Proc. Natl. Acad. Sci. USA
Vol. 89, pp. 4285-4289, May 1992
Humanization of an anti-p185HER2 antibody for human
(antibody engineering/site-directed mutagenesis/c-erbB-2/neu)
PAUL CARTER*, LEN PRESTA*, CORNELIA M. GORMANt, JOHN B. B. RIDGWAYt, DENNIS HENNERt,
WAI LEE T. WONGt, ANN M. ROWLANDf, CLAIRE KoTTs*, MONIQUE E. CARVERt,
AND H. MICHAEL SHEPARD§
Departments of *Protein Engineering, tCell Genetics, tMedicinal and Analytical Chemistry, and §Cell Biology, Genentech Inc., 460 Point San Bruno
Boulevard, South San Francisco, CA 94080
Communicated by Hilary Koprowski, January 16, 1992 (receivedfor review February 15, 1991)
directed against human epidermal growth factor receptor 2
(pl85"m), specifically inhibits proliferation of human tumor
cells overexpressing p185HER2. However, the efficacy of
mumAb4D5 in human cancer therapy is likely to be limited by a
human anti-mouse antibody response and lack of effector func-
tions. A "hum" antibody, humAb4D5-1, containing only
the antigen binding loops from mumAb4D5 and human variable
region framework residues plus IgG1 constant do
constructed. Light-andheavy-chainvariableregionswere simul-
taneously humned in one step by "gene conversion mutagen-
esis" using 311-mer and 361-mer preassembled oligonudleotides,
respectively. The humAb4D5-1 variant does not block the pro-
liferation of human breast carcinoma SK-BR-3 cells, which
overexpress pl85mm, despite tight antigen binding (Kd = 25
nM). One of seven additiona humai
molecular modeling (humAb4D5-8) binds the pl85"IM2 antigen
250-fold and 3-fold more tightly than humAb4D5-1 and
mumAb4D5,respectively. In addition, humAb4D5-8 has potency
comparable to the uinre antibody in blocking SK-BR-3 cell
proliferation. Furthermore, humAb4D5-8 ismuch more efficient
in supporting antibody-dependent cellular cytotoxicity against
SK-BR-3 cells than mumAb4D5, but it does not efficiently kill
WI-38 cells, which express p185HFR2 at lower levels.
The protooncogene HER2 encodes a protein tyrosine kinase
(pl85HER2) that is homologous to the human epidermal
growth factor receptor (1-3). Amplification and/or overex-
pression of HER2 is associated with multiple human malig-
nancies and appears to be integrally involved in progression
of 25-30%o of human breast and ovarian cancers (4, 5).
Furthermore, the extent of amplification is inversely corre-
lated with the observed median patient survival time (5). The
murine monoclonal antibody mumAb4D5 (6), directed
against the extracellular domain (ECD) of p185HER2, specif-
ically inhibits the growth of tumor cell lines overexpressing
p185HER2 in monolayer culture or in soft agar (7, 8).
mumAb4D5 also has the potential of enhancing tumor cell
sensitivity to tumor necrosis factor (7, 9). Thus, mumAb4D5
has potential for clinical intervention in carcinomas involving
the overexpression of p185HER2.
A major limitation in the clinical use of rodent mAbs is an
anti-globulin response during therapy (10, 11). A partial
solution to this problem is to construct chimeric antibodies by
coupling the rodent antigen-binding variable (V) domains to
human constant (C) domains (12-14). The isotype of the
human C domains may be varied to tailor the chimeric
antibody for participation in antibody-dependent cellular
cytotoxicity (ADCC) and complement-dependent cytotoxic-
ity (CDC) (15). Such chimeric antibody molecules are still
=30% rodent in sequence and are capable of eliciting a
significant anti-globulin response.
Winter and coworkers (16-18) pioneered the "humaniza-
tion" of antibody V domains by transplanting the comple-
mentarity determining regions (CDRs), which are the hyper-
variable loops involved in antigen binding, from rodent
antibodies into human V domains. The validity of this ap-
proach is supported by the clinical efficacy of a humanized
antibody specific for the CAMPATH-1 antigen with two
non-Hodgkin lymphoma patients, one of whom had previ-
ously developed an anti-globulin response to the parental rat
antibody (17, 19). In some cases, transplanting hypervariable
loops from rodent antibodies into human frameworks is
sufficient to transfer high antigen binding affinity (16, 18),
whereas in other cases it has been necessary to also replace
one (17) or several (20) framework region (FR) residues. For
a given antibody, a small number of FR residues are antici-
pated to be important for antigen binding. First, there are a
few FR residues that directly contact antigen in crystal
structures of antibody-antigen complexes (21). Second, a
number of FR residues have been proposed (22-24) as
critically affecting the conformation of particular CDRs and
thus their contribution to antigen binding.
