Experimental Biochemistry

425 Pages·1999·3.384 MB·English

by  Robert L. Switzer, Liam F. Garrity

572 SWI 3rd ed.
CONTENTS

Section I Basic Techniques of Experimental Biochemistry 1
Introduction 3
Experiment 1 Photometry 15
Experiment 2 Chromatography 25
Experiment 3 Radioisotope Techniques 45
Experiment 4 Electrophoresis 61
Section II Proteins and Enzymology 79
Introduction 81
Experiment 5 Acid-Base Properties of Amino Acids 105
Experiment 6 Sequence Determination of a Dipetide 111
Experiment 7 Study of the Properties of ß-Galactosidase 123
Experiment 8 Purification of Glutamate Oxaloacetate Transaminase from Pig Heart 135
Experiment 9 Kinetic and Regulatory Properties of Aspartate Transcarbamylase 149
Experiment 10 Affinity Purificaiton of Glutathione-S-Transferase 157
Section III Biomolecules and Biological Systems 163
Introduction 165
Experiment 11 Microanalysis of Carbohydrate Mixtures by Isotopic Enzymatic, and Colorimetric
Methods 195
Experiment 12 Glcose-1-Phosphate: Enzymatic Formation from Starch and Chemical
Characterization 205
Experiment 13 Isolation and Characterization of Erythrocyte Membranes 217
Experiment 14 Electron Transport 227
Experiment 15 Strudy of the Phosphoryl Group Transfer Cascade Goferning Glucose Metabolism
Allosteric and Covalent Regulation of Enzyme Activity 243
Experiment 16 Experiments in Clinical Biochemistry and Metabolism 253
Section IV Immunochemistry 261
Introduction 263
Experiment 17 Partial purification of a Polyclonal Antibody, Determination of Titer, and
Quantitation of an Antigen Using the ELISA 279
Experiment 18 Western Blot to Identify an Antigen 291
Section V Nucleic Acids 301
Introduction 303
Experiment 19 Isolation of Bacterial DNA 333
Experiment 20 Transformation of a genetic Character with Bacterial DNA 339
Experiment 21 Constructing and Characterizing a Recombinant DNA Plasmid 345
Experiment 22 In Vitro Transcription from a Plasmid Carrying a T7 RNA Polymerase-Specific
Promoter 359
Experiment 23 In Vitro Translation: mRNA tRNA, and Ribosomes 369
Experiment 24 Amplification of a DNA Fragment Using Polymerase Chain Recation 385
Section VI Information Science 397
Introduction 399
Experiment 25 Obtaining and Analyzing Genetic and Protein Sequence Information via the World
Wide Web, Lasergene, and RasMol 405
Appendix Supplies and Reagents 409
Index 437
q /
SECTION I
Basic Techniques of
Experimental Biochemistry
Introduction
Biochemistry is the chemistry of biological sys- in biochemistry. However, students will find that a
tems. Biological systems are complex, potentially review of the basic principles and units used in the
involving a variety of organisms, tissues, cell types, quantitative aspects of experimental biochemistry is
subcellular organelles, and specific types of mole- quite useful. This section is intended to provide
cules. Consequently, biochemists must separate such a review. In addition, it is valuable for students
and simplify these systems to define and interpret to understand the methods often used in experi-
the biochemical process under study. For example, mental biochemistry. Experiments 1 to 4 of this
biochemical studies on tissue slices or whole or- section deal specifically with these techniques: spec-
ganisms are followed by studies on cellular systems. trophotometry, chromatography, radioisotope trac-
Populations of cells are disrupted, separated, and ing, and electrophoresis. Finally, it is imperative
their subcellular organelles are studied. Biological that students understand the intricacies of data
molecules are studied in terms of their specific analysis. The final part of this Introduction dis-
mechanisms of action. By dividing the system un- cusses the principles underlying the basics of sta-
der study and elucidating the action of its compo- tistical analysis that are critical to the ability to de-
nent parts, it is possible to then define the func- termine the precision or error associated with
tion of a particular biological molecule or system quantitative data obtained in biochemical experi-
with respect to the cell, tissue, and/or organism as ments.
a whole.
