In the Classroom
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Glycolysis in Wonderland: The Importance
of Energy Dissipation in Metabolic Pathways
J. Carlos Aledo* and Alicia Esteban del Valle
Departamento de Biología Molecular y Bioquímica, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga,
Spain; *caledo@uma.es
Living beings convert energy from one form to another
as they carry out the business of life. Within the context of
cellular metabolism, any energy transformation process has
two sides which must be considered by biochemists: energy
conservation and energy dissipation, both equally necessary
for life. Biochemistry textbooks pay adequate attention to the
energy-conservation aspects. However, it is rather less common to find a suitable discussion of the importance of energy dissipation. The purpose of this essay is to develop a
strategy to conduct a discussion of energy dissipation in the
classroom. As glycolysis is essential for the majority of cells
and taught in every course in biochemistry, we will use this
metabolic pathway as a concrete model. Nevertheless, the
conclusion we may reach working with the glycolysis can, in
fact must, be extrapolated to other pathways of the cellular
metabolism.
Heinrich and co-workers, making use of basic irreversible thermodynamic considerations, developed the concept
of metabolic optimization (1). This concept is critical for
understanding that energy dissipation is as necessary as energy conservation. Despite the fact that students perceive thermodynamics as an important subject, they find it difficult
to comprehend the concepts expressed by mathematical formulae. Consequently, lectures on thermodynamics are frequently met by fear and hopelessness. Herein, the concept
of metabolic optimization will be introduced in such a way
that irreversible thermodynamics and mathematics will not
be a problem for undergraduate students. That objective can
be achieved if we carry out a trip to Wonderland, an imaginary place where any form of life can be found as long as it
meets with all the known scientific laws.
Background of the Problem
Before travelling to Wonderland, to illustrate that energy dissipation is far from being a futile waste of energy, we
need to introduce the problem in suitable terms. It is assumed
that we have already studied glycolysis, which means we know
the sequence of reactions by which glucose is converted to
the end products of the pathway, the mechanisms of the enzymatic conversion, the energetics of each single reaction, and
the mechanisms controlling the activity of the glycolytic enzymes. In other words, glycolysis has already been presented
to the students as in most biochemistry textbooks (2, 3). Now,
we commence the current discussion summarizing and stressing those aspects of glycolysis that will lead us to formulate
the relevant question: Why has evolution not led to a less
energetically dissipative glycolytic pathway?
Anaerobic glycolysis, also called fermentation, is one of
the oldest energy-yielding mechanisms in living organisms,
with a history of thousands of millions of years behind it.
From a teleological point of view, the main function of
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anaerobic glycolysis is rapid ATP production. We also know
that the breakdown of glucose to lactic acid (homolactic fermentation) involves an electronic redistribution. As a consequence of this electronic redistribution a large amount of
energy is released. Taking physiological values for the concentrations of reactants and products, the released energy is
calculated to be around 205 kJ/mol (2, 3). We have also
learned that part of this released energy can be trapped in
the energy-storage compound ATP:
Glc
Glc
∆Gglc = −205kJ
2 ∆G ATP = 2 ( 50 ) = 100kJ
2 Lact
2 ADP
+ 2 Pi
+ 2 ADP + 2 Pi
2ATP
2 Lact
+ 2 ATP
∆Gnet = ∆Gglc + 2 ∆GATP
(1)
Therefore, glycolysis constitutes a clear example of an exergonic process (splitting of glucose to lactic acid, ∆Gglc < 0 )
coupled to an endergonic process (formation of ATP, ∆GATP
> 0), where the efficiency of the coupling, ␩, can be easily
calculated as
η =
n ∆GATP
∆Gglc
(2)
which is derived from the definition of efficiency as the proportion of the energy released by the exergonic process
(|⌬Gglc|), which is sequestered in form of ATP (n⌬GATP). In
this equation n is the number of moles of ATP formed per
mol of glucose consumed. As we know, n is equal to two for
glycolysis in the biosphere. At actual intracellular concentrations of ATP, ADP, and Pi, where the ⌬GATP will be close to
50 kJ/mol (3), homolactic fermentation is 49% efficient; that
is, nearly half of the free energy released by the splitting of
glucose to lactic acid is retained in the form of ATP. The rest
of the energy will be lost as heat and represents the actual
change of free energy for glycolysis (⌬Gnet). If we admit that
the main goal of anaerobic glycolysis is the production of
energy in the form of ATP, and that this pathway has been
evolving through thousands of millions of years, then why
has evolution not improved the glycolytic efficiency in order
to dissipate less energy as heat and produce more moles of
ATP per mol of glucose consumed?
