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sisting of four essay questions relating to the preceding course, together with a brief practical examination of a series of written short answer questions covering practical skills and laboratory calculations.

It had been planned that the final course-work exami- nation, consisting of two three-hour papers, one with short answers and one for essay questions, would be held during the 30th week of the course to allow the maximal amount of time for the students to prepare their theses without distraction. In the event, it did not prove possible to hold this formal examination earlier than the 32nd week. Marking of examination responses was performed by the staff members who set the question and the external examiner. The projects were assessed by one internal examiner, not otherwise involved in the course, and one external examiner. In addition, supervisors were asked to submit a report. The BMSc is an honours degree and was classified in the usual manner.

Resources The Department of Biochemical Medicine in Dundee is a joint University/Health Service Department and senior staff employed by both the University and the Health Service contributed extensively. In addition, staff from outwith the Department , particularly clinicians with special relevant expertise, took part from time to time. Examples of such individuals were a radiotherapist with a special interest ~in tumour markers and a clinical endocrin- ologist with a special interest in diabetes. Clinical Bio- chemists and Medical Laboratory Scientific Officers not directly involved with the course gave considerable help with the project work.

Discussion The extent to which clinical biochemistry is taught in medical schools varies greatly. In the University of Dundee, the members of the Department of Biochemical Medicine contribute to undergraduate medical teaching in the second, third, fourth and fifth (final) years, through lectures, tutorials and bedside teaching. The major thrust in the limited time available is directed towards the competent interpretation of results obtained in patients. The limited time in the curriculum unfortunately does not allow significant expansion into the very necessary dis- cussion of analytical techniques or of the principles of interpretation, except in the most elementary way. When there is severe competition for contact time in the medical curriculum, it is unlikely that the much increased amount of clinical biochemistry recommended by the Inter- national Federation of Clinical Chemistry t will be re- alised. Nevertheless, it seems important to us that a small number of medical undergraduates should be encouraged to consider the possibility of careers in clinical biochem- istry and be provided with sufficient insight to allow a reasoned choice later. We believe that the course we have described may serve in this way much as previously prepared courses in microbiology and pathology fre- quently encourage students to return after qualification.

We recognised that there was a conflict between what was desirable for a 'vocational course' and what was required for an honours degree in a scientific subject. The course we have described was inevitably a compromise to some extent. On review of the first such course con- ducted, we now believe that the proportion of time used for formal teaching and practical work was probably too large, while that available for the project work was probably too small. Nevertheless, we feel that the pattern we devised may be of assistance to others planning the introduction of a similar intercalated degree course and the wider availability of such courses could make a real contribution to the recruitment of academically com- petent and well motivated medical graduates into bio- medical research and clinical biochemistry.

Acknowledgements The very many members of staff of the Department of Biochemical Medicine who gave of their time are sincerely thanked, particularly Drs J D Baty, T E Isles, P E G Mitchell and J P Moody. Professors I W Percy- Robb and P D Griffiths, the external and internal examiners, are thanked for their considerable efforts.

Reference 1Fraser C G, Zinder O, deCediel N, Porter C J, Schwartz M K and Worth H G J (1985) 'Guidelines (1985) for Teaching of Clinical Chemistry to Medical Students', J Clin Chem Clin Biochem 23 697-703

Reservoir Model of Metabolic Crossroads as a Teach- ing Tool in Enzyme Kinetics

ENRIQUE CRESPO,* ALBERTO SOLS ° and ANTONIO SILLERO*

* Departamento de Bioqu#nica, Facultad de Medicina Universidad de Extremadura 06071 Badajoz, Spain and

°Departarnento de Enzimologia del Instituto de Invest# gaciones, Facultad de Medicina Biom(dicas del CSIC y Departarnento de Bioquimica Universidad Aut6noma de Madrid 28029 Madrid, Spain

Introduction In 1969 we developed a method to quantify the glycer- aldehyde "metabolic crossroads. ''1 The method may be useful both for metabolic studies and as a pedagogic tool to teach enzyme kinetics. This last aspect of the problem has remained somewhat hidden probably due to the basic nature of the journal in which that work was originally published. The object of this article is to recall the existence of this procedure and to extend its application to allosteric enzymes.

