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J Biol Chem, Vol. 274, Issue 40, 28206-28212, October 1, 1999
From Hexagonal bilayer hemoglobins (Hbs) are
~3.6-MDa complexes of ~17-kDa globin chains and 24-32-kDa,
nonglobin linker chains in a ~2:1 mass ratio found in annelids and
related species. Studies of the dissociation and reassembly of
Lumbricus terrestris Hb have provided ample evidence for
the presence of a ~200-kDa linker-free subassembly consisting of
monomer (M) and disulfide-bonded trimer (T) subunits. Electrospray
ionization mass spectrometry (ESI-MS) of the subassemblies obtained by
gel filtration of partially dissociated L. terrestris and
Arenicola marina Hbs showed the presence of noncovalent
complexes of M and T subunits with masses in the 213.3-215.4 and
204.6-205.6 kDa ranges, respectively. The observed mass of the
L. terrestris subassembly decreased linearly with an
increase in de-clustering voltage from ~215,400 Da at 60 V to
~213,300 Da at 200 V. In contrast, the mass of the A. marina complex decreased linearly from 60 to 120 V and reached an
asymptote at ~204,600 Da (180-200 V). The decrease in mass was
probably due to the progressive removal of complexed water and alkali
metal cations. ESI-MS at an acidic pH showed both subassemblies to
consist of only M and T subunits, and the experimental masses
demonstrated them to have the composition M3T3.
Because there are three isoforms of M and four isoforms of T in
Lumbricus and two isoforms of M and 5 isoforms of T in
Arenicola, the masses of the M3T3
subassemblies are not unique. A random assembly model was used to
calculate the mass distributions of the subassemblies, using the known
ESI-MS masses and relative intensities of the M and T subunit isforms.
The expected mass of randomly assembled subassemblies was 213,436 Da
for Lumbricus Hb and 204,342 Da for Arenicola
Hb, in good agreement with the experimental values.
The giant extracellular
HBL1 Hbs found in most
terrestrial, aquatic, and marine annelids and in deep sea annelids and
vestimentiferans are ~3.6-MDa complexes of globin subunits and
nonglobin, linker chains and represent a summit of complexity for
oxygen-binding heme proteins (1-4). The most extensively studied
complex is the Hb from the common earthworm Lumbricus
terrestris. Based on the finding of a ~200-kDa globin
subassembly upon mild, partial dissociation of the Hb at neutral pH, a
"bracelet" model of its quaternary structure was proposed to
consist of twelve ~200-kDa globin subassemblies attached to a central
scaffolding of 36-42 linker chains (24-32 kDa) (5). Scanning
transmission electron microscopy mass mapping of the isolated globin
subassembly showed it to have a mass of 202 ± 26 kDa, consonant
with it being a dodecamer of globin chains (~17 × 12 = 204 kDa), [d]3[bac]3, consisting of three
copies each of the monomer M (chain d) and the disulfide-bonded trimer T (chains b + a + c) (6); in addition, this subassembly was
found to be an obligate intermediate in the dissociation and reassembly
of the HBL structure (7). A complete ESI-MS determination of the masses
of the constituent globin and linker chains and the disulfide-bonded
trimer subunit of Lumbricus Hb provided a calculated mass of
213.434 kDa for the subassembly [M]3[T]3
(8). Furthermore, the calculated masses for the Hb comprised of 12 subassemblies and 36 or 42 linker chains, 3.523 and 3.687 MDa, respectively, were in good agreement with the masses determined by
scanning transmission electron microscopy and sedimentation equilibrium
(3.56 ± 0.13 and 3.41 ± 0.39 MDa, respectively) (8). ESI-MS
studies of several other HBL Hbs by Green and his collaborators (9-15)
have provided accurate masses for all the constituent subunits as well
as their relative proportions. The masses calculated based on the model
proposed for Lumbricus Hb are in satisfactory agreement with
the experimentally determined masses of the native Hbs. Furthermore, three-dimensional reconstructions of several HBL Hbs using cryoelectron microscopy have demonstrated unequivocally the overall correctness of
the bracelet model (16-21). Concurrent studies of
Lumbricus Hb and its reassembly subsequent to dissociation
at an alkaline pH by A. F. Riggs and his group have yielded quite
different results (22-24). Multiple angle laser light scattering was
used to determine the mass of the Hb, 4.1 ± 0.1 MDa, and
reassembly of the isolated M and T subunits was interpreted to indicate
a hexadecamer subassembly [M]4[T]4, ~285
kDa (22-24). Based on these results, a Hb model was proposed
consisting of 12 hexadecamer subassemblies and 24 linker chains. A key
point in resolving the differences is a reliable mass for the globin
subassembly. We present the results of an ESI-MS study that provides
accurate masses for the globin subassemblies isolated from the HBL Hbs
of L. terrestris and the marine polychaete Arenicola
marina.
