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Structure Prediction of CPPs and Iterative Development of Novel CPPs 195 x, y, and z (where the xy plane is that of the membrane). However, on the time scale of peptide–bilayer interactions the peptide is assumed to be influenced by a potential averaged in the membrane plane: (9.7) where the integral in Equation 9.7 is extended on the surface of the xy plane over an area S. When the dielectric function is dependent upon z, the average potential Φ(z) is the solution of Equation 9.6 with an average charge distribution: where 1 Φ()= z Φ() r dxdy S 2 d Φ() z dε Φ z ρ z ε() z + 2 dz dz dz ε (9.8) (9.9) and where the definition of the integral and of S are the same as in Equation 9.7. To make an average charge distribution, the mean and standard deviations of the z coordinate of each phospholipid atom type were calculated. The contribution from each atom type to the overall charge density of the bilayer was approximated as a Gaussian function with mean and standard deviations as calculated, and normalized to the partial charge per unit area of that atom type: (9.10) where A is the area per head group, 49 q i is the partial charge of atom type i, G is a Gaussian function of the z coordinate for atom type i, and the sum is extended over all atom types of the phospholipid molecule. The resultant charge density of the bilayer is localized in a plane at –15.75 and +15.75 Å. Imagine that a charge is distributed uniformly over the entire xy-plane (Figure 9.3), with a charge per unit area or surface density of charge, δ. We wish to calculate the electric intensity at the point P. Let the charge be subdivided into narrow strips parallel to the y-axis and of dx width. Each strip can be considered as a charged line. The area of a portion of a strip of length L is L dx, and the charge dq on the strip is dq = δLdx The charge per length unit, dλ, is therefore ∫ () = () 1 ρ()= z ρ() z dxdy S ∑ 1 ρ()= z qG i i() z A i 0
196 Cell-Penetrating Peptides: Processes and Applications FIGURE 9.3 Schematic model for calculation of the electric intensity at P in the presence of a superficial density of charge δ. and at point P, a field dE, has a magnitude of The field can be solved into two components dE x and dE z. By symmetry, the components dE x will sum to zero for the entire sheet of charge. The resultant field at P is therefore in the z-direction, perpendicular to the sheet of charge. It is seen from the diagram that and hence dq dλ = = δdx L dE k dx q = 2 δ r dE z = dE sin θ E = dEz = 2kδ q +∞ ∫ ∫ −∞ sin θ. dx r
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CELL- PENETRATING PEPTIDES Processe
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Pharmacology and Toxicology: Basic
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Library of Congress Cataloging-in-P
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to the handbook are prominent resea
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REFERENCES 1. Green, M. and Loewens
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Contributors Mats Andersson Microbi
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Erin T. Pelkey Department of Chemis
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Contents Section I Classes of Cell-
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Chapter 16 Cell-Penetrating Peptide
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The Tat-Derived Cell-Penetrating Pe
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24 Cell-Penetrating Peptides: Proce
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3 Transportans Margus Pooga, Mattia
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Transportans 55 Indeed, galparan is
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Transportans 57 especially the endo
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Transportans 59 In the penetration
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Transportans 61 A 21-mer antisense
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Transportans 63 Commonly, the prote
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Transportans 65 antibiotin antibodi
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Transportans 67 For cross-linking o
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Transportans 69 and still retain ef
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Model Amphipathic Peptides 73 its D
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Model Amphipathic Peptides 75 pmol/
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TABLE 4.1 Internalization of Peptid
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TABLE 4.2 Internalization of Peptid
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Model Amphipathic Peptides 81 relat
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Model Amphipathic Peptides 87 A cat
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Model Amphipathic Peptides 89 At th
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Model Amphipathic Peptides 91 16. H
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Signal Sequence-Based Cell-Penetrat
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116 Cell-Penetrating Peptides: Proc
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Page 186 and 187: Interactions of Cell-Penetrating Pe
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Page 210 and 211: Structure Prediction of CPPs and It
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Toxicity and Side Effects of Cell-P
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Kinetics of Uptake of Cell-Penetrat
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Cell-Penetrating Peptide Conjugatio
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FIGURE 15.9 (Color Figure 15.9 foll
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Cell-Penetrating Peptides as Vector
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TABLE 16.1 Examples of Transport of
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CPP 2 Cargo or mRNA CAP Antisense A
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Microbial Membrane-Permeating Pepti
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Index A Abaecin, 129 Abz radiolabel
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Index 399 Diffraction, 168 Disulphi
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Index 401 structure prediction, 187
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Index 403 pRB proteins, Tat-E1A bin
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Index 405 lipid perturbation (secon
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