General Application A metabolic crossroads refers to the situation in which a metabolite may be transformed by more than one enzyme. Illustrative examples are the crossroads of acetyl- CoA, glucose-6-phosphate, pyruvate, glutamate, glycer-

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aldehyde, etc. Let us imagine a simple metabolic cross- roads such as

e ~--'- [ a b c ~ f

A ~ B - C ~ O - F

in which metabolite D is synthesized through a unique pathway starting with metabolite A. The synthesis of D is dependent on the availability of A and on the kinetic characteristics of enzymes a, b and c. Considering all these variables, the rate of synthesis of D may oscillate between 0 and a maximum of, say, 3 i.zmol/min/g of tissue. Once formed, metabolite D is withdrawn by the three enzymes constituent of the crossroads. In our model, this can be viewed as a metabolite (D) flowing into a reservoir (metabolic pool), reaching a certain level (concentration) and being drained through holes present in the wall of the reservoir (Fig 1). The amount of D flowing through each hole will depend, disregarding hydrostatic pressure, on its

-2

A

i

°[e , 9

- 4

-6

0 e

-2

-8

0 ? g e

-e I

f 9 f

31 . . / ....... ~r, OO

I "°

| ,o

E 3" / f " r ~lJ ioo

/

' i ' . ' ' i :: r ri" tO

io o , . ~ _ . : : ~ " .

. / loo

I.~ 60 40 20

3 / I: 10o /

/" so f I

1,5, ~ 2o4°e° O'e[ ¢ 9 3 i ~

E . . - . - . i r '.5 .

• / Bo 4)

I o g [ s u b l t r a t e ] ~ )

Figure 1 Computer representation of six metabolic cross- roads (A-F) . On the left are represented the three draining holes in the wall of a metabolic reservoir, drawn according to the Hill equation and considering the kinetics character- istics (Table 1) of the three enzymes acting on the common substrate. The graphs at the right represent both the percentage contribution of each of the enzymes to the metabolism of the common substrate, and the sum (~) of the activities of the three enzymes, expresses as u/g

level and both the outlet area (Vm.x of each enzyme) and its relative height (Kin). The shape of the exit holes are such that half-maximum velocity is attained at the height of liquid (metabolite concentration) corresponding to the widest part of the orifice (Km or So.5 value). The draining holes have been drawn with the help of a computer program according to the equation

V m a x . S n V = (1)

S ° + K'

where K' = (So.5)". n = 1 corresponds to enzymes with hyperbolic kinetics, in which case K' = K,, = So._s; n > 1 corresponds to enzymes with positive cooperative kinetics, 2 n < 1 corresponds to negative cooperative kinetics. 2

Different examples can be given for metabolic cross- roads (Table l , Fig 1). In crossroads A (Table 1, Fig 1), the three enzymes have the s a m e V m a x but different Km values. In this case, it is clear that at low substrate concentration the more active enzyme will be that with the lowest Km value.

Table 1 Examples of theoretical metabolic crossroads' (A-F), composed of three enzymes, e, f and g represent three enzymes acting on a common substrate. For the purpose of this work V .. . . and Km values can be given in arbitrary units. Nevertheless, and for reasons of simplicity, Vm,x is expressed here as txmol of substrate transformed per min and per g of wet tissue (u/g), and KIn(So.5) as mM. So.5 refers to enzyme f of crossroads C-F; K,, refers to the rest of the enzymes; n is the Hill coefficient. Computer treatment of these crossroads is shown in Fig 1

Crossroads Enzymes V, ..... (u/g) Km(S,.5)mM n

e 1 0.01 1 A f 1 0.1 1

g 1 1 1

e 0.5 1 1 R f 1 1 1

g 2 1 1

e 1 0.01 1 C f 1 0.1 4

g 1 1 1

e 1 0.01 1 D f 1 0.1 0.5

g 1 1 1

e 0.5 1 1 E f 1 l 4

g 2 1 1

e 0.5 1 1 F f 1 1 0.5

g 2 1 1

B I O C H E M I C A L E D U C A T I O N 14(3) 1986

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A quantitative treatment of each crossroads is rep- resented in the right part of Fig 1. The percent contri- bution of each enzyme has been evaluated at different concentrations of the common substrate. This percentage is easily derived by applying the Hill Equation (1) to each of the enzymes at the given substrate concentration. The total sum of the three enzymatic activities (the overall removal of substrate D) is also represented in Fig 1. Supposing that the rate of influx of the common meta- bolite into the metabolic reservoir equals that of its exit, the steady state concentration of metabolite D corres- ponds to the point where the sum of the three enzymes of the crossroads equals the velocity of influx of metabolite.

