An Efficient Protocol for the Palladium-Catalyzed Asymmetric Decarboxylative Allylic Alkylation Using Low Palladium Concentrations and a Palladium(II) Precatalyst

Article abstract of DOI:10.1002/adsc.201500253

Enantioselective catalytic allylic alkylation for the synthesis of 2-alkyl-2-allylcycloalkanones and 3,3-disubstituted pyrrolidinones, piperidinones and piperazinones has been previously reported by our laboratory. The efficient construction of chiral all

Full text of DOI:10.1002/adsc.201500253

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DOI: 10.1002/adsc.201500253
An Efficient Protocol for the Palladium-Catalyzed Asymmetric
Decarboxylative Allylic Alkylation Using Low Palladium
Concentrations and a Palladium(II) Precatalyst
Alexander N. Marziale,a Douglas C. Duquette,a Robert A. Craig II,a Kelly E. Kim,a
Marc Liniger,a Yoshitaka Numajiri,a and Brian M. Stoltza,*
a
The Warren and Katharine Schlinger Laboratory for Chemistry and Chemical Engineering, Division of Chemistry and
Chemical Engineering, California Institute of Technology, 1200 E. California Blvd, MC 101-20, Pasadena, CA 91125, USA
Fax: (+1)-626-395-8436; e-mail: stoltz@caltech.edu
Received: March 13, 2015; Revised: May 21, 2015; Published online: July 14, 2015
Dedicated to Professor Stephen L. Buchwald on the occasion of his 60th birthday.
Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/adsc.201500253.
Abstract: Enantioselective catalytic allylic alkyla-
tion for the synthesis of 2-alkyl-2-allylcycloalkan-
ones and 3,3-disubstituted pyrrolidinones, piperidi-
nones and piperazinones has been previously re-
ported by our laboratory. The efficient construction
of chiral all-carbon quaternary centers by allylic al-
kylation was previously achieved with a catalyst de-
rived in situ from zero-valent palladium sources and
chiral phosphinooxazoline (PHOX) ligands. We
now report an improved reaction protocol with
broad applicability among different substrate
classes in industry-compatible reaction media using
loadings of palladium(II) acetate as low as
0.075 mol% and the readily available chiral PHOX
ligands. The novel and highly efficient procedure
enables facile scale-up of the reaction in an eco-
nomical and sustainable fashion.
action conditions is limited. The palladium-catalyzed
decarboxylative asymmetric allylic alkylation is a pow-
erful and reliable approach to bridge this gap.[3]
This class of reactions was developed in the 1980s
by Tsuji and co-workers, employing various sub-
strates, such as allyl enol carbonates[4] or b-keto
esters.[5] Over the past decade our group has made
significant contributions to this field; our initial ef-
forts resulted in the first catalytic enantioselective
Tsuji allylic alkylation of simple alkanone derivatives
in 2004.[6] We have since expanded the scope of this
transformation considerably[7] and elucidated the cata-
lytic cycle through mechanistic investigations.[8] Nu-
merous applications of this technology in the field of
natural product synthesis have been demonstrated by
our group[9] and others,[10] highlighting the power and
broad applicability of this reaction.
Despite the importance of palladium-catalyzed de-
carboxylative asymmetric alkylation in total synthesis,
its application on an industrial scale is hampered by
the need for high catalyst loadings (5.0–10.0 mol%).
The high cost of palladium significantly increases the
cost of each reaction. Furthermore, high catalyst load-
ings also increase the risk of poisoning downstream
Keywords: allylic alkylation; asymmetric catalysis;
palladium; quaternary center; scale-up
The catalytic enantioselective construction of all- chemistry or contaminating active pharmaceutical in-
carbon quaternary centers represents a considerable gredients.[11]
challenge in synthetic organic chemistry.[1,2] A new
carbon carbon bond must be formed in the face of enantioselective allylic alkylation on a larger scale.
significant steric hindrance to accomplish this goal.
These drawbacks have prevented application of the
À
The application of transition metal catalysis to indus-
Synthetic methods for the generation of quaternary try-scale synthesis requires transformations that are
stereocenters are extremely desirable given their safe, robust, cost-effective, and scalable.[12] Conse-
prevalence in a broad variety of biologically active quently, there remains a significant need to develop
natural products.[2] Despite their importance, the new reaction protocols that employ lower catalyst
number of highly enantioselective transformations concentrations and hence facilitate the scale-up of
that construct quaternary stereocenters under mild re- such transformations.
