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• W2024014666 abstract "Neutron scattering exploits the enormous scattering difference between protons and deuterons. A set of 42 x-ray and neutron solution scattering curves from hybrid Escherichia coli ribosomes was obtained, where the proteins and rRNA moieties in the subunits were either protonated or deuterated in all possible combinations. This extensive data set is analyzed using a novel method. The volume defined by the cryoelectron microscopic model of Frank and co-workers (Frank, J., Zhu, J., Penczek, P., Li, Y. H., Srivastava, S., Verschoor, A., Radermacher, M., Grassucci, R., Lata, R. K., and Agrawal, R. K. (1995) Nature 376, 441–444) is divided into 7890 densely packed spheres of radius 0.5 nm. Simulated annealing is employed to assign each sphere to solvent, protein, or rRNA moieties to simultaneously fit all scattering curves. Twelve independent reconstructions starting from random approximations yielded reproducible results. The resulting model at a resolution of 3 nm represents the volumes occupied by rRNA and protein moieties at 95% probability threshold and displays 15 and 20 protein subvolumes in the 30 S and 50 S, respectively, connected by rRNA. 17 proteins with known atomic structure can be tentatively positioned into the protein subvolumes within the ribosome in agreement with the results from other methods. The protein-rRNA map enlarges the basis for the models of the rRNA folding and can further help to localize proteins in high-resolution crystallographic density maps. Neutron scattering exploits the enormous scattering difference between protons and deuterons. A set of 42 x-ray and neutron solution scattering curves from hybrid Escherichia coli ribosomes was obtained, where the proteins and rRNA moieties in the subunits were either protonated or deuterated in all possible combinations. This extensive data set is analyzed using a novel method. The volume defined by the cryoelectron microscopic model of Frank and co-workers (Frank, J., Zhu, J., Penczek, P., Li, Y. H., Srivastava, S., Verschoor, A., Radermacher, M., Grassucci, R., Lata, R. K., and Agrawal, R. K. (1995) Nature 376, 441–444) is divided into 7890 densely packed spheres of radius 0.5 nm. Simulated annealing is employed to assign each sphere to solvent, protein, or rRNA moieties to simultaneously fit all scattering curves. Twelve independent reconstructions starting from random approximations yielded reproducible results. The resulting model at a resolution of 3 nm represents the volumes occupied by rRNA and protein moieties at 95% probability threshold and displays 15 and 20 protein subvolumes in the 30 S and 50 S, respectively, connected by rRNA. 17 proteins with known atomic structure can be tentatively positioned into the protein subvolumes within the ribosome in agreement with the results from other methods. The protein-rRNA map enlarges the basis for the models of the rRNA folding and can further help to localize proteins in high-resolution crystallographic density maps. cryo-electron microscopy TP50, RNA30, and RNA50, the total proteins and the rRNA moieties in the 30 S and 50 S subunits, respectively dummy atoms model simulated annealing total proteins Ribosomes are supramolecular complexes responsible for protein synthesis in all organisms. Each of the two unequal ribosomal subunits is a complicated assembly of proteins and nucleic acids. Thus, the prokaryotic 70 S ribosome from Escherichia coli has a total molecular mass of about 2.3 × 106 Da and consists of a 30 S and 50 S subunit (1.Wittmann H.G. Annu. Rev. Biochem. 