Looking for the Answer in Wonderland
Wonderland is an imaginary place where you can find
almost any form of life that you can imagine. There is only
one limitation for diversity: all these forms of life are subjected to the same physical laws that exist on Earth. In this
scenario, scientists have isolated and characterized four species of bacteria from Lake Sweet in Wonderland. They belong to the same genus called Glucolitica because they obtain
Journal of Chemical Education • Vol. 79 No. 11 November 2002 • JChemEd.chem.wisc.edu
In the Classroom
the ATP they need for life by converting glucose to lactate:
Glc
+ n ADP + n Pi
2 Lact
+ n ATP
(3)
∆Gnet = ∆Gglc + n ∆GATP
The difference between species lies in the stoichiometry. That
is, n, the number of ATP produced per glucose, runs from
one to four. The steady-state concentrations of glucose and
lactate, however, are the same in all of the species and hence
the actual change of free energy for the splitting of glucose
to lactate (⌬Gglc) is also the same, let us say ᎑205 kJ/mol.
Similarly, the intracellular concentrations of ADP, Pi, and ATP
are equivalent in the four prokaryotic species and consequently the energy required for the phosphorylation of one
mol of ADP (⌬GATP) is the same in all the cases; that is, 50
kJ/mol.
The glycolytic efficiency for each of these singular species of bacteria can be calculated introducing the corresponding value of n in eq 2. Thus, we observe that the efficiency
value rises from 24 to 97% when n moves from one to four.
Not surprisingly, these extreme species have been designated
as Glucolitica inefficians and Glucolitica efficians, respectively.
It seems obvious that G. inefficians is a wasteful organism,
with only one mol of ATP formed per mol of glucose consumed. On the contrary, G. efficians has managed to couple
the formation of four moles of ATP to the breakdown of glucose and thus as much as 97% of the energy released during
the catabolism of glucose is conserved as ATP.
Rather less obvious may be the statement that G.
inefficians shows a more successful glycolysis than its relative
G. efficians. To prove such an affirmation will be our
immediate aim. A good starting point would be to define
unequivocally what we mean by more successful. If we check
the dictionary it can be found “something that is ‘successful’
achieves what was intended to be achieved”. Therefore, the
question is: what is intended to be achieved by glycolysis? As
stated above, the main goal of glycolysis is the rapid
production of ATP. The word rapid is important here. It is
very reasonable to assume that on Earth, glycolysis has evolved
under the selective pressure of yielding ATP rapidly. For
instance, the rate of ATP production by anaerobic glycolysis
can be up to 100 times faster than that of oxidative
phosphorylation (2). Then, we can say that a successful
glycolysis will be a glycolysis with a high capacity to speed
up the rate of ATP production. From now on, this rate of
ATP production will be referred to as flux of ATP production
(JATP) which is defined as the number of ATP moles formed
per unit time. Similarly, the glycolytic flux (Jglc) is defined as
the moles of glucose consumed per unit time. Glucose
consumption and ATP formation are coupled processes and
therefore their fluxes are related by the stoichiometry
coefficient n:
(4)
JAT
ATP = n Jglc
In accordance with eq 4, it could be concluded that the bacterium G. inefficias (n = 1) shows a flux of ATP production
equal to its glycolytic flux, while the flux of ATP production
is four-fold the glycolytic flux in G. efficians (n = 4). If we
could assume that the glycolytic fluxes are the same in both
prokaryotic species, then the most efficient bug would be the
most successful, which would be in contrast with the main
point of this paper that energy dissipation is important in
biological systems. However, the assumption of equal
glycolitic fluxes is indeed unacceptable even in Wonderland
because we would infringe an important physical law that
maintains that the glycolytic flux is inversely proportional to
the glycolytic efficiency. Since we have accorded that physical laws are as valid in Wonderland as they are on Earth, it is
worth making a break to consider the above-mentioned law
in detail.
