Tài liệu Báo cáo khoa học: Reaction mechanisms of thiamin diphosphate enzymes: redox reactions pdf

MINIREVIEW
Reaction mechanisms of thiamin diphosphate enzymes:
redox reactions
Kai Tittmann
Albrecht-von-Haller-Institut fu
¨
r Pflanzenwissenschaften und Go
¨
ttinger Zentrum fu
¨
r Molekulare Biowissenschaften, Georg-August-Universita
¨
t
Go
¨
ttingen, Germany
Introduction
The oxidative decarboxylation of 2-keto acids, such
as pyruvate, branched-chain keto acids and ketoglu-
tarate, is a key reaction of intermediary metabolism
in virtually all organisms and is catalyzed by thiamin
diphosphate (ThDP)-dependent enzymes [1]. In view
of the central metabolic role of pyruvate, the various
biochemical reactions involving pyruvate are the
most intensely studied and are well understood.
Thus, they serve as prototypical reactions for the
enzymic oxidative conversion of 2-keto acids. Hence,
the present review mainly focuses on the reaction
mechanisms of ThDP enzymes that directly oxidize
pyruvate. Special emphasis is devoted to the nature
and reactivity of transient intermediates, the coupling

of oxidation–reduction and acyl group transfer and
electron transfer between cofactors. The review
includes a discussion of general aspects of enzyme
catalyzed pyruvate oxidation, in addition to individ-
ual sections on the different ThDP enzymes that act
on pyruvate.
Pathways of pyruvate oxidation by
ThDP enzymes
Generally, there are at least four major different path-
ways of ThDP enzyme catalyzed pyruvate oxidation.
Keywords
electron transfer; flavin; intermediate;
iron-sulfur cluster; lipoamide; oxidative
decarboxylation; phosphorolysis; pyruvate;
radical; X-ray crystallography
Correspondence
K. Tittmann, Albrecht-von-Haller-Institut fu
¨
r
Pflanzenwissenschaften und Go
¨
ttinger
Zentrum fu
¨
r Molekulare Biowissenschaften,
Georg-August-Universita
¨
tGo
¨
ttingen, Ernst-

Caspari-Haus, Justus-von-Liebig-Weg 11,
D-37077 Go
¨
ttingen, Germany
Fax: +49 551 39 5749
Tel: +49 551 39 14430
E-mail:
(Received 7 November 2008, revised 3
February 2009, accepted 13 February 2009)
doi:10.1111/j.1742-4658.2009.06966.x
Amongst a wide variety of different biochemical reactions in cellular car-
bon metabolism, thiamin diphosphate-dependent enzymes catalyze the oxi-
dative decarboxylation of 2-keto acids. This type of reaction typically
involves redox coupled acyl transfer to CoA or phosphate and is mediated
by additional cofactors, such as flavins, iron-sulfur clusters or lipoamide
swinging arms, which transmit the reducing equivalents that arise during
keto acid oxidation to a final electron acceptor. EPR spectroscopic and
kinetic studies have implicated the intermediacy of radical cofactor
intermediates in pyruvate:ferredoxin oxidoreductase and an acetyl phos-
phate-producing pyruvate oxidase, whereas the occurrence of transient
on-pathway radicals in other enzymes is less clear. The structures of pyru-
vate:ferredoxin oxidoreductase and pyruvate oxidase with different enzymic
reaction intermediates along the pathway including a radical intermediate
were determined by cryo-crystallography and used to infer electron tunnel-
ing pathways and the potential roles of CoA and phosphate for an intimate
coupling of electron and acyl group transfer. Viable mechanisms of reduc-
tive acetylation in pyruvate dehydrogenase multi-enzyme complex, and of
electron transfer in the peripheral membrane enzyme pyruvate oxidase
from Escherichia coli, are also discussed.
Abbreviations

AcThDP, 2-acetyl-ThDP; HEThDP, 2-(1-hydroxyethyl)-ThDP; PDHc, pyruvate dehydrogenase multi-enzyme complex; PFOR,
pyruvate:ferredoxin oxidoreductase; POX, pyruvate oxidase; Q
8,
ubiquinone 8; ThDP, thiamin diphosphate.
2454 FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS
Pyruvate dehydrogenase multi-enzyme complex
In mitochondria and respiratory eubacteria, the pyru-
vate dehydrogenase multi-enzyme complex (PDHc)
catalyzes the essentially irreversible conversion of pyru-
vate, CoA and NAD
+
into CO
2
, NADH and acetyl-
CoA (Eqn 1) [2]. The latter is utilized as a precursor
for the Krebs cycle and the biosynthesis of fatty acids
and steroids, whereas NADH feeds the reducing equiv-
alents into the respiratory chain for oxidative phos-
phorylation (i.e. ATP synthesis).
PDHc:pyruvate þ CoA + NAD
þ
! acetyl-CoA+CO
2
þ NADH ð1Þ
PDHc is the largest molecular machine known (M
r
of $ 10
6
–10
7

) and is composed of multiple copies of
three enzyme components: a ThDP-dependent pyru-
vate dehydrogenase (termed the E1 component), a
dihydrolipoamide transacetylase (E2 component),
which carries lipoyl groups covalently attached to
lysine residues [N
6
-(lipoyl)lysine, lipoamide], and lipoa-
mide dehydrogenase (E3 component) with a nonco-
valently yet tightly bound FAD cofactor [3]. In
mammals, PDHc contains an additional E3 binding
protein and specific kinases and phosphatases, which
control the activity of the complex by reversible phos-
phorylation ⁄ dephosphorylation of serine side chains in
E1 [4]. Initially, E1 catalyzes the irreversible decarbox-
ylation of pyruvate and the subsequent reductive acet-
ylation of an N
6
-(lipoyl)lysine in E2. E2 itself catalyzes
acyl group transfer from the reduced S-acety-
ldihydrolipoyl-lysine to CoA. Finally, E3 regenerates
the oxidized form of lipoamide and transfers the two
reducing equivalents to NAD
+
.
Pyruvate:ferredoxin oxidoreductase
In anaerobic organisms, acetyl-CoA is synthesized by
the enzyme pyruvate:ferredoxin oxidoreductase
(PFOR), which may contain one or multiple
[Fe