Materials--
L. terrestris Hb was prepared as
described previously (25). A. marina blood was obtained by
direct puncture of the ventral vessel of live animals collected near
Roscoff, and the Hb was prepared as described elsewhere (12). The Hbs
were dissociated at a neutral pH in the presence of ~4 M
urea and subjected to low-pressure, isocratic gel filtration at room
temperature (20 ± 2 °C) using a fast protein liquid
chromatography system (Amersham Pharmacia Biotech) and 2.5 × 50-cm columns of Superose S12 or S6 (Amersham Pharmacia Biotech). The
flow rate was 0.5 ml/min, and the absorbance of the eluate was
monitored at 280 nm. The concentrations of the Hb and the globin
subassembly were determined from the absorbance of the cyanmet forms at
540 nm using the extinction coefficients 0.442 and 0.656 ml·mg Electrospray Ionization Mass Spectrometry--
Sample solutions
in 10 mM ammonium acetate were introduced at 4 µl/min
into the ESI source of either a Quattro LCZ, a tandem quadrupole
instrument whose m/z range was specially extended
to 8000, or a quadrupole time-of-flight instrument (Q-Tof) (Micromass UK Ltd., Wythenshawe, Manchester, United Kingdom) with a
m/z range of 14,000. Data were accumulated over
5-10 min. Mass scale calibration used the
Cs(n+1)In+ ions from separate
introductions of a solution of CsI (1 mg/ml) in 50% aqueous
acetonitrile. The protein samples were diluted to a concentration of
0.5 mg/ml in high pressure liquid chromatography-grade water and
desalted by manually shaking 200 µl of each solution for about 1 min
with ~3 mg of previously washed mixed-bed ion exchange resin beads
(Type AG 501-X8; Bio-Rad), and ammonium acetate was added to a
concentration of 10 mM. The multiply charged data produced
by the mass spectrometer on the m/z scale were
converted to the mass (molecular weight) scale using either Maximum
Entropy-based software (27) or the transformation software (28)
supplied with the instrument. The latter deconvolution method was used for the spectra shown in Fig. 3, because it faithfully preserves the
peak shapes observed in the m/z spectra. Masses
were determined as peak tops in the transformed spectra.
ESI-MS of Lumbricus Hb Subassembly--
Fig.
1 shows the ESI m/z
spectrum (~pH 7) of the ~200-kDa globin subassembly isolated from
Lumbricus Hb by gel filtration of the partially dissociated
Hb as performed repeatedly in our earlier studies (5-7). It was
obtained on the quadrupole time-of-flight instrument at a de-clustering
voltage of 145 V. Three sets of peaks were observed: (a) one
set of peaks corresponding to the intact subassembly with charge states
ranging from 29+ to 38+, with the
34+ and 35+ states being the most abundant; and
(b) two other sets of peaks corresponding to the two
subunits comprising the subassembly, i.e. the ~55-kDa
trimer T with charge states ranging from 14+ to
18+ and the ~17-kDa monomer M with charge states ranging
from 6+ to 9+, respectively. The
inset in Fig. 1 shows the result of deconvoluting the part
of the spectrum containing the multiply charged subassembly peaks by
MaxEnt: a single peak with a mass of 213,909 Da is observed in the
100-330 kDa range.
ESI-MS of Arenicola Hb Subassembly--
The gel filtration elution
profile of partially dissociated Arenicola Hb at a neutral
pH was very similar to the elution profile obtained with
Lumbricus Hb by a variety of means (5-7) and also exhibited
a ~200-kDa subassembly peak. Fig.
