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Parkinson's disease (PD) is a neurodegenerative disorder that is pathologically characterized by the presence of intracytoplasmic Lewy bodies, the major components of which are filaments consisting of α-synuclein. Two recently identified point mutations in α-synuclein are the only known genetic causes of PD. α-Synuclein fibrils similar to the Lewy body filaments can be formedin vitro, and we have shown recently that both PD-linked mutations accelerate their formation. This study addresses the mechanism of α-synuclein aggregation: we show that (i) it is a nucleation-dependent process that can be seeded by aggregated α-synuclein functioning as nuclei, (ii) this fibril growth follows first-order kinetics with respect to α-synuclein concentration, and (iii) mutant α-synuclein can seed the aggregation of wild type α-synuclein, which leads us to predict that the Lewy bodies of familial PD patients with α-synuclein mutations will contain both, the mutant and the wild type protein. Finally (iv), we show that wild type and mutant forms of α-synuclein do not differ in their critical concentrations. These results suggest that differences in aggregation kinetics of α-synucleins cannot be explained by differences in solubility but are due to different nucleation rates. Consequently, α-synuclein nucleation may be the rate-limiting step for the formation of Lewy body α-synuclein fibrils in Parkinson's disease. Parkinson's disease (PD) is a neurodegenerative disorder that is pathologically characterized by the presence of intracytoplasmic Lewy bodies, the major components of which are filaments consisting of α-synuclein. Two recently identified point mutations in α-synuclein are the only known genetic causes of PD. α-Synuclein fibrils similar to the Lewy body filaments can be formedin vitro, and we have shown recently that both PD-linked mutations accelerate their formation. This study addresses the mechanism of α-synuclein aggregation: we show that (i) it is a nucleation-dependent process that can be seeded by aggregated α-synuclein functioning as nuclei, (ii) this fibril growth follows first-order kinetics with respect to α-synuclein concentration, and (iii) mutant α-synuclein can seed the aggregation of wild type α-synuclein, which leads us to predict that the Lewy bodies of familial PD patients with α-synuclein mutations will contain both, the mutant and the wild type protein. Finally (iv), we show that wild type and mutant forms of α-synuclein do not differ in their critical concentrations. These results suggest that differences in aggregation kinetics of α-synucleins cannot be explained by differences in solubility but are due to different nucleation rates. Consequently, α-synuclein nucleation may be the rate-limiting step for the formation of Lewy body α-synuclein fibrils in Parkinson's disease. Parkinson's disease wild type Parkinson's disease (PD)1 is a neurodegenerative disorder that predominantly affects dopaminergic neurons in the nigrostriatal system but also several other regions of the brain. A pathological hallmark of PD are Lewy bodies (1Lewy F.H. Lewandowski M. Handbuch der Neurologie. Springer, Berlin1912: 920-933Google Scholar, 2Pollanen M.S. Dickson D.W. Bergeron C. J. Neuropathol. Exp. Neurol. 1993; 52: 183-191Crossref PubMed Scopus (390) Google Scholar, 3Forno L.S. J. Neuropathol. Exp. Neurol. 1996; 55: 259-272Crossref PubMed Scopus (1256) Google Scholar), which also accumulate in dementia with Lewy bodies (4Spillantini G.M. Crowther R.A. Jakes R. Hasegawa M. Goedert M. Proc. Natl. Acad. Sci. 1998; 95: 6469-6473Crossref PubMed Scopus (2443) Google Scholar) and multiple system atrophy (5Arima K. Uéda K. Sunohara N. Arakawa K. Hirai S. Nakamura M. Tonozuka-Uehara H. Kawai M. Acta Neuropathol. 1998; 96: 439-444Crossref PubMed Scopus (235) Google Scholar, 6Wakabayashi K. Hayashi S. Kakita A. Yamada M. Toyoshima Y. Yoshimoto M. Takahashi H. Acta Neuropathol. 1998; 96: 445-452Crossref PubMed Scopus (320) Google Scholar), but not in a variety of other neurodegenerative disorders. The major filamentous component of Lewy bodies is α-synuclein (4Spillantini G.M. Crowther R.A. Jakes R. Hasegawa M. Goedert M. Proc. Natl. Acad. Sci. 1998; 95: 6469-6473Crossref PubMed Scopus (2443) Google Scholar, 7Arai T. Uéda K. Ikeda K. Akiyama H. Haga C. Kondo H. Kuroki N. Niizato K. Iritani S. Tsuchiya K. Neurosci. Lett. 1999; 259: 83-86Crossref PubMed Scopus (76) Google Scholar), a 140-amino acid protein (8Uéda K. Fukushima H. Masliah E. Xia Y. Iwai A. Yoshimoto M. Otero D. Kondo J. Ihara Y. Saitoh T. Proc. Natl. Acad. Sci. U. S. A. 1993; 90: 11282-11286Crossref PubMed Scopus (1239) Google Scholar). Lately, two dominant mutations in α-synuclein causing familial early onset PD have been described (9Polymeropoulos M.H. Lavedan C. Leroy E. Ide S.E. Dehejia A. Dutra A. Pike B. Root H. Rubenstein J. Boyer R. Stenroos E.S. Chandrasekharappa S. Athanassiadou A. Papapetropoulos T. Johnson W.G. Lazzarini A. Duvoisin R.C. Di Iorio G. Golbe L.I. Nussbaum R. Science. 