rotation. Peristaltic pumps provide a constant flow rate, which is controlled by the drum’s speed of rotation and the inner diameter of the tubing. Flow rates from 0.0005–40 mL/min are possible, which is more than adequate to meet the needs of FIA where flow rates of 0.5–2.5 mL/min are common. One limitation to a peristaltic pump is that it produces a pulsed flow—particularly at higher flow rates—that may lead to oscillations in the signal.

## Instrumentation for Flow Injection Analysis

The basic components of a flow injection analyzer are shown below and include a pump for propelling the carrier stream and reagent streams, a means for injecting the sample into the carrier stream, and a detector for monitoring the composition of the carrier stream (the detector’s flow cell is shown here; fiber optic cables, which are not shown, connect the flow cell to the detector). Connecting these units is a transport system that brings together separate channels and provides time for the sample to mix with the carrier stream and to react with the reagent streams. We also can incorporate separation modules into the transport system. The particular configuration shown here has two channels: the carrier stream and a reagent line.

## Fiagrams

An FIA curve, or fiagram, is a plot of the detector’s signal as a function of time. The illustration below shows a typical fiagram for conditions in which both convection and diffusion contribute to the sample’s dispersion. Also shown on the figure are several parameters for characterizing a sample’s fiagram.

Two parameters define the time for a sample to move from the injector to the detector. Travel time, ta, is the time between the sample’s injection and the arrival of its leading edge at the detector. Residence time, T, on the other hand, is the time required to obtain the maximum signal. The difference between the residence time and travel time is t′, which approaches zero when convection is the primary means of dispersion, and increases in value as the contribution from diffusion becomes more important.

The time required for the sample to pass through the detector’s flow cell—and for the signal to return to the baseline—also is described by two parameters. The baseline-to-baseline time, Δt, is the time between the arrival of the sample’s leading edge to the departure of its trailing edge. The elapsed time between the maximum signal and its return to the baseline is the return time, ′. The final characteristic parameter of a fiagram is the sample’s peak height, h.

Of the six parameters illustrated here, the most important are peak height and return time. Peak height is important because it is directly or indirectly related to the analyte’s concentration. The sensitivity of an FIA method, therefore, is determined by the peak height. The return time is important because it determines the frequency with which we may inject samples. As illustrated below, if we inject a second sample at a time ′ after injecting the first sample, there is little overlap of the two FIA curves.

By injecting samples at intervals of ′, we obtain the maximum possible sampling rate.

## Flow Profile in Flow-Injection Analysis

When we first inject a sample into an FIA’s carrier stream it has the rectangular flow profile of width w as shown  below in (a). As the sample moves through the mixing zone and reaction zone, the width of its flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes: convection due to the flow of the carrier stream and diffusion due to the concentration gradient between the sample and the carrier stream. Convection occurs by laminar flow. The linear velocity of the sample at the tube’s walls is zero, but the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in (b). Convection is the primary means of dispersion in the first 100 ms following the sample’s injection.

The second contribution to the sample’s dispersion is diffusion due to the concentration gradient between the sample and the carrier stream. As shown in the illustration below, diffusion occurs parallel (axially) and perpendicular (radially) to the direction in which the carrier stream is moving. Only radial diffusion is important in flow injection analysis. Radial diffusion decreases the sample’s linear velocity at the center of the tubing, while the sample at the edge of the tubing experiences an increase in its linear velocity. Diffusion helps to maintain the integrity of the sample’s flow profile, as shown in (c) above, preventing samples in the carrier stream from dispersing into one another. Both convection and diffusion make significant contributions to dispersion from approximately 3–20 s after the sample’s injection. This is the normal time scale for a flow injection analysis. After approximately 25 s, diffusion is the only significant contributor to dispersion, resulting in a flow profile similar to that shown in (d) above.

## Flow-Injection Analysis

Flow injection analysis (FIA) was developed in the mid-1970s as a highly efficient technique for the automated analyses of samples. Unlike a centrifugal analyzer, in which the number of samples is limited by the transfer disk’s size, FIA allows for the rapid, sequential analysis of an unlimited number of samples. FIA is one example of a continuous-flow analyzer, in which we sequentially introduce samples at regular intervals into a liquid carrier stream that transports them to the detector.

A schematic diagram detailing the basic components of a flow injection analyzer is shown here. The reagent serving as the carrier is stored in a reservoir, and a propelling unit maintains a constant flow of the carrier through a system of tubing that comprises the transport system. We inject the sample directly into the flowing carrier stream, where it travels through one or more mixing and reaction zones before reaching the detector’s flow-cell.

This is the simplest design for a flow injection analyzer, consisting of a single channel and a single reagent reservoir. Multiple channel instruments that merge together separate channels, each introducing a new reagent into the carrier stream, also are possible.

## Kinetic Analysis of a Mixture

The figure below illustrates how we can use a kinetic analysis to determine the concentration of two analytes, A and B, provided that there is a difference in their reaction rates. In this example, B reacts more slowly (kB = 0.1 min–1) than A (kA = 1 min–1).

Extrapolating the linear part of the curve back to t = 0 gives ln[B]0 as –2.3, or a [B]0 of 0.10 M. At t = 0, ln[C]0 is –1.2, corresponding to a [C]0 of 0.30 M. Because [C]0 = [A]0 + [B]0, the concentration of A in the original sample is 0.20 M.