2A presents the ESI m/z spectrum of the Arenicola Hb
subassembly obtained at neutral pH on the extended
m/z range quadrupole instrument. The noncovalent complex is observed with charge states similar to those of
Lumbricus (Fig. 1), but it is the dominant species in this
case, with almost insignificant levels of M and T, suggesting that the
Arenicola subassembly is more stable under ESI-MS conditions
than that of Lumbricus. The inset in Fig.
2A shows the result of deconvoluting the raw
m/z data by MaxEnt and exhibits a principal peak
at 204,753 Da with a much smaller subsidiary peak at 205,308 Da. Fig.
2B shows the ESI m/z spectrum of the
Arenicola Hb subassembly obtained under the same mass
spectrometer conditions as described for Fig. 2A but with
the pH value reduced to pH 3.5. Approximately half of the complex was
dissociated into its constituent M and T subunits existing in charge
states similar to those observed in the case of Lumbricus
(Fig. 1). It was found that the addition of ammonium acetate to the
sample solutions was essential in order to observe the subassembly at
adequate sensitivity, with an optimum concentration of 10 mM. Thorough desalting using the ion exchange beads was also necessary, otherwise the peaks were significantly broader, presumably due to the multiple addition of alkali metal ions, mainly
Na+. Although these latter ligands could not be directly
observed in the subassembly, they were distinguishable in association
with the monomer and were significantly reduced after desalting but were not completely eliminated.
Effect of De-clustering Voltage on Mass--
It was also found
that the measured masses of the subassemblies depended to some extent
(<1%) on the amount of de-clustering voltage applied to the ions.
De-clustering occurs when the ions are accelerated through a region
that is intermediate in pressure between their generation at
atmospheric pressure and analysis under high vacuum. This acceleration
by a potential across the intermediate pressure region has the effect
of imparting internal energy to the ions by collisions with the
nitrogen gas in this region, causing them to lose weakly bound ligands
at low potentials, followed by more strongly bound ligands as the
potential is increased. Thus, at low de-clustering potentials, the mass
tends to be higher than at high potentials. Fig.
3 shows a series of mass spectra obtained
on the time-of-flight instrument for the Lumbricus (Fig. 3A) and Arenicola (Fig. 3B)
subassemblies that illustrate the way in which the mass and appearance
of the subassembly peaks change with the de-clustering voltage.
Although the Lumbricus subassembly mass decreased linearly
from ~215,400 Da at 60 V to ~213,300 Da at 200 V, the mass of the
Arenicola subassembly decreased linearly from ~205,570 at
60 V to ~205,100 at 120 V and then tended toward an asymptote at
~204,600 Da in the range 180-200 V. In addition, above about 140 V,
a series of peaks appeared below the major peak that can be attributed
to the loss of up to three heme groups. In the case of
Lumbricus, discrete peaks corresponding to the loss of heme
groups were not observed, although above 140 V, there is an obvious
broadening of the peak on the low mass side of its maximum. Also, the
heme group itself (m/z 616.5) was observed to
appear in the spectra from both samples at about 120 V and then
increased in intensity at higher voltage. The decrease in mass with
increasing de-clustering voltage is most likely due to the loss of
complexed water molecules and possibly some cations. The inability to
observe the distinct loss of heme groups in the case of
Lumbricus could be due in part to the heterogeneity of the
components composing the subassembly, which is substantially greater
than is the case with Arenicola.