1997; 276: 2045-2047Crossref PubMed Scopus (6734) Google Scholar,10Krüger R. Kuhn W. Müller T. Woitalla D. Graeber M. Kösel S. Przuntek H. Epplen J.T. Schöls L. Riess O. Nat. Genet. 1998; 18: 106-108Crossref PubMed Scopus (3344) Google Scholar), suggesting that Lewy bodies contribute mechanistically to the degeneration of neurons in PD. Very recent in vitro studies have shown that recombinant α-synuclein can indeed form Lewy body-like fibrils (11Conway K.A. Harper J.D. Lansbury P.T. Nat. Med. 1998; 4: 1318-1320Crossref PubMed Scopus (1271) Google Scholar, 12El-Agnaf O. Jakes R. Curran M. Wallace A. FEBS Lett. 1998; 440: 67-70Crossref PubMed Scopus (241) Google Scholar, 13Hashimoto M. Hsu L. Sisk A. Xia Y. Takeda A. Sundsmo M. Masliah E. Brain Res. 1998; 799: 301-306Crossref PubMed Scopus (249) Google Scholar, 14Giasson B.I. Uryu K. Trojanowski J.Q. Lee V.M.-Y. J. Biol. Chem. 1999; 274: 7619-7622Abstract Full Text Full Text PDF PubMed Scopus (457) Google Scholar, 15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar). Most importantly, both PD-linked α-synuclein mutations accelerate this aggregation process (11Conway K.A. Harper J.D. Lansbury P.T. Nat. Med. 1998; 4: 1318-1320Crossref PubMed Scopus (1271) Google Scholar, 15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar), which immediately suggests that such in vitro studies may have relevance for PD pathogenesis. We therefore decided to address the kinetic mechanism of α-synuclein fibrillogenesis. We have shown before that in a complete aggregation time course α-synuclein aggregation is slow and displays a distinct lag phase (15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar). This might be indicative of a nucleation-dependent polymerization mechanism consisting of an initial lag phase (nucleation) followed by a growth phase (elongation) and a steady state phase in which the ordered aggregate and monomer are at equilibrium. In the lag phase a supersaturated protein solution remains stable while soluble pre-nucleus oligomers build up. Once nuclei are formed, the aggregates grow rapidly (elongation phase) until a thermodynamic equilibrium between aggregate and monomer is reached. Under these steady state conditions the growth equilibrium constant describes the solubility of the protein, which is equivalent to its critical concentration (16Andreu J.M. Timasheff S.N. Methods Enzymol. 1986; 130: 47-59Crossref PubMed Scopus (79) Google Scholar). At concentrations above the critical concentration the nucleation step can be bypassed by the addition of exogenous nuclei (17, 18, 20, for review see Ref. 19Harper J.D. Lansbury P.T. Annu. Rev. Biochem. 1997; 66: 385-407Crossref PubMed Scopus (1420) Google Scholar). To rigorously demonstrate the nucleation dependence of α-synuclein aggregation, we needed to show a lag phase, a seeding effect, and a critical concentration of monomer at equilibrium. We report here that α-synuclein aggregation fulfills all criteria of a nucleation-dependent polymerization process. In this regard α-synuclein fibril formation resembles that of β-amyloid (Aβ) fibers (20Jarrett J.T. Berger E.P. Lansbury Jr., P.T. Biochemistry. 1993; 32: 4693-4697Crossref PubMed Scopus (1768) Google Scholar, 21Lomakin A. Chung D.S. Benedek G.B. Kirschner D.A. Teplow D.B. Proc. Natl. Acad. Sci. U. S. A. 1996; 93: 1125-1129Crossref PubMed Scopus (736) Google Scholar, 22Wood S.J. Chan W. Wetzel R. Biochemistry. 1996; 35: 12623-12628Crossref PubMed Scopus (106) Google Scholar) and paired helical filaments (18Friedhoff P. von Bergen M. Mandelkow E.