1982; 51: 155-183Crossref PubMed Scopus (151) Google Scholar). The 30 S subunit contains 21 individual proteins and a single 16 S rRNA molecule, and the 50 S subunit, 33 proteins and two rRNA molecules (5 S rRNA + 23 S rRNA). In both subunits the rRNA moieties account for about two-thirds of the mass. A better description of the interactions between proteins and rRNA in the ribosome is of paramount importance for the understanding of the structural mechanism of protein synthesis. The structure of the ribosome has been extensively studied for decades using various methods. In the last years, cryoelectron microscopy (cryo-EM)1yielded models of the overall shape of the ribosome at a resolution of 1.5 nm (2.Frank J. Zhu J. Penczek P. Li Y.H. Srivastava S. Verschoor A. Radermacher M. Grassucci R. Lata R.K. Agrawal R.K. Nature. 1995; 376: 441-444Crossref PubMed Scopus (359) Google Scholar, 3.Malhotra A. Penczek P. Agrawal R.K. Gabashvili I.S. Grassucci R.A. Jünemann R. Burkhardt N. Nierhaus K.H. Frank J. J. Mol. Biol. 1998; 280: 103-116Crossref PubMed Scopus (163) Google Scholar, 4.Stark H. Mueller F. Orlova E.V. Schatz M. Dube P. Erdemir T. Zemlin F. Brimacombe R. Heel M.V. Structure. 1995; 3: 815-821Abstract Full Text Full Text PDF PubMed Scopus (210) Google Scholar, 5.Stark H. Rodnina M.V. Rinke-Appel J. Brimacombe R. Wintermeyer W. Heel M.V. Nature. 1997; 389: 403-406Crossref PubMed Scopus (313) Google Scholar). Recent tremendous progress in the x-ray crystallography provided electron density maps down to 0.78 nm for ribosomal complexes containing tRNAs (6.Cate J.H. Yusupov M.M. Yusupova G.Z. Earnest T.E. Noller H.F. Science. 1999; 285: 2095-2104Crossref PubMed Scopus (524) Google Scholar) and to 0.45 nm for the individual ribosomal subunits (7.Tocilj A. Schlünzen F. Janell D. Glühmann M. Hansen H.A.S. Harms J. Bashan A. Bartels H. Agmon I. Franceschi F. Yonath A. Proc. Natl. Acad. Sci. U. S. A. 1999; 96: 14252-14257Crossref PubMed Scopus (101) Google Scholar, 8.Ban N. Nissen P. Hansen J. Capel M. Moore P.B. Steitz T.A. Nature. 1999; 400: 841-847Crossref PubMed Scopus (348) Google Scholar, 9.Ban N. Freeborn B. Nissen P. Penczek P. Grassucci R.A. Sweet R.A. Frank J. Moore P.B. Steitz T.A. Cell. 1998; 93: 1105-1115Abstract Full Text Full Text PDF PubMed Scopus (218) Google Scholar, 10.Clemons Jr., W.M.J. May J.L. Wimberly B.T. McCutcheon J.P. Capel M.S. Ramakrishnan V. Nature. 1999; 400: 833-840Crossref PubMed Scopus (313) Google Scholar). Despite these remarkable achievements, limited information has so far been obtained about the spatial distribution of rRNA and proteins in the ribosome. Using the x-ray maps, six ribosomal proteins were positioned in the small (7.Tocilj A. Schlünzen F. Janell D. Glühmann M. Hansen H.A.S. Harms J. Bashan A. Bartels H. Agmon I. Franceschi F. Yonath A. Proc. Natl. Acad. Sci. U. S. A. 1999; 96: 14252-14257Crossref PubMed Scopus (101) Google Scholar, 10.Clemons Jr., W.M.J. May J.L. Wimberly B.T. McCutcheon J.P. Capel M.S. Ramakrishnan V. Nature. 1999; 400: 833-840Crossref PubMed Scopus (313) Google Scholar) and four in the large subunit (8.Ban N. Nissen P. Hansen J. Capel M. Moore P.B. Steitz T.A. Nature. 1999; 400: 841-847Crossref PubMed Scopus (348) Google Scholar). The low contrast between ribosomal proteins and rRNA for both electrons and x-rays makes it difficult to distinguish between the two components even at relatively high resolution. Moreover, disordered or flexible domains do not show up in the electron density maps obtained by the x-ray crystal analysis (6.Cate J.H. Yusupov M.M. Yusupova G.Z. Earnest T.E. Noller H.F. Science. 1999; 285: 2095-2104Crossref PubMed Scopus (524) Google Scholar, 8.Ban N. Nissen P. Hansen J. Capel M. Moore P.B. Steitz T.A. Nature. 1999; 400: 841-847Crossref PubMed Scopus (348) Google Scholar). Neutron scattering in solution, although yielding only low-resolution information (11.Feigin L.A. Svergun D.I. Structure Analysis by Small-angle X-ray and Neutron Scattering. Plenum Press, New York1987Crossref Google Scholar), is a powerful tool to study complexes of proteins and nucleic acids. Scattering from a particle or its component is proportional to the squared contrast (difference between the scattering density of the particle/component and that of the solvent), and measurements at different contrasts provide additional information about the object (12.Stuhrmann H.B. Kirste R.G. Z. Phys. Chem. Neue. Folge. 