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Palladium-Catalyzed Asymmetric Decarboxylative Allylic Alkylation
Table 1. Comparison between palladium precursors in differ-
ent oxidation states.
Scheme 1. Pd-catalyzed enantioconvergent decarboxylative
allylic alkylation.
Entry Ligand
[mmol]
Pd source
[mol%]
Yield
[%][a]
ee
[%][b]
Therefore, we began to question the existing proto-
cols and reinvestigated critical reaction parameters
such as the palladium source, catalyst loading, solvent
and temperature, with respect to the scalability of our
reaction and its compatibility with industry require-
ments.
We first turned our attention to the palladium
source in an effort to replace the oxygen-sensitive
Pd2(dba)3 used in our original conditions. Therefore,
the original catalytic enantioconvergent decarboxyla-
tive allylic alkylation of allyl 1-methyl-2-oxocyclohex-
anecarboxylate (1a) was chosen as a model reaction
(Scheme 1).[13]
1
2
3
4
5
6
7
8
3 10.0
4 10.0
3 10.0
4 10.0
3 1.0
4 1.0
3 1.0
Pd(OAc)2 1.0
Pd(OAc)2 1.0
Pd2(dba)3 1.0
Pd2(dba)3 1.0
Pd(OAc)2 0.1
Pd(OAc)2 0.1
Pd2(dba)3 0.1
Pd2(dba)3 0.1
99
99
99
90
99
99
12
14
86
82
84
82
79
83
n.d.
n.d.
4 1.0
[a]
[b]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by chiral GC.[17]
The catalytic cycle of the allylic alkylation operates selectivities at only 0.10 mol% Pd (Table 1, entries 5
starting from a zero-valent palladium source and is and 6). When 0.10 mol% Pd2(dba)3 was used to form
believed to involve a palladium(0/II) redox cycle.[8]
the catalyst, a dramatic decrease in yields was ob-
While utilization of Pd2(dba)3 renders in situ reduc- served (Table 1, entries 7 and 8).
tion of the catalyst obsolete, its application is ham-
We then became interested to see if other palladiu-
pered not only by increased sensitivity to oxygen but m(II) sources were equally suited to catalyze the de-
also by difficulties in separating the dibenzylideneace- carboxylative allylic alkylation. Consequently, a total
tone ligand from non-polar reaction products.
of eight different commercially available Pd(II) pre-
In their original reports Tsuji and co-workers per- cursors were examined in our model reaction in the
formed the allylic alkylation reactions in the presence presence of ligand 3.[16] While with Pd(OAc)2 a quanti-
of Pd(OAc)2 and PPh3.[4,5a] We adopted this strategy tative yield for the desired allylic alkylation product
and started screening a variety of Pd(II) sources in was obtained, none of the other palladium(II) sources
combination with the chiral phosphinooxazoline li- promoted any conversion of the substrate. We reason
gands (S)-t-BuPHOX 3[14] and (S)-(CF3)3-t-BuPHOX that the limited solubility of these palladium salts in
4 (Figure 1).[15]
TBME likely prevented product formation.
When comparing Pd(OAc)2 and Pd2(dba)3 at
Limited to Pd(OAc)2 as the only viable palladium
1.0 mol% palladium in combination with a ten-fold precursor, we turned our attention to minimizing the
excess of PHOX ligands 3 or 4, respectively, in catalyst loading. A screening of six different catalyst
TBME at 808C, we were pleased to find that both loadings, ranging from 0.05 mol% to 1.0 mol%, was
palladium sources exhibited comparable catalytic per- performed (Table 2). All reactions were conducted in
formance (Table 1, entries 1–4). At lower palladium the presence of a ten-fold excess of ligand with re-
concentrations, however, Pd(OAc)2 was clearly supe- spect to palladium, in TBME at 408C.[18]
rior, delivering quantitative yields and good enantio-
Under these reaction conditions, palladium loadings
as low as 0.10 mol% were sufficient to deliver the de-
sired allylic alkylation product in 90% yield and with
high enantioselectivity (Table 2, entry 5). To obtain
a quantitative yield of ketone 2a, the catalyst loading
was increased to 0.15 mol% of Pd(OAc)2 (Table 2,
entry 4). Enantioselective allylic alkylation reactions
are typically performed in solvents such as THF,[6,19]
DCM,[19b,c] dioxane[2,20] or diethyl ether.[13] While these
solvents are common for academic laboratory scale,
their use prohibits conducting the reaction in an in-
dustrial setting.[21] We sought to overcome this limita-
tion and performed a solvent screening with a total of
Figure 1. Chiral phosphinooxazoline ligands applied in this
investigation.