In crossroads B (Table 1, Fig 1), the enzymes have different Vm,x and the same K,,, values. In this case the percent contribution of each of the three enzymes remain constant at different substrate concentrations. The metabolic crossroads for glyceraldehyde (four enzymes with different Vm,x and Km values) have been previously published. 1

This treatment can also be applied to metabolic crossroads in which allosteric enzymes of the cooperative type 2 participate. In this case it is convenient to emphasize the shape of the hole in the metabolic reservoir model as a function of the Hill coefficient (n) of the enzyme. For illustration, enzymes with the same V,,,,,~ and S0.5 values, but with theoretical n values of 0.2, 0.5, 0.7, 1, 3, 4 and 7 are represented in Fig 2. It can be seen that as n increases, the enzyme tends to reach maximum velocity between narrower ranges of substrate concentration. In negative homotropic kinetics, as n decreases, it becomes more difficult for second and subsequent molecules of substrate to be bound to the enzyme and hence more difficult to attain maximum velocity. When n = 0.2, the shape of the hole, on the scale used in Fig 2, is a long breach in the wall of the reservoir. The presence of one cooperative enzyme (with n X 1) in a metabolic crossroads greatly modifies the percentage that the common substrate is transformed by each one of the enzymes of the crossroads. Compare, for example, crossroads A, C and D (Table 1, Fig 1). The sole difference between them is that e n z y m e f h a s n values of 1, 4 and 0.5, respectively. In crossroads C, the contri- bution of enzyme f increases sharply as the substrate concentration approaches its S0.5 value. In crossroads D,

" I

ion. I J

Y ,i

7'

Figure 2 Shape of the draining hole on the wall of a reservoir depending on the Hill coefficient (n) of the enzyme. In all cases V,,,x and So.5 have been kept constant. n values as specified in the Figure

enzyme f, in spite of having a S0.5 value one order of magnitude higher than enzyme e, is the more active enzyme of the crossroads at the lowest substrate concen- tration. The comparison of crossroads B, E and F (Table 1, Fig 1) is also significant. Between each crossroads, the enzymes have the same Km(S0.5) but different Vma x

values. Values for n of 1, 4 and 0.5 have been assigned to enzyme f in crossroads B, E and F respectively. In crossroads E the percentage of enzyme f increases sharply at substrate concentrations approaching So.5 and con- sequently the contribution of enzyme g decreases. The comparison of crossroads B and F shows well how an enzyme with negative cooperativity can drastically change the overall picture of a metabolic crossroads, taking control of the metabolism of the common metabolite at low substrate concentration.

Special Circumstances The simple reservoir model is centred on a common substrate potentially shared by several enzymes in a metabolic crossroads. Its use to visualize simply the predominant flux(es) should be made paying attention to a variety of limitations. First of all, most intracellular enzymes have two (or even more) cosubstrates, and the actual activity of an enzyme in the cell might be limited by a second substrate, as is the case for dehydrogenases that use NADP + as substrate, such as glucose-6-phosphate dehydrogenase in the glucose-6-phosphate crossroads. There is a large potential excess of the dehydrogenase, but actual activity is geared to N A D P H consumption and hence to NADP + regenerating pathways. What is signifi- cant is that its large potential ensures that the enzyme will use as much glucose-6-phopshate out of the pool as required to maintain most of the NADP + pool as NADPH. Other common instances are the dehydro- genases depending on N A D H as second substrate, as happens in the pyruvate crossroads in animal tissues. An outstanding case is the family of aminoacyl-tRNA syn- thetases, whose activity is geared to regeneration of the cosubstrate, the corresponding tRNA, by synthesis of peptide bonds on nascent proteins. Whenever the second substrate is generally plentiful, be it NADPH, NAD +, or ATP, there is no problem, 3 and the model can be used without reservations.

A second limitation to the simple reservoir model based on the intrinsic kinetic parameters (V, ........ K,,, or So.5 and n) is the frequent occurrence in first enzymes of pathways - - those most frequently involved in metabolic crossroads - - of regulatory mechanisms that could markedly affect one or several of the above parameters. They could be either allosteric effectors (in the restricted sense that involve specific regulatory sites), 2 metabolic intercon- versions by covalent modification, or both. Thus, in the case of the glucose-6-phosphate crossroads, phospho- fructokinase, linked to glucose 6-phosphate by a large excess of the freely reversible glucose phosphate isomer- ase, is a multi-allosteric enzyme 2 that in addition can be regulated by phosphorylation in certain tissues. 4

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Acknowledgement This work was supported by the Comision Asesora de Investigaci6n Cientffica y T6cnica

References ISillero, M A G, Sillero, A and Sols, A (1969) Eur J Biochem 10, 345-350

2Sols, A (1981) Curr Top Cell Regul 19, 77-101

3Sols, A and Marco, R (1970) Curr Top Cell Regul 2, 227-273

4Hofer, H W Schlaner, G and Graefe, M (1985) Biochem Biophys Res Comm 129,892-897