Lumbricus Hb contains four globin chains (chains a An additional and very important point that needs to be considered in
comparing the experimental masses of the subassemblies with the masses
calculated from their subunits is the fact that these subassemblies do
not have a unique mass. Because each dodecamer subassembly consists of
three monomers and three trimers, there are essentially two levels of
mass distribution: (a) one for each of the two subunits; and
(b) another for their combination into a dodecamer. In the
case of the Lumbricus Hb subassembly, there are 10 possible
ways of forming three monomers from three different chains (d1-d3),
and the four different trimers (chains b and c with each of chains
a1-a4) provide 20 possible combinations of three trimers; thus, the
total number of possible dodecamer subassemblies (i.e. 3M
and 3T) is 200. For the Arenicola Hb subassembly, there are
4 possible combinations of 3M from two different monomers (chains a1
and a2) and 35 possible combinations of 3T from five different trimers,
leading to 140 possible M3T3 subassemblies. Because the proportions of the subunit isoforms are known
experimentally from previous ESI-MS studies (8, 12), it is possible to
calculate a mass distribution based on a straightforward combinatorial
model (see "Appendix"). The calculated histograms for the
subassembly masses of the two Hbs incorporating only masses with a
probability
Electrospray Ionization Mass Spectrometric Determination of the
Molecular Mass of the ~200-kDa Globin Dodecamer Subassemblies in
Hexagonal Bilayer Hemoglobins*
,,
**
Micromass UK Limited, 3 Tudor Road, Altrincham,
Cheshire WA14 5RZ, United Kingdom, § Department of Mathematics,
Idaho State University, Pocatello, Idaho 83209-8085, ¶ Equipe
Ecophysiologie, Observatoire Océanologique de Roscoff, Station
Biologique, 29682 Roscoff, France, and Department of
Biochemistry and Molecular Biology, Wayne State University School of
Medicine, Detroit, Michigan 48201
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
REFERENCES
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
REFERENCES
EXPERIMENTAL PROCEDURES
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
REFERENCES
1·cm1, respectively (12, 26).
RESULTS
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
REFERENCES
View larger version (26K):
[in a new window]
Fig. 1.
ESI m/z spectrum of the
~200-kDa subassembly from Lumbricus Hb in an aqueous
10 mM ammonium acetate solution at pH 6.5. Inset, result of deconvoluting the ESI spectrum over the
m/z range 5700-7050 by MaxEnt. M and
M1, monomer chain peaks with 0 and 1 heme groups,
respectively. T3, trimer subunit peaks with three heme
groups. D, the dodecamer subassembly peaks. The number
after the colon indicates the number of charges on the ion.
View larger version (27K):
[in a new window]
Fig. 2.
ESI m/z spectrum of the
~200-kDa subassembly from Arenicola Hb in an aqueous
10 mM ammonium acetate solution at pH 6.5 (A) and pH 3.5 (B).
Inset in A, result of deconvoluting the ESI
spectrum over the m/z range 5450-6280 by MaxEnt.
T, T1, and T2, trimer subunit peaks with 0, 1, and 2 heme groups, respectively. Other peak annotation nomenclature is
the same as that described in the Fig. 1 legend.
View larger version (25K):
[in a new window]
Fig. 3.
ESI mass spectra of the subassemblies from
(A) Lumbricus and
(B) Arenicola showing the way in
which the mass and peak shape were calculated using the transformation
software (28) change with de-clustering voltage over the 60-200 V
range.
DISCUSSION
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
REFERENCES
d)
ranging in mass from 15,962 to 19,390 Da, with the monomer subunit
(chain d) existing as three isoforms (d1-d3), and chain a occurring as four glycosylated isoforms (a1-a4); the latter form four different disulfide-bonded trimer subunits with chains b and c (8).
Arenicola Hb contains eight different globin chains (a1, a2,
b1, b2, b3, c, d1, and d2) ranging in mass from 15,922 to 17,032 Da,
with the b, c, and d chains forming five of the six possible
disulfide-bonded trimers (T1-T5) (c + b1 + d1, c + b1 + d2, c + b2 + d1, c + b2 + d2, and c + b3 + d2) (12). Table
I shows the range of masses observed for
the two subassemblies and the selected representative masses together
with the calculated masses for dodecamer subassembly compositions
M9T, M6T2, and
M3T3 and a hexadecamer subassembly M4T4 using the globin chain and subunit masses
determined previously (8, 12). For the Lumbricus Hb
subassembly, the mass 214,190 Da at a de-clustering voltage of 140 V
was taken to be representative, assuming a behavior similar to that of
the Arenicola Hb subassembly, which displays minimal heme
loss at this voltage. For the Arenicola Hb subassembly, the
asymptotic mass 204,600 Da was taken to be representative. The results
shown in Table I demonstrate unequivocally that the
M3T3 subassembly compositions provide the best
agreement between the calculated masses and the experimental masses,
even though the latter are somewhat higher, depending on the
de-clustering voltage used. Although adduct formation with alkali metal
cations cannot be excluded, the mass differences can be ascribed to
noncovalent complexation of Lumbricus and
Arenicola subassemblies with approximately 42 and 14 water
molecules, respectively. It is now known that water molecules play an
important role in the formation of biomolecular complexes (29).