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Table 2. Optimization of the Pd(OAc)2 loading for the de-
carboxylative allylic alkylation.
Table 4. Optimization of the palladium loading for the de-
carboxylative allylic alkylation at various temperatures.
Yield [%][a]
ee [%][b]
Entry
Pd [mol%]
T [8C]
Yield [%][a]
ee [%][b]
Entry
Pd [mol%]
3 [mol%]
1
2
3
0.075
0.10
0.125
80
60
40
99
99
99
84
88
89
1
2
3
4
5
6
1.00
0.50
0.25
0.15
0.10
0.05
10.0
5.0
2.50
1.50
1.0
99
99
99
99
90
10
90
90
90
89
89
89
[a]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by chiral GC.[17]
[b]
0.50
[a]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by chiral GC.[17]
[b]
Table 5. Scale-up experiments.
Table 3. Optimization of the reaction medium.
Entry Substrate
Scale
T
Pd
Yield ee
[mol] [8C] [mol%] [%] [%]
1
2
cyclohexanone 1a 0.01 60
tetralone 1b 0.02 40
0.150
0.125
95[a] 89[c]
95[b] 88[d]
Entry
Solvent
Yield [%][a]
ee [%][b]
1
2
3
4
5
6
7
8
9
10
TBME
EtOAc
88
89
74
–
64
–
[a]
[b]
[c]
[d]
12[c]
trace
28
Isolated yield, purification by distillation.
Isolated yield, purification by flash chromatography.
Enantiomeric excess measured by chiral GC.
Enantiomeric excess measured by chiral SFC.[17]
acetonitrile
isopropyl acetate
isobutyl acetate
dimethylacetamide
toluene
2-Me-THF
t-amylOH
acetone
17
trace
52
–
80
89
–
sequently, all further experiments were carried out in
TBME.
21
[c]
–
At this point, we considered that the palladium
concentration could be lowered further by performing
the reaction at higher temperatures, and we were in-
terested in the influence of increased reaction temper-
ature on stereoselectivity. All experiments were per-
formed in TBME with a ten-fold excess of ligand 3
(Table 4). A palladium loading as low as 0.075 mol%
12[c]
47
[a]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by chiral GC.
Reaction performed at 608C.[17]
[b]
[c]
ten different solvents that are considered to be safe, afforded ketone 2a in 99% yield when the reaction
sustainable and cost-efficient (Table 3).[21,22]
was performed at 808C, which corresponds to a turn-
Conversion of allyl 1-methyl-2-oxocyclohexanecar- over number of 1320 for the in situ formed catalyst.
boxylate (1a) in TBME resulted in a high yield and Nevertheless, a slightly lower enantioselectivity of
good enantioselectivity (Table 3, entry 1) for com- 84% was observed in this case (Table 4, entry 1). At
pound 2a. When the reaction was performed in vari- 608C and 408C, palladium loadings of 0.10 and
ous alkyl acetates the yields dropped dramatically, to 0.125 mol%, respectively, were sufficient to deliver
12%, 28% and 17% (Table 3, entries 2, 4 and 5, re- the desired product in quantitative yield and retain
spectively). Similarly low yields were observed for re- high enantioselectivity (Table 4, entries 2 and 3).
actions performed in acetonitrile, dimethylacetamide,
To assess the utility of our findings on a large scale,
2-Me-THF, and acetone (Table 3, entries 3, 6, 8 and we then applied the protocol to the 10 and 20 mmol
10). Moderate conversion was found when the reac- scale synthesis of a-quaternary ketones 2a and 2b
tion was performed in toluene (Table 3, entry 7). Con- (Table 5). Both reactions were performed in TBME
with a ten-fold excess of ligand 3. Cyclohexanone 1a
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Palladium-Catalyzed Asymmetric Decarboxylative Allylic Alkylation
Table 6. Optimization of the ligand loading for the decar-
Table 7. Optimization of the reaction concentration.
boxylative allylic alkylation.