The Role of Water in Glycolysis

JOHN L MEGO

Biology Department University of Alabama University, AL 35486, USA

Introduction The formula for the complete oxidation of glucose is:

CBHI206 * 602 ÷ 6H20 ~ 12H20 * 6C0 a (1)

As the formula indicates, there is an uptake of 6 moles of wate/ per mole of glucose oxidized to water and CO2. Furthermore, not obvious from this formula, the oxygen attached to carbon in CO2 comes from water. The sole function of molecular oxygen in glycolysis is to re-oxidize FADH2 and NADH. What is the function of water in this process? Where is water taken up and how does the oxygen from water appear in CO2? A balanced equation for the aerobic catabolism of glucose does not require an uptake of 6 moles of water:

C6HI206 * 602- -~ - I " 6H20 * 6C02 (2)

The uptake of 6 waters (equation (1)) means that 12 additional electron pairs are transferred to NAD + and FAD thus doubling the yield of ATP by oxidative phosphorylation in the electron transport chain. The concept involved is therefore of fundamental importance, yet it is ignored by every biochemistry textbook with which I am familiar. Some textbooks discuss the addition of water to double bonds followed by removal of electrons and protons (eg Wood and Pickering, Introducing Bio- chemistry; de Duve, A Guided Tour of the Living Cell) but none emphasizes the extra ATP yield resulting from this process.

Oxidation of aldehydes When an aldehyde is oxidized by NAD + or FAD, for example the aldehyde dehydrogenase reaction, the extra oxygen appearing in the product comes from water:

CH3CHO * NAD* * H20 ~ CH3CO0- -" NADH ÷ H" (3)

It is a well known fact that aldehydes become hydrated in aqueous solution. This is the basis for the formation of the

cyclic pyranose and furanose forms of monosaccharides in which internal hemiacetals are formed. The structures of aldehydes in solution should therefore be written as follows:

OH R-CHO * H20 ~ R-~-OH (4)

One reaction occurs in the Embden-Meyerhof pathway in which an aldehyde is oxidized to an organic acid. This is the glyceraldehyde-phosphate dehydrogenase reaction. The mechanism of this reaction involves the formation of a thiohemiacetal at the active site of the enzyme. This is then oxidized by NAD + and the energy of this oxidation is conserved by the formation of the acyl phosphate, 1,3- bisphosphoglycerate. In this reaction, an aldehyde is clearly oxidized to an acid, yet there is no net uptake of water:

OH OH R-(~-OH * ENZ-SH ~ ENZ-S-C-R • H20 (5)

OH 0 ENZ-S-C-IR * NAD" - HO-PO; ~ R-C-O-PO; "- NADH * H* (6)

Origin of the water In the next reaction, catalyzed by phosphoglycerate kinase, the phosphate is transferred to ADP. The alde- hyde has been oxidized to an acid but no water is involved. Where, then, does the oxygen come from? The answer is from phosphate. When phosphate is transferred from 1,3-bisphosphoglycerate to ATP, an oxygen is left behind to form the carboxyl group:

0 0 ~ 0 0 0 Ad-Rib-O-P-O-P-O- ,P,-O-C-R ~ ATP * -O-C-R

6- 6- o-o- (7)

The carboxyl group of glycerate-3-phosphate, the product of the phosphoglycerate kinase reaction, ultimately is released as CO2 in the pyruvate dehydrogenase reaction. It would appear, therefore, that at least part of the oxygen in CO2 has its origin in phosphate. However, when ATP is hydrolyzed, the oxygen lost to the carboxyl of glycerate-3- phosphate is replaced in the phosphate by the water taken up from the medium. Thus, the source of oxygen in the oxidation of glyceraldehyde-3-phosphate to glycerate-3- phosphate, and ultimately in the CO2 released in the pyruvate dehydrogenase reaction, orginates in water from the medium.

There is no net uptake of water in the fermentation of glucose (the Embden-Meyerhof pathway). A molecule of water is taken up in the aldolase reaction and the products are hydrated glyceraldehyde-3-phosphate and dihydroxy- acetone phosphate. The conversion of dihydroxyacetone phosphate to the aldehyde in the triosephosphate isomer- ase reaction also requires an uptake of water. This uptake of two molecules of water is balanced by the two waters released in the enolase reaction. The formation of two thiohemiacetals in the glyceraldehydephosphate dehydro- genase reaction release two waters which are balanced by

BIOCHEMICAL EDUCATION 14(3) 1986