1965; 46: 247-250Crossref Scopus (107) Google Scholar). As the neutron scattering lengths of hydrogen and deuterium differ drastically, isotopic H/D substitution is widely employed for the contrast variation. In earlier studies using H2O/D2O mixtures (13.Stuhrmann H.B. Koch M.H.J. Parfait R. Haas J. Ibel K. Crichton R.R. J. Mol. Biol. 1978; 119: 203-212Crossref PubMed Scopus (46) Google Scholar, 14.Koch M.H.J. Stuhrmann H.B. Methods Enzymol. 1979; 59: 670-706Crossref PubMed Scopus (50) Google Scholar), integral parameters of the protein and rRNA moieties were established. Yet more information is provided by selective deuteration of the ribosomal components. Triangulation of labeled protein pairs in the ribosomal subunits so far provided the most comprehensive information about the protein positions (15.Capel M.S. Engelman D.M. Freeborn B.R. Kjeldgaard M. Langer J.A. Ramakrishnan V. Schindler D.G. Schneider D.K. Schoenborn B.P. Sillers I.-Y. Yabuki S. Moore P.B. Science. 1987; 238: 1403-1406Crossref PubMed Scopus (213) Google Scholar, 16.May R.P. Nowotny V. Nowotny P. Voss H. Nierhaus K.H. EMBO J. 1992; 11: 373-378Crossref PubMed Scopus (63) Google Scholar). In a recent study (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar), 42 solution scattering curves from the hybrid E. coli ribosomes were measured, where the proteins and rRNA moieties in the subunits were selectively deuterated. This is probably the most extensive set of consistent x-ray and neutron contrast-variation data collected on a single object. The curves permitted to validate cryo-EM models of the ribosome (2.Frank J. Zhu J. Penczek P. Li Y.H. Srivastava S. Verschoor A. Radermacher M. Grassucci R. Lata R.K. Agrawal R.K. Nature. 1995; 376: 441-444Crossref PubMed Scopus (359) Google Scholar, 4.Stark H. Mueller F. Orlova E.V. Schatz M. Dube P. Erdemir T. Zemlin F. Brimacombe R. Heel M.V. Structure. 1995; 3: 815-821Abstract Full Text Full Text PDF PubMed Scopus (210) Google Scholar) and they were further interpreted in terms of a solid body model constructed from the envelopes of the subunits and those of the rRNA moieties. Here, we exploit the data set further using a new analysis method (19.Svergun D.I. Biophys. J. 1999; 76: 2879-2886Abstract Full Text Full Text PDF PubMed Scopus (1755) Google Scholar), where an overall shape of the object provided by cryo-EM is filled by densely packed small spheres. The algorithm assigns each sphere to the rRNA or protein moieties (or to the solvent) to simultaneously fit the available scattering data. Its efficiency was illustrated (19.Svergun D.I. Biophys. J. 1999; 76: 2879-2886Abstract Full Text Full Text PDF PubMed Scopus (1755) Google Scholar) by anab initio restoration of a model structure representing the envelope of the 30 S ribosomal subunit with several embedded proteins. The application of the new method significantly improves the resolution of the neutron-scattering maps of the ribosomal structure. A three-dimensional map of the protein-rRNA distribution is established which, in particular, reveals the likely positions of individual ribosomal proteins or protein complexes in the 70 S E. coliribosome. The sample preparation and scattering experiments are described in detail elsewhere (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar). The 70 S samples of the E. coli ribosome were made by in vitro association of selectively deuterated ribosomal subunits and checked for structural integrity and biological activity. The neutron experiments were performed at the Risø Laboratory (Roskilde, Denmark (20.Lebech B. Neutron News. 1990; 1: 7-13Google Scholar)) and at the GKSS Research Center (Geesthacht, Germany (21.Stuhrmann H.B. Biochimie (Paris). 