Yield [%][a]
ee [%][b]
Entry
Concentration [M]
Yield [%][a]
ee [%][b]
Entry
Ligand 3 [mol%]
1
2
3
4
5
0.40
0.20
0.10
0.05
0.033
99
99
99
99
91
88
88
89
89
87
1
2
3
4
5
1.00
0.80
0.60
0.40
0.20
99
99
99
99
99
88
89
88
88
86
[a]
[a]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by chiral GC.[17]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by chiral GC.[17]
[b]
[b]
was converted on a 10.0 mmol scale (1.96 g) in the
presence of 0.15 mol% (3.37 mg) of Pd(OAc)2 at
608C. The corresponding product 2a was isolated by
distillation in excellent yield and high enantioselectiv-
ity (Table 5, entry 1). Similarly, tetralone substrate 1b
was subjected to enantioselective allylic alkylation
conditions at 408C on a 20 mmol scale (4.89 g). The
desired product 2b was purified by flash chromatogra-
phy and isolated in 95% yield and 88% ee (Table 5,
entry 2).
Table 8. Optimization of the palladium loading for the de-
carboxylative allylic alkylation of lactams.
Entry
Pd [mol%]
4 [mol%]
Yield [%][a]
ee [%][b]
Satisfied with the scalability of our new allylic alky-
lation conditions, we turned our attention to reducing
the ligand loading. A series of six experiments, em-
ploying different quantities of ligand, from 0.20 mol%
to 1.0 mol%, in the presence of 0.10 mol% Pd(OAc)2
was performed (Table 6).
1
2
3
0.50
0.30
0.10
5.0
3.0
1.0
87
85
77
96
97
84
[a]
GC yield relative to an internal standard (tridecane).
Enantiomeric excess measured by HPLC.[17]
[b]
A ligand loading of 0.40 mol%, which corresponds
to a four-fold excess of ligand with respect to palladi- active alkaloids and their potential importance in
um, was sufficient to provide the desired product in pharmaceutical agents.[23] Initial experiments suggest-
quantitative yield and high enantioselectivity (Table 6, ed that higher palladium loadings were required for
entry 4). At a loading of only 0.20 mol% of ligand 3, the decarboxylative allylic alkylation of piperidinones.
however, a slight decrease in enantioselectivity was Consequently, a brief study was performed to deter-
observed (Table 6, entry 5).
mine the minimal palladium loading needed to effi-
Finally, we investigated the influence of concentra- ciently catalyze the reaction (Table 8). The electron-
tion on reactivity. A brief study across five different poor ligand (S)-(CF3)3-t-BuPHOX 4 was applied in
substrate concentrations was executed (Table 7).
the presence of varying amounts of Pd(OAc)2 in
We were pleased to find that the decarboxylative TBME at 608C.[23]
alkylation reaction could be performed in high con-
At 0.10 mol% of Pd(OAc)2 the desired product was
centrations of up to 0.40M without any negative obtained in only 77% yield and a reduced enantiose-
impact on yield or enantiomeric excess (Table 7, lectivity of 84% ee. (Table 8, entry 3) Nevertheless,
entry 1). When the reaction was performed at higher a catalyst concentration of only 0.30 mol% was suffi-
dilution (0.033M) a slight decrease in yield and opti- cient to render the chiral lactam 6a in 85% yield and
cal purity was observed (Table 7, entry 5).
97% ee (Table 8, entry 2). Compared to the original
After optimizing all critical reaction parameters for report, in which 5.0 mol% of Pd2(dba)3 were applied,
the conversion of cyclohexanone substrate 1a we this constitutes a more than thirty-fold decrease in
sought to investigate the substrate scope of this novel palladium loading.
protocol. In particular, the decarboxylative allylic al-
To demonstrate the broad applicability of this novel
kylation of lactams is important, given the prevalence protocol, a total of ten compounds were subjected to
of quaternary nitrogen heterocycles in biologically the improved reaction parameters (Table 9). Asym-
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Alexander N. Marziale et al.
