Biophysical studies of membrane proteins/peptides. Interaction with ...

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APPENDIX – Derivation of the FRET rate between a donor at the outer radius of a cylindrical transmembrane protein to a plane of acceptors distributed around the latter Fig. A1 shows the geometry relevant to this problem. Our derivation of the FRET rate law begins with the general expression for the average decay for a donor located in the centre of a finite disk with radius R d , N , taking into account all statistical arrangements of the N acceptor molecules located inside the disk (26): 2 2 N w + R 6 d ⎡ t ⎛ R 0 ⎞ ⎤ < ρ(t) > N = exp( − t / τ) ⋅∏ ∫ exp⎢− ⎜ ⎥W(R i )dR i i= 1 R ⎟ (A1) w ⎢ τ ⎣ ⎝ i ⎠ ⎥⎦ where W(R i )dR i is the probability of finding acceptor molecule A i in the ring of inner radius R i and outer radius R i +dR i . The acceptor distribution function is normalized, in the sense that ∫ w 2 2 w + R d W (R i )dR i = 1 (A2) We now proceed as previously done by Davenport et al. (20) and Capeta et al. (27) for similar (albeit simpler) geometries. Because all acceptors have the same distribution function, W(R i )dR i = W(R j )dR j = simply W(R)dR, all integrals in Eq. (A1) are identical, and denoting them by J(t), we can write ⎛ t ⎞ < ρ( t ) > [ ] N N = exp ⎜− ⎟ ⋅ J ( t) (A3) ⎝ τ D ⎠ As pointed out by Davenport et al. [20], the probability of finding an acceptor at a distance between R and R + dR to the donor in question, given by W(R)dR, is equal to that of finding an acceptor in the ring between R’ and R’ + dR’ in the acceptors plane, given by W(R’)dR’. The acceptor distribution function, in terms of R’ = Rsinθ (see Fig. A1A), is given by 122
[ 1+ (2 / π)arcsin( R' / 2R )] BINDING OF A QUINOLONE ANTIBIOTIC TO BACTERIAL PORIN OmpF ⎧ p R' ⎪ 0 < R' < 2R '2 2 p ⎪ Rd − Rp W ( R' ) = ⎨ (A4) ⎪ 2R' ⎪ '2 2 2Rp < R' < R' d ⎪⎩ Rd − Rp Note that, whereas for R’ > 2R p (where R p is the cylindrical protein radius) W(R’) is as expected for a uniform distribution of acceptors in a planar disk (only corrected in the denominator for the excluded area resulting from the existence of a protein molecule inside R d ), for R’ < 2R p the more complex expression denotes that only a fraction of the region between R’ and R’ + dR is available to acceptors (the shaded area in Fig. A1B). Insertion of this distribution function in the definition of J(t) (the integral in Eq. A1), together with the substitution α = cosθ = w/R, leads to ⎡ 2 1 6 2w ⎛ t ⎞⎛ R0 ⎞ 6 −3 J ( t) = ∫ exp⎢ ⎜− ⎟⎜ ⎟ α ⎥ f ( α) α dα (A5) '2 2 Rd − R p + ⎢⎣ ⎝ τ 2 ' 2 ⎠⎝ ⎠ w / w R D w d ⎥⎦ ⎤ where ⎧ ⎪ w w ⎪ 1 < α < 2 '2 2 2 w + Rd w + 4Rp ⎪ f ( α) = ⎨ (A6) ⎪ w ⎪ ⎛ 2 1 1 ⎞ < α < ⎪ ⎜ w 1− α 1 + arcsin ⎟ 2 2 + π ⎜ ⎟ w 4Rp 2 ⎩ ⎝ 2αRp ⎠ We now rearrange Eq. A5 into 123
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UNIVERSIDADE TÉCNICA DE LISBOA INS
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Fernandes, F., Loura, L. M. S., Fed
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Ao Pedro e Hugo, amigos de longa da
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2.2. - Peptides as models 2.3. - Am
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ABBREVIATIONS AND SYMBOL LIST ABBRE
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RESUMO RESUMO As biomembranas são
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SINOPSE SINOPSE Nas últimas duas d
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SINOPSE podem fornecer informação
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SINOPSE aceitantes. Dadores mais pr
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OUTLINE OUTLINE The last two decade
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OUTLINE membranes with a distributi
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OUTLINE BAR domains (tubulation of
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ion diffusion, as the energy requir
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acid. If no more groups are linked
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sphingomyelin, the most abundant sp
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signal for neighbouring cells to ph
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functional role in process such as
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in the L α phase, while lateral di
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1.7. Lateral heterogeneity in lipid
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the vesicle through bilayer deforma
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Figure I.9 - Depiction of the sever
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Figure I.11 - Experimentally obtain
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drying into a film and ressuspensio
