205
Table 1 Optimization of the function q
d, No. of ATP
1
2
3
4
Energyyield (%)
23.9
47.8
71.7
95.6
AGnet (kJ/mol)
156
107
58
9
q (eqn 2)
37.3
51.2
41.6
8.6
show that the flux of ATP production is proportional to r/.s
Thus, in addition to representing a worthy goal of natural
selection, ~/has a real physical meaning. We can consider
eqn 2 as a function to maximize ATP flux.
It can be calculated (from actual cellular concentrations of glucose, lactate, ATP, ADP, Pi) 9 that, under
cellular conditions, AGATP= +49kJ/mol and AGony=
- 2 0 5 . 2 kJ/mol. Parenthetically, even if these values are
not exactly accurate, the results of this paper are not
changed. Then, coupling eqn 4 to phosphorylation
(1,2,3,4... ATPs produced), as in eqn 3, a set of AGnet
values is calculated according to eqn 2. For example, AGnc,
values become - 1 5 6 , - 1 0 7 , - 5 8 , - 9 k J / m o l for
increasing d (1,2,3,4, respectively). Table 1 illustrates
these results.
Is the function r/maximized as proposed? Is glycolysis,
indeed, optimized at the ATP yield d = 2? It is clear from
Table 1 that the function r/, a measure of the ATP flux
during glycolysis,8 has its maximum value when the degradation of glucose to 2lactate is coupled to the production
of 2 ATP. Cellular glycolysis is optimized!
Conclusion and re-iteration
The optimization of metabolism is a concept introduced
by Melendez-Hevia in 19851° and further developed to
demonstrate optimization in the design of the pentose
phosphate pathway, 1°'11 the Calvin cycle of photosynthesis," and the structure of glycogenJ 2 We have
previously discussed how the chemical design of glycolysis
indicates an optimized structure. 13 Studies such as these
can provide answers to the fundamental questions: 'Why
is metabolism the way it is? Could it have been any other
way and accomplish the same purpose? How did it get to
its present design?'
We have demonstrated herein that the process of
glycolysis evolution has maximized the ATP yield (d = 2)
and has maintained the most negative AGnet. Glycolysis is
optimized in terms of its energy coupling to phosphorylation. We emphasize that this view of glycolysis efficiency
has much more scientific meaning than the common
textbook calculations. In fact, the text calculations do not
reflect the remarkably optimized and perfected energy
coupling in glycolysis) 4
Ever run the short way; and the short way is the way of
Nature.
Marcus Aurelius (AD 121-180)
References
1 Lupianez J.A., Garcia-Salguero L., Torres N.V., Peragon J. and
Melendez-Hevia E. (1996) Comp. Biochem. Physiol. l13B, 439-443
BIOCHEMICAL EDUCATION 25(4) 1997
2 Garrett, R. H. and Grisham, C. M. (1995) Biochemistry, pp. 569-596.
Saunders, New York
3 Campbell, M. K. (1995) Biochemistry, 2nd edn, p. 362. Saunders, New
York
4 Voet, D. and Voet, J. G. (1995) Biochemistry, 2nd edn, p. 469. Wiley,
New York
5 Lehninger, A. L., Nelson, D. L. and Cox, M. M. (1993) Principles of
Biochemistry, 2nd edn, pp. 375, 404. Worth, New York
6 Fell D. (1983) Biochem. Soc. Trans. 11, 44-45
7 Gnaiger, E. (1983) J. Exp. Zoo. 228, 471-490. See also Fields, J. H. A.
(1988) Can. J. Zool. 66, 1036-1040
8 Heinrich R., Montero F., Klipp E., Waddell T.G. and Melendez-Hevia
E. (1997) Eu~ J. Biochem. 243, 191-201
9 Lehninger, A. L., Nelson, D. L. and Cox, M. M. (1993) Principles of
Biochemistry, 2nd edn, p. 426. Worth, New York
10 Melendez-Hevia E. and Isidoro A. (1985)J. Theo. Bio. 117, 251-263
11 Melendez-Hevia E. (1990) Biomed. Biochim. Acta 49, 903-916
12 Melendez-Hevia E., Waddell T.G. and Shelton E. (1993) Biochem. J.
295, 477-483
13 Melendez-Hevia E., Waddell T.G., Heinrich R. and Montero F. (1997)
Eur J. Biochem. 244, 527-543
14 For a discussion of optimization of metabolism see Melendez-Hevia E.,
Waddell T.G. and Montero F. (1994) J. Theor Biol. 166, 201-220
PII: S0307-4412(97)00118-0
A Guided Discovery Approach for Learning
Glycolysis
EMERIC SCHULTZ
Department of Chemistry
Bloomsburg University
Bloomsburg, PA 17815
USA
Introduction
Metabolic pathways are, at the most basic level, a set of
successive chemical transformations. For those in the
know however, each pathway is pregnant with possibilities
for concept development. From the simple beauty of
'naked reactions', connections can be made to many
unifying principles including: (1) the energetics of each
transformation and of the overall process; (2) the balance
between entropy and enthalpy effects; (3) the multi-level
control aspects of the process; (4) the overall strategy of
the process in relationship to other pathways.