Table 9. Scope of the decarboxylative allylic alkylation.[a]
Entry
1
Product
Protocol
Pd [mol%]
Yield [%]
ee [%]
old
new
5.00
0.125
89
88
89
99[b]
2
old
new
8.00
0.125
97
92
89
85[b]
3
4
5
6
7
old
new
10.0
0.30
97
99
97
85[f]
old
new
10.0
0.50
85
99
95
81[f]
old
new
10.0
0.125
91
94
88
99[f]
old
new
10.0
0.125
89
99
99
80[f]
old
new
5.00
0.10
83
87
70
97[e,f]
8
9
old
new
5.00
0.125
83
93
90
95[f]
old
new
–
0.10
–
–
90
79[c,e,f]
10
old
new
5.00
0.25
78
99
97[d,e,f,h]
99[g]
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Palladium-Catalyzed Asymmetric Decarboxylative Allylic Alkylation
metric allylic alkylation to generate products 2a, 2b in trapped Pd(0)-olefin species that lie outside of the
and 6a was discussed previously in detail (Table 9, en- catalytic cycle.[8b] Furthermore, a variety of critical re-
tries 1–3). Allylmethylpiperidinone 6b and allylfluoro- action parameters such as temperature, concentration,
piperidinone 6d were synthesized in a similar fashion. ligand stoichiometry and choice of solvent were opti-
Yields of 81% and 80%, respectively, and enantiose- mized to increase the scalability and lower the cost
lectivities of up to 99% could be obtained (Table 9, basis for palladium-catalyzed allylic alkylation reac-
entries 4 and 6). In the latter case, a catalyst loading tions. The method is broadly applicable among a varie-
as low as 0.125 mol% was sufficient to yield the prod- ty of substrate classes for both inter- and intramolecu-
uct in near to perfect enantioselectivity. Despite the lar allylic alkylations, and is tolerant of most function-
80-fold reduction in palladium loading compared to al groups because of the neutral reaction conditions
the original procedure, no erosion of enantioselectivi- and modest reaction temperatures. We anticipate
ty was observed (Table 9, entry 6).
these advances will promote the continued use of pal-
Gratifyingly, the novel allylic alkylation protocol ladium-catalyzed allylic alkylation reactions as means
could be applied to seven-membered rings as well; of installing quaternary stereocenters in multi-step
however, despite a near quantitative yield only a re- syntheses in academic laboratories, and hope to see
duced enantiomeric excess of 70% was observed for these reactions used to synthesize valuable molecules
ketone 2c (Table 9, entry 7). Nevertheless, seven- in the chemical and pharmaceutical industries.
membered caprolactam 6e was isolated in 95% yield
and high enantioselectivity (Table 9, entry 8). Notably,
despite the low catalyst loading, cyclohexyl ketal 2d Experimental Section
was generated in 79% yield and good enantioselectiv-
ity through intermolecular allylic alkylation of the General Procedure
corresponding silyl enol ether and allyl methanesulfo-
nate (Table 9, entry 9).
In a nitrogen-filled glove box, a stock solution of Pd(OAc)2
(1.1 mg, 4.9 mmol, in 20 mL TBME) was prepared in a 20-
Finally, cyclohexanedione 2e, which is a critical in-
termediate in the synthesis of (À)-cyanthiwigin F,[9b]
could be accessed through double enantioselective al-
lylic alkylation of the bis(b-keto ester) 1e in excellent
yield and near perfect enantioselectivity using only
0.25 mol% palladium. This corresponds to 5% of the
palladium loading used in the original protocol. De-
spite the considerable reduction in catalyst concentra-
tion the yield for this reaction was improved to 97%
(Table 9, entry 10).