Here we report the rapid and simultaneous humanization of
heavy-chain (VH) and light-chain (VL) V region genes of
mumAb4D5 by using a "gene conversion mutagenesis" strat-
egy (43). Eight humanized variants (humAb4D5) were con-
structed to probe the importance of several FR residues
identified by our molecular modeling or previously by others
(22-24). Efficient transient expression of humanized variants
in nonmyeloma cells allowed us to rapidly investigate the
relationship between binding affinity for pl85HER2 ECD and
antiproliferative activity against p185HER2 overexpressing car-
MATERIALS AND METHODS
Cloning of V Region Genes. The mumAb4D5 VH and VL
genes were isolated by PCR amplification ofmRNA from the
corresponding hybridoma (6) as described (25). N-terminal
sequencing ofmumAb4D5 VL and VH was used to design the
sense-strand PCRprimers, whereas the anti-sense PCR prim-
ers were based on consensus sequences of murine FR resi-
Abbreviations: mumAb4D5 and humAb4D5, murine and humanized
versions of the monoclonal antibody 4D5, respectively; ECD, ex-
tracellular domain; ADCC, antibody-dependent cellular cytotoxic-
ity; CDC, complement-dependent cytotoxicity; CDR, complemen-
tarity-determining region; FR, framework region; VH and VL, vari-
able heavy and light domains, respectively; C region, constant
region; V region, variable region.
The publication costs of this article were defrayed in part by page charge
payment. This article must therefore be hereby marked "advertisement"
in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Proc. Natl. Acad. Sci. USA 89 (1992)
DVNTAV A WY
QVQQQS NIK TYIWV
dues (25, 26) incorporating restriction sites for directional
cloning shown by underlining and listed after the sequences:
VL sense, 5'-TCCGATATCCAGCTGACCCAGTCTCCA-3'
EcoRV; VL antisense, 5'-GTTTGATCTCCAGCTTGG-
TACCHSCDCCGAA-3' Asp718; VH sense, 5'-AGGTSM-
ARCTGCAGSAGTCWGG-3' Pst I; VH antisense, 5'-
BstEII; where H is A, C, or T; S is C or G; D is A, G, or T;
M isA orC; R is A orG;W is A orT. The PCR products were
cloned into pUC119 (27) and five clones for each V domain
were sequenced by the dideoxynucleotide chain-termination
Molecular Modeling. Models of mumAb4D5 VH and VL
domains were constructed by using seven Fab crystal struc-
tures from the Brookhaven Protein Data Bank (entries 2FB4,
2RHE, 2MCP, 3FAB, 1FBJ, 2HFL, and 1REI) (29). VH and
VL of each structure were superimposed on 2FB4 by using
main-chain atom coordinates (INSIGHT program, Biosym
Technologies, San Diego). The distances from each 2FB4 Ca
to the analogous Ca in each of the superimposed structures
was calculated. For residues with all Ca-Ca distances '1A,
the average coordinates for individual N, Ca, C, 0, and CB
atoms were calculated and then corrected for resultant de-
viations from standard bond geometry by 50 cycles ofenergy
minimization (DISCOVER program, Biosym Technologies) us-
ing the AMBER forcefield (30) and fixed Ca atoms. Side chains
ofFR residues were then incorporated, followed by inclusion
of five of the six CDR loops (except VH-CDR3) using
tabulations ofCDR conformations (23) as a guide. Side-chain
conformations were chosen on the basis of Fab crystal
structures, rotamer libraries (31), and packing consider-
ations. Three possible conformations of VH-CDR3 were
taken from a search of similar sized loops in the Brookhaven
Protein Data Bank or were modeled by using packing and
solvent exposure considerations. Models were then sub-
jected to 5000 cycles of energy minimization.