Linear Phenomenological Laws
In 1811 Baron Joseph Fourier won the prize of the
French Academy of Sciences for his mathematical description of the propagation of heat. The result stated by Fourier
was surprisingly simple and elegant: heat flow is proportional
to the thermal disequilibrium given by the gradient of temperature. Fourier’s law was the first example describing an
irreversible process. Table 1 shows some irreversible processes
that are well characterized, such as electrical conduction
(Ohm’s law), chemical diffusion (Fick’s law), or heat conduction (Fourier’s law). A general theory based on linear relations between disequilibrium degrees, D, and flows, J, can
be deduced.
(5)
J = LD
where L is a constant of proportionality called phenomenological coefficient. For example, Ohm’s law, I = (1/R)V, for
the electrical conduction, is a particular expression of this
Table 1. Linear Relations between Disequilibrium Degrees and Flows
for Some Irrevesible Processes
Process
Electrical conduction
Law
I = V/R
Flow
Disequilibrium
Degree
Phenomenological
Coefficient
I
V
1/R
Chemical diffusion
J k = ᎑Dk(dCk/dx)
Jk
dCk/dx
᎑Dk
Heat conduction
J q = ᎑␬(dT/dx)
Jq
dT/dx
᎑␬
J
⌬G
᎑L
Chemical reaction
J = ᎑L ⌬G
JChemEd.chem.wisc.edu • Vol. 79 No. 11 November 2002 • Journal of Chemical Education
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In the Classroom
Although this claim is basically correct, students must be informed that the conditions under which it is true are limited
to closed systems, where only equilibrium states and infinitely
small perturbations are considered. By contrast, biochemical
reactions are out of equilibrium and therefore their reaction
rates are functions of the Gibbs free-energy changes (5).
general phenomenological law. Here, the electric charge flow
or current intensity, I, is proportional to the disequilibrium
degree which is given by the voltage, V. The phenomenological coefficient is called conductance and is the inverse of the
resistance, (1/R). Fick’s law, Jk = ᎑Dk(dCk/dx), which describes
the diffusion of a chemical substance, is another example of
a linear phenomenological law, where the flow of the substance k, Jk, is proportional to the disequilibrium degree given
by the concentration gradient, dCk/dx. In this equation the
phenomenological coefficient receives the name of diffusion
coefficient, Dk; the negative sign preceding this coefficient is
just to indicate that the flow of the substance k takes place
in the direction that decreases the concentration. The third
example illustrated in Table 1 is heat conduction, a process
governed by Fourier’s law, Jq = ᎑κ(dT/dx), which, of course,
is a linear phenomenological law. In this equation κ, the heat
conductivity, is the phenomenological coefficient, while the
disequilibrium degree is given by the gradient of temperature, dT兾dx. Again, the negative sign in this equation is to
indicate that heat flows in the direction that decreases the
temperature.
What has glycolytic flux in common with chemical diffusion or heat and electrical conduction? For a chemical reaction, or a set of coupled reactions like glycolysis, the flow
rate can be also governed by a linear phenomenological law,
where the disequilibrium degree is given by the free-energy
change (∆G), and the phenomenological coefficient (L) may
incorporate attributes of chemical rate constants (4). Thus,
the glycolytic flux is related to the Gibbs free-energy change
in the following way:
Jglc = −L ∆Gnet
Returning to Wonderland
At this point it may be convenient to remember where
we want to go and where we are now. The purpose of this
paper is to illustrate that energy dissipation fulfills an important role in metabolism. To do this, we went to Wonderland,
where we found that different organisms exhibit glycolytic
pathways with different efficiencies (see Table 2). We focused
our attention on two extreme species, G. inefficians and G.
efficians, possessing glycolytic efficiencies of 24 and 97%, respectively. Then, we affirmed that the less efficient (more dissipative) glycolysis is more successful than the glycolysis with
the highest efficiency. In other words, G. inefficians can form
ATP faster than G. efficians. Now, armed with eqs 4 and 6
we are equipped to prove it. Using eq 6 to substitute the term
Jglc in eq 4, the flux of ATP production can be expressed as:
JATP = −n L ∆Gnet
The values of ⌬Gnet for each species of bacterium can be easily calculated using eq 3 and are listed in Table 2. Introducing these values of Gibbs free-energy into eq 7 will give us
the fluxes of ATP formation. For example, for G. efficians
(omitting units for the sake of clarity), n = 4, ⌬Gnet = ᎑205 +
4 × 50 = ᎑5, and JATP = ᎑4 × (᎑5) × L = 20L. We conclude
that the flux of ATP formation is 20-times the value of L. If
we carry out similar calculations for G. inefficians, we will
find that the flux of ATP formation is now 155-times the
value of L. Taking advantage of being in Wonderland, we
postulate the same value of L for all the species. That means
that the most dissipative bug (G. inefficians) can show a flux
of ATP formation nearly 8-fold higher than that of the most
efficient bug (G. efficians).