1991; 73: 899-910Crossref PubMed Scopus (7) Google Scholar, 22.Stuhrmann H.B. Burkhardt N. Diedrich G. Jünemann R. Meerwinck W. Schmitt M. Wadzack J. Willumeit R. Zhao J. Nierhaus K.H. Nucl. Instr. Methods Phys. Res. 1995; 356: 124-132Crossref Scopus (80) Google Scholar)). Using two sample-detector distances (“low angle” and “high angle” setting), the range of momentum transfer 0.09 < s < 2.3 nm−1 was covered (s = (4π/λ)sinθ, where λ is the wavelength, and2θ is the scattering angle). The x-ray synchrotron radiation scattering data were collected on the EMBL beamline (23.Koch M.H.J. Bordas J. Nucl. Instrum. Methods. 1983; 208: 461-469Crossref Scopus (287) Google Scholar, 24.Boulin C. Kempf R. Koch M.H.J. McLaughlin S.M. Nucl. Instrum. Methods Sect. A. 1986; 249: 399-407Crossref Scopus (296) Google Scholar, 25.Boulin C.J. Kempf R. Gabriel A. Koch M.H.J. Nucl. Instrum. Methods Sec. A. 1988; 269: 312-320Crossref Scopus (232) Google Scholar) at HASYLAB (Hamburg, Germany) in the range 0.08 < s < 1.6 nm−1. The full list of samples is presented in TableI.Table ISamples measured in this study and the contrasts of ribosomal componentsSampleTP30RNA30TP50RNA50Conventional neutron scattering, hybrid 70 S particles1HH30 + HH50, Y = 0% D2O2.3094.2452.3094.2452HH30 + HH50, Y = 35% D2O.3782.207.3782.2073HH30 + HH50, Y = 50% D2O−.4461.328−.4461.3284HH30 + HH50, Y = 75% D2O−1.819−.129−1.819−.1295HH30 + HH50, Y = 100% D2O−3.199−1.586−3.199−1.5866HH30 + DD50, Y = 0% D2O2.3094.2457.1857.1437HH30 + DD50, Y = 35% D2O.3782.2075.2505.0868HH30 + DD50, Y = 50% D2O−.4461.3284.4254.2269HH30 + DD50, Y = 75% D2O−1.819−.1293.0572.76810DD30 + HH50, Y = 0% D2O7.1217.1432.3484.24511DD30 + HH50, Y = 35% D2O5.1995.086.4222.20712DD30 + HH50, Y = 50% D2O4.3734.226−.4021.32813DD30 + HH50, Y = 75% D2O3.0062.768−1.780−.12914DD30 + HH50, Y = 100% D2O1.6251.309−3.148−1.58615DD30 + DD50, Y = 0% D2O7.1217.1437.1857.14316DD30 + DD50, Y = 35% D2O5.1995.0865.2505.08617DD30 + DD50, Y = 50% D2O4.3734.2264.4254.22618DD30 + DD50, Y = 75% D2O3.0062.7683.0572.76819DD30 + DD50, Y = 100% D2O1.6251.3091.6771.30920DH30 + HH50, Y = 0% D2O7.1214.2452.3484.24521DH30 + HH50, Y = 40% D2O4.9281.907.1501.90722DH30 + HH50, Y = 60% D2O3.818.744−.949.74423DH30 + HH50, Y = 100% D2O1.625−1.586−3.148−1.58624HH30 + DH50, Y = 0% D2O2.3094.2457.1854.24525HH30 + DH50, Y = 40% D2O.1111.9074.9921.90726HH30 + DH50, Y = 60% D2O−.988.7443.883.74427HH30 + DH50, Y = 100% D2O−3.199−1.5861.677−1.586Spin-dependent neutron scattering, hybrid 70 S particles28HH30 + DD50, P = 0%1.290.748−.116−.03729HH30 + DD50, P = 100%1.290.729.013.00030DD30 + HH50, P = 0%−.116−.0371.290.76731DD30 + HH50, P = 100%.013.0001.290.72932HD30 + HD50, P = 0%−.0521.870−.0521.87033HD30 + HD50, P = 100%.2711.870.2711.870Conventional neutron scattering, free subunits34HH30, Y = 0% D2O2.3094.245.000.00035HH30, Y = 100% D2O−3.199−1.586.000.00036DD30, Y = 0% D2O7.1217.143.000.00037HH50, Y = 0% D2O.000.0002.3094.24538HH50, Y = 100% D2O.000.000−3.199−1.58639DD50, Y = 0% D2O.000.0007.1857.143X-ray curves from all 70 S samples and from free subunits4070 S2.264.232.264.234130 S2.264.23.000.0004250 S.000.0002.264.23Sample abbreviations: H, protonated; D, deuterated; first letter, TP, second letter, rRNA (e.g. DH30 + HH50 denotes hybrid ribosome with the TP30 deuterated, the rest protonated). For neutron scattering experiments, D2O concentration in the solvent Y (conventional scattering) or sample polarization P (spin dependent scattering) is indicated. The contrasts are given in units 1010 cm−2. Contrasts for the spin dependent scattering and for the x-ray scattering are scaled to those of the conventional contrast variation data as described (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar). Open table in a new tab Sample abbreviations: H, protonated; D, deuterated; first letter, TP, second letter, rRNA (e.g. DH30 + HH50 denotes hybrid ribosome with the TP30 deuterated, the rest protonated). For neutron scattering experiments, D2O concentration in the solvent Y (conventional