Biochemical approaches to the simplification
Requirements for a Student of
and understanding of biological systems require
two types of background. First, biochemists must Experimental Biochemistry
be thoroughly skilled in the basic principles and
techniques of chemistry, such as stoichiometry, This course is aimed at developing your interest in
photometry, organic chemistry, oxidation and re- and understanding of modern biochemical and
duction, chromatography, and kinetics. Second, molecular biological experimentation. This goal
biochemists must be familiar with the theories and necessitates a careful emphasis on the experimen-
principles of a wide variety of biological and phys- tal design, necessary controls, and successful com-
ical disciplines often used in biochemical studies, pletion of a wide variety of experiments. This goal
such as genetics, radioisotope tracing, bacteriology, will require additional efforts if you are to benefit
and electronics. This need reflects the biochemists’ fully from Experimental Biochemistry. First, you
ready acceptance and use of theories and techniques should familiarize yourself with general back-
from allied areas and disciplines. ground material concerning each experiment.
It is not possible or appropriate for this book to Three elements have been incorporated into the
summarize the many disciplines and principles used text to aid you in this effort: (1) Each experiment
3
4 SECTION I Basic Techniques of Experimental Biochemistry
is preceded by a short introduction designed to aid data, such as computer-derived graphs, chro-
you in understanding the various theories and tech- matograms, dried SDS-PAGE gels, and pho-
niques underlying the exercises. (2) The experi- tographs.
ments are divided into sections that deal with a spe- 2. Never record your data on separate sheets of
cific class of biological molecules. The introduction paper. Rather, record all your data directly in
preceding each section will serve as a review to pro- your notebook. You may consider using one
vide you with enough information to understand side of the notebook for raw data and calcula-
the experiments. This material is intended to rein- tions and the other side for results and inter-
force and supplement the knowledge you have pretation.
gained from biochemistry lecture courses and text- 3. All graphs and tables must be clearly and un-
books of general biochemistry, which you should ambiguously labeled. Be particularly careful to
review as needed. (3) Each experiment is followed specify units on the ordinate (y-axis) and ab-
by a set of exercises and related references that will scissa (x-axis) of every graph.
allow you to further develop your interest and un- 4. The laboratory report for all experiments
derstanding of a particular method, technique, or should include:
topic.
a. a brief statement of purpose (why you are
Second, you must keep in mind that the ability
doing the experiment and what you wish to
to complete the experiments within allocated times
determine);
requires you to be familiar with the protocol of the
b. a brief account of the theory and design of
experiment before the start of the laboratory session.
the experiment, including a summary or
Each of the experiments contains a detailed, class
flow chart of the principal manipulative
tested, step-by-step protocol that will enable you to
steps;
perform, analyze, and interpret the experiments on
c. the raw data;
your own. Your success will depend on your ability
d. all calculations (if analysis requires a single,
to organize and understand the experimental pro-
repetitive calculation, a sample calculation
cedures, making efficient use of your time.
for one of a series is acceptable);
Third, efficient use of Experimental Biochemistry
e. results;
requires that you perform and interpret many cal-
f. conclusions and interpretations (the infor-
culations during the course of the laboratory sessions.
mation that you can derive from the results
Specifically, laboratory work for introductory bio-
of the experiment).
chemistry, unlike many introductory laboratory
courses, frequently requires you to use the results As stated earlier, all the experiments in this text-
of one assay to prepare and perform additional as- book have been class tested by hundreds of students.