-M. Davies P. Mandelkow E. Proc. Natl. Acad. Sci. U. S. A. 1998; 95: 15712-15717Crossref PubMed Scopus (287) Google Scholar), two protein aggregates characteristic for Alzheimer's disease. Interestingly, the critical concentrations of wild type and mutant α-synuclein do not differ significantly, suggesting that the accelerated aggregation of the α-synuclein mutations is not due to a decreased solubility of mutant monomer or increased stability of mutant fiber, respectively, but rather due to different nucleation rates. Therefore, α-synuclein nucleation may be the rate-limiting step for the formation of Lewy body α-synuclein fibrils in Parkinson's disease. In this light it was of interest to show that nuclei formed of mutant α-synuclein can function as a seed for elongation by wild type α-synuclein, which is a situation similar to the one found in familial PD cases. Bacterial expression and purification of α-synuclein was done as described before (15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar). Briefly, Escherichia coli cell paste was homogenized in 20 mm Tris, 100 mm NaCl, pH 7.5, with protease inhibitor mixture Complete (Roche Molecular Biochemicals). Cells in suspension were broken by passaging through a Microfluidizer, and a clarified lysate supernatant was collected after centrifugation at 18,000 × g for 45 min. E. colicontaminating proteins were precipitated by acid precipitation of the lysate supernatant. The pH was adjusted to 3.5, and after stirring for 20–30 min, the mixture was centrifuged for 1 h at 27,000 ×g. After adjusting the pH of the resulting supernatant to 7.5, the sample was applied to Q-Sepharose FF (Amersham Pharmacia Biotech), equilibrated in 20 mm Tris, pH 7.5, and eluted with a NaCl gradient in equilibration buffer. α-Synuclein-containing fractions were identified by SDS-polyacrylamide gel electrophoresis and are >99% pure. The concentration of α-synuclein was determined by measuring absorbance at 280 nm and employing ε2800.1% of 0.354, determined by using Genetics Computer Group software. Purified samples of α-synuclein were concentrated to >7 mg/ml in Tris-buffered saline (20 mm Tris, pH 7.5, and 200 mm NaCl) + 0.05% sodium azide and sterile filtered through 0.22-μm filters to remove any particulate matter. The filtrates were all adjusted to a final concentration in the range of 2–7 mg/ml in Tris-buffered saline + 0.05% sodium azide and incubated at 37 °C in parafilm-sealed, 1.5-ml Beckman ultracentrifuge tubes. At various time points, the samples were centrifuged at 100,000 × g for 10 min, and the α-synuclein content of their supernatants was analyzed by measuring their absorbance at 280 nm. The concentration of α-synuclein was then determined employing ε2800.1% = 0.354. Supernatants of samples with concentrations 4 mg/ml or higher were first diluted 1:10 with Tris-buffered saline (11 μl of sample + 99 μl of buffer) whereas supernatants of samples at concentrations below 4 mg/ml were analyzed directly (100 μl). The remainder of the sample was vortexed for 30 s to resuspend pelleted material and then allowed to continue incubation at 37 °C. If the supernatant was analyzed neat, the 100-μl aliquot used for absorbance measurements was returned to the original incubation tube that was then vortexed for 30 s and placed back at 37 °C. Curve fits for aggregation time courses (i.e. A 280 versus time) were drawn manually. Solutions of wt or A53T α-synuclein at 7 mg/ml were incubated at 37 °C for 3 days in an Eppendorf Thermomixer with continuous shaking (high speed); under these conditions the equilibrium was reached. Reported seed concentrations are based on the amount of monomeric protein used, assuming complete aggregation of the starting material. The material was stored frozen at −20 °C until needed. Incubations of soluble α-synuclein at concentrations ranging from 2–7 mg/ml in Tris-buffered saline + 0.05% sodium azide were spiked with various amounts of preformed α-synuclein aggregates to serve as nuclei for fibril formation. The final concentration of seed is reported as a percentage of the soluble α-synuclein in the incubation (e.g. a 2 mg/ml incubation seeded at a level of 10% contains 0.2 mg/ml seed). Loss of soluble α-synuclein is measured byA 280 of soluble material following ultracentrifugation as described above. Critical concentrations were determined for wt and A53T mutant α-synuclein as described in Jarrett et al. (20Jarrett J.T. Berger E.P. Lansbury Jr., P.T. Biochemistry. 