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Biophysical Studies of Cell-Penetrating Peptides 229 number of H-bonding water molecules are removed, therefore promoting intramolecular H-bonds. The most common alcohols used in such studies are trifluoroethanol (TFE) and hexafluoroisopropanol (HFP), which are water mixible; however, it has also been suggested that some aggregated solvent clusters could exist in aqueous mixtures. 25 Whether this type of solvent mixture should be considered a good membrane mimetic can be debated. 10.4 INTERFACIAL PHENOMENA — ELECTROSTATICS Outside the charged membrane surface is the so-called interphase region, a region of solvent more strongly associated with the membrane than the bulk region, which is far away (∞) from the surface. In the theoretical treatment of the diffuse double layer one assumes that the interphase is also composed of two regions. Close to the surface is the Stern layer, where ions are attracted or repelled. Outside this region is a diffuse layer of ions, within which all the ionic particles, including charged peptides like CPPs, are assumed to obey a Boltzmann distribution. With an electrical potential φ(r) at a position r, the mean-field electrical interaction energy becomes z ieφ(r), where z i is valency of the ion (±) and e is electronic charge (F/N A). For each ion, concentration (mol/dm 3 ) is assumed to become c i(r) = c i(∞) exp [–z ieφ(r)/kT] The net charge density (charges/m 3 ) in the aqueous phase at a point r is then A all ∑ i i A all ∑ i i i i i ()= ( ) ()= ( ) ∞ 3 3 ρ r 10 N e zc r 10 N e zc exp zeφ r kT The Poisson equation is a fundamental result (from Gauss laws) in electrostatics connecting the electrical potential φ(r) and charge density ρ(r): ∆φ(r) = – ρ(r)/ε οε r [ ] ( ) − () In the one-dimensional case, the Laplace operator becomes ∆ = d 2 /dx 2 , where x is the distance from the Stern layer. With x = ∞, the limit is out in the bulk phase. When the medium is not a perfect dielectricum, variation in the permittivity (ε r) can exist. Even in the one-dimensional case, the combined Poisson–Boltzmann equation has no simple analytical solution; we must assume certain boundary conditions. A useful relation between the surface charge density, σ 0, and the surface potential φ(0), at x = 0, was derived by Grahame: 26 2 3 σ = 210 ⋅ ε ε RT c ( ∞) exp( − z eφ( 0) kT)−1 0 all ∑ o r i i { i }
230 Cell-Penetrating Peptides: Processes and Applications In this ex<strong>press</strong>ion the ionic concentrations c i(∞) of all ions in the bulk phase should be accounted for. At a fixed surface density (charges/m 2 ), the surface potential (volt) will become dependent on the concentration and valency of all the ions present in the bulk phase. The equation above is more general than the early Gouy–Chapman equation where, e.g., the exponent is simplified as a serial expansion (linearization). In the simplest theories the surface charge density is smeared out, without considering any “discreteness-of-charge” effects. 27,28 At the Stern layer (x = 0) the surface potential is defined as φ(0). At a distance x = 1/κ from the surface, the potential has decayed to φ(0)/e. This characteristic length is the so-called Debye length, which is a measure of the extension of the diffuse layer. The full ex<strong>press</strong>ion for the parameter κ includes the ionic strength, defined by all I= ∑zici 1 2 2 Since κ ∝ I ½ it is clear that a higher ionic strength will result in a shorter Debye length (1/κ). Moreover, the surface potential φ(0) will become reduced due to screening. In this respect a multivalent ion will be very potent. Besides the nonspecific screening effect, specific interactions (bindings) may exist between charged particles and a charged membrane. For instance, weak intrinsic bindings exist among the alkali ions to acidic phospholipids. This situation will result in reduced value of the surface potential and is not accounted for in the doublelayer theory. The experimental surface potential (measured by electrophoresis as a zeta-potential) of a fully charged phospholipid vesicle (100 mol% PS, or PG) in 0.1 M NaCl is about –60 mV. With only 20 mol% of negative phospholipids, a value more relevant for many biological membranes, the surface potential of a bilayer becomes reduced to about –30 mV at the same salt concentration. If the salt concentration is decreased to only 0.01 M NaCl the surface potential of the low charge density vesicle will now also become about –60 mV. Hence, it is extremely important to have good control of the ionic strength when doing studies on the charged CCPs in model systems. The relevant concentration in a membrane process is the local surface concentration. This should be used in order to understand intrinsic properties of the CPPs. Applying bulk concentration of ions will lead to apparent parameters, which will be dependent on the experimental conditions. Without proper corrections for the electrical potential effects, an apparent value for the binding constant (K app) is measured. This value is related to the intrinsic (true) value (K int) by K app = K int exp[–z ieφ(0)/kT] The apparent binding constant will be orders of magnitude larger than the intrinsic one for a polycationic molecule (like a CPP) when φ(0) is negative (–mV). The i
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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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1 CONTENTS 0-8493-1141-1/02/$0.00+$
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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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Interactions of Cell-Penetrating Pe
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Page 200 and 201: Interactions of Cell-Penetrating Pe
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Page 210 and 211: Structure Prediction of CPPs and It
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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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