scattering) or sample polarization P (spin dependent scattering) is indicated. The contrasts are given in units 1010 cm−2. Contrasts for the spin dependent scattering and for the x-ray scattering are scaled to those of the conventional contrast variation data as described (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar). The 70 S ribosome consists of four components representing the total proteins (TP) and the rRNA moieties in the 30 S and 50 S subunits (denoted below as TP30, TP50, RNA30, and RNA50, respectively). The search volume was defined by drawing a regular grid of points in space corresponding to dense hexagonal packing of spheres of radius r 0 = 0.5 nm inside a parallelepiped determined by the gabarites of the cryo-EM reconstruction of the 70 S E. coli ribosome (2.Frank J. Zhu J. Penczek P. Li Y.H. Srivastava S. Verschoor A. Radermacher M. Grassucci R. Lata R.K. Agrawal R.K. Nature. 1995; 376: 441-444Crossref PubMed Scopus (359) Google Scholar). If the distance between a point and the closest pixel in the EM reconstruction did not exceed 1.5 r 0, a dummy atom is placed at this point. This procedure expands the original model and thus reduces the bias and allows for deviations from the EM shape. The structure of the four component dummy atoms model (DAM) is defined by assigning a number (component index) 0 ≤ X j ≤ 4 to each dummy atom. As the subunits are well resolved in the cryo-EM model, the 30 S and 50 S subvolumes are defined where the dummy atoms may have the component index 0,1,2 (solvent, TP30 or RNA30) and 0,3,4 (solvent, TP50 or RNA50), respectively. The atoms at the subunit interface can belong to any component. The DAM in Fig. 1 contains 2644 atoms in the 30 S subvolume, 5020 atoms in the 50 S subvolume, 196 atoms at the interface, and encloses the volume of 5560 nm3 (that of the original cryo-EM model is 3920 nm3). In keeping with the low resolution of the solution scattering data, the model must be constrained to have low resolution with respect tor 0. For this, a list of neighbors (i.e atoms at an offset 2r 0) is defined for each dummy atom. Looseness (degree of isolation) of a non-solvent atom is calculated asP(N e) = exp(−0.5N e) − exp(−0.5N c), where N e is the number of neighbors having the same index and N c = 12 is the coordination number for hexagonal packing. Looseness of the configuration X (i.e. its non-compactness) is characterized by the average value P(X) = <P(N e)> over all non-solvent atoms. Another condition requires connectivity, i.e. a possibility to connect two arbitrarily selected atoms belonging to a component by successively connecting neighboring atoms belonging to this component. The measure of connectivity of the k-th component is computed as Gk(X) = ln(N k/M k)≥0, whereN k and M k are the numbers of dummy atoms in the entire component and in the longest connected fragment, respectively. Using the multipole expansion, the scattering intensity from a four component ribosomal DAM in solution is (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar, 26.Svergun D.I. Acta Crystallogr. Sec. A. 1994; 50: 391-402Crossref Scopus (50) Google Scholar), I(s)=2π2 ∑l=0∞ ∑m=−ll∑k=14[ΔρkAlm(k)(s)] 2+2 ∑n>k ΔρkAlm(k)(s)Δρn[Alm(n)(s)]*Equation 1 where Δρk andA (k) lm(s) denote the contrast and the partial amplitudes of the k-th component, respectively. The contrasts of the “dry” protonated and deuterated ribosomal components in different solvents (Table I) were computed from their chemical composition as described elsewhere (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar). The partial amplitudes are expressed as (19.Svergun D.I. Biophys. J. 1999; 76: 2879-2886Abstract Full Text Full Text PDF PubMed Scopus (1755) Google Scholar), Alm(k)(s)=il2/πva ∑j jl(srj)Ylm*(ωj)Equation 2 where the sum runs over the atoms of the k-th component, (r j ωj) = r jare their polar coordinates, v a = (4πr 03/3)/0.74 is the displaced volume per dummy atom, j