says. Thus, you will have to understand fully what The experiments, therefore, show a high rate of
you are doing at each step and why you are doing success. Still, there may be times when your exper-
it. imental results are not particularly useful, or when
Finally, it is imperativethat you maintain a com- they yield unexpected results that require an expla-
plete research notebook containing all your data, nation. If this is the case for a particular experiment,
calculations, graphs, tables, results, and conclu- discuss in the results section of your laboratory re-
sions. Your notebook should be so clear and com- port what may have gone wrong. Did you make an
plete that anyone can quickly understand what was improper dilution of one of the reagents? Did you
done and what results were obtained. Your instruc- accidentally omit one of the experimental steps? In
tor may provide additional specific instructions for the conclusion section, discuss what you may have
your laboratory reports; the following suggestions expected to see if the experiment had been suc-
may be helpful: cessful. Your knowledge of the theory underlying
the techniques, along with your understanding of
1. Use a large, bound notebook, preferably one the experimental protocol, should be sufficient to
with gridded pages. Such notebooks permit allow you to determine what type of data you may
the direct construction of data tables and allow have obtained under ideal conditions. By doing this,
you to attach records of primary accessory you are likely to turn what appears to be a failed
SECTION I Introduction 5
experiment into a valuable learning opportunity. It side the laboratory. When working with radioiso-
is never sufficient to say, “the experiment did not topes such as 32P, it is necessary to check your hands
work.” Attempt to understand why a particular ex- and shoes with a Geiger counter before leaving the
periment may not have worked as expected. laboratory.
The laboratory will be equipped with safety
showers, eyewash stations, emergency exits, sharps
Laboratory Safety containers, and fire extinguishers. Take the time to
become familiar with the location of all of these
Experimental Biochemistry employs the use of po- safety components. All “sharps” (razor blades, Pas-
tentially hazardous reagents. Strong acids, strong teur pipettes, broken glass, etc.) should be placed
bases, volatile compounds, flammable compounds, in the labeled “sharps” containers. Your laboratory
mutagenic compounds, corrosive compounds, ra- supervisor will instruct you on the proper use and
dioisotopes, electricity, and sharp objects are the disposal of all hazardous reagents. If you do become
tools of the biochemist. Like any other tool, these injured or have any questions about your health risk
are hazardous only when handled improperly. At during the course of the experiment, immediately
the beginning of each experimental protocol, we notify the laboratory instructor. Most laboratory
draw your attention to potential hazards that may supervisors have had training in dealing with fires
be associated with a particular reagent you are about and exposure to different chemicals. Have fun with
to use. the experiments, be safe, and always leave a clean
Safety goggles/glasses must be worn in the lab- laboratory workbench for the beginning of the next
oratory at all times. The main purpose of eye pro- laboratory session.
tection is to prevent chemical damage to the eye.
Laboratory eye protection should also be shatter-
Units of Biochemistry
proof to protect against debris that would be pro-
duced from broken glass in the event of an acci-
dent. Although you may feel confident that you will Biochemistry employs a decade system of units
not be the cause of such an accident, it is impossi- based on the metric system. Thus, biochemists use
ble to ensure that your laboratory partner or neigh- units such as the mole or the liter and various sub-
boring groups will not have accidents. divisions that differ by three orders of magnitude
It is advised that you wear latex or vinyl exam (Table I-1). With knowledge of the molecular
gloves at all times in the laboratory. Even if a par- weight of a particular molecule and equation I-1, a
ticular experiment does not require the use of haz- given mass of a molecule can be converted to units
ardous chemicals, one can never be sure that those of moles:
from a previous experiment have been properly dis-
posed of. If volatile compounds are used, they (I-1)
should be stored under a fume hood at all times. If number of grams of molecule
Number of moles(cid:2)(cid:5)(cid:5)(cid:5)(cid:5)
possible, students should work with these materials molecular weight of molecule
under the fume hood as well. The large amounts of
materials that are often required for a laboratory As indicated in Table I-1, grams may be converted
group may soon fill the room with unpleasant and to milligrams and moles can be converted to mil-
potentially hazardous vapors. This is particularily limoles simply by multiplying each of the appro-
important if the reagent vapors are flammable (see priate values by 103. For example, 0.025 mol of a
Experiment 6) or radioactive (see Experiment 12). molecule is equal to 25 mmol:
Laboratory coats may be worn if desired. It is a
good idea to wear them when working with ra- 103 mmol
0.025 mol(cid:3)(cid:5)(cid:5)(cid:2)25 mmol
dioisotopes, since very small quantities of a ra- 1 mol
dioactive solution can carry a significant amount of
activity. It is also a good idea to wash your hands Volume and mole values define the concentration
thoroughly with soap before leaving the laboratory terms of molar (M), millimolar (mM), and micro-
to ensure that you do not take any chemicals out- molar ((cid:4)M) as shown in equation I-2:
6 SECTION I Basic Techniques of Experimental Biochemistry
Table I-1 Basic Units Used in Biochemistry
Mole Units Liter Units
1 mole 1 liter
1 millimole (mmol)(cid:2)10(cid:6)3moles 1 milliliter (ml)(cid:2)10(cid:6)3liter
1 micromole ((cid:4)mol)(cid:2)10(cid:6)6moles 1 microliter ((cid:4)l)(cid:2)10(cid:6)6liter
1 nanomole (nmol)(cid:2)10(cid:6)9moles 1 nanoliter (nl)(cid:2)10(cid:6)9liter
1 picomole (pmol)(cid:2)10(cid:6)12moles
Gram Units Equivalent Units
1 gram 1 equivalent (Eq)
1 milligram (mg)(cid:2)10(cid:6)3g 1 milliequivalent (mEq)(cid:2)10(cid:6)3Eq
1 microgram ((cid:4)g)(cid:2)10(cid:6)6g 1 microequivalent ((cid:4)Eq)(cid:2)10(cid:6)6Eq
1 nanogram (ng)(cid:2)10(cid:6)9g
1 picogram (pg)(cid:2)10(cid:6)12g
1 femtogram (fg)(cid:2)10(cid:6)15g
(I-2) of water or dilute aqueous solution weighs approx-
number of moles imately 1 g and occupies 1 cc of volume (1 ml(cid:2)
Concentration (molar)(cid:2)(cid:5)(cid:5)
volume (in liters) 1.000027 cc).
These simple interrelationships of moles,
Concentration (millimolar)(cid:2)
weights, volumes, and so forth are often covered in
number of millimoles number of micromoles introductory or freshman level college chemistry
(cid:5)(cid:5)(cid:5)(cid:2)(cid:5)(cid:5)(cid:5)
volume (in liters) volume (in milliliters) textbooks. Yet, practical experience reveals that
these basic concepts are a major source of difficulty
Concentration (micromolar)(cid:2)
for many students in their initial exposure to ex-
number of micromoles number of nanomoles
(cid:5)(cid:5)(cid:5)(cid:2)(cid:5)(cid:5)(cid:5) perimental biochemistry. Therefore, we strongly
volume (in liters) volume (in milliliters) suggest that students thoroughly review these con-
cepts before conducting the experiments described
Similarly, volume and equivalent values define
in this textbook.
the concentration term of normality (N) commonly
used in the expression for acid (H(cid:7)) or base (OH(cid:6)) Analysis and Interpretation of
strength, as indicated by equation I-3:
Experimental Data
(I-3) In nearly all of the experiments outlined in this text-
book, you will be asked to collect, analyze, and in-
Concentration (normal)(cid:2)
terpret experimental data. Whether you are deter-
number of equivalents number of milliequivalents mining the concentration of a molecule in an
(cid:5)(cid:5)(cid:5)(cid:2)(cid:5)(cid:5)(cid:5)(cid:5)
volume (in liters) volume (in milliliters) unknown solution, the activity of an enzyme, the
absorbance of a solution at a particular wavelength,
Because these units involve basic metric princi- or the activity of a particular isotope in a biologi-
ples, one can make use of the metric interconver- cal sample, the exercise will require you to perform
sions of mass (grams), fluid volumes (liters or mil- a quantitative measurement and calculate a specific
liliters), and spatial volumes (cubic centimeters, cc). value. There are several questions that frequently
Specifically, under most laboratory conditions, 1ml arise during the analysis of experimental data: How
SECTION I Introduction 7
do you determine the level of precision of a set of In performing an assay, the biochemist aims for
measurements? How many data values or trials of accuracy. An assay method is accurate when the
an experiment must you perform before a mea- chance is high that its result will be quite close to
surement can be deemed precise? If you have a sin- the true value being measured. Since individual as-
gle value in a data set that is not in agreement with say results invariably fluctuate, an accurate assay
other members of the set, how do you determine method must be (1) highly precise (equivalently, re-
whether it is statistically acceptable to ignore the producible), having little variability when repeated,
aberrant value? In the subsections below, each of and (2) nearly unbiased, meaning that almost all of
these issues is addressed. the time the average result from a large number of
repeated assays of the same sample must be very
close to correct. Conversely, an assay method can
Accuracy, Precision, and Bias of a
be poor because it is imprecise, biased, or both. For
Quantitative Measurement
instance, a highly reproducible assay based on a very
When interpreting laboratory data, it is important poorly calibrated instrument may yield almost the
to recognize that individual measurements, such as same, but grossly incorrect result, every time it is
the concentration of a biological molecule observed applied to a given sample. Another assay may be
in an assay, are never entirely accurate. For instance, unbiased but also never close to correct, because its
the serum cholesterol measured by a medical labo- frequently large overestimates are balanced out by
ratory from a blood sample is not the exact average equally large and frequent underestimates.
serum cholesterol in the patient’s blood at the time The above concepts become more precise when
the sample was drawn. There are a number of rea- expressed mathematically. Let the Greek letter (cid:4)
sons for this, the most obvious being that choles- represent the true characteristic of a sample that we
terol may not have been quite uniformly mixed are trying to measure, and suppose the n observa-
throughout the bloodstream. The patient’s blood tions x, i(cid:2)1, . . . , n, represent the results of en-
i
and the sample drawn from it are never totally ho- tirely separate executions of an assay procedure.
mogeneous, the reagents used in the test are never Then (x (cid:6)(cid:4)) is the error of the ith assay. If we
i
totally pure or totally stable if repeatedly used, and square these errors and take their arithmetic mean,
the calibration of the autoanalyzer is never exactly we obtain the mean squared error(cid:2)(1/n)(cid:8)(x (cid:6)(cid:4))2
i
correct or totally stable. Even such small deviations of the group of nrepetitions. If we could repeat the
from the ideal execution of the assay may some- assay an extremely large number of times, so that
times noticeably affect the results, and additional nis very large, the average result (cid:2)x(cid:2)(1/n)(cid:8)xiwould
undetected errors in execution sometimes produce eventually stabilize at a limiting value X(cid:2), the “long-
substantial errors. For these reasons, carrying out run” average value of the assay for the given sam-
the same experiment more than once, or even re- ple. The mean squared error would similarly stabi-
peatedly assaying the same sample, is bound to pro- lize at a value, MSE, that can be used as an index
duce somewhat different numerical results each of the assay’s inherent accuracy. In principle, a per-
time. fect assay method has MSE(cid:2)0 for all samples, but
Now, although the quantity being measured is no such assay exists. The bias of the assay is ((cid:2)X(cid:6)
a property of the particular sample under study, the (cid:4)) and its square, ((cid:2)X(cid:6)(cid:4))2, is a component of the
degree of expected fluctuation from one measure- MSE. The difference MSE(cid:6)Bias2(cid:2)MSE(cid:6)
ment to another depends most fundamentally on ((cid:2)X(cid:6)(cid:4))2(cid:2)(cid:9)2 is a measure of inherent variability
the measurement process itself—that is, how the of the assay, known as its variance. While we can
assay is conducted—rather than on the particular never determine the variance of an assay exactly, be-
sample. Since, depending on the circumstances, the cause that would require performing the assay an
amount of fluctuation among attempts to measure impossibly large number of times, we can estimate
the same quantity may be trivial or crucially im- it by
portant, we now consider briefly some basic con-
cepts that help the biochemist deal with variability 1
among measurements. s2(cid:2)(cid:5)n(cid:6)1 (cid:3)(xi(cid:6)(cid:2)x)2
8 SECTION I Basic Techniques of Experimental Biochemistry
known technically as the sample variance.By taking provement in precision obtained by replicating an
its square root, assay n times is a reduction in the SD by a factor
of [1(cid:6)(1/(cid:6)(cid:2)n)], meaning that two repetitions yield
s(cid:2)(cid:4)(cid:5)(cid:5)n(cid:6)11(cid:5)(cid:3)(cid:5)(cid:5)(x(cid:5)i(cid:5)(cid:6)(cid:5)(cid:2)x)(cid:5)2 a4b2o%u tr ead 2u9c%tio nre, dauncdt ifoonu ri nr eSpDet,i ttihonrese a r5e0p%eti trieodnusc a-
tion. However, the reduction obtained by A rel-
n(cid:7)1
we obtain a measure of variability in the same units ative to that achieved by A is [1(cid:6)((cid:6)(cid:2)n/(cid:6)(cid:2)n(cid:2)(cid:7)(cid:2)1)],
n
as the individual assay results. This measure of
or 18%, for three versus two repetitions, 13% for
fluctuation among repeated assays is known as the
four versus three, and 11% for five versus four.