A model ofthe humAb4D5 was generated by using consen-
sus sequences derived from the most abundant human sub-
classes-namely, VL K subgroup I and VH subgroup III (26).
The six CDRs were transferred from the mumAb4D5 model
onto a human Fab model. All humAb4D5 variants contain
acid sequences ofmumAb4D5 and
humAb4D5-5 VL (A) and VH (B)
(numbered according to ref. 26).
The CDR residues according to a
sequence definition (26) and a
structural definition (22) are un-
derlined and overlined, respec-
tively. The 5' and 3' ends of the
oligonucleotides used for gene
conversion mutagenesis are
shown by arrows and mismatches
between genes are shown by as-
terisks. The asparagine-linked gly-
cosylation site (#) in mumAb4D5
VLis used in some mumAb4D5
molecules derived from the corre-
sponding hybridoma. However,
mumAb4D5 variants, which are
glycosylated or aglycosylated in
VL, areindistinguishablein their
binding affinity for the p185HER2
ECD and in their antiproliferative
activity with SK-BR-3 cells (C.K.,
M. Spellman, and B. Hutchins,
Nucleotide and amino
humanreplacements ofmumAb4D5 residues atthree positions
within CDRs as defined by sequence variability (26) but not as
defined by structural variability (22): VL-CDR1 K24R, VL-
CDR2 R54L and VL-CDR2 T56S.1 Differences between
mumAb4D5 and the human consensus FR residues (Fig. 1)
were individually modeled to investigate their possible influ-
ence on CDR conformation and/or binding to pl85HER2 ECD.
Construction of Chimeric Genes. Genes encoding the chi-
meric mAb4D5 light and heavy chains were separately as-
sembled in previously described phagemid vectors contain-
ing the human cytomegalovirus enhancer and promoter, a 5'
intron, and simian virus 40 polyadenylylation signal (32).
Briefly, gene segments encoding mumAb4D5 VL (Fig. 1A)
and REI human K1 light-chain CL (33) were precisely joined
as were genes for mumAb4D5 VH (Fig. 1B) and human IgGl
C region (34) by subcloning (35) and site-directed mutagen-
esis as described (36). The IgG1 isotype was chosen, as it is
the preferred human isotype for supporting ADCC and CDC
by using matched sets of chimeric (15) or humanized anti-
bodies (17). The PCR-generated VL and VH fragments (Fig.
1) were subsequently mutagenized so that they faithfully
represent the sequence of mumAb4D5 determined at the
protein level: VH, Q1E; VL, V104L and T109A. The human
IgG1 C regions are identical to those reported (37) except for
the mutations E359D and M361L (Eu numbering; ref. 26),
which we installed to convert the antibody from the naturally
rare A allotype to the much more common non-A allotype
(26). This was an attempt to reduce the risk of anti-allotype
antibodies interfering with therapy.
Construction of Humaniz
meric mAb4D5 light-chain and heavy-chain Fd fragment (VH
and CH1 domains) were subcloned together into pUC119 (27)
to create pAK1 and were simultaneously humanized in a
single step (43). Briefly, sets of six contiguous oligonucleo-
tides were designed to humanize VH and VL (Fig. 1). These
oligonucleotides are 28-83 nucleotides long, contain 0-19
mismatches to the murine antibody template, and are con-
Genes. Genes encoding chi-
Variants are denoted by the amino acid residue and number
followed by the replacement amino acid.
Immunology:Carter et al.
Proc. Natl. Acad. Sci. USA 89 (1992)
strained to have 8 or 9 perfectly matched residues at each end
to promote efficient annealing and ligation of adjacent oligo-
nucleotides. The sets of VH and VL humanization oligonu-
cleotides (5 pmol each) were phosphorylated with eitherATP
or [y-32P]ATP (36) and separately annealed with 3.7 pmol of
pAK1 template in 40 ,ul of 10 mM Tris HCl (pH 8.0) and 10
mM MgCl2 by cooling from 100°C to =20°C over =20 min.