Expected student learning of metabolic pathways runs
the gamut from the very superficial to the very inclusive.
For some nursing students, as well as other students in
allied health sciences, often only the names of a small
number of the key compounds in the pathway (most
usually glycolysis and the citric acid cycle), and perhaps
the names of a few enzymes are required. The learning
here is essentially rote. For students in a junior/senior
level biochemistry course or sequence, especially one
taught from a chemical perspective, a thorough understanding of the actual transformations as well as the
energy and control connections is routinely expected.
Unfortunately, in this case also, most of the learning is
rote.
The clientele for our biochemistry sequence consists of
primarily biology majors (greater than 90%). For this
206
audience the nuances of structural changes are often lost,
if indeed they have ever been comprehended. These
students often default to a wholly inadequate rote
memorization of names, enzymes and structures. The
structures of intermediates presented on examinations by
these students often range from the inept, to the bizarre,
to the comical. Students handicapped in this way seldom
see the forest of integrated concepts from the trees of
individual reactions.
A recent editorial in this journal I celebrated the 25th
anniversary of the Metabolic Pathways Charts and
commented on student strategies for studying metabolic
pathways. In the same issue, Nicholson, the leading
'inventor' of the Charts, in addition to describing the
history behind the development of the modern Charts,
presented the pentose phosphate pathway in a manner
that separated the two overlapping 'missions' of this
pathway. 2 The argument was made that the pathway
needed to be assimilated by the student in a way that was
non arbitrary. The suggested way of learning this pathway
was highlighted by considering the different possibilities
that would arise given different cellular requirements.
Another recent paper described three different styles by
which the essentials of the urea cycle could be learned by
students? One of these styles involved the use of a
nmenonic in order to help students remember the
different components of the cycle.
Ryder and Leach describe a unique tutorial approach
that 'requires students to move away from a view of glycolysis and gluconeogenesis as sequences of metabolites and
enzymes, towards an appreciation of the links between
metabolic pathways.. ?.4 1 agree. The challenge for me in
teaching a metabolic pathway is to impart both the
chemical sense in the specific transformations (you can
not walk away from bonding), the energetic sense in the
thermodynamics of each step and the overall process, and
the biological sense in terms of economy of effort dictated
by evolutionary perfection. However, this cannot occur
unless the essentials of the pathway have been assimilated
by the student. In my opinion, more attention needs to be
paid to teaching students how to learn the rudiments of
specific pathways. We need to have a greater assurance
that students understand these nuts and bolts aspects
before attending to the more difficult concepts detailed
above.
This communication describes a unique way of learning
the glycolytic pathway in step-wise fashion. The pedagogy
involves clear rote components that are connected to a set
of generalizations that develop and deepen important
biochemical concepts.
Expected starting information and some useful guiding
generalizations
In order to learn anything one has to build upon the
knowledge base that is in place. Specifically, to start the
study of glycolysis the following memorized essentials are
required: the structures D-glucose (open chain form),
D-glyceraldehyde, dihydroxy-acetone and pyruvate; an
BIOCHEMICAL EDUCATION 25(4) 1997
ability to convert between open chain and ring forms of
sugars. I approach these in a holistic way.
o-glyceraldehyde is the starting point; the structure is
given in Fischer form: aldehyde group at the top; the other
carbons having their O H groups pointing to the right.
Dihydroxyacetone is just the keto isomer of
o-glyceraldehyde, p-glucose is o-glyceraldehyde with a 3
carbon unit with alternating O H groups right, left, right
inserted between the aldehyde and the rest of the
D-glyceraldehyde chain (common to all p-family sugars).
Finally, pyruvate is dihydroxyacetone that has been
oxidized at one end (to the carboxylate group) and
reduced at the other end (to the methyl group).
Throughout my course I develop what I call 'guiding
generalizations'. As with all generalizations, there are of
course exceptions. However, these generalizations serve
as a way in which students can integrate large amounts of
seemingly unrelated information. The generalizations I
use to guide discovery of glycolysis are given below. A
short description of how these apply is also given. (1)
Every biological process has some overall sense and can
be divided into different components that have unique
features and/or missions. This notion has the effect of
compartmentalizing the memory load into do-able quantities. (2) An economy of effort is characteristic of
biological systems. This idea has several aspects. First,
don't fool around; get to the task right away; pathways
have been perfected by evolution, therefore expect the
minimum number of steps needed to do the job. Secondly,
always make a minimal change on a small part of the
molecule--do not even consider massive changes. Third,
keep track of the changes that have occurred and compare
them to the final product in the pathway. If one end of the
molecule already has the structure of one end of the final
product, then there will be no more changes on that part
of the molecule. (3) Enzyme design is related to enzyme
function. Specifically, enzymes in catabolic pathways act
on small molecules and the changes that occur on the
substrate molecule are usually at or near one of the ends
of the molecule because the catalytic site is usually at the
bottom of the active site. (4) 'Low energy' biological
compounds have more stable structures than 'high energy'
biological compounds. Specifically, low energy phosphates are usually found connected to carbon chains at
primary alcohol positions; high energy phosphates are
connected to carbon chains through other types of
linkages.
The step by step guided discovery of the pathway
A distillation of what is presented in lecture follows.
Step 1 Count the number of reactions and organize these
in a way that is easy to remember:
(1) There are nine reactions (actually there are ten, but
one of the reactions is not a part of the main
sequence; we'll get back to this later).
(2) Divide the pathway in terms of missions; consider a
story--it has a beginning, a middle and an end.
207
(a) Beginning = setting up substrates from which
energy can be extracted by phosphate transfer;
this will be a top row of four reactions = upper
tier.
(b) M i d d l e = a unique event (like the top of a
mountain from which we can see both sides) that
connects one mission to another; this reaction
connects the top row of four reactions to the
bottom row of four reactions.
(c) E n d = u s i n g the high energy substrate compounds to generate metabolic energy in the form
of ATP; this will be a bottom row of four reactions = lower tier.
(3) Number each of the reactions in the pathway.
The result of this discussion is shown in Figure 1.
Step 2 Identify the reactions in which ATP, ADP and
phosphate are involved either as substrates or as products
of reactions:
The result of this discussion is shown in Figure 2.
Step 3 Do a number of molecules/number of phosphates
inventory for each of the reactions in the pathway:
(1) Write in the known structures of the starting
substance, glucose and the final product, pyruvate.
(2) Establish that since no carbons are lost, 2 pyruvates
must have arisen from 1 glucose.
(3) Establish the following notation, X - Y , where
X = the number of molecules of a given species, and
Y = the number of phosphates that are 'on' that
molecule (referred to as species/phosphate [S/P]
value).
(4) Label under the structure of glucose 1 - 0 and under
the structure of pyruvate 2 - 0 .
(5) Start along the pathway assigning S/P values to each
of the metabolite spaces in the figure (specific structures will be placed in these positions later); carry out
the following dialog:
(a) The product of reaction 1 has S/P = 1 - 1 since
one phosphate has been added.
(b) There is no change at reaction 2, therefore S/P
does not change and is still 1 - 1.
(c) At reaction 3 an additional phosphate is added
therefore the product has S/P = 1 - 2 .
(d) Since we expect that phosphates have been added
on each end of the 6 carbon unit (enzyme
generalization), it would seem logical that this is
the spot where we split our 6 carbon unit into two
3 carbon units; therefore the products' of this
reaction should have the label S/P = 2 - 1 (each 3
carbon unit has one phosphate).
(1) Invoking the economy of effort principle, the mission
of the pathway starts right away and finishes as soon
as possible therefore both the first and the last
reaction (1 and 9) involve ATP since energy generation is the mission of this pathway.
(2) Since the upper tier is to set up high energy substrate
compounds, ATP is a reactant and ADP is a
product.
(3) Likewise since the lower tier extracts metabolic
energy from high energy substrate compounds, ATP
is a product and ADP is a reactant.
(4) The other reactions that involve ATP are easy--3 and
6: one can remember reaction 1 and then going up in
3s.
(5) The position of ATP (as product or reactant) is
dictated by what tier the reaction is in.
(6) Since this pathway generates an excess of ATP,
somewhere in the pathway phosphate has to be added
if more ATPs are to be made than are used; the only
logical place to add this extra phosphate is at reaction
4 (as we will see later there is an additional energy
connection at this reaction).
(i) Actually what happens is that the split is into
two different 3 carbon units that are very
closely related.
(ii) Show this split into two different 3 carbon
units by adding a little loop in the pathway
and labeling the isomerization reaction that
gives the main glycolytic intermediate as 4a.
[]
[]
[]
[]
[]
7-V
[]
ATP
[]
--
ADP
[]
?W"
ATP
ADP
[]
[]
[]
[]
[]
[]
[]
[]
ATP
Figure 1 Blackboard or overhead result after Step 1 in the
guided discovery approach to glycolysis
BIOCHEMICAL EDUCATION 25(4) 1997
[]
ADP
ATP
ADP
Figure 2 Blackboard or overhead result after Step 2 in the
guided discovery approach to glycolysis
208
(a) Glycolysis yields not only biological energy in the
form of ATP, but also biological energy in the
form of reducing power, specifically NADH.
(b) Since this reaction is the 'special' one in the
middle of the pathway, its logical to infer that this
is where the N A D H is made.
(c) N A D H is made from NAD + (a reduction); therefore the glycolytic intermediate has to be
oxidized.
(d) Since there are 2 molecules of glyceraldehdye3-phosphate that are going to be oxidized, 2
molecules of NAD + will be reduced to NADH;
the reaction is updated to reflect this fact.
(e) Given our guiding principles, we expect the oxidation to occur at the end of the molecule where
there is no phosphate; we also expect the
phosphate to be added at this end; (the type of
linkage that results, a mixed anhydride, is similar
to the high energy phosphate anhydrides that the
students have already had experience with in
ATP); the resulting compound is 1,3-bisphosphoglycerate.
(f) The logic of this compound and its high energy
status as the first compound in the lower tier in
the pathway is emphasized.
(e) Reaction 5 is the special reaction in the pathway;
phosphate is being added in this reaction but
since we have two 3 carbon units we have to add
2 phosphates (one to each); the result afterwards
is S/P = 2 - 2.
(f) Reaction 6 involves the removal of phosphate
from a glycolytic intermediate to ADP to make
ATP; make sure we indicate 2 ADP and 2 ATP
and the result afterwards is S/P = 2 - 1 .
(g) No change in the phosphate status occurs until
the last reaction, therefore S/P for the products of
reactions 7 and 8 is also 2 - 1 (although something
obviously must be happening here).
(h) The last reaction (No 9) is the same type of
reaction as No 6 and the final products are 2
pyruvates (2 - 0).
The result of this discussion is shown in Figure 3. The
remainder of the pathway is worked out in parts that are
detailed below.
Step 4 Focus in on the region that is the middle of the
pathway and give it structural definition.
(1) The two three carbon compounds that follow reaction
4 are easy; they are phosphates of the two three
carbon sugars that are the building blocks of the
aldose and ketose family of sugars (D-glyceraldehyde
and dihydroxyacetone).
(a) Since both these compounds are in the low
energy upper tier, the placement of the
phosphates on these compounds as directed by
S/P is easy--they go on the primary alcohols.
(b) The structures are placed in the boxes in which
they belong; the reason glyceraldeyde is in the
main pathway will soon become obvious; it is also
easy to see how the ketone can be isomerized to
the aldehyde.
(2) Reaction 5 is the 'central' reaction in glycolysis; it is
also the one that if you commit to memory, really
helps you figure out the reactions of the lower tier.
[]
ATP
[]
ADP
[]
ATP
[]
ADP
2 Pi-~.
[]
[]
[]
[]
[]
Step 5 Give definition to the rest of the structures in the
pathway.
There is a logical dialogue that goes step by step
(invoking components of the guiding principles given
above) that completes the presentation of the pathway.
For the sake of brevity and the fact there is nothing
especially unique or innovative about this part of glycolysis as I do it, these details are not reported here. They
are available upon request.
Evaluation of guided approach
The bottom line, when it comes to student understanding
of a topic area, is student performance on that topic on an
examination. After I adopted this approach, there was a
remarkable increase in student performance when the
reactions of glycolysis were assessed. This improved
performance was most dramatic for lower aptitude
students. Especially noteworthy was the obvious attempt
by many students to use the S/P values as a means of
'figuring out' the right answer. This would suggest that the
rote memory devices present in this approach are being
used by students to learn the pathway in a non rote
fashion. Lastly, students who have had glycolysis in other
courses (in biology), comment very favorably about this
approach. Many statements along the line 'this is the first
time I have understood glycolysis' have been made by
students.
References
2 ATP 2 ADP
2 ATP 2 ADp
Figure 3 Blackboard or overhead result after Step 3 in the
guided discovery approach to gkycolysis
BIOCHEMICAL EDUCATION 25(4) 1997
1
2
3
4
Wood E.J. (1997) Biochem. Educ. 25, 61
Nicholson D.E. (1997) Biochem. Educ. 25, 62-70
Patel M.B. and Shastri N.V. (1996) Biochem. Educ. 24, 15-16
Ryder J. and Leach J.T. (1996) Biochem. Educ. 24, 21-25