## Elucidating Mechanisms for the Inhibition of Enzyme Catalysis

When an inhibitor interacts with an enzyme it decreases the enzyme’s catalytic efficiency. An irreversible inhibitor covalently binds to the enzyme’s active site, producing a permanent loss in catalytic efficiency even if we decrease the inhibitor’s concentration. A reversible inhibitor forms a noncovalent complex with the enzyme, resulting in a temporary decrease in catalytic efficiency. If we remove the inhibitor, the enzyme’s catalytic efficiency returns to its normal level.

There are several pathways for the reversible binding of an inhibitor to an enzyme, as shown here.

In competitive inhibition the substrate and the inhibitor compete for the same active site on the enzyme. Because the substrate cannot bind to an enzyme–inhibitor complex, EI, the enzyme’s catalytic efficiency for the substrate decreases. With noncompetitive inhibition the substrate and the inhibitor bind to different active sites on the enzyme, forming an enzyme–substrate–inhibitor, or ESI complex. The formation of an ESI complex decreases catalytic efficiency because only the enzyme–substrate complex reacts to form the product. Finally, in uncompetitive inhibition the inhibitor binds to the enzyme–substrate complex, forming an inactive ESI complex.

We can identify the type of reversible inhibition by observing how a change in the inhibitor’s concentration affects the relationship between the rate of reaction and the substrate’s concentration. As shown here

when we display kinetic data using as a Lineweaver-Burk plot it is easy to determine which mechanism is in effect. For example, an increase in slope, a decrease in the x-intercept, and no change in the y-intercept indicates competitive inhibition. Because the inhibitor’s binding is reversible, we can still obtain the same maximum velocity—thus the constant value for the y-intercept—by adding enough substrate to completely displace the inhibitor. Because it takes more substrate, the value of Km increases, which explains the increase in the slope and the decrease in the x-intercept’s value.

## Lineweaver-Burk Plots

For an enzyme–substrate reaction following a simple mechanism

E + S ↔ E–S ↔ E + P

consisting of the initial formation of an enzyme–substrate complex, ES, and its subsequent decomposition to form the product, P, and to release the enzyme to react again, the rate of product formation for this reaction is

$\textup{rate}&space;=&space;\frac{d[P]}{dt}&space;=&space;\frac{k_{2}[E]_{0}[S]}{K_{\textup{m}}+[S]}$

where k2 is the rate of the conversion of the enzyme-substrate complex, E–S, to product, [E]0 is the enzyme’s initial concentration, [S] is the substrate’s concentration, and Km is a constant called the Michaelis constant. A plot of this equation is shown here.

As suggested above, we can find values for Vmax and Km by measuring the reaction’s rate at very small and very large concentrations of the substrate. Unfortunately, this is not always practical as the substrate’s limited solubility may prevent us from using the large substrate concentrations needed to determine Vmax. Another approach is to rewrite the reaction’s rate equation by taking its reciprocal

$\frac{1}{dP/dt}=\frac{1}{v}=\frac{K_{\textup{max}}}{V_{\textup{max}}}\times&space;\frac{1}{[S]}+\frac{1}{V_{\textup{max}}}$

where v is the reaction’s rate. As shown below, a plot of 1/v versus 1/[S], which is called a double reciprocal or Lineweaver–Burk plot, is a straight line with a slope of Km/Vmax, a y-intercept of 1/Vmax, and an x-intercept of –1/Km.

## Enzyme Kinetics

Enzymes are highly specific catalysts for biochemical reactions, with each enzyme showing a selectivity for a single reactant, or substrate. For example, the enzyme acetylcholinesterase catalyzes the decomposition of the neurotransmitter acetylcholine to choline and acetic acid. Many enzyme–substrate reactions follow a simple mechanism that consists of the initial formation of an enzyme–substrate complex, ES, which subsequently decomposes to form product, P, releasing the enzyme to react again.

E + S ↔ E–S ↔ E + P

The rate of product formation for this reaction is

$\textup{rate}&space;=&space;\frac{d[P]}{dt}&space;=&space;\frac{k_{2}[E]_{0}[S]}{K_{\textup{m}}+[S]}$

where k2 is the rate of the conversion of the enzyme-substrate complex, E–S, to product, [E]0 is the enzyme’s initial concentration, [S] is the substrate’s concentration, and Km is a constant called the Michaelis constant. A plot of this equation is shown here.

For high concentration of substrate, highlighted in green, the rate equation simplifies to

$\textup{rate}&space;=&space;\frac{d[P]}{dt}&space;=&space;k_{2}[E]_{0}&space;=&space;V_{\textup{max}}$

where Vmax is the reaction’s maximum rate. Under these conditions we can use the reaction’s rate to determine the concentration of enzyme. For small concentrations of substrate, the area highlighted in red, the rate equation simplifies to

$\textup{rate}&space;=&space;\frac{d[P]}{dt}&space;=\frac{k_{2}[E]_{0}[S]}{K_{\textup{m}}}=\frac{V_{\textup{max}}[E]_{0}}{K_{\textup{m}}}$

and we can use the rate to determine the concentration of substrate.