The annealed oligonucleotides were joined by incubation
with T4 DNA ligase (12 units; New England Biolabs) in the
presence of2 ,l4 of5 mM ATP and 2Alof0.1 M dithiothreitol
for 10 min at 14°C. After electrophoresis on a6% acrylamide
sequencing gel, the assembled oligonucleotides were located
by autoradiography and recovered by electroelution. The
assembled oligonucleotides (-0.3 pmol each) were simulta-
neously annealed to 0.15 pmol of single-stranded deoxyuri-
dine-containing pAK1 prepared as described (38) in 10 pul of
40 mM Tris HCl (pH 7.5) and 16 mM MgCl2 as described
above. Heteroduplex DNA was constructed by extending the
primers with T7 DNA polymerase and transformed into
Escherichia coli BMH 71-18 mutL as described (36). The
resultant phagemid DNA pool was enriched first for human
VL by restriction purification usingXho I and then for human
VH by restriction selection using Stu I as described (36, 39).
Resultant clones containing both human VL and human VH
genes were identified by nucleotide sequencing (28) and
designated pAK2. Additional humanized variants were gen-
erated by site-directed mutagenesis (36). The mumAb4D5 VL
and VH gene segments in the transient expression vectors
described above were then precisely replaced with their
Expression and Purification of mAb4D5 Variants. Appro-
priate mAb4D5 light- and heavy-chain cDNA expression
vectors were cotransfected into adenovirus-transformed hu-
man embryonic kidney cell line 293 by a high-efficiency
procedure (32). Media were harvested daily for up to 5 days
and the cells were refed with serum-free medium. Antibodies
were recovered from the media and affinity purified on
protein A-Sepharose CL-4B (Pharmacia) as described by the
manufacturer. The eluted antibody was buffer-exchanged
into phosphate-buffered saline by G25 gel filtration, concen-
trated by ultrafiltration (Amicon), sterile-filtered, and stored
at 4°C. The concentration of antibody was determined by
both total IgG and antigen binding ELISAs. The standard
used was humAb4D5-5, whose concentration had been de-
termined by amino acid composition analysis.
Cell Proliferation Assay. The effect ofmAb4D5 variants on
proliferation of the human mammary adenocarcinoma cell
line SK-BR-3 was investigated as described (6) by using
saturating mAb4D5 concentrations.
Affinity Measurements. mAb4D5 variant antibodies and
p185HER2ECD were prepared as described (40) and incubated
in solution until equilibrium was found to be reached. The
concentration of free antibody was then determined by
ELISA using immobilized p185HER2 ECD and was used to
calculate affinity (Kd) as described (41). The solution-phase
equilibrium between p185HER2 ECD and mAb4D5 variants
was found not to be grossly perturbed during the immobilized
ECD ELISA measurement of free antibody.
Humanization of mumAb4D5. The mumAb4D5 VL and VH
gene segments were firstclonedbyPCRand sequenced (Fig. 1).
The V region genes were then simultaneously humanized by
gene conversion mutagenesis using preassembled oligonucleo-
tides. A 311-mer oligonucleotide containing 39 mismatches to
the template directed 24 simultaneous amino acid changes
required to humanize mumAb4D5 VL. Humanization of
mumAb4D5 VH required 32 amino acid changes, which were
installed with a 361-mer containing 59 mismatches to the
mumAb4D5 template. Two ofeight clones sequenced precisely
encode humAb4D5-5, although one ofthese clones contained a
single nucleotide imperfection. The six other clones were es-
sentially humanized but contained a small numberoferrors: <3
nucleotide changes and <1 single nucleotide deletion per kilo-
base. Additional humanized variants (Table 1) were constructed
by site-directed mutagenesis of humAb4D5-5.
Expression levels ofhumAb4D5 variants were 7-15 ,g/ml
as judged by ELISA using immobilized p185HER2 ECD.
Successive harvests offive 10-cm plates allowed 200-500 ,g
ofeach variant to be produced in a week. Antibodies affinity
purified on protein A gave a single band on a Coomassie
blue-stained SDS/polyacrylamide gel of mobility consistent
with the expected mass of -150 kDa. Electrophoresis under
reducing conditions gave two bands consistent with the
expected mass of free heavy (48 kDa) and light (23 kDa)
chains (data not shown). N-terminal sequence analysis (10
cycles) gave the mixed sequence expected (see Fig. 1) from
an equimolar combination of light and heavy chains.