1993; 32: 4693-4697Crossref PubMed Scopus (1768) Google Scholar). α-Synuclein was incubated at 7 mg/ml in Tris-buffered saline, pH 7.5 + 0.05% sodium azide at 37 °C for 3 days with continuous shaking in an Eppendorf Thermomixer (high speed) to ensure complete aggregation. Following this treatment, the samples were centrifuged for 10 min at 100,000 ×g, the supernatants were collected, filtered through 0.22-μm filters and analyzed by quantitative amino acid analysis to determine protein content. Samples were transferred to pyrolyzed glass vial inserts, dried, and transferred to a Water's Picotag reaction vial, which contained 1 ml of a hydrolysis mixture (6n hydrochloric acid, 0.05% phenol, 0.001% β-mercaptoethanol). The reaction vial was purged with nitrogen and then sealed under hydrolysis at °C for The sample glass were and dried, and the samples were in sample the and analyzed on a Beckman amino acid was used to concentrations from the amino and The a and an percentage between the and of To study the kinetics of α-synuclein the aggregated material was pelleted by centrifugation and the concentration of the soluble material in the supernatant was determined The of soluble material was by an in In we followed α-synuclein aggregation by measurements not and by and phase that the material is (15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar). We have shown that α-synuclein forms vitro and that this aggregation is by a lag phase that is followed by a of aggregate formation (15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google both are and in as a of soluble wild type α-synuclein This kinetic is indicative of a process. In such a addition of exogenous nuclei elongation and aggregation. with this the addition of preformed wild type α-synuclein aggregates indeed seed soluble α-synuclein resulting in aggregation as shown in 1 versus concentrations in this from 0.001% of the soluble α-synuclein amount to 10% and it is that the aggregation of soluble α-synuclein is by the seed content in a the from 1 as the time to of the soluble starting material a quantitative of the seeding At 2 mg/ml under aggregation conditions wild type α-synuclein aggregated with a of the seed content consisting of only 0.001% of the soluble α-synuclein, the decreased to At seed the days and seed concentrations of 1 and 10% seed in a of to and Once the nuclei are by formation or exogenous α-synuclein fibril elongation is to the of soluble α-synuclein the by these This process be with respect to the soluble α-synuclein We this by a amount of preformed seed to various concentrations of soluble α-synuclein and followed its aggregation time In all concentrations the initial of soluble α-synuclein were or until to level due to of soluble and at the critical the decreased with α-synuclein In a seeded the of soluble α-synuclein are to the elongation rates. initial elongation from this are shown in 2 as a function of soluble α-synuclein The suggests that α-synuclein elongation is a first process with respect to α-synuclein The described above have wild type α-synuclein aggregation. that α-synuclein the dominant A53T can also be seeded versus and also aggregates by a nucleation-dependent with wild type α-synuclein the of is seed 10% seed). The dominant A53T α-synuclein is with familial Parkinson's disease and with the wild type form in We have shown that A53T as as the only other known familial PD displays accelerated aggregation and a in the lag phase of this process. was of interest to the that the mutant α-synuclein as seed for the soluble wild type protein. In 4 we preformed aggregates of A53T α-synuclein to wild type α-synuclein and incubated under aggregation with the shown in 1 the not aggregate the time course of this A53T seed concentrations or 10% of the soluble α-synuclein in the incubation in fibril The of seeding in seed at and 10% seed of the soluble material was aggregated at and 2 To determine the critical concentrations of α-synuclein wild type and A53T mutant were incubated for 3 days at 37 °C and continuous shaking to ensure complete aggregation and equilibrium between fibers and soluble material. After centrifugation the supernatants were analyzed by quantitative amino acid The critical concentrations for wild type and A53T α-synuclein were mg/ml and mg/ml respectively, between these two Lewy bodies that contain α-synuclein as their major component are one of the of Parkinson's dementia with Lewy bodies, and multiple system If and Lewy bodies degeneration is not the that two α-synuclein mutations dominant familial PD an α-synuclein for PD. This that mutant α-synuclein the formation of Lewy bodies that in the PD for this from vitro which demonstrate that α-synuclein can indeed form fibrils similar to found in Lewy bodies (11Conway K.A. Harper J.D. Lansbury P.T. Nat. Med. 1998; 4: 1318-1320Crossref PubMed Scopus (1271) Google Scholar, 13Hashimoto M. Hsu L. Sisk A. Xia Y. Takeda A. Sundsmo M. Masliah E. Brain Res. 1998; 799: 301-306Crossref PubMed Scopus (249) Google Scholar, 14Giasson B.I. Uryu K. Trojanowski J.Q. Lee V.M.