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deactivating agents. Zwitterionic d
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amphipatic helices (see Section 2.3
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size corresponding to the hydrophob
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changes abruptly in the interfacial
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thickness of the bilayer (Section 1
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some α-helical membrane proteins a
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The formation of a lipid population
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homogeneous distribution of lipids
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Figure I.20 - Relative binding cons
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2.9. Lipid phase preferential parti
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In Figure I.21, theoretical simulat
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PROTEIN-PROTEIN AND PROTEIN-LIPID I
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2430 Biophysical Journal Volume 85
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2432 Fernandes et al. Coat protein
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2434 Fernandes et al. leads to an a
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2436 Fernandes et al. FIGURE 4 (A)
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2438 Fernandes et al. section of th
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2440 Fernandes et al. tein oligomer
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QUANTIFICATION OF PROTEIN-LIPID SEL
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FRET Study of Protein-Lipid Selecti
Page 100 and 101: FRET Study of Protein-Lipid Selecti
Page 107 and 108: BINDING OF INHIBITORS TO A PUTATIVE
Page 109 and 110: BINDING OF INHIBITORS TO A PUTATIVE
Page 111: INTERACTION OF THE INDOLE CLASS OF
Page 114 and 115: 5272 Biochemistry, Vol. 45, No. 16,
Page 123: BINDING ASSAYS OF INHIBITORS TOWARD
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Page 140 and 141: Introduction Quinolones are broad-s
Page 142 and 143: [9-12]. Having this into considerat
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Page 146 and 147: placement of the protein around the
Page 148 and 149: ⎛ II t ⎛ R ⎞ 0 ρ () t = exp
Page 152 and 153: 2 2w J ( t) = '2 R − R + w / 1
Page 154 and 155: [14] L. Plançon, M. Chami, L. Lete
Page 156 and 157: acceptors) (Eqs. 4-6) (⋅-⋅-⋅)
Page 158 and 159: FIGURE 1A FIGURE 1B 130
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Page 166 and 167: dynamin. Soon after, the same group
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Page 172 and 173: Introduction Control of membrane re
Page 174 and 175: Steady-state fluorescence measureme
Page 176 and 177: Rho-DOPE (acceptor). The increase o
Page 178 and 179: where η is the viscosity of the me
Page 180 and 181: ound conformation of the BAR domain
Page 182 and 183: 19. Fernandes, F., L. M. S. Loura,
Page 184 and 185: Figure Legends Fig.1: N-terminal am
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Page 188 and 189: FIG. 3A FIG. 3B 19
Page 190 and 191: FIG.5A 21
Page 192 and 193: FIG 6. 23
Page 194 and 195: FIG. 8 A B 25
Page 196 and 197: The signalling functions of PI(4,5)
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174
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zoxadiazol (NBD)-PC were obtained f
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Fig. 3. Fluorescence decays of diph
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CONCLUSIONS VII CONCLUSIONS Chapter
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CONCLUSIONS constants recovered by
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CONCLUSIONS Chapter IV ‐ Binding
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CONCLUSIONS Chapter VI - Clustering
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FINAL CONSIDERATIONS AND PROSPECTS
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BIBLIOGRAPHY IX BIBLIOGRAPHY Albert
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BIBLIOGRAPHY Phosphatidylinositol 4
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BIBLIOGRAPHY Glaubitz, C., Grobner,
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BIBLIOGRAPHY Koehorst, R. B. M., Sp
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BIBLIOGRAPHY Mishra, V. K., Palguna
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BIBLIOGRAPHY Pluschke, G., Hirota,
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BIBLIOGRAPHY Sperotto, M. M., and M
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BIBLIOGRAPHY Williamson, I. M., Alv
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