humAb4D5 Variants. In general, FR residues were chosen
from consensus human sequences (26) and CDR residues
were chosen from mumAb4D5. Additional variants were
constructed by replacing selected human residues in
humAb4D5-1 with their mumAb4D5 counterparts. These are
VH residues 71, 73, 78, 93, plus 102 and VL residues 55 plus
66. VH residue 71 has previously been proposed by others
(24) to be critical to the conformation of VH-CDR2. Amino
acid sequence differences between humAb4D5 variant mol-
ecules are shown in Table 1 togetherwith theirp185HER2 ECD
p185HER2 ECD binding affinity and anti-proliferative activities of mAb4D5 variants
Human and murine residues are shown in one-letter and three-letter amino acid codes, respectively. Kd values for the pl85HER2 ECD were
determined by the method of Friguet et al. (41) and the standard error of each estimate is ±10%. Proliferation of SK-BR-3 cells incubated for
96 hr with mAb4D5 variants is shown as a percentage of the untreated control as described (7). Data represent the maximal antiproliferative
effect for each variant (see Fig. 2) calculated as the mean of triplicate determinations at a mAb4D5 concentration of8Ag/ml.Data are all taken
from the same experiment and the estimated standard error is ±15%.
Immunology:Carter et al.
Immunology: Carter et al.
[MAb4D5 variant] jig/ml
Relative cell proliferation was determined as described (7) and data
(average of triplicate determinations) are presented as a percentage
ofresults with untreated cultures for mumAb4D5, humAb4D5-8, and
Inhibition ofSK-BR-3 proliferation by mAb4D5 variants.
binding affinity and maximal antiproliferative activities
against SK-BR-3 cells. Very similar Kd values were obtained
for binding mAb4D5 variants to either SK-BR-3 cells (C.K.
and N. Dua, unpublished data) or to p185HER2 ECD (Table 1).
The most potent humanized variant designed by molecular
modeling, humAb4D5-8, contains five FR residues from
mumAb4D5. This antibody binds the p185HER2 ECD 3-fold
more tightly than does mumAb4D5 itself (Table 1) and has
comparable antiproliferative activity with SK-BR-3 cells
(Fig. 2). In contrast, humAb4D5-1 is the most humanized but
least potent mumAb4D5 variant, created by simply installing
the mumAb4D5 CDRs into the consensus human sequences.
humAb4D5-1 binds the pl85HER2 ECD 80-fold less tightly
than does the murine antibody and has no detectable antipro-
liferative activity at the highest antibody concentration in-
The antiproliferative activity of humAb4D5 variants
against pl85HER2 overexpressing SK-BR-3 cells is not simply
correlated with theirbinding affinity for the p185HER2 ECD-
e.g., installation ofthree murine residues into the VH domain
of humAb4D5-2 (D73T, L78A, and A93S) to create
humAb4D5-3 does not change the antigen binding affinity but
does confer significant antiproliferative activity (Table 1).
The importance of VH residue 71 (24) is supported by the
observed 5-fold increase in affinity for pl85HER2 ECD on re-
placementofR71 inhumAb4D5-1 withthecorrespondingmurine
residue, A71(hum.Ab4D5-2). Incontrast, replacing VH L78 in
humAb4D54 with the murine residue A78(humAb4D5-5) does
notsignificantly changetheaffinityfor thep185HER2 ECD or
change antiproliferative activity, suggestingthat residue 78 is not
of critical functionalsignificance to humAb4D5 ininteracting
VL residue 66 isusuallyaglycine in human and murine
K-chainsequences (26)but anarginine occupies thisposition
in themumAb4D5 Klightchain. The side chain of residue 66
islikelyto affect the conformation ofVL-CDR1 and VL-
CDR2 and thehairpinturn at residues 68-69(Fig. 3). Con-
sistent with theimportanceof thisresidue, the mutationVL
G66R (humAb4D5-3 -+ humAb4D5-5) increases theaffinity
for thep185HER2ECDby4-fold with a concomitant increase
From molecularmodeling,itappearsthat the side chain of
mumAb4D5 VLY55mayeither stabilize the conformation of
VH-CDR3orprovidean interaction at theVL-VH interface.
The latter functionmaybedependenton thepresence ofVH
Y102. In the context ofhumAb4D5-5 the mutationsVL ESSY
(humAb4D5-6) and VH V102Y (humAb4D5-7) individually
increase theaffinityforpl85HER2 ECDby 5-fold and 2-fold,
respectively, whereastogether (humAb4D5-8) they increase
theaffinity by11-fold. This is consistent with eitherproposed
roleof VL Y55 andVHY102.
