Vibrations and fractional vibrations of rods, plates and Fresnel pseudo-processes

Different initial and boundary value problems for the equation of vibrations of rods (also called Fresnel equation) are solved by exploiting the connection with Brownian motion and the heat equation. The analysis of the fractional version (of order $\nu$) of the Fresnel equation is also performed and, in detail, some specific cases, like $\nu=1/2$, 1/3, 2/3, are analyzed. By means of the fundamental solution of the Fresnel equation, a pseudo-process $F(t)$, $t>0$ with real sign-varying density is constructed and some of its properties examined. The equation of vibrations of plates is considered and the case of circular vibrating disks $C_R$ is investigated by applying the methods of planar orthogonally reflecting Brownian motion within $C_R$. The composition of F with reflecting Brownian motion $B$ yields the law of biquadratic heat equation while the composition of $F$ with the first passage time $T_t$ of $B$ produces a genuine probability law strictly connected with the Cauchy process.Comment: 33 pages,8 figure

Using zeta-potential measurements to quantify peptide partition to lipid membranes

© The Author(s) 2011. This article is published with open access at Springerlink.com.Open Access: This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.Many cellular phenomena occur on the biomembranes. There are plenty of molecules (natural or xenobiotics) that interact directly or partially with the cell membrane. Biomolecules, such as several peptides (e.g., antimicrobial peptides) and proteins, exert their effects at the cell membrane level. This feature makes necessary investigating their interactions with lipids to clarify their mechanisms of action and side effects necessary. The determination of molecular lipid/water partition constants (Kp) is frequently used to quantify the extension of the interaction. The determination of this parameter has been achieved by using different methodologies, such as UV-Vis absorption spectrophotometry, fluorescence spectroscopy and ζ-potential measurements. In this work, we derived and tested a mathematical model to determine the Kp from ζ-potential data. The values obtained with this method were compared with those obtained by fluorescence spectroscopy, which is a regular technique used to quantify the interaction of intrinsically fluorescent peptides with selected biomembrane model systems. Two antimicrobial peptides (BP100 and pepR) were evaluated by this new method. The results obtained by this new methodology show that ζ-potential is a powerful technique to quantify peptide/lipid interactions of a wide variety of charged molecules, overcoming some of the limitations inherent to other techniques, such as the need for fluorescent labeling.This work was partially supported by project PTDC/QUI/ 69937/2006 from Fundação para a Ciência e Tecnologia-Ministério da Ciência, Tecnologia e Ensino Superior (FCT-MCTES, Portugal), and by Fundação Calouste Gulbenkian (Portugal). JMF and MMD also thank FCT-MCTES for grants IMM/BT/37-2010 and SFRH/BD/41750/2007, respectively

Free energy barrier for melittin reorientation from a membrane-bound state to a transmembrane state

An important step in a phospholipid membrane pore formation by melittin antimicrobial peptide is a reorientation of the peptide from a surface into a transmembrane conformation. In this work we perform umbrella sampling simulations to calculate the potential of mean force (PMF) for the reorientation of melittin from a surface-bound state to a transmembrane state and provide a molecular level insight into understanding peptide and lipid properties that influence the existence of the free energy barrier. The PMFs were calculated for a peptide to lipid (P/L) ratio of 1/128 and 4/128. We observe that the free energy barrier is reduced when the P/L ratio increased. In addition, we study the cooperative effect; specifically we investigate if the barrier is smaller for a second melittin reorientation, given that another neighboring melittin was already in the transmembrane state. We observe that indeed the barrier of the PMF curve is reduced in this case, thus confirming the presence of a cooperative effect

Small Changes in the Primary Structure of Transportan 10 Alter the Thermodynamics and Kinetics of its Interaction with Phospholipid Vesicles

ABSTRACT: The kinetics and thermodynamics of binding of transportan 10 (tp10) and four of its variants to phospholipid vesicles, and the kinetics of peptide-induced dye efflux, were compared. Tp10 is a 21-residue, amphipathic, cationic, cell-penetrating peptide similar to helical antimicrobial peptides. The tp10 variants examined include amidated and free peptides, and replacements of tyrosine by tryptophan. Carboxy-terminal amidation or substitution of tryptophan for tyrosine enhance binding and activity. The Gibbs energies of peptide binding to membranes determined experimentally and calculated from the interfacial hydrophobicity scale are in good agreement. The Gibbs energy for insertion into the bilayer core was calculated using hydrophobicity scales of residue transfer from water to octanol and to the membrane/ water interface. Peptide-induced efflux becomes faster as the Gibbs energies for binding and insertion of the tp10 variants decrease. If anionic lipids are included, binding and efflux rate increase, as expected because all tp10 variants are cationic and an electrostatic component is added. Whether the most important effect of peptide amidation is the change in charge or an enhancement of helical structure, however, still needs to be established. Nevertheless, it is clear that the changes in efflux rate reflect the differences in the thermodynamics of binding and insertion of the free and amidated peptide groups. We have recently reported a detailed investigation (1) o

