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