Furthermore, recent ESI-MS studies of complexes formed between SH2
domains from tyrosine kinase Src with tyrosyl phosphopeptides (30) and
of insulin hexamers (31) have shown that one to three water molecules
in the former case and three to six water molecules in the latter were
incorporated into the observed protein complexes.
Measured and calculated masses (in Da) of globin subassemblies
0.002 are shown in Fig.
4. The calculated mass range for the Lumbricus Hb subassembly (212,624-214,176 Da) is much
greater than that for the Arenicola Hb subassembly
(203,934-204,495 Da) (Table I). The subassembly masses with the
highest probability are 213,512 Da for Lumbricus and 204,375 and 204,425 Da for Arenicola. The expected masses of
the randomly assembled subassemblies are 213,436 Da (S.D. = 319 Da) and
204,342 Da (S.D. = 80 Da), respectively. The substantially broader mass
distribution of the Lumbricus Hb subassembly as compared
with that of the Arenicola Hb subassembly may be a
contributing factor to the greater uncertainty in the observed mass of
the former.
View larger version (39K):
[in a new window]
Fig. 4.
Histogram of random mass distribution of
dodecamer subassemblies (A, from
Lumbricus Hb; B, from Arenicola Hb) calculated using monomer and trimer masses from
previous ESI-MS studies (8, 12). To avoid an overcrowding of
points along the abcissa, only masses with probabilities of 0.002
were plotted, and the number of points shown represent about half the
number of calculated subassembly masses (200 for Lumbricus
and 140 for Arenicola, respectively).
It is appropriate at this point to briefly discuss the disagreement concerning the structure of Lumbricus Hb between our group and that of A. F. Riggs that has persisted for over a decade. In 1991, Fushitani and Riggs reassembled at a neutral pH the trimer and monomer subunits isolated by dissociation of the Hb at pH > 9, observed a 5.8 S species using sedimentation velocity, and suggested it to be an octamer globin complex M2T2. In subsequent experiments, the CO forms of the trimer and monomer subunits isolated by dissociation at an alkaline pH were mixed at a neutral pH to obtain a subassembly with a mass of ~280 kDa as determined by multiple angle laser light scattering, in agreement with a mass of 286 kDa calculated for a hexadecamer [M]4[T] 4 (22-24). Based on a weight proportion of linker chains of 0.163, Riggs and his colleagues have proposed a model of Lumbricus Hb comprising 12 hexadecamers [d]4 [abc]4 (192 globin chains) and 24 linkers, with a calculated mass in agreement with the 4.1 ± 0.1 MDa mass for the native Hb determined only by multiple angle laser light scattering (22-24). Apart from the fact that the proposed globin to linker stoichiometry corresponds to iron and heme contents that are higher than those generally observed for over 30 HBL Hbs by many different investigators (4, 32), the most telling shortcoming of this model is that the proposed hexadecamer subassembly cannot have a 3-fold symmetry and is thus unable to account for the 12 local 3-fold axes observed in the three-dimensional reconstructions based on cryoelectron microscopy images in frozen, hydrated samples of Lumbricus Hb obtained by the groups of Van Heel and colleagues (16) and Lamy and colleagues (21). Our findings, which are summarized in Table I, do not provide any support for the Riggs model of the globin subassembly.
It should be pointed out that the three-dimensional reconstructions
obtained by De Haas et al. for the chlorocruorin from Eudistylia vancouverii (17) and the Hbs from the leech
Macrobdella decora (18), the vestimentiferan Riftia
pachyptila (19), and the deep sea polychaete Alvinella
pompejana (20) indicate that the quaternary structures are very
similar at a resolution of ~3 nm. Hence, it is likely that the
dodecamer subassembly demonstrated to occur in the Hbs from
Lumbricus and the marine polychaete Arenicola also occurs in other HBL Hbs, including chlorocruorins. This proposal is supported by the good agreement between the available experimental masses and the masses calculated for our model consisting of 12 dodecamer subassemblies and 36 or 42 linkers using the accurate masses
obtained by ESI-MS of the HBL Hbs (9-15).