In conclusion, we have reported a novel and highly
efficient protocol for the decarboxylative enantiose-
lective allylic alkylation using palladium acetate and
loadings below 0.50 mol%. For simple quaternary
ketone products metal loadings as low as 0.075 mol%
effectively catalyzed the reaction and generated the
desired products in high yields and enantioselectivi-
ties. Thereby, turnover numbers (TON) of up to 1320
could be reached. We envision that the key for high
catalytic turnover in this system involves the lack of
dba in the reaction mixture, which would likely result
mL scintillation vial. In a separate 1-dram vial, (S)-t-
BuPHOX (1.9 mg, 4.9 mmol) was dissolved in TBME
(1 mL). To a 2-dram vial equipped with a magnetic stirbar,
1.02 mL of the Pd(OAc)2 solution was added (56 mg, 0.25
mmol, 0.125 mol%) followed by 0.51 mL of the (S)-t-
BuPHOX solution (0.97 mg, 2.5 mmol, 1.25 mol%). This
mixture was stirred at ambient temperature (288C) in the
glove box for 30–40 min. Substrate (0.20 mmol, 1.0 equiv.)
was taken up in TBME (0.5 mL) and added to the stirring
catalyst solution. In reactions analyzed by GC, tridecane
(24 mL, 0.1 mmol, 0.5 equiv.) was added. The reaction was
sealed with a Teflon-lined cap, removed from the glove box
and stirred at the indicated temperature for the indicated
duration of time. At this point, the reaction was analyzed by
GC, or passed through a silica plug, concentrated under
vacuum, and purified by distillation or column chromatogra-
phy.
[a]
Conditions: reactions were performed according to the “general procedure” in TBME at 608C with a ten-fold excess of
ligand 3 with respect to Pd.
Temperature: 408C.
Temperature: 328C.
Temperature: 278C.
Reaction performed in toluene.
Ligand 4 was used.
Diketone 2e was obtained in 4.85:1.00 dr.
[b]
[c]
[d]
[e]
[f]
[g]
[h]
Isolated yield. GC yield relative to an internal standard (tridecane). Enantiomeric excess measured by chiral GC, HPLC or
SFC.[17]
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Alexander N. Marziale et al.
Iwashita, S. C. Virgil, B. M. Stoltz, Chem. Eur. J. 2011,
17, 14199–14223.
Acknowledgements
[8] a) J. A. Keith, D. C. Behenna, J. T. Mohr, S. Ma, S. C.
Marinescu, J. Oxgaard, B. M. Stoltz, W. A. Goddard III,
J. Am. Chem. Soc. 2007, 129, 11876–11877; b) N. H.
Sherden, D. C. Behenna, S. C. Virgil, B. M. Stoltz,
Angew. Chem. 2009, 121, 6972–6975; Angew. Chem.
Int. Ed. 2009, 48, 6840–6843; c) J. A. Keith, D. C. Be-
henna, N. Sherden, J. T. Mohr, S. Ma, S. C. Marinescu,
R. J. Nielsen, J. Oxgaard, B. M. Stoltz, W. A. Goddar-
d III, J. Am. Chem. Soc. 2012, 134, 19050–19060.
[9] For examples of total syntheses, see: a) R. M. McFad-
den, B. M. Stoltz, J. Am. Chem. Soc. 2006, 128, 7738–
7739; b) J. A. Enquist Jr, B. M. Stoltz, Nature 2008, 453,
1228–1231; c) J. J. Day, R. M. McFadden, S. C. Virgil,
H. Kolding, J. L. Alleva, B. M. Stoltz, Angew. Chem.
2011, 123, 6946–6950; Angew. Chem. Int. Ed. 2011, 50,
6814–6818; d) A. Y. Hong, B. M. Stoltz, Angew. Chem.
2012, 124, 9812–9816; Angew. Chem. Int. Ed. 2012, 51,
9674–9678.
We wish to thank the NIH-NIGMS (R01M080269), Amgen,
AbbVie, Boehringer Ingelheim, and Caltech for financial sup-
port. This material is based upon work supported by the
German National Academy of Sciences Leopoldina under
Grant No. LPDS 2011-12 (fellowship to A.N.M.). D.C.D. is
grateful for financial support from the National Science
Foundation (Predoctoral Research Fellowship, No. DGE-
1144469). We also wish to thank the National Cancer Institute
of the National Institutes of Health under Award Number
F31A174359 (fellowship to R.A.C.), and the Swiss National
Science Foundation (SNSF, fellowship for M.L.). Y.N. thanks
Toray Industries, Inc. for a postdoctoral fellowship. Dr. Scott
Virgil is acknowledged for assistance with instrumentation.
Dr. John A. Enquist and Dr. Nathaniel H. Sherden are ac-
knowledged for preliminary experimental work related to
these results. Dr. Douglas C. Behenna is acknowledged for in-
sightful discussions.
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