Low number of ATP produced per glucose molecule
means bad coupling, and thus low energy conservation as
(6)
Here, again the negative sign is to indicate that the reaction
takes place in the direction that decreases Gibbs free energy.
The statement that a reaction rate may be proportional
to the actual free-energy change is a troublesome idea for
many students. They have been told, during classical thermodynamics courses, that Gibbs free-energy changes give information on whether a reaction or conversion can proceed,
that is, whether it is feasible in a certain direction, but it gives
no information on the rate of reaction or conversion.
Table 2. Metabolic Characteristics of Glucolitica Speciesa
Stoichiometry
n
Efficiency,
␩ (%)
⌬Gnet /
(kJ/mol)
Jglc (a.u.)b
G. inefficians
1
24
᎑155
31
7.8
G. optima
2
49
᎑105
21
10.5
G. suboptima
3
73
᎑ 55
11
8.2
G. efficians
4
97
᎑5
1
Species
JATP (a.u.)b
1
a
The relationships between stoichiometry, efficiency, Gibbs free-energy change, and flux
are given in the text by eqs 2, 3, and 6.
b
The ATP production and glycolytic fluxes are normalized dividing each flux by the one
shown by G. efficians. a.u.: arbitrary units.
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(7)
Journal of Chemical Education • Vol. 79 No. 11 November 2002 • JChemEd.chem.wisc.edu
In the Classroom
opposed to dissipation. However, this is kinetically good because the dissipated energy promotes a high disequilibrium
degree, giving a large flux. From the simple inspection of
Table 2, some important conclusions can be drawn. The glycolytic flux is positively correlated to energy dissipation. However, although the flux of ATP production is also a function
of the dissipated energy, this function exhibits a maximum
when half of the energy is conserved as ATP and the remaining half dissipated as heat. This leads to the conclusion that
the degradation of glucose into two molecules of lactate
coupled to the production of two molecules of ATP, as found
in most organisms in real life (eq 1), represents an optimal
state with respect to the rate of ATP production.
biological entities that are at equilibrium may be considered
to be dead and hence energy dissipation must not be regarded
as a futile waste of energy.
Conclusions
Literature Cited
A hallmark of living matter is the ability to extract and
transform energy from its environment. Glycolysis fulfills
both requirements, extracting energy from glucose and
transforming it, part as heat and part as ATP. Contemporary
glycolysis shows about 50% efficiency. This value represents
a compromise between energy conservation (as ATP) and
energy dissipation (as heat). Energy conservation is necessary
to transform the potential energy trapped in glucose into the
most common cellular energy currency: ATP. On the other
hand, energy dissipation is absolutely essential, as we have
seen, to drive the flow of matter throughout the glycolytic
pathway, avoiding chemical equilibrium (⌬Gnet = 0). Indeed,
Acknowledgements
JCA is grateful for the financial support from the
SAF2001-1894.
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Supplemental Material
A thermokinetic discussion regarding the relationship between flux and net free energy is available in this issue of
JCE Online.
1. Heinrich, R.; Meléndez-Hevia, E.; Montero, F.; Nuño, J. C.;
Stephani, A.; Waddell, T. G. Biochem. Soc. Trans. 1999, 27,
294–298.
2. Voet, D.; Voet, J. G. Biochemistry, 2nd ed.; Wiley: New York,
1995.
3. Mathews, C. K.; van Holde, K. E.; Ahern, K. G. Biochemistry, 3rd ed.; Addison Wesley Longman: San Francisco, 2000.
4. Westerhoff, H.; van Dam, K. Thermodynamics and Control of
Biological Free-Energy Transduction; Elsevier: Amsterdam, 1987.
5. Aledo, J. C. Biochem. Mol. Biol. Educ. 2001, 29, 142–143.
6. Nielsen, J. Biochem. J. 1997, 321, 133–138.
7. Ebenhöh, O.; Heinrich, R. Bull. Math. Biol. 2001, 63, 21–55.
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