4
S
4
]
2+
clusters in addition to ThDP [5]. The two
electrons, which arise during oxidation of pyruvate at
the ThDP site, are sequentially transferred via the iron-
sulfur cluster(s) to final electron acceptors ferredoxin
(Fd) or flavodoxin (Eqn 2) [6]. Unlike PDHc, PFOR
also carries out the reverse reaction, namely the reduc-
tive carboxylation of acetyl-CoA to yield pyruvate.
PFOR: pyruvate þ CoA + 2Fd
ox

!
acetyl - CoA
þ CO
2
þ2Fd
red
ð2Þ
The low-potential electrons of Fd
red
formed in the
forward direction (E
o
of pyruvate oxidation
$ )540 mV) are used to drive several low-potential
transformations such as CO reduction or hydrogen

formation [7]. The reverse synthase reaction (pyruvate
formation) is central to CO
2
fixation in acetogenic and
green photosynthetic bacteria [8].
Acetyl phosphate-producing pyruvate oxidases
In Lactobacillae such as Lactobacillus plantarum or
Lactobacillus delbrueckii, which are unable to synthe-
size hemes and thus lack a respiratory chain for oxi-
dative phosphorylation, ATP is mainly generated by
fermentation of carbohydrates with lactic acid as a
final product. Under aerobic growth conditions, some
Lactobacillae convert carbohydrates to the high-
energy metabolite acetyl phosphate, which in turn is
used for ATP synthesis. A key reaction of this path-
way is the oxidative decarboxylation of pyruvate by
the enzyme pyruvate oxidase (POX) that requires
ThDP, Mg
2+
and FAD as cofactors [9,10]. After
binding and decarboxylation of pyruvate, the reduc-
ing equivalents are transferred to the neighboring
FAD cofactor. The flavin is then reoxidized by the
final electron acceptor dioxygen to yield hydrogen
peroxide (Eqn 3).
POX : pyruvate þ phosphate + oxygen + H
þ
! acetyl phosphate + CO
2
+H

2
O
2
ð3Þ
Phosphate-independent pyruvate oxidase from
E. coli
In E. coli , a related ThDP and FAD-dependent pyru-
vate oxidase (EcPOX) feeds electrons from the cytosol
directly into the respiratory chain at the membrane
[11,12]. EcPOX is considered to be a backup system to
PDHc and was shown to be important for aerobic
growth of E. coli. Unlike POX from Lactobacillae,
EcPOX produces acetate rather than acetyl phosphate
and its reduced flavin is unreactive towards oxygen.
Two-electron reduction of the flavin has been sug-
gested to induce a structural rearrangement of the
enzyme that exposes a lipid-binding site at the C-termi-
nus. After binding to the membrane, the flavin reduces
the membrane-bound mobile electron carrier ubiqui-
none 8 (Q
8
) (Eqn 4).
EcPOX : pyruvate + Q
8
+OH
À
! acetate + CO
2
+Q
8

H
2
ð4Þ
K. Tittmann Redox reactions of thiamin diphosphate enzymes
FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS 2455
Reaction intermediates in the ThDP
catalyzed oxidation of pyruvate
The oxidative decarboxylation of pyruvate in PDHc,
PFOR and POX involves a series of covalent ThDP
intermediates and analogous elementary reactions
(Fig. 1) [13]. In pioneering studies on models, Breslow
[14] identified C2 of the ThDP thiazolium as the
reactive center that, in its carbanionic form, attacks
the substrate carbonyl yielding, in the case of pyru-
vate, the tetrahedral pre-decarboxylation intermediate
2-lactyl-ThDP. Decarboxylation of the latter gives the
resonant a-carbanion ⁄ enamine forms of 2-(1-hydroxy-
ethyl)-ThDP (HEThDP). The enamine is sometimes
(and more accurately) referred to as 2-(1-hydroxye-
thylidene)-ThDP and formally represents the C2a-
deprotonated conjugate base of HEThDP in a
resonance stabilized form. Essentially, all steps
encompassing binding and decarboxylation of pyru-
vate are common to PDHc, PFOR and POX. Reac-
tion sequences diverge at the HEThDP
carbanion ⁄ enamine intermediate, which is highly
reducing and may undergo one-electron or two-elec-
tron oxidation by proximal redox cofactors. The
[Fe
4

S
4
] clusters in PFOR are exclusive one-electron
acceptors, whereas the flavin in POX may function as
a one-electron and two-electron capacitor. Model
studies suggest that reduction of the redox active
dithiolane moiety of lipoic acid is a two-electron
process linked to atom transfer [15].
One-electron oxidation of the HEThDP carban-
ion ⁄ enamine results in the formation of a ThDP cat-
ion radical (termed the HEThDP radical) with
different resonance contributors (the most relevant
ones are shown in Fig. 1). In principle, the unpaired
spin may be delocalized over the hydroxyethyl and
thiazolium moieties but it appears likely that the
active sites in enzymes are poised to stabilize just one
Fig. 1. Intermediates in the ThDP-catalyzed oxidative decarboxylation of pyruvate.
Redox reactions of thiamin diphosphate enzymes K. Tittmann
2456 FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS
or few electronic states. If electron transfer is coupled
to proton transfer (i.e. deprotonation of the Ca-OH),
the neutral 2-acetyl-ThDP (AcThDP)-type radical will
be formed with a set of resonant forms similar to
those described for the HEThDP radical. Two-elec-
tron reduction or stepwise one-electron reduction
yields the AcThDP intermediate that exists in three
distinct forms: the keto form, the hydrate and the tri-
cyclic carbinolamine [16]. The keto form undergoes
acyl transfer to nucleophilic acceptors or is hydroly-
sed with the geminal diol (hydrate) as a transitory

state.
The occurrence of 2-lactyl-ThDP, HEThDP and
AcThDP as reaction intermediates in ThDP enzymes
has been confirmed by 1H NMR spectroscopy after
acid quench isolation [17]. EPR spectroscopy was
employed to detect radical ThDP intermediates [18].
Thermodynamic aspects of pyruvate
oxidation
In PDHc, PFOR and POX, the thermodynamically
favorable oxidation of pyruvate is coupled to forma-
tion of the ‘energy-rich’ metabolites acetyl-CoA and
acetyl-phosphate, which serve either as chemically acti-
vated building blocks in anabolic pathways, or for
ATP synthesis because the group transfer potential of
the acetyl-CoA thioester (DG°
¢
= )35.7 kJÆmol
)1
) and
the acetyl phosphate acid anhydride (DG°
¢
= )44.8
kJÆmol
)1
) exceeds that of ATP (DG°
¢
= 31.8 kJÆmol
)1
)
[19].

Electrochemical studies on thiazolium models
revealed very low subsequent one-electron oxidation
potentials of the presumed pyruvate-derived enamine
(E°
ox(1)
= )0.96 V and E°
ox(2)
= )0.73 V versus satu-
rated calomel electrode; E°
ox(1)
= )0.72 V and
E°
ox(2)
= )0.49 V versus standard hydrogen electrode)
[20]. Thus, the high reducing power of the enamine
intermediate is by far sufficient to initiate downhill
transfer of the reducing equivalents to the final elec-
tron acceptors ferredoxin (E°
¢
[Fe
++
⁄ Fe
+++
] $
)0.4 V versus standard hydrogen electrode at pH 7),
NAD
+
(E°
¢
[NADH, H

+
⁄ NAD
+
,2H
+
]=
)0.32 V), ubiquinone (E°
¢
[dihydroquinone ⁄ quinone,
2H
+
] = +0.10 V) or oxygen (E°
¢
= +0.29 V for
the O
2
⁄ H
2
O
2
couple). The redox potentials of
additional cofactors directing electron transfer from
the ThDP enamine onto final electron acceptors may
be modulated to some degree by the protein environ-
ment but are suspected to lie in between. Redox
potentials of [Fe
4
S
4
] clusters in PFOR and FAD in

POX will be discussed in the sections on the different
enzymes.
Reaction mechanism of pyruvate:
ferredoxin oxidoreductase
Evidence for a free radical mechanism
In the early 1980s, Oesterhelt et al. discovered that
mixing PFOR from Halobacterium halobium with its
substrate pyruvate led to the formation of an organic
free radical that gives rise to a continuous wave
X-band EPR signal centered at g = 2.006 [21]. The
radical was reported to be stable even at room temper-
ature, but was readily depleted upon addition of the
second substrate CoA. Quantitative analysis of sub-
strate turnover revealed that two moles of final one-
electron acceptor ferredoxin are reduced per mole of
pyruvate in the presence of CoA. There are several
lines of evidence indicating that the organic radical is a
HEThDP radical resulting from one-electron oxidation
of the HEThDP carbanion ⁄ enamine intermediate by
the neighboring FeS cluster (i.e. this PFOR contains a
single [Fe
4
S
4
] cluster). At first, additional experiments
with selectively
14
C-labeled pyruvate revealed that
radioactivity remained tightly bound to the enzyme
when PFOR was reacted with [3-

14
C]pyruvate, whereas
no label could be detected after addition of
[1-
14
C]pyruvate, clearly suggesting the radical to be
formed after decarboxylation [18]. Second, the hyper-
fine splitting of the radical EPR signal was shown to
be dependent on the chemical nature of the substrate
methyl substituent (i.e. the number of nuclear spins at
C3 of pyruvate) [5]. When the EPR spectra were
recorded at temperatures below 20 K, spin coupling
between the ThDP-derived radical and the reduced
[Fe
4
S
4
]
1+
cluster was observable, indicating that the
two paramagnetic centers are located at a distance of
approximately 1 nm or less [18].
Subsequently, kinetic and spectroscopic studies on
PFORs from different organisms including Desulfovib-
rio africanus and Clostridium thermoaceticum suggested
a common reaction mechanism with an obligate tran-
sient ThDP-based radical, the lifetime of which criti-
cally depends on the presence of CoA [22]. Unlike the
archetypical PFOR from H. halobium, these PFORs
contain three [Fe

4
S
4
] clusters with slightly different
midpoint potentials (E
1
= )540 mV, E
2
= )515 mV,
E
3
= )390 mV) [23]. Thermodynamics suggest an elec-
tron transfer chain from the thiamin radical to the
final electron acceptor ferredoxin via the three iron-
sulfur clusters involving the initial reduction of the
lowest-potential iron-sulfur cluster (suspected to be
located in close proximity to the ThDP cofactor), fol-
lowed by sequential reduction of the other two clusters
leading towards the surface of the protein, where
K. Tittmann Redox reactions of thiamin diphosphate enzymes
FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS 2457
ferredoxin will be reduced. Remarkably, in the absence
of CoA, addition of pyruvate to D. africanus PFOR
eventually resulted in the reduction of only the highest
potential [Fe
4
S
4
] cluster (E
3

= )390 mV). No mag-
netic interaction between this cluster and the ThDP
radical was detectable, and it was concluded that the
reduced cluster is distant from the thiamin binding site
[23]. In the presence of pyruvate and CoA, all three
clusters become reduced. This exciting discovery on
different PFORs pinpointed a crucial role of CoA for
facilitating transfer of the second electron from the
ThDP radical to the iron-sulfur clusters.
Structural studies on PFOR and its ThDP radical
intermediate
In 1999, Fontecilla-Camps et al. solved the X-ray crys-
tallographic structure of the homodimeric PFOR from
D. africanus in the resting state at 2.3 A
˚
resolution
[24]. The ThDP cofactor is deeply buried within the
protein, and its reactive center, the thiazolium nucleus
of ThDP, is located approximately 10 A
˚
from the most
proximal [Fe
4
S
4
] cluster (referred to as cluster A, prox-
imal) (Fig. 2). Clusters A, B (medial) and C (distal) of
each subunit are separated by approximately 10–12 A
˚
,

thus allowing for facile electron transfer in a suitably
organized redox chain (Dutton’s empirical analysis [25]
predicts electron tunneling to take place when
donor ⁄ acceptor pairs are within 14 A
˚
edge-to-edge
distance). Cluster C is located close to the enzyme
surface, where the final electron acceptor ferredoxin
is suspected to bind. Electron tunneling is likely to
proceed dominantly in a through-bond mechanism
involving the backbone and coordinating cysteinyl
ligands of the iron-sulfur clusters. Clusters B and C
are covalently linked to each other via the protein, and
only few gaps with edge-to-edge distances close to van-
der-Waals distance (< 4 A
˚
) exist between ThDP and
cluster B, such that through-space tunneling will be
scarcely required.
Fontecilla-Camps et al. then reported the high-reso-
lution X-ray structure of the free AcThDP radical
trapped at the active center of PFOR from D. afric-
anus [26]. The electron density maps suggested the
thiazolium moiety of the cofactor intermediate to be
markedly puckered, a structural feature that indicates
reduction or even loss of aromaticity. Therefore, the
thiazolium ring was proposed to adopt an unprece-
dented tautomeric form, in which a proton from the
4-methyl group has undergone transfer to C5
(Fig. 3A). Also, the C2-C2a bond that connects C2 of

ThDP with the substrate C2 was reported to be excep-
tionally long (1.86 A
˚
) prompting the authors to
suggest a r ⁄ n-type AcThDP radical in which the
unpaired spin is mostly confined to the acetyl moiety
and, to a lesser degree, to C2 of the cofactor [26].
Fig. 2. Stereo drawing of PFOR structure
(Protein Data Bank code: 1kek) in transpar-
ent surface representation. The ThDP radical
and the three [Fe
4
S
4
] clusters are shown as
sticks. Edge-to-edge distances between all
cofactors are indicated.
Redox reactions of thiamin diphosphate enzymes K. Tittmann
2458 FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS
After fragmentation of the r ⁄ n-type cation radical and
formation of an acetyl radical, radical recombination
with a CoA thiyl radical was proposed to occur. By
contrast to p-type radicals with extensive delocalization
of the unpaired spin over aromatic systems, the pro-
posed r ⁄ n-type AcThDP radical must be regarded,
especially in view of the tenuously bonded acetyl moi-
ety, as an unstable high-energy intermediate and, thus,
its long lifetime, as demonstrated experimentally both
in the crystalline phase and in solution, is seemingly
counterintuitive.

EPR studies on the free radical in PFOR and role
of CoA for electron transfer
Ragsdale and Reed [27] thoroughly examined the
HEThDP radical in PFOR from Moorella thermoacetica
by X-band and D-band EPR spectroscopy. EPR spec-
tra of PFOR were recorded for different combinations
of native and isotopically labeled cofactor ([2-
13
C],
[3-
15
N]) and substrate ([3-
2
H
3
], [2-
13
C], [3-
13
C]), and
further analyzed by spectral simulations. The obtained
g-values and
14
N ⁄
15
N hyperfine-splittings are in good
agreement with a planar p-type radical and extensive
delocalization of the unpaired spin over the thiazolium
ring. The EPR spectra and associated simulations on
simplified thiazolium models are not consistent with a

r ⁄ n-type AcThDP radical proposed on the basis of
pure structural data [26]. Although which protonation
state pertains to the radical intermediate cannot be
clarified unambiguously, the observed
1
H- and
13
C-hyperfine splittings of the C2ß protons and C2
and C2a carbons would best correspond to an interme-
diate state between C2a O-protonated (HEThDP radi-
cal) and O-deprotonated (AcThDP radical) forms. The
close proximity of the cofactor’s exocyclic 4¢-amino
group demonstrated in the X-ray structure favors a
hydrogen-bonding interaction between C2a-O and N4¢
(Fig. 3B).
As noted above, addition of pyruvate to PFOR gen-
erates a stable ThDP radical and one reduced [Fe
4
S
4
]
cluster, which was more recently demonstrated to be
the medial cluster [28]. Rapid depletion of the thiamin
radical and reduction of all clusters is only achieved
after addition of CoA. What is the special role of CoA
for propagation of the second electron and the associ-
ated 10
5
-fold rate enhancement of electron transfer? In
pursuit of this question, Ragsdale proposed several

viable mechanisms [7,29].
At first, he considered that CoA itself could comprise
part of the electron transfer chain by wiring the HEThDP
radical and one iron-sulfur cluster, followed by nucleo-
philic attack of the AcThDP formed in that process and
eventual release of acetyl-CoA. The observation that the
CoA analogue desulfo-CoA induces no rate enhancement
of electron transfer, despite only marginally compro-
mised binding energy compared to CoA, renders the
above-considered mechanism unlikely. In line with that
argument, if indeed CoA were to lend its orbitals for
bridging the pathway and effective through-bond tunnel-
ing, why then does transfer of the first electron proceed
so facilely from the HEThDP enamine to cluster B via
cluster A in the absence of CoA?
Second, a biradical mechanism was proposed that
involves one-electron reduction of one iron-sulfur
cluster by CoA and subsequent recombination of the
Fig. 3. Chemical structures of the
HEThDP ⁄ AcThDP radical in PFOR proposed
on the basis of structural data (A) [26] or
EPR spectroscopic analysis (B) [27].
K. Tittmann Redox reactions of thiamin diphosphate enzymes
FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS 2459
resultant CoA thiyl radical and the HEThDP radical
to form acetyl-CoA. Support for this comes from the
observation that CoA reduced one [Fe
4
S
4

] cluster in
PFOR from C. thermoaceticum, even in the absence of
pyruvate [22]. However, such behavior has not been
reported for all PFORs and there was no EPR spectro-
scopic evidence for the putative CoA sulfur-based thiyl
radical. An additional intricacy of this mechanism is
the necessity of a structural rearrangement of CoA in
the course of catalysis: initially, the reactive thiol
group of CoA must be positioned proximal to an iron-
sulfur cluster and distant to ThDP but, after oxida-
tion–reduction, it would have to swing closer to ThDP.
Although a simple bond rotation could account for
such conformational transition, diffusion of the CoA
radical out of the active site and abortive side
reactions of the highly reactive thiyl radical could
successfully compete with radical recombination.
Furthermore, direct access to the clusters is sterically
occluded by different loops, so the structural confine-
ments of the active site channel render the proposed
double duty of CoA (cluster reduction and radical
recombination) unlikely, unless binding of CoA would
enforce large structural rearrangements of the protein.
Third, it was proposed that the rate enhancement of
electron transfer by CoA could result from a chemical
and kinetic coupling of oxidation–reduction and acyl
group transfer [7]. This mechanism would generate a
covalent adduct between the AcThDP-type radical and
CoA to form an anion radical, the reducing power of
which can be anticipated to be much higher than of a
charge-neutral AcThDP radical, thus increasing the

driving force of the redox reaction. As noted earlier
above, in model studies, it was established that the
potential of the thiazolium enamine ⁄ radical couple
(E°
ox(1)
= )0.72 V versus standard hydrogen elec-
trode) is more negative than that of the radical ⁄ acetyl
couple (E°
ox(2)
= )0.49 V). It is conceivable that the
redox potential of the former is low enough to reduce
the lowest potential PFOR cluster (E
1
= )0.54 V),
whereas the reducing ability of the latter might be
insufficient in that concern. Thus, conclusively, the
formation of a low potential anion radical may be
thermodynamically mandatory to drive re-reduction of
the lowest potential clusters in PFOR.
Mechanism of pyruvate oxidation in
pyruvate dehydrogenase multi-enzyme
complex
As noted earlier, oxidation of pyruvate in the E1 com-
ponent of PDHc is coupled to reductive acetylation of
lipoic acid covalently attached in amide linkage to the
e-amino function of a lysine in the E2 component. By
contrast to iron-sulfur clusters in PFOR or FAD in
POX, the N
6
-(lipoyl)lysine conjugate is structurally

flexible, a ‘swinging arm’ that permits active site cou-
pling between E1, E2 and E3 components by rotation
of the lipoyl moiety itself and by additional movement
of the whole protein domain (‘swinging domain’) that
carries the lipoyl-lysine, thus providing a ‘super arm’
that is capable to span the gaps between the active
centers on the different components [2,30].
Oxidation–reduction chemistry of lipoic acid in
models and implications for reductive acetylation
in pyruvate dehydrogenase
Lipoic acid exists in an oxidized disulfide form with a
slightly strained five-membered dithiolane ring (LipS
2
)
and in the two-electron reduced acyclic dithiol form
(dihydrolipoic acid, Lip(SH)
2
). The standard redox
potential of the Lip(SH
2
) ⁄ LipS
2
couple has been
determined by polarographic analysis to be approxi-
mately )0.32 V (pH 7) and is thus more positive than
the two subsequent one-electron oxidation potentials
of thiazolium enamine models, making oxidation of
the enamine by LipS
2
thermodynamically favorable

[31]. However, LipS
2
will be electrochemically reduced
only at extremely negative potentials in acetonitril
solution ()1.92 V versus saturated calomel electrode)
and it even resists reduction in water [15]. Low-poten-
tial single-electron reductants such as reduced methyl
viologen do not undergo oxidation–reduction with
LipS
2
, clearly indicating that sequential one-electron
reduction is an unlikely mechanism for two-electron
reduction of LipS
2
[15]. A lipoic acid disulfide anion
radical can be generated by one-electron reduction
using hydrated electrons as reductants, but the reduc-
ing power of the disulfide radical is much higher than
that of the HEThDP enamine, disfavoring its
one-electron oxidation by LipS
2
[32]. Because the
complete reduction of LipS
2
was easily achieved by
reaction with molecular hydrogen, it was concluded
that reduction and concomitant cleavage of the
disulfide linkage must be coupled to atom (proton)
transfer [15].
In line with these early investigations, Jordan et al.

observed that, in chemical models, reductive acetyla-
tion of lipoic acid by thiazolium enamine occurs
extremely slowly and requires the addition of a
mercury trapping reagent [33]. Subsequently, the
same laboratory used S-methylated lipoic acid
[LipS(SCH
3
)
+
] as a viable chemical model for the
S-protonated form of LipS
2
[34]. MS analysis revealed
the existence of a tetrahedral adduct with an S-C
Redox reactions of thiamin diphosphate enzymes K. Tittmann
2460 FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS
linkage formed between lipoic acid and the thiazolium
C2a [34]. Very remarkably, LipS(SCH
3
)
+
easily oxi-
dizes thiazolium enamine models with second-order
rate constants that, in view of the effective molarity
of the lipoyl-lysine in the multi-enzyme complex, can
account for the observed turnover number of PDHc.
This intriguing observation suggests that reductive
acetylation in PDHc requires an acid ⁄ base catalyst to
protonate the dithiolane part of lipoamide. Two dif-
ferent mechanisms were envisioned to explain the cat-

alytic role of a proton donor. At first, the ThDP
enamine might attack at one of the sulfurs to form
the tetrahedral adduct, and the free thiolate anion
would then be protonated by a proximal proton
source. Alternatively, LipS
2
could be protonated in a
pre-equilibrium to give a highly reactive thiolanium
cation LipS
2
H
+
, followed by nucleophilic attack by
the enamine and concomitant cleavage of the disulfide
bond. An important factor concerning the latter
mechanism is the low pKa of the thiolanium cation,
so that only minor fractions will be present in equili-
brium under physiological conditions.
Mechanistic analysis of reductive acetylation
in PDHc
A key question related to the mechanism of reductive
acetylation in PDHc is whether enzyme-bound
dihydrolipoamide is acetylated at S6 or S8 by the
HEThDP enamine. It has been impossible, thus far, to
directly test the two alternatives or to disprove one of
them for the reconstituted multi-enzyme complex;
however, elaborate studies conducted by Frey et al. on
the E2-catalyzed acetylation of free dihydrolipoamide
by acetyl-CoA clearly revealed formation of the 8-S
isomer, followed by non-enzymatic isomerization and

formation of the 6-S isomer [35]. By invoking the prin-
ciple of microscopic reversibility, 8-(S)-acetyl-
dihydrolipoylamide is the chemically (and kinetically)
competent isomer for the physiologically relevant for-
ward reaction of E2 (i.e. the formation of acetyl-CoA)
and this must be formed in the preceding reductive
acetylation at E1.
A further compelling question concerns a possible
coupling of oxidation–reduction and acyl group trans-
fer. In principle, the two elementary reactions of reduc-
tive acetylation could occur simultaneously in a
tightly-coupled mechanism or, alternatively, in a step-
wise manner. Both mechanisms would involve the
tetrahedral adduct between reduced lipoamide and
AcThDP; however, AcThDP would be a compulsory
on-pathway intermediate only in the stepwise mecha-
nism. Frey et al. could isolate AcThDP in the steady
state of the overall reaction of PDHc by acid quench
trapping [36]. This finding is consistent with a stepwise
mechanism of oxidation–reduction and acyl group
transfer; however, it cannot disprove a coupled mecha-
nism because AcThDP could be generated from the
tetrahedral thiamin-lipoamide adduct in an equilibrium
side reaction.
Further support for a stepwise mechanism comes
from the observation that E1-bound AcThDP (formed
by enzymic conversion of 3-flouropyruvate) is a chemi-
cally competent acyl group donor to externally added
dihydrolipoamide [37]. In search of putative free radi-
cal intermediates that could be transiently formed in

the course of sequential one-electron transfer from the
enamine to oxidized lipoyl-lysine, a p-type HEThDP
radical could be detected by EPR spectroscopic studies
on PDHc from different organisms [13,38]. There was,
however, no spectroscopic evidence for a correspond-
ing lipoamide sulfur-centered thiyl radical, and the for-
mation of the ThDP-based radical appeared to result
from an oxygenase side reaction of the HEThDP
enamine with dioxygen rather than from on-pathway
oxidation by lipoamide.
X-ray crystallographic studies on E1 from different
dehydrogenase complexes have provided the structural
framework for our mechanistic understanding of
reductive acetylation and active site coupling between
E1 and E2 [39,40]. The active center of E1 with the
ThDP cofactor is located at the bottom of a long fun-
nel-shaped substrate channel, which is suitable orga-
nized to accommodate a flexible E2-linked lipoamide
swinging arm for chemical coupling and intermediate
channeling. As noted earlier above, reductive acetyla-
tion is likely to involve acid ⁄ base chemistry from the
protein and ⁄ or ThDP cofactor. General acid catalysis
is required for protonation of the lipoamide disulfide,
and a general base must be involved to deprotonate
the a-OH of the HEThDP enamine. Structural and
functional data implicate highly-conserved His side
chains at E1 to fulfil this function. Some of the His
residues such as His407 in E. coli E1 are located in
loops that are flexible in the resting state but become
ordered upon binding and processing of pyruvate

[41,42]. A probable (and partially modeled) structural
snapshot of catalysis showing E2-bound lipoamide
prior to reaction with the planar HEThDP enamine
intermediate (atomic coordinates of HEThDP enamine
taken from POX) at the active center of E1 from
E. coli is illustrated in Fig. 4. The lipoamide molecule
was modeled into the substrate channel of E1 such
that (a) formation of 8-(S)-acetyl-dihydrolipoylamide
is more likely than of the 6-S isomer and (b)
protonation of the lipoamide dithiolane by His407
K. Tittmann Redox reactions of thiamin diphosphate enzymes
FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS 2461
may occur (on the basis of structural considerations
and previously available functional data [41]). The
resultant model invokes active center residue His640 to
be important for deprotonation of the a-OH of the
HEThDP enamine.
Reaction mechanism of acetyl
phosphate-producing pyruvate oxidases
Chemical considerations of acetyl phosphate
formation by pyruvate oxidases
In phosphate-dependent pyruvate oxidases, such as
that from L. plantarum (LpPOX), thermodynamically
favorable oxidation of pyruvate is coupled to forma-
tion of the ‘energy-rich’ metabolite acetyl phosphate
that carries an acid anhydride linkage [10]. Owing to
its high group transfer potential, acetyl phosphate
may undergo favorable phosphotransfer to ADP to
give ATP, a process that is catalyzed by the enzyme
acetate kinase [19]. Besides ThDP and a divalent cat-

ion (Mg
2+
) required for anchoring the former, pyru-
vate oxidases contain FAD as an additional cofactor,
of which the apparent catalytic role is to oxidize the
HEThDP carbanion ⁄ enamine formed after binding
and decarboxylation of pyruvate at the thiamin site.
Two-electron oxidation of the HEThDP carban-
ion ⁄ enamine by FAD gives AcThDP, an intermediate
that was initially suspected to be highly unstable but,
in chemical models (AcThDP and 2-acetyl-thiazolium
salts), was shown to be relatively stable at low
hydroxide ion concentrations or in the absence of
trapping nucleophiles [16,43]. Water and other less
basic nucleophiles, such as the phosphate dianion,
were demonstrated to add to 2-acetyl-thiazolium salts
and result in tetrahedral adducts; however, only the
water adduct underwent further decomposition to
acetate, whereas reactions with phosphate gave back
the starting material rather than acylated phosphates
[43]. This is because phosphate is a better leaving
group than the thiazolium ylid, and electron donation
to C2 in the tetrahedral phospho adduct is not as
extensive as in the water adduct to enable expulsion
of the thiazolium ylide. In the case of AcThDP,
phosphate did not even form a tetrahedral addition
compound [16]. Conclusively, these model studies
indicate that acetyl phosphate-producing pyruvate
oxidase may not utilize simple oxidation–reduction
chemistry followed by acyl transfer to phosphate.

Besides overcoming the large barrier for expelling
acetyl phosphate from the tetrahedral phospho
adduct, the enzyme must also suppress hydrolytic
cleavage of the presumed AcThDP intermediate to
avoid decoupling of oxidation and acid anhydride
bond formation.
Molecular architecture of phosphate-dependent
pyruvate oxidases and implications for electron
transfer
The X-ray crystal structure of the homotetrameric
LpPOX was solved by Muller and Schulz [44] in the
early 1990s and serves as the structural prototype for
acetyl phosphate-producing POXs. As in all ThDP-
dependent enzymes that have been structurally charac-
terized to date, the active site is located at the interface
of two corresponding subunits constituting the cata-
lytic dimer (Fig. 5). The thiazolium of ThDP and the
redox active isoalloxazine of FAD are bound at
approximately 7 A
˚
edge-to-edge distance, with the
dimethylbenzene part of FAD pointing directly
towards the thiazolium. The flavin isoalloxazine is
markedly bent over the N5–N10 axis ($ 10–15°),
which is a structural feature that increases the driving
force of oxidation–reduction because the distorted con-
formation resembles the reduced state of the flavin,
thus increasing its oxidizing power. The widely-
accepted theoretical framework for biological electron
transfer (Dutton’s ruler) predicts that pure electron

(quantum-chemical) tunneling between both cofac-
tors in POX would occur extremely rapidly
(k
theo
$ 10
8
s
)1
) when assuming ‘normal’ free and
reorganization energies [25]; however, the packing
Fig. 4. Putative structure of E2-bound lipoamide attacking the HET-
hDP enamine at the active center of E1 from E. coli in stereo view.
A lipoamide molecule in the oxidized state was modeled into the
substrate channel of PDHc-E1 from E. coli (Protein Data Bank code:
2g25), thus representing the catalytic state prior to reductive acety-
lation. To adequately illustrate the confinements of the substrate
channel, the protein is shown in surface representation with a
sliced active center pocket and substrate funnel. The HEThDP
enamine (modeled according to [47]) and selected His residues
implicated as participating in general acid ⁄ base catalysis are shown
in a stick representation.
Redox reactions of thiamin diphosphate enzymes K. Tittmann
2462 FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS
density (i.e. a measure of the volume in the inter-reac-
tant space occupied by protein atoms) between the
thiazolium and the isoalloxazine is very small so that
electron transfer would mostly occur as through-space
tunneling. Because of this structural observation, it has
been alternatively suggested that electron tunneling
might involve the side chains of two Phe residues

(Phe479 and Phe121) contributed by different mono-
mers as way stations for electron transfer in a com-
bined through-space ⁄ through-bond mechanism [44]. In
support of this proposal, an arginine side chain sitting
atop Phe479 could partially offset the transiently
formed negative charge at the phenyl ring. These dif-
ferent possible modes notwithstanding, theoretical
treatment of oxidation–reduction between the HET-
hDP enamine and FAD might not be as straightfor-
ward as in other systems because electron transfer in
POX is definitely coupled to proton transfer (i.e.
deprotonation of C2a-OH of HEThDP and proton-
ation of FAD at N5 and N1). The tight and rigid
binding of both cofactors excludes a direct carbanion
mechanism with covalent linkage between C2a of the
HEThDP enamine and C4a of FAD, as suggested for
FAD-catalyzed oxidation of other organic substrates
(e.g. amino acids).
Besides the different hydrophobic active center resi-
dues considered above as being involved in electron
transfer, there are a few polar side chains (Glu, Gln)
in close vicinity to the ThDP cofactor, which are likely
to play important roles for catalysis and binding of
phosphate. This initially premature functional assign-
ment has been corroborated by kinetic and structural
analysis of different LpPOX variants (G. Wille and
K. Tittmann, unpublished results).
Kinetic and spectroscopic analysis of
oxidation–reduction in pyruvate oxidase
As considered above, the structural confinements of

the active site and the long distance between the two
cofactors ($ 11 A
˚
between ThDP-C2 and FAD-N5 or
FAD-C4a) relegate a direct carbanion mechanism with
covalent HEThDP-FAD linkage or an alternative
hydride transfer mechanism to minor probability. Fur-
ther experimental evidence arguing against a hydride
transfer mechanism comes from the finding that no
oxidation–reduction can be detected in LpPOX recon-
stituted with 5-deaza-5-carba-FAD, which is a FAD
analogue that functions as a good hydride acceptor
but does not catalyze single electron transfer [45]. Fur-
thermore, FAD reduction kinetics exhibits no kinetic
solvent isotope effect. Conclusively, two-electron
reduction of the flavin by the HEThDP carban-
ion ⁄ enamine should take place in two sequential one-
electron transfer steps coupled to proton transfer.
Stopped-flow kinetics and spectroscopic analysis of the
reductive half-reaction (i.e. single turnover reduction
of the flavin under anaerobic conditions) could not
demonstrate transient formation of flavin radicals
[45,46]. Two-electron reduction of the flavin occurred
with a k
obs
of approximately 10
2
s
)1
at saturating

pyruvate concentrations. The inability to observe radi-
cal intermediates cannot, however, rule out a two-step
sequential electron transfer mechanism because a
kinetic stabilization of radical intermediates requires
the transfer of the second electron (k
red
2
) to proceed at
a comparable rate or slower than that which occurs
for the first electron (k
red
1
). No transient radicals will
be kinetically stabilized when k
red
2
» k
red
1
. Initial
Fig. 5. Stereo drawing of the active site of
pyruvate oxidase from L. plantarum (Protein
Data Bank code: 1pox) showing the cofac-
tors ThDP and FAD and selected proximal
amino acid residues. The amino acid resi-
dues contributed by the corresponding
subunits are colored individually (green or
pink). The two Phe residues suggested to
be involved in electron transfer are
indicated.

K. Tittmann Redox reactions of thiamin diphosphate enzymes
FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS 2463
kinetic investigations of the reductive half-reaction of
LpPOX were conducted in phosphate buffer [45].
Although phosphate is a substrate for the overall reac-
tion, it was not suspected a priori to play a catalytic
role for FAD reduction under the chosen single turn-
over conditions (i.e. it was added as a stabilizing agent
to the reaction mixture).
Much to our surprise, transient FAD radicals could
be detected in the course of the reductive half-reaction
when the experiments were conducted in buffer devoid
of phosphate (i.e. in PIPES or MES buffer) [46].
Kinetic analysis at substrate saturation and different
temperatures, and treatment of the two observed rate
constants of flavin reduction (radical formation and
radical depletion) according to Marcus theory,
revealed radical formation to occur with a k
obs
of
approximately 10
2
s
)1
. Electron transfer is gated (rate-
limited) by a slower preceding chemical (adiabatic)
step of catalysis (i.e. pyruvate addition to ThDP
and ⁄ or decarboxylation). By contrast, decay of the
putative HEThDP–FAD radical pair (k
obs

$ 3s
)1
)isa
true electron transfer reaction [46]. In summary, the
kinetic experiments pinpointed a crucial role of phos-
phate for facilitating transfer of the second electron
from the HEThDP radical to the FAD radical,
whereas no such role is evident for transfer of the first
reducing equivalent from the HEThDP enamine to
FAD in the oxidized state.
A coupling mechanism of oxidation–reduction
and acyl transfer?
What could be the catalytic role of phosphate as a
mediator for electron transfer between HEThDP and
FAD? By theory, an enhanced rate of electron transfer
could result from a larger driving force of the reaction
(i.e. a change of the redox potentials of the donor
and ⁄ or acceptor pair), a shorter tunneling pathway
between donor and acceptor, a decreased reorganiza-
tion energy, an increased packing density in the inter-
reactant space, or as a result of a change in chemistry
of oxidation–reduction. At first, a scenario could be
envisioned in which phosphate bridges the pathway
(i.e. it binds in the active center crevice right inbetween
of HEThDP and FAD). Cryo-crystallographic studies
on LpPOX clearly argue against this mechanism. In
the X-ray structure of LpPOX with the HEThDP
enamine resembling the situation prior to electron
transfer, phosphate is not bound in the presumed
through-space tunneling pathway but rather in close

proximity to the essentially planar HEThDP enamine
in an almost perfect orientation for later nucleophilic
attack onto C2a [47]. On account of fluorescence
resonance energy transfer experiments employing the
fluorescent ThDP analogue N
3
¢-pyridyl-ThDP and
X-ray crystallographic studies, binding of phosphate
could be shown to not induce structural changes of the
active center, and neither cofactor orientation nor
edge-to-edge distance are different in the presence or
absence of phosphate [46,47]. The same observation
holds true for the packing density between the two
cofactors. It was also established that phosphate has
no impact on the midpoint redox potential of enzyme-
bound FAD (E
m
$ )0.06 V) and the thermodynamic
stabilization of FAD radicals by LpPOX [46].
Conclusively, many of the mechanisms considered
above are highly unlikely to explain the role of phos-
phate for facilitating transfer of the second reducing
equivalent.
A mechanism that could account for the observed
rate enhancement of electron transfer by phosphate is
a coupling mechanism of oxidation–reduction and acyl
transfer. Accordingly, after one-electron reduction of
FAD by the HEThDP enamine, phosphate could
attack the neutral AcThDP-type radical to give a tetra-
hedral phospho anion radical adduct (Fig. 6A), the

negative charge of which would certainly make it a
low-potential intermediate and thus increase the free
driving force of the reaction [46,47]. In an alternative
mechanism (Fig. 6B), phosphate could add to the
HEThDP cation radical, followed by homolytic frag-
mentation to the ThDP ylide and an O-protonated
acetyl phosphate radical [13,46]. The latter would then
transfer the second electron to FAD yielding O-pro-
tonated acetyl phosphate and two-electron reduced
FAD. The reaction is then completed by deprotona-
tion of acetyl phosphate.
Reaction mechanism of pyruvate
oxidase from Escherichia coli
Pyruvate oxidase from E. coli (EcPOX) catalyzes a
similar intramolecular redox reaction as LpPOX, also
involving two-electron oxidation of the HEThDP
enamine by a neighboring FAD cofactor. Unlike
LpPOX, EcPOX does not produce the energy-rich
product acetyl phosphate, but rather acetate [11].
Analysis of the reductive half-reaction by transient
kinetics revealed that no radical intermediates are
kinetically stabilized under all sets of conditions tested
[46]. This result, however, is not unexpected because
there is no chemical need for a kinetically stabilized
HEThDP radical as in PFOR or LpPOX, where nucle-
ophiles (CoA, phosphate) add to the ThDP-based radi-
cal in a coupling mechanism of acyl transfer and
oxidation–reduction.
Redox reactions of thiamin diphosphate enzymes K. Tittmann
2464 FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS

It was noted earlier above that EcPOX is a peri-
pheral membrane protein that locates to the cytosol in
the resting state and becomes recruited to the biologi-
cal membrane only after reduction of the flavin cofac-
tor. At the membrane, electrons are transferred to final
acceptor Q8, a mobile electron carrier of the respira-
tory chain. Binding to the membrane in vivo or, alter-
natively, mild proteolytic digestion in vitro stimulate
the catalytic proficiency of EcPOX by a few hundred-
fold [48]. Transient kinetic studies undertaken by
Bertagnolli and Hager [49] suggested that an approxi-
mately 100-fold enhanced oxidation–reduction between
HEThDP and FAD is the major source of catalytic
stimulation related to this activation phenomenon. The
X-ray structure of EcPOX could be solved in the rest-
ing and in the activated state and revealed a Phe resi-
due to swing into the active site upon activation,
occupying the position observed for a conserved Phe
in the constitutively active POXs from Lactobacillae
(Fig. 7). It is premature to make any definitive conclu-
sions about the discrete chemical role of the suspicious
Phe residue for electron transfer, although it is clear
that the structural transition and functional activation
are somehow linked [50]. Noteworthy, in the related
enzymes glyoxylate carboligase and acetohydroxy acid
synthase, which also contain ThDP and FAD as cofac-
tors but do not catalyze redox chemistry, no such Phe
residue exists as it does in EcPOX or LpPOX [51,52].
Fig. 6. Alternative reaction mechanisms of phosphorolysis in LpPOX taking into account the addition of phosphate to a neutral AcThDP
radical (A) or HEThDP cation radical (B).

Fig. 7. Superposition of the active sites of
EcPOX in the resting state (green; Protein
Data Bank code: 3ey9) and after proteolytic
activation (yellow; Protein Data Bank code:
3eya) in stereo view. The position of residue
Phe465 suspected to be involved in oxida-
tion–reduction is highlighted.
K. Tittmann Redox reactions of thiamin diphosphate enzymes
FEBS Journal 276 (2009) 2454–2468 ª 2009 The Author Journal compilation ª 2009 FEBS 2465
Conclusions
ThDP-dependent enzymes catalyze an amazing variety
of different chemical reactions, among which the
oxidative decarboxylation of 2-keto acids is a funda-
mental process of intermediary metabolism in all
organisms. ThDP enzyme-catalyzed oxidation of keto
acids is coupled to the formation of energy-rich meta-
bolites such as acyl-CoA conjugates or acyl phosphate
and the concomitant generation of reducing equiva-
lents. The underlying chemistry is demanding, as
demonstrated by the poor yields and rates observed in
models. ThDP enzymes have evolved a sui generis
versatility in combining the elegant radical chemistry
of ThDP in tandem with iron-sulfur clusters, flavins,
lipoic acid and CoA; delicately balanced acid ⁄ base
catalysis; and perfectly organized redox chains to
successfully meet this challenge.
Acknowledgements
Insightful discussions with Perry Frey, Sandro Ghisla,
Wolfgang Buckel and Steve Ragsdale are gratefully
acknowledged. This review is dedicated to Professor

Alfred Schellenberger on the occasion of his 80th
birthday.
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