Determining Peptide Partitioning Properties via Computer Simulation

The transfer of polypeptide segments into lipid bilayers to form transmembrane helices represents the crucial first step in cellular membrane protein folding and assembly. This process is driven by complex and poorly understood atomic interactions of peptides with the lipid bilayer environment. The lack of suitable experimental techniques that can resolve these processes both at atomic resolution and nanosecond timescales has spurred the development of computational techniques. In this review, we summarize the significant progress achieved in the last few years in elucidating the partitioning of peptides into lipid bilayer membranes using atomic detail molecular dynamics simulations. Indeed, partitioning simulations can now provide a wealth of structural and dynamic information. Furthermore, we show that peptide-induced bilayer distortions, insertion pathways, transfer free energies, and kinetic insertion barriers are now accurate enough to complement experiments. Further advances in simulation methods and force field parameter accuracy promise to turn molecular dynamics simulations into a powerful tool for investigating a wide range of membrane active peptide phenomena

Membrane Permeabilization by Oligomeric α-Synuclein: In Search of the Mechanism

Background: \ud The question of how the aggregation of the neuronal protein α-synuclein contributes to neuronal toxicity in Parkinson's disease has been the subject of intensive research over the past decade. Recently, attention has shifted from the amyloid fibrils to soluble oligomeric intermediates in the α-synuclein aggregation process. These oligomers are hypothesized to be cytotoxic and to permeabilize cellular membranes, possibly by forming pore-like complexes in the bilayer. Although the subject of α-synuclein oligomer-membrane interactions has attracted much attention, there is only limited evidence that supports the pore formation by α-synuclein oligomers. In addition the existing data are contradictory.\ud \ud Methodology/Principal Findings:\ud Here we have studied the mechanism of lipid bilayer disruption by a well-characterized α-synuclein oligomer species in detail using a number of in vitro bilayer systems and assays. Dye efflux from vesicles induced by oligomeric α-synuclein was found to be a fast all-or-none process. Individual vesicles swiftly lose their contents but overall vesicle morphology remains unaltered. A newly developed assay based on a dextran-coupled dye showed that non-equilibrium processes dominate the disruption of the vesicles. The membrane is highly permeable to solute influx directly after oligomer addition, after which membrane integrity is partly restored. The permeabilization of the membrane is possibly related to the intrinsic instability of the bilayer. Vesicles composed of negatively charged lipids, which are generally used for measuring α-synuclein-lipid interactions, were unstable to protein adsorption in general.\ud \ud Conclusions/Significance:\ud The dye efflux from negatively charged vesicles upon addition of α-synuclein has been hypothesized to occur through the formation of oligomeric membrane pores. However, our results show that the dye efflux characteristics are consistent with bilayer defects caused by membrane instability. These data shed new insights into potential mechanisms of toxicity of oligomeric α-synuclein species

Extrinsic Fluorescent Dyes as Tools for Protein Characterization

Noncovalent, extrinsic fluorescent dyes are applied in various fields of protein analysis, e.g. to characterize folding intermediates, measure surface hydrophobicity, and detect aggregation or fibrillation. The main underlying mechanisms, which explain the fluorescence properties of many extrinsic dyes, are solvent relaxation processes and (twisted) intramolecular charge transfer reactions, which are affected by the environment and by interactions of the dyes with proteins. In recent time, the use of extrinsic fluorescent dyes such as ANS, Bis-ANS, Nile Red, Thioflavin T and others has increased, because of their versatility, sensitivity and suitability for high-throughput screening. The intention of this review is to give an overview of available extrinsic dyes, explain their spectral properties, and show illustrative examples of their various applications in protein characterization

Non-Metabolic Membrane Tubulation and Permeability Induced by Bioactive Peptides

BACKGROUND: Basic cell-penetrating peptides are potential vectors for therapeutic molecules and display antimicrobial activity. The peptide-membrane contact is the first step of the sequential processes leading to peptide internalization and cell activity. However, the molecular mechanisms involved in peptide-membrane interaction are not well understood and are frequently controversial. Herein, we compared the membrane activities of six basic peptides with different size, charge density and amphipaticity: Two cell-penetrating peptides (penetratin and R9), three amphipathic peptides and the neuromodulