Document1
Page 1
7/28/2017
Understanding Reversible Molecular Binding
GEORGE P. SMITH
GEORGE P. SMITH is Professor Emeritus of Biological Sciences, and was freshman coordinator of the
Mathematics in Life Sciences Program, at the University of Missouri, Tucker Hall, Columbia, MO 65211;
e-mail [email protected].
Abstract
Reversible binding between biomolecules—for example, between a cell-surface receptor such as the
insulin receptor and its corresponding natural ligand such as insulin—is central to innumerable
physiological transactions. Binding of the dye HABA to egg-white avidin is a simple, reliable, and
colorful laboratory model for introducing beginning biology students to the principles underlying
reversible binding. They can probe the reaction quantitatively with a spectrophotometer, and model it
mathematically using only high-school algebra and a spreadsheet program such as Microsoft Excel.
Keywords: receptor, ligand, drug, avidin, biotin, HABA, mass action law, association rate constant,
dissociation rate constant, dissociation equilibrium constant, spectrophotometer, absorbance, absorption
coefficient, parameter estimation, least squares
Recommended for Beginning college biology majors
Document1
Page 2
7/28/2017
Introduction
For 6 years, we offered an alternative freshman biology lab called Mathematics in Life Sciences (MLS)
that emphasized investigation while integrating simple mathematics more intimately into the curriculum.
One of its modules has previously been described in these pages (Smith et al., 2015). Here I describe
another module, in which students explored a reversible molecular binding reaction.
Reversible, non-covalent binding interactions are a ubiquitous component of physiological processes,
both inside and outside cells. A familiar example is the interaction between a cellular receptor and its
natural ligand (the hormone or other biomolecule that naturally binds that receptor). For instance, the
hormone insulin is the natural ligand for the insulin receptor on muscle, liver, and adipose cells. When
insulin engages the receptor, the cell is stimulated to import glucose from the surrounding fluid, thus
lowering blood glucose level. Many drugs also bind reversibly to their targets in the body. Acid-base
equilibria and antibody-antigen reactions are other instances.
In this investigation students explored the binding of the protein avidin to an artificial ligand. In the
module’s first hour, they followed detailed instructions to quantify the reaction. These measurements
were followed by guided student investigation, which spanned ~6 hours of class time spread out over
several weeks and interspersed with other modules, but which can be shortened as needed. In the course
of this investigation, students came to understand the reaction in increasing depth, ultimately modeling it
mathematically using only high-school algebra. Detailed instructor’s guides and teaching materials are
available at a companion website https://mls.missouri.edu/equilibrium-binding/.
Document1
Page 3
7/28/2017
Avidin, Biotin, and HABA
Avidin is a biotin-binding protein in the oviducts of birds, reptiles and amphibians that is deposited in the
whites of their eggs. Its adaptive function isn’t known, but is suspected to be antibiotic: by sequestering
biotin, it slows the growth of microbes that require that vitamin. Because the binding interaction is noncovalent, it’s reversible; avidin and biotin can associate to form the avidin-biotin complex (the forward
reaction), and at the same time the complex can dissociate to release the two individual molecules again
(the reverse reaction). Such systems come to a natural equilibrium state, in which the forward and reverse
reactions exactly balance, so that the net concentrations of the reactants remain constant even though
individual molecules continue to associate and dissociate. In the case of the avidin-biotin interaction,
dissociation is so slow (half-life 6–7 weeks; Green, 1975) and association so fast that actually measuring
them is technically challenging. Super-slow dissociation plus super-fast association = super-super-high
affinity (binding strength).
Avidin consists of 4 identical subunits. Each subunit (molecular mass 16,500 Da) is a polypeptide of 128
amino acids with carbohydrate attached to one of its amino acid side chains. The subunits bind biotin
independently of one another; as far as binding equilibrium is concerned, therefore, each tetramer acts the
same as would four separate monomers. Consequently, avidin concentration is expressed in terms of
individual monomer subunits. Biotin bound to avidin is buried in a deep pocket in the protein’s threedimensional structure (Figure 1).
Document1
Page 4
7/28/2017
Figure 1. Three-dimensional structure of biotin
bound to an avidin subunit (Livnah et al.,
1993b; Protein Data Base accession 2AVI). The
avidin is rendered in a format that traces only
the main backbone of the polypeptide chain.
The biotin is rendered in space-filling format.
HABA is a dye that binds reversibly to avidin with weak affinity, inhabiting the same binding pocket as
does biotin (Green, 1965; Livnah et al., 1993a). Avidin-HABA binding results in a dramatic change in
HABA’s spectral properties that’s easy to measure with a spectrophotometer. Whereas HABA dissolved
in aqueous solution absorbs light maximally at a wavelength max = 348 nm, and has a pale yellow color;
the avidin-HABA complex absorbs light maximally at max = 500 nm, and has a bright red color. The
avidin-HABA system is an attractive experimental model for introducing students to binding interactions
(e.g., Ninfa et al., 2010).
Performance and Results
Before the first session (100 min), students read a handout covering the information in the first two
sections of this article. This prepared them to participate in discussion during the session.
Document1
Page 5
7/28/2017
Each student was supplied with four 1.5-mL microtubes containing exactly 1.2 mL of HABA at a
particular concentration in buffer (Table 1); the HABA concentrations for different students ranged from
1.1 to 100 µM in logarithmic progression. Each student was also supplied with a 500-µL microtube
containing 100 µL of an avidin solution in water (Table 1; the same avidin concentration for all students);
a 500-µL microtube with 100 µL water; a 500-µL microtube with 100 µL biotin at the same concentration
as avidin in the avidin microtube (Table 1); four disposable 1.5-mL polystyrene spectrophotometer
cuvettes (e.g., Fisher 14-955-127); pipetters and tips for pipetting 40- and 1000-µL volumes; access to a
vortex mixer and to a beaker for discarding used disposable labware. All supplies were at room
temperature. A single Jenway model 6705 spectrophotometer adjusted to 500 nm served the entire class;
any comparable instrument can be substituted.
Working as accurately as possible, students pipetted exactly 40 µL water into two of their 1.5-mL
microtubes of HABA (the reference tubes), and exactly 40 µL avidin into the other two 1.5-mL HABA
microtubes (the sample tubes). The microtubes were vortexed (equilibrium is attained almost instantly),
and exactly 1 mL from each was pipetted into a disposable cuvette (two reference cuvettes, two sample
cuvettes). They compared the color in the reference and sample cuvettes visually; the latter should be red
compared to the former, the contrast being more and more pronounced the higher the HABA
concentration. In order to quantify the color change, they took the four cuvettes to the spectrophotometer,
rapidly zeroing with one of the reference cuvettes, reading and recording A500 with one of the sample
cuvettes, zeroing with the other reference cuvette, and reading and recording A500 with the other sample
cuvette. One reference and one sample cuvette were discarded; the other two cuvettes were brought back
to the workbenches, where each student pipetted 40 µL from the biotin microtube into each (a 24 percent
molar excess of biotin over the avidin in the sample cuvette) and stirred the contents with the pipette tip;
Document1
Page 6
7/28/2017
students were forewarned to note any visible color change (the red color should disappear in all sample
cuvettes, regardless of HABA concentration) in anticipation of discussion later in the session. The two
cuvettes (now containing biotin) were brought back to the spectrophotometer, zeroing with the reference
cuvette and reading and recording A500 with the sample cuvette as before.
The foregoing steps consumed ~70 min of lab time; the time could be reduced by skipping the duplicate
reads (only one reference and one sample), and by the instructor doing the post-biotin spectrophotometric
reads after the lab. The module’s investigative phase began immediately in the remaining ~30 min, when
students were asked to explain why the red color disappears after adding biotin, even when the amount of
biotin added is much less than the amount of HABA already in the cuvette. The class as a whole was
always able to arrive at a cogent answer, setting the tone for the entire investigation.
If we think of avidin as a model for a cellular receptor (e.g., a hormone receptor on the surface of a cell),
HABA as a model for that receptor’s natural ligand (e.g., the hormone that binds to and activates the
receptor), and the color change as a model for the physiological effect triggered by receptor engagement;
then biotin could be thought of as a model for a drug that antagonizes the natural ligand, thus blocking its
physiological effect. The antagonist drug occupies the receptor’s binding site, preventing the natural
ligand from binding. The antagonist drug and the natural ligand thus compete for the same binding site
on the receptor. Biotin thought of in this way is an extraordinarily potent antagonist drug because of its
super-high affinity for the target receptor. Competitive inhibitors are a major category of drugs, though
there are many other categories. (Of course, we’re distorting reality to make our analogy here, since the
biotin “antagonist” is actually avidin’s presumed natural ligand.)
Document1
Page 7
7/28/2017
After the lab, the instructor entered the students’ spectrophotometric data (duplicate pre-biotin readings, a
single post-biotin reading for each student) into a spreadsheet such as Microsoft Excel; the spreadsheet
also had the HABA and avidin concentrations during the pre-biotin readings (these are the total input
concentrations of the respective molecules, regardless of whether or not they are bound to a partner). The
spreadsheet document was distributed to the students so they had access to the entire class’s results.
Students were assigned the homework task of graphing the data-points as in Figure 2 (open circles, closed
triangles, and open squares only; other features were created later), using a logarithmic scale for the x-axis
to match the logarithmic distribution of HABA concentrations. This exercise required prior experience
with the spreadsheet program, which in the MLS course occurred in computer labs in previous modules.
An exemplar student worksheet is provided on the companion website.
Figure 2. Results of the binding equilibrium experiment for a
recent semester. The x-axis plots the total input concentration
of HABA molecules, regardless of whether or not they are
bound to an avidin partner. Filled triangles and open circles
represent the duplicate absorbance measurements for each
student (the two outliers at 11 µM HABA were traced to a
defective pipetter, and were not included in the subsequent
analysis). The open squares represent the absorbance
Document1
Page 8
7/28/2017
measurements after adding biotin. The dashed line marks 0
absorbance. The solid curve and the best-fitting KD will be
explained in the section on Parameter Estimation.
Reversible binding studies like that in Figure 2 are ubiquitous in biochemistry, physiology and
pharmacology. In each case, the concentration of a ligand analogous to HABA is varied, and some
binding measurement analogous to A500 is made at each ligand concentration.
Mathematical Model
The 100-minute lab described in the previous section can stand on its own, but in the MLS course it was
followed by an investigative phase (~300 minutes of classroom time) devoted to understanding the
reaction and modeling it mathematically. The instructor’s guides and teaching materials on the
companion website detail the steps by which this was achieved.
Letting A stand for free avidin, B for free HABA, and AB for the avidin-HABA complex (“free” avidin
and HABA are molecules that aren’t part of AB complexes), the reversible binding reaction can be
diagrammed as in Figure 3.
Figure 3. Reversible binding of free
avidin (A) and free HABA (B) to form the
avidin-HABA complex (AB). The upper
and lower expressions represent the
forward (association) and reverse
(dissociation) reactions, respectively.
Document1
Page 9
7/28/2017
Graphing and defining variables
To begin their investigation, students were asked to sketch graphically how the concentration of avidinHABA complex will change with time in the course of one of the binding reactions, starting at its initial
value of 0. With some guidance from the instructor, they were able to come up with something
qualitatively like the ascending curve in Figure 4 (the variable definitions in that graph emerge only later).
Why does the curve flatten out with time, asymptotically approaching an upper boundary? Part of the
reason is that as more and more avidin-HABA complex accumulates, the rate at which complexes
dissociate increases in concert, slowing the overall rate at which the complex accumulates.
Concomitantly, accumulation of avidin-HABA complex also reduces the concentrations of free avidin and
free HABA, slowing the rate at which they can associate to make more complex. Eventually, dissociation
and association reactions come to balance each other; that’s the equilibrium state. These effects are a
qualitative expression of the mass action law (next subsection).
Once a satisfactory graph of complex concentration had been developed, students were asked to sketch
how the free avidin concentration evolves with time on the same graph. The purpose of this task was to
reveal a key stoichiometric constraint: that at any point in time, the amount by which the complex
concentration has increased from its initial value of 0 must equal the amount by which the free avidin and
free HABA concentrations have decreased from their non-zero initial values. The descending avidin and
HABA concentration curves are thus the same as the ascending complex concentration curve flipped
upside down, as depicted in Figure 4.
Document1
Page 10
7/28/2017
Students found it much easier to define the algebraic variables of their mathematical model, and to
express the stoichiometric constraint in the previous paragraph, with the curves sketched in Figure 4 in
hand than without them. Their notation systems were equivalent to the one in this paragraph and in
Figure 4, though the particular choice of algebraic symbols differed. We let a, b and c stand for the
concentrations of free A, free B and AB complex, respectively, at any moment in time (all concentrations
in the lab are expressed in µM units). We call the initial concentrations of free A and free B (before any
binding reactions have occurred) a0 and b0, which equal the known total input concentrations of avidin
and HABA, respectively (the initial concentration of the avidin-HABA complex is 0). The momentary
concentrations a, b and c change with time from their initial values at time 0, ultimately attaining their
final equilibrium values, which we’ll call aeq, beq and ceq, respectively. The stoichiometric constraint in
the previous paragraph implies that at any moment during the reaction, a0 – a = b0 – b = c. The time
course for c thus completely determines the time course for a and b: a = a0 – c and b = b0 – c. As students
develop their own systems of algebraic symbols, the instructor must help them avoid the confusions that
arise from using the same symbol for two different quantities (e.g. using b for both b0 and beq).
Document1
Page 11
7/28/2017
Figure 4. Time course of the binding reaction. At all times, including at
equilibrium, the concentrations must obey the stoichiometric constraint
a0 – a = b0 – b = c.
Mass action law
Applied to the bimolecular forward (association) reaction, mass action implies that the forward reaction
rate at any moment in time is proportional to both a and b at that moment. Using a conventional
abbreviation for the proportionality constant, the forward reaction rate = k1ab, where the value of the
proportionality constant k1 is not specified by the law of mass action. In chemistry, k1 is called the
association rate constant.
Applied to the unimolecular reverse (dissociation) reaction, mass action implies that the reverse reaction
rate at any moment in time is proportional to c at that moment. Using a conventional abbreviation for the
proportionality constant, the reverse reaction rate = k–1c, where the value of the proportionality constant
k–1 is not specified by the law of mass action, and is independent of the value of k1. In chemistry, k–1 is
called the dissociation rate constant.
Document1
Page 12
7/28/2017
From the two rate equations, the entire time course of a reaction (as graphed in Figure 4) can be modeled
with the aid of calculus. In the MLS module, however, we considered only the final equilibrium state,
which can be modeled using high-school algebra.
Equilibrium is attained when the concentrations a, b and c have changed from their initial values (a0, b0
and 0) to final equilibrium values (aeq, beq and ceq) that bring the forward and reverse reaction rates into
balance: k1aeqbeq = k–1ceq. Rearranging,
aeqbeq
ceq

k1
 K D , where the constant KD defined in the second
k1
part of the equation is called the dissociation equilibrium constant, and has units of concentration (here
µM). This equation shows that the equilibrium state doesn’t depend on the magnitudes of the k–1 and k1
rate constants individually, but only on their ratio KD.
The stoichiometric constraints a0  aeq  b0  beq  ceq (Figure 4) allow the unknown variables aeq and beq
to be eliminated, leaving a single unknown variable, ceq, on the left-hand side:
(a0  ceq )(b0  ceq )
ceq
 KD
Equation 1
When students were asked in class to solve Equation 1 for ceq, they found that it is quadratic with solution
ceq 
a0  b0  K D 
a0  b0  K D 2  4a0b0
2
Equation 2
Document1
Page 13
7/28/2017
(The expression inside the radical is non-negative; the quadratic solution with a plus sign preceding the
radical is physically impossible.)
Beer’s law and the absorption coefficient
Students did not measure the complex concentration ceq directly. Instead, they measured A500 (absorbance
at 500 nm), which according to Beer’s law (the subject of a previous module in the MLS course) is
proportional to ceq, the proportionality constant being the complex’s absorption coefficient :

A 500    ceq   
a0  b0  K D 
a0  b0  K D 2  4a0b0
2
Equation 3
Equation 3 gives predicted values of the dependent variable A500 in terms of a known constant (the total
input avidin concentration a0), an independent variable with known values (the total input HABA
concentrations b0), and two constants with unknown values (the dissociation equilibrium constant KD and
the absorption coefficient ). Unknown constants such as KD and  are called parameters; the next section
focuses on using the available data to estimate their values.
Parameter Estimation
If the mathematical model in Equation 3 accurately describes binding equilibrium, there should be values
of its two parameters KD and  that bring the predicted values of the dependent variable A500 into
agreement with the observed values of that dependent variable. Conversely, parameter values that bring
Document1
Page 14
7/28/2017
the model’s predictions into agreement with the observations can be considered estimates of those
parameters. The final session in the MLS binding equilibrium module was a 100-minute computer lab
centered on estimating KD and . Students had already encountered a simpler estimation problem
involving a single parameter, in the Beer’s law module mentioned earlier.
Using the spreadsheet with the observed absorbances A500 for each total input HABA concentration b0
(the open circle and filled triangle data-points in Figure 2; an exemplar spreadsheet is provided on the
companion website), students wrote a formula that gives the mathematical model’s predicted absorbance
for each HABA concentration. The formulae’s predictions were graphed (smooth solid curve in Figure 2)
in order to compare them visually to the observed measurements. The formulae obtained values of the
parameters KD and  from two of the spreadsheet’s cells. Initially, the parameter values in those cells
were just guesses (e.g., KD = 10 µM,  = 0.1 µM–1), and the predicted absorbances in the solid curve
consequently diverged greatly from the corresponding observed absorbances. The students were given
the task of finding values of the parameters that brought the predictions into as close agreement as
possible with the observations. To supplement their visual assessment of agreement, they entered a
formula for a conventional badness of fit criterion in one of the spreadsheet’s cells: S = the sum of the
squares of the deviations of the predictions from the corresponding measurements. Their goal was thus
more clearly defined: to find the optimal pair of parameter values according to the least-squares criterion
(i.e. the pair of values that minimized S). They soon learned that optimizing two parameters
simultaneously by trial and error is a challenging task. In the Beer’s law module, they had been
introduced to least-squares optimization, and learned to use Solver, a Microsoft Excel add-in utility that
automates this task for any number of parameters. The solid curve in Figure 2 is the optimal fit of the
Document1
Page 15
7/28/2017
mathematical model to the data (the two outliers at 11 µM HABA were excluded from the optimization);
the optimal values of KD and  were 5.9 µM and 0.0308 µM–1, respectively.
The foregoing parameter values are estimates, of course, not exact measurements. Suboptimal parameter
values result in systematic deviations from the data, but small deviations may plausibly be attributed to
systematic errors in the data and thus do not convincingly exclude the corresponding parameter values.
Indeed, even the optimal fit deviates systematically from the data to a slight degree. Unsurprisingly,
somewhat different optimal parameter values emerged from the students’ data in different years (optimal
KD 4.9–10.6 µM; optimal  0.0308–0.0352 µM–1). The companion website includes suggestions for an
optional in-class discussion of uncertainty in parameter values.
The fit of the solid curve to the data in Figure 2 seems excellent, its systematic deviations very slight.
That accuracy, in conjunction with the well-established physical principles from which the mathematical
model was developed (mass action and Beer’s law), give us considerable confidence in Equation 3 as an
explanation of the hidden physical processes underlying the observed results. By the same token, we can
be relatively confident of predictions based on that equation. Those predictions are extensive. The model
allows the equilibrium state to be predicted for different concentrations of avidin and HABA than those
actually investigated. Moreover, it is the end-point of an even deeper mathematical model describing the
entire time-course along which the system attains equilibrium (Figure 4).
Document1
Page 16
7/28/2017
Pedagogical Strategy
The lab module described here is an example of “inquiry learning” (e.g., Hmelo-Silver et al., 2007), but
the focus of inquiry was not the physical process of acquiring data; the spectrophotometric measurements
were acquired via step-by-step instructions, as in traditional “cookbook” labs. Inquiry was focused
instead on the mental process of developing scientific understanding from the data, from relevant
scientific principles presented in reading and lectures (e.g., mass action) or expounded in previous
modules (e.g., Beer’s law), and from students’ background knowledge (especially high-school algebra).
The inquiry was highly guided or “scaffolded” (Hmelo-Silver et al., 2007; Kirschner et al., 2006) in
important ways. First, the inquiry evolved in planned stages, each class session and homework
assignment focusing on a restricted part of the overall inquiry. Second, short lectures and readings
introduced specific scientific principles (e.g., the mass action law) just as needed in the inquiry. Third,
prior modules provided worked examples that could be applied to the problem at hand. In particular, the
Beer’s law module not only introduced students to spectrophotometry and to the law itself, but also
included a computer lab in which least-squares optimization was used to estimate the absorption
coefficient parameter; at the same time, that computer lab served to enhance their mastery of the
spreadsheet program.
In spite of extensive guidance, there was a great deal of intellectual distance for students themselves to
traverse. For instance, they had to recognize that their prior module on Beer’s law taught them not just
about the absorption coefficient for the particular chromophore in that module, but about the absorption
coefficients for chromophores in general, including the avidin-HABA complex; and not just about
Document1
Page 17
7/28/2017
estimating absorption coefficients, but about estimating parameters in general, of any kind and in any
number. Such generalizations, which come so naturally to experienced scientists, and which are so
central to scientific progress, are a revelation to beginning science students.
As important as mathematics was to MLS’s ambitions, the MLS course did not emphasize new
mathematical techniques, as in traditional modeling courses. We sought instead to show students how
even the elementary mathematics they had already learned in high school illuminates a great diversity of
biological phenomena. At this early stage in their education, we hoped, students would come to
understand the scientific enterprise as a great web of deeply interconnected ideas (including mathematical
ones) rather than a collection of “disciplines” with distinct “professional skills.”
Acknowledgments
My colleagues Carmen Chicone, Michael Henzl, Miriam Golomb, Ricardo Holdo and Jeni Hart helped
critique the manuscript. The University of Missouri Mathematics in Life Sciences Program was
supported by U.S. National Science Foundation grant DMS 0928053, Dix H. Pettey Principal
Investigator.
References
Green, N.M. (1965). A spectrophotometric assay for avidin and biotin based on binding of dyes by avidin.
Biochem. J., 94, 23C–24C.
Green, N.M. (1975). Avidin. Adv. Protein Chem., 29, 85–133.
Hmelo-Silver, C.E., Duncan, R.G., and Chinn, C.A. (2007). Scaffolding and achievement in problembased and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational
Psychologist, 42, 99–107.
Document1
Page 18
7/28/2017
Kirschner, P.A., Sweller, J., and Clark, R.E. (2006). Why minimal guidance during instruction does not
work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquirybased teaching. Educational Psychologist, 41, 75–86.
Livnah, O., Bayer, E.A., Wilchek, M., and Sussman, J.L. (1993a). The structure of the complex between
avidin and the dye, 2-(4'- hydroxyazobenzene) benzoic acid (HABA). FEBS Lett., 328, 165–168.
Livnah, O., Bayer, E.A., Wilchek, M., and Sussman, J.L. (1993b). Three-dimensional structures of avidin
and the avidin-biotin complex. Proc. Natl. Acad. Sci. USA, 90, 5076–5080.
Ninfa, A.J., Ballou, D.P., and Benore, M. (2010). Fundamental Laboratory Approaches for Biochemistry
and Biotechnology, 2nd Edition. John Wiley & Sons, Hoboken, NJ, Chapter 11.
Smith, G.P., Golomb, M., Billstein, S.K., and Montgomery Smith, S. (2015). The Luria-Delbrück
fluctuation test as a classroom investigation in Darwinian evolution. American Biology Teacher, 77, 614–
619.
Document1
Page 19
7/28/2017
Table 1. Advance preparation. Detailed instructions are available on the companion website.
HABA stock solution. Into a 16 × 100 mm glass test tube dissolve 140 mg of HABA [2-(4hydroxyphenylazo)benzoic acid; e.g. Sigma H5126-5G] in 7 ml ethanol; transfer the 20 mg/mL
ethanolic solution to a 15-mL polypropylene screw-cap centrifuge tube (or other tightly sealed
polypropylene vessel); measure 24.75 mL Dulbecco’s phosphate-buffered saline without calcium or
magnesium (DPBS; e.g., Fisher Scientific SH30028FS) into a 50-mL polypropylene screw-cap
centrifuge tube; start the tube vortexing with the cap off, and pipette 250 µL of the 20-mg/mL HABA
solution directly into the vortexing buffer (a fine yellow precipitate forms temporarily but disperses
immediately); continue vortexing until the precipitate is fully dissolved; measure A348 (absorbance at
348 nm) of a 1/40 dilution, and calculate the true HABA concentrations in the 15- and 50-mL tubes
assuming a molar absorption coefficient of 20,700 M–1 (should be about 75 mM and 750 µM,
respectively); store the tubes with caps on securely in the dark –20ºC. Upon thawing and before
opening a tube, mix to ensure homogeneity and centrifuge briefly at low speed to drive all liquid to the
bottom.
Biotin stock solution. The 10-mM biotin stock solution is used to titrate avidin (see below); therefore
biotin solid of high purity should be used (e.g., Fisher BP2321), and the 10-mM stock solution in DPBS
should be prepared as accurately as practicable; the stock solution is stored at –20ºC, and thawed and
refrozen as needed. Upon thawing and before opening a tube, mix to ensure homogeneity and
centrifuge briefly at low speed to drive all liquid to the bottom.
Avidin stock solution. Avidin can be purchased in 10- or 100-mg quantities (Merck-Millipore
189725), enough for 1 and 10 20-student labs, respectively; the smaller amount is about twice as
expensive per mg as the larger amount. Here I describe the stock solution for the smaller amount, to be
used within a few days without freezing (the preparation document on the companion website describes
preparing frozen aliquots of the larger amount, to be used over a period of years.) The entire contents
of the vial (nominally 10 mg) is dissolved in 1.2 mL water (all water is distilled or deionized),
transferred to a 1.5-mL microtube, and microfuged for a few minutes to collapse bubbles and pellet
particulates; the supernatant is transferred to a larger vessel (capacity at least 3 mL) and diluted with 1
mL additional water (total volume 2.2 mL, enough for 20 students). The nominal avidin subunit
concentration is 275.5 µM, but it is advisable to determine the concentration of biotin-binding sites
empirically by titration with biotin (Green, 1965). The stock solution can be stored at 4ºC for a few
days before use in the student lab.
Document1
Page 20
7/28/2017
Preparations just before lab (a Microsoft Excel spreadsheet on the companion website automates the
calculations below).
 Starting with the 10-mM biotin stock above, make at least 2.2 mL of a dilution in DPBS with a
biotin concentration equal to the avidin concentration in the avidin stock solution above.
 Dispense 100 µL water, 100 µL of the avidin stock solution (previous subsection), and 100 µL of
the biotin dilution (previous bullet) into 500-µL microtubes for each student.
 Calculate the volume of 100-µM HABA dilution needed = 0.2  5.5  1  f n  1  f  mL, where n
is the number of students and f is defined in the next bullet. Thaw the 50-mL tube of HABA stock
solution above, vortex the tube vigorously and centrifuge it briefly to drive solution to bottom. In a
50-mL polypropylene conical centrifuge tube, mix HABA stock solution and DPBS diluent in
appropriate volumes to give the calculated final volume with a final HABA concentration of 100
µM (it is significantly more accurate to measure the DPBS diluent into the tube by weight rather
than by volume). Screw the cap on the 50-mL stock solution tube securely and return that tube to
the –20ºC freezer.
 In n – 1 vessels make a logarithmic (geometric) serial dilution series of 5.5-mL HABA solutions by
mixing DPBS diluent and the 100-µM HABA solution (previous bullet) in appropriate volumes.
The HABA concentration in each dilution in the series is a fraction f of the HABA concentration in
the previous dilution, where the serial dilution fraction f  n 1 11 / 1000 ; the final dilution in the
series has a HABA concentration of 1.1 µM. The actual HABA concentrations can differ slightly
from the target concentrations if convenient, and the volumes can differ slightly from 5.5 mL; but it
is important that the actual HABA concentrations be known as accurately as practicable. Dispense
exactly 1.2 mL of the 100-µM solution and of each dilution into 4 1.5-mL microtubes, which will
be used by one of the students (4 × n microtubes altogether).