| |
FOOTNOTES |
|---|
* The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
** To whom correspondence should be addressed. Tel.: 313-577-1501; Fax: 313-577-2765; E-mail: svinogra@med.wayne.edu.
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ABBREVIATIONS |
|---|
The abbreviations used are: HBL, hexagonal bilayer; M, monomer subunit; T, disulfide-bonded trimer subunit; ESI, electrospray ionization; ESI-MS, electrospray ionization mass spectrometry.
| |
APPENDIX |
|---|
Random Assembly Model of Lumbricus Dodecamer Subassemblies
Each dodecamer subassembly consists of three M and three T subunits. The M subunit consists of chains d1-d3, and the T subunits are comprised of chains b and c and one of the four a1-a4 chains. Previous ESI-MS studies have established that the relative proportions of the three M chains are d1:d2:d3 = 0.55:0.28:0.17, and the proportions of the four a chains of T subunits are a1:a2:a3:a4 = 0.24:0.40:0.08:0.28 (8). We assume that the M and T subunits are incorporated into the subassembly independently of each other. Let D = (D1, D2, D3) be the vector of random numbers of d1-d3 monomers contained in the subassembly. D1-D3 are nonnegative integer-valued random variables subject to the restriction that D1 + D2 + D3 = 3. The random vector D takes 10 values corresponding to the following combinations: 3d1, 3d2, 3d3, 2d1d2, 2d2d1, 2d1d3, 2d3d1, 2d2d3, 2d3d2, and d1d2d3. It follows from our assumption that the random vector D has a multinomial distribution B(3; p(d1), p(d2), p(d3)), that is:
|
(Eq. 1) |
= (1, 2, 3) is a vector of nonnegative
integers such that 1 + 2 + 3 = 3 (31). Similarly, let
T = (T1, T2, T3, T4) be the vector of random numbers of trimers
(t1-t4) contained in a dodecamer subassembly. T1-T4 are nonnegative
integer-valued random variables such that T1 + T2 + T3 + T4 = 3. The random vector T takes 20 values that correspond to the following
combinations of trimer subunits in a dodecamer: 3t1, 3t2, 3t3, 3t4,
2t1t2, 2t2t1, 2t1t3, 2t3t1, 2t1t4, 2t4t1, 2t2t3, 2t3t2, 2t2t4, 2t4t2, 2t3t4, 2t4t3, t1t2t3, t1t2t4, t1t3t4, and t2t3t4. Likewise, the random
vector T has a multinomial distribution B(3; p(a1), p (a2), p(a3),
p(a4)), that is:
|
(Eq. 2) |
= (1, 2, 3, 4) is a vector of
nonnegative integers such that 1 + 2 + 3 + 4 = 3. The
number of different dodecamers is the product of the numbers of
possible values of vectors D and T, 10 × 20 = 200; each is
determined by the two integer vectors and , and the probability
of its occurrence is equal to the product of probabilities given by
Equations 1 and 2. The mass of a dodecamer subassembly is given by
(33):
|
(Eq. 3) |
The expected mass of a randomly assembled dodecamer can also be easily calculated from Equation 3. Because the random variables Di and Tj for all i = 1,2,3 and j = 1,2,3,4 follow the binomial distributions B(3, p(di)) and B(3, p(aj)), the expected total masses of monomers di and aj in a dodecamer are equal to 3 m(di)p(di) and 3 m(aj)p(aj), respectively. Therefore, the expected mass of a randomly assembled dodecamer is Em = 3[m(d1)p(d1) + m(d2)p(d2) + m(d3)p(d3) + m(a1)p(a1) + m(a2)p(a2) + m(a3)p(a3) + m(a4)p(a4) + m(b) + m(c)] + h = 213,436 Da.
The S.D. 
of the mass distribution (3) is given by:--
|
(Eq. 4) |
and , m(,) = m(d1)1 + m(d2) m(d3) 3 + m(a1) 1 + m(a2)2 + m(a3)3 + m(a4)4 + 3 m(b) + 3 m(c) + h is the mass
of a randomly assembled dodecamer with D = and T = ,
and p(), p() are defined by Equations 1 and 2, respectively. A
calculation using MAPLE provided = 319 Da.
| |
REFERENCES |
|---|
|
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL PROCEDURES
RESULTS
DISCUSSION
APPENDIX
REFERENCES
|
|---|
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