Secondary Immune Functio
efficientlymediates ADCCagainstSK-BR-3 breast carcinoma
cells, whichoverexpress p185HER2 athighlevels asanticipated
from itsIgG1 isotype (Table 2). Incontrast, humAb4D5-8 is
very inefficient inmediating ADCC against the normallung
epithelium cell lineWI-38, whichexpresses p185HER2 at100-
fold lower levels than SK-BR-3 cells (Table 2). The murine
parentantibodyis notveryeffective inmediatingADCCagainst
either SK-BR-3 or WI-38 cells.
mumAb4D5 ispotentially useful for humantherapy since it is
cytostatic toward human breast and ovarian tumor linesover-
expressing pl85HER2. Here we have humanized mumAb4D5 in
anattempttoimproveitspotential clinicalefficacy by reducing
Rapid humanization of humAb4D5 was facilitated by the
gene conversionmutagenesis strategy developed hereusing
long preassembled oligonucleotides. This method uses less
bon tracing for model of hum-
Ab4D5-8 VL and VH. The CDR
residues(26)are shown in boldface
and side chains of VH residues
A71, T73, A78, S93, and Y102 and
VL residues Y55 and R66 (see Ta-
ble 1) are shown.
Stereoview of a-car-
Proc. Natl. Acad Sci. USA 89(1992)
Proc. Natl. Acad. Sci. USA 89 (1992)
Selectivity of ADCC mediated by mAb4D5 variants
mumAb4D5 humAb4D5-8 mumAb4D5 humAb4D5-8
Antibody concentration, 100 ng/ml
Antibody concentration, 10 ng/ml
Sensitivity to ADCC of human cell lines WI-38 (normal lung
epithelium) and SK-BR-3 (breast tumor), which express 0.6 and 64
pg ofp185HER2 perggofcell protein, respectively, as determined by
ELISA (40). ADCC assays were carried out as described (15) using
interleukin 2 activated human peripheral blood mononuclear cells as
effector cells and either WI-38 or SK-BR-3 target cells in 96-well
microtiter plates for4 hr at37C at different antibody concentrations.
Values given represent percentage specific cell lysis as determined
by 51Cr release. The estimated standard error in these quadruplicate
determinations was ±+10o.
than half the amount of synthetic DNA, as does total gene
synthesis, and does not require convenient restriction sites in
the target DNA. Our method appears to be simpler and more
reliable than a similar protocol recently reported (42). Tran-
sient expression of humAb4D5 in human embryonic kidney
293 cells permitted the isolation of0.2- to 0.5-mg humAb4D5
variants for rapid characterization by growth inhibition and
antigen binding affinity assays. Furthermore, different com-
binations of light and heavy chain were readily tested by
cotransfection of corresponding cDNA expression vectors.
The crucial role ofmolecular modeling in the humanization
humAb4D5-8, which binds the p185HER2 ECD 250-fold more
tightly than the simple CDR loop swap variant humAb4D5-1.
It has previously been shown that the antigen binding affinity
of a humanized antibody can be increased by mutagenesis
based on molecular modeling (17, 20). Here we have designed
a humanized antibody that binds its antigen 3-fold more
tightly than the parent antibody and is almost as potent in
blocking the proliferation ofSK-BR-3 cells. While this result
is gratifying, assessment of the success of molecular model-
ing must await the outcome ofongoing x-ray crystallographic
humAb4D5-8 also supports cytotoxicity via ADCC against
SK-BR-3 tumorcells in the presence ofhuman effector cells but
is not effective in directing the killing of normal (WI-38) cells,
which express p185HER2 at much lower levels. This augurs well
for the ongoing treatment of human cancers overexpressing
pl85HER2 by using humAb4D5-8.
is illustrated by the designed variant
We thank Bill Henzel forN-terminal sequence analysis ofmAb4D5
variants; Nancy Simpson for sequencing the cDNAs formumAb4D5
V-region genes; Maria Yang for providing the CL-containing clone;
Susie Wong for performing amino acid composition analysis; Irene
Figari for performing the ADCC assays; Mark Vasser, Parkash
Jhurani, Peter Ng, and Leonie Meima for synthesizing oligonucleo-
tides; Bob Kelley for helpful discussions; and Tony Kossiakoff for
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