-Y. J. Biol. Chem. 1999; 274: 7619-7622Abstract Full Text Full Text PDF PubMed Scopus (457) Google Scholar, 15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar) and which suggest conditions M. Hsu L. Xia Y. Takeda A. Sundsmo M. Masliah E. 1999; PubMed Scopus Google Scholar). Most importantly, both mutations accelerate the formation of these fibrils (11Conway K.A. Harper J.D. Lansbury P.T. Nat. Med. 1998; 4: 1318-1320Crossref PubMed Scopus (1271) Google Scholar, 15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar). the in vitro a critical of the The mechanism of this not been In this study we show that α-synuclein aggregation follows a 1 and 3 demonstrate that aggregation of both wild type and A53T mutant α-synuclein is by a nucleation The addition of which as nuclei, to supersaturated of α-synuclein the lag phase and causes aggregation. The aggregation are by the seed content in a the seed concentration constant and the soluble α-synuclein concentration we show that its aggregation is also on the soluble α-synuclein concentration The results suggest that α-synuclein elongation is a first process with respect to α-synuclein Interestingly, the elongation of (Aβ) which been by and Lee Biochemistry. 1996; 35: PubMed Scopus Google Scholar, 1997; PubMed Scopus Google Scholar), follows first that both and α-synuclein may the We have determined the critical concentrations for wild type and A53T mutant forms of α-synuclein and found to be This that the aggregation of the mutant forms is a kinetic and not due to an solubility or higher is to that the mutations the of critical regions of α-synuclein to from to the in the aggregate (15Narhi L. Wood S.J. Steavenson S. Jiang Y. Wu G.M. Anafi D. Kaufman S.A. Martin F. Sitney K. Denis P. Louis J.C. Wypych J. Biere A.L. Citron M. J. Biol. Chem. 1999; 274: 9843-9846Abstract Full Text Full Text PDF PubMed Scopus (630) Google Scholar), and that this causes the rate-limiting nuclei to results do not the that the nucleation of wild type and mutant α-synuclein forms be mechanistically may a as as differences between wild type and mutant α-synuclein, α-synuclein A. J.M. J. Biol. Chem. 1998; Full Text Full Text PDF PubMed Scopus Google Scholar, M.S. Jakes R. Goedert M. J. Biol. Chem. 1998; Full Text Full Text PDF PubMed Scopus Google Scholar). will be of interest to study the early of nuclei formation and determine the nuclei as as the and of have been reported for different of other fibril and in and (18Friedhoff P. von Bergen M. Mandelkow E.-M. Davies P. Mandelkow E. Proc. Natl. Acad. Sci. U. S. A. 1998; 95: 15712-15717Crossref PubMed Scopus (287) Google Scholar, J.D. Lansbury Jr., P.T. Chem. Biol. 1997; 4: Full Text PDF PubMed Scopus Google Scholar, A. Benedek G.B. Teplow D.B. J. Biol. Chem. 1997; PubMed Scopus Google Scholar). Interestingly, al. M. Hsu L. Sisk A. Xia Y. Takeda A. Sundsmo M. Masliah E. Brain Res. 1998; 799: 301-306Crossref PubMed Scopus (249) Google Scholar) and oligomers of α-synuclein with SDS-polyacrylamide gel electrophoresis and their to material. and other (11Conway K.A. Harper J.D. Lansbury P.T. Nat. Med. 1998; 4: 1318-1320Crossref PubMed Scopus (1271) Google Scholar) other phase do indeed suggest the of other soluble α-synuclein not Most importantly, wild type α-synuclein cannot only be seeded by its fibrils but can also be by mutant α-synuclein fibrils differences at the elongation or of the two This was and after recent studies reported differences in fibers of wild type and A53T mutant α-synuclein B.I. Uryu K. Trojanowski J.Q. Lee V.M.-Y. J. Biol. Chem. 1999; 274: 7619-7622Abstract Full Text Full Text PDF PubMed Scopus (457) Google Scholar), and it will be to study the of the that seeding is suggests that not only mutant α-synuclein and aggregate wild type but that in a in situation the lag phase of wild type α-synuclein aggregation is to the one of the mutant the mutant protein its on the α-synuclein on this we the that the Lewy bodies of will contain both the mutant and the wild type α-synuclein protein. to that under α-synuclein show in of This not be the wild type α-synuclein be from Lewy body formation by the lag phase of the α-synuclein mutations or the lag phase by the of nuclei fibril growth and causing their In this α-synuclein nucleation be at the of Lewy body formation and nucleation at in have We are to Sitney for the expression of recombinant proteins and to for the quantitative amino acid
Wood et al. (Thu,) studied this question.
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