l(x) andY lm(ω) denote the spherical Bessel function and the spherical harmonics, respectively. Equations 1 and 2 permit one to rapidly compute the scattering curves from the DAM for an arbitrary configuration X under the given contrasts of the components. To fit the data with a low resolution model one should find a configuration Xminimizing f(X) = χ2 +αP(X), where the overall discrepancy is, χ2=1M ∑i=1M 1N(i)−1∑j=1N(i)[(Iexp(i)(sj)−Icalc(i)(sj))/ς(sj)] 2Equation 3 M = 42 is the number of experimental curves,N(i) is the number of points in the i-th curve,I exp(s), I calc(s), and ς(s) are the experimental and calculated intensity and the experimental errors, respectively, and α>0 is the weight of the looseness penalty. The experimental data were scaled to the total dry volume of the ribosome 2350 nm3 expected from its molecular weight and fitted in the range up to s max = 0.2 nm−1. Series (1.Wittmann H.G. Annu. Rev. Biochem. 1982; 51: 155-183Crossref PubMed Scopus (151) Google Scholar) over spherical harmonics was truncated atl = 14 and the calculated intensities were appropriately smeared to account for instrumental effects (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 588-601Crossref PubMed Scopus (26) Google Scholar, 18.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G. Nierhaus K.H. J. Mol. Biol. 1997; 271: 602-618Crossref PubMed Scopus (26) Google Scholar). The minimization was performed using simulated annealing (SA (27.Kirkpatrick S. Gelatt Jr., C.D. Vecci M.P. Science. 1983; 220: 671-680Crossref PubMed Scopus (31633) Google Scholar, 28.Press W.H. Teukolsky S.A. Wetterling W.T. Flannery B.P. Numerical Recipes. University Press, Cambridge, MA1992Google Scholar, 29.Ingber L. Math. Comp. Model. 1993; 18: 29-57Crossref Scopus (888) Google Scholar)). Starting from a random configuration X 0, the assignment of a single atom is changed randomly (a move fromX to X′). If Δ =f(X′) − f(X) < 0, the move is accepted, if not, it can be accepted with a probability exp(-Δ/T), where T is annealing temperature. The latter is held constant for 70N moves or 7N accepted moves, whichever occurs first, then it is decreased (T′ = 0.9T). The procedure starts at a sufficiently high temperature T ≅ 101 and runs down toT ≅ 10−3 until no further reduction inf(X) is observed. A complete run takes about 3 weeks CPU time on a 180 MHz SGI machine. After preliminary calculations, the penalty weight α ≅ 20 was selected so that the penalty term amounted to about 5–10% of f(X) at the end of minimization (independent runs yielded discrepancy about χ ≅ 4.1 and looseness P(X) ≅ 0.08). Each of the dummy atoms filling the search volume in Fig.1 was assigned to a specific component (solvent, TP30, TP50, RNA30, or RNA50) by simultaneously fitting the available scattering curves in Table I. Already preliminary computations without using connectivity constrain yielded well separated volumes for the protein and rRNA moieties. For all independent restorations starting from random initial approximations, proteins in both subunits converged to several isolated subvolumes, whereas the distribution of the dummy atoms belonging to the rRNAs was more uniform and featureless (see example in Fig.2, top). To further constrain the model, the connectivity requirement was imposed on the rRNA moieties in both subunits and also on the entire subunit (see details under “Experimental Procedures”). Corresponding connectivity factorsG k(X) were added to the looseness penaltyP(X) during minimization and 12 independent restorations yielded very consistent results. The positions of the individual protein subvolumes differ slightly in different restorations (typical deviations are illustrated in Fig. 2, bottom). Given that the restorations provide the same overall discrepancy χ ≅ 4.1 (typical fit to the experimental data is presented in Fig.3), this uncertainty has to be attributed to the low resolution of the solution scattering data. A similar ambiguity has been observed in model calculations on a ribosome-like structure (19.Svergun D.I. Biophys. J. 1999; 76: 2879-2886Abstract Full Text Full Text PDF PubMed Scopus (1755) Google Scholar).Figure 3Typical fit of the neutron (A) and x-ray (B) scattering data by the SA models. Successive curves are displaced up by one logarithmic unit corresponding to the distance between theordinate tick marks (in panel A, also by Δs = 0.05 nm−1 along theabscissa) for better visualization. For the neutron scattering data in panel A, fits to the low angle and high angle settings are displayed separately, and the sequence of curves, from bottom to top, corresponds to that in TableI.View Large Image Figure ViewerDownload Hi-res image Download (PPT) The reliability of the results is assessed by the analysis of the 12 independently obtained configurations. For each dummy atom, the number of repetitions (i.e. the number of times a given position was attributed to the same specific component) was counted. The frequency histogram (numbers of atoms having the given number of repetitions) is presented in Fig. 4 along with the histogram computed from 12 randomly generated DAMs. The two distributions are principally different and that obtained from the SA has much higher proportion of atoms with high repetition rates. In particular, the random generations indicate that the probability for a dummy atom to be occasionally assigned to one and the same component 12 times out of 12 is about 2 × 10−6. Alone the fact that the frequency histogram contains 1755 such atoms underlines the statistical significance and reproducibility of the results. The uncertainty illustrated in Fig. 2 (bottom), indicates that the assignment of the dummy atoms close to the protein-rRNA interface or to the subunit border may differ in different reconstructions. Given also that closely positioned proteins may be joined in single globules at low resolution, the method does not yield exact positions and shapes of all individual proteins. Nevertheless, the analysis of the independent reconstructions permits one to distinguish between the volumes occupied by proteins and rRNA in the ribosomal subunits with a reasonable probability. For each of the four ribosomal components (TP30, RNA30, TP50, and RNA50) we build a volume from the atoms that were ascribed to a specific component at least once in the 12 reconstructions. It is conceivable that these 4 volumes enclose the true volumes of the corresponding ribosomal components. In each of these volumes we now discard the atoms that appeared only once and keep those atoms ascribed to the given component twice and more. Simulations with randomly generated structures show that the remaining volumes would enclose the true volumes with the probability of 95%. The rRNA and protein moieties thus obtained are well separated in both subunits: the overlap (relative number of dummy atoms found in the two moieties simultaneously) is less than 17 and 20% in the 30 S and 50 S subunit, respectively. The overlapping positions are resolved by selecting the component with higher number of repetitions. The final map of the protein-rRNA distribution in the ribosome at a resolution of about 2π/s max ≅ 3 nm is presented in Fig. 5. Given that no distinction is made between proteins and rRNA at the first stage (see Fig. 2,top), the mere fact that the proteins reproducibly converge to separated volumes connected by the rRNA moiety underlines the soundness of the restoration. The integral parameters of the ribosomal components in Table II are in a good agreement with those reported in (17.Svergun D.I. Burkhardt N. Pedersen J.S. Koch M.H.J. Volkov V.V. Kozin M.B. Meerwinck W. Stuhrmann H.B. Diedrich G." @default.
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• W2024014666 title "A Map of Protein-rRNA Distribution in the 70 SEscherichia coli Ribosome" @default.
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