sample standard deviation, abbreviated SD. The
Thus, the relative benefit of each additional repe-
mean, x(cid:2), and standard deviation, SD, together tition declines with n, and the comparison of the
represent a compact summary of a group of re-
benefit to the cost of an additional repetition gen-
peated assays. For example, if the absorbance val-
erally becomes less favorable to additional repeti-
ues of three identically prepared solutions at a
tions as n increases. Nevertheless, in principle any
particular wavelength are determined to be 0.50,
desired level of precision may be achieved by using
0.44, and 0.32, then their mean value is x(cid:2)(cid:2)0.42 enough repetitions, although the extra repetitions
and their SD is
will not change the bias of the assay.
The quantity s2/n, which represents the vari-
(cid:4)(cid:5)0.082(cid:7)0.0(cid:5)22(cid:7)0.102
s(cid:2) (cid:5)(cid:5)(cid:5)(cid:2)(cid:6)(cid:2)0.(cid:2)00(cid:2)8(cid:2)4(cid:2)(cid:2)0.09 ability among arithmetic means (i.e., simple aver-
2
ages) of n repetitions, is known as the standard
error of the mean, and is abbreviated either as SEM
It is common to report such results as x(cid:2)(cid:10)SD, for
or SE. Results of assays involving n repetitions,
example, 0.42(cid:10)0.09, although this notation can
such as the absorbance results reported earlier as
lead to some unfortunate confusion, as we shall see
x(cid:2)(cid:10)SD(cid:2)0.42(cid:10)0.09 are also frequently reported
below.
as (cid:2)x(cid:10)SE, which in this case is 0.42(cid:10)
(0.09/(cid:6)(cid:2)3)(cid:2)0.42(cid:10)0.05. Confusion can arise if ei-
Precision of a Replicated Assay
ther this (cid:2)x(cid:10)SE or the (cid:2)x(cid:10)SD format is used with-
Intuitively, it seems that one way to improve the ac- out specific indication of whether it is SD or SE
curacy of an assay is to do it more than once and that follows the reported mean. The latter is prefer-
take the average of the repetitions as your result. In able whenever the purpose is to represent the pre-
principle, random overestimation and underesti- cision of the assay’s summary result rather than the
mation by the individual results will cancel one an- variability of the individual measurements that have
other out in the average, leaving a more accurate contributed to it. This is almost always the case with
result than can be obtained from only one mea- chemical analyses, and we recommend the (cid:2)x(cid:10)SE
surement. This is true if the assay has been prop- notation, supplemented by the number of repli-
erly calibrated, so that its bias is very low. In that cates, n, for general use. Thus, in the example, we
case, the accuracy of the assay depends almost en- would report an absorbance of 0.42(cid:10)0.05 (SE),
tirely on its precision, which is represented by the from three replications.
SD, with a precise assay having a small SD. Using When faced with a choice between two assays
the SD, we may determine how precision improves you may compare either their SDs, or their stan-
with each additional repetition. Suppose we replace dard errors for any fixed n, to determine which as-
the procedure of a single assay Awith standard de- say is most useful. The more precise assay is gen-
viation sby a new procedure, which involves nrep- erally preferred if biases are similar, assuming costs
etitions of A, with only the average result reported. and other practical considerations are comparable
Call this “improved” assay A . Thus, each single re- as well. In such circumstances, an assay with SD(cid:2)
n
sult of the assay A is an average of n results of A. s(cid:2)0.09 is much preferable to one with s(cid:2)0.36;
n
Though it is beyond the scope of this book to similarly, a triplicate assay procedure with SE(cid:2)
demonstrate, it may be shown that the standard de- 0.02 is greatly preferable to another triplicate pro-
viation of the assay A is just s/(cid:6)n(cid:2). Thus, the im- cedure with SE(cid:2)0.07.
n
SECTION I Introduction 9
For an unbiased assay the SE may also often be Outlying Data Values
used to form a range, centered on the reported as-
say result, that has a known probability of contain- Suppose that you perform an identical assay four
ing the true value (cid:4)for the sample being studied. times and obtain the following values: 0.47, 0.53,
This range, known as a confidence interval, sum- 1.53, and 0.45. Within this small data set, the value
marizes the information that the assay provides of 1.53 stands out as apparently different. If all four
about the sample in a manner that incorporates the of these values are included in the reported assay
underlying fuzziness of our knowledge due to ran- result, we report 0.75(cid:10)0.26 (SE) from four repli-
dom variability in the assay process. For instance, cates. This measurement does not appear particu-
x(cid:2)(cid:10)4.31(cid:3)SE gives a 95% confidence interval for larly precise, since the error associated with the
the true value estimated by a triplicate assay, and measurement is about 35% of its value. By ignor-
x(cid:2)(cid:10)3.19(cid:3)SE gives a 95% confidence interval for ing the apparently aberrant value of 1.53, however,
an assay in quadruplicate. For the triplicate ab- you may report 0.48(cid:10)0.02. It is tempting to as-
sorbance data, we have 0.42(cid:10)4.31(cid:3)0.05(cid:2) sume that the 1.53 must have resulted from a mis-
0.42(cid:10)0.22, or 0.20 to 0.64. In the long-run, 19 of take, and that the latter result is likely more accu-
20 (95%) of such ranges obtained from triplicate rate and far more precise than the former.
assays using the given method will include the true Unfortunately, in many such instances this is falla-
absorbance of the sample, though we cannot say ex- cious, and deleting the apparently outlying number
actly where within the interval that true value lies. results in a less accurate assay result with misrep-
However, for 1 in 20 assays (5%), the true ab- resentation of its precision. The problem results
sorbance will be outside the interval. For a higher from our intuitive inclination to regard the 1.53 as
confidence such intervals may be widened, while in- probably wrong because it is so deviant from the
tervals obtained using a smaller multiplier will ex- other three values, when an alternative plausible ex-
clude the true concentration more than 5% of the planation is that any of the other three values is
times they are employed. The appropriate multi- somewhat, but not unusually, lower than might be
plier of the SEM depends on both n and the de- expected. When three or four numbers are obtained
sired degree of confidence, here 95%. When the from a situation partially governed by chance, it is
SD of an assay is known to good accuracy (e.g. re- not at all unusual for one of them to depart further
ported by an instrument manufacturer based on from the others than intuition might suggest. When
considerable data on the performance of the in- such numbers are deleted, the resulting report may
strument over the range of likely values) confidence be very misleading.
intervals may be constructed using reported rather Yet there are circumstances in which single
than observed variability. These intervals require gross errors contaminate otherwise valid assays, and
smaller multipliers, and hence will tend to be nar- it is desirable to be able to delete such errors and
rower, than those based only on the observed repli- use the remaining repetitions of the assay. How can
cations for an individual assay. The choice of mul- we tell when to delete such outlying values, and
tiplier is beyond the scope of this book. when it is necessary to retain them and accept the
A consequence of the above ideas is a rule of possibility that our assay is less precise than we had
thumb that to obtain adequate precision with some hoped?
assurance that gross error has been avoided, at rea- The first and best approach should be to exam-
sonable cost, you will often be well served to per- ine the assay procedure that was used to try to find
form three or four trials of a single experiment. The an explanation (e.g., a technical error or even a data
experiments outlined in this textbook rarely call for recording error) for the outlying value. If a sub-
such replication, due to time and financial con- stantial technical error is found, then the outlying
straints of the educational process. Remember, how- value may be discarded, and if possible the assay
ever, that a properly designed experiment should be per- should be run again to replace it. If no such expla-
formed multiple times, and that the data should be nation is found, however, we still may wish to dis-
presented with a well-defined statistical analysis to allow card grossly aberrant values rather than repeat the
the reader to ascertain the precision of the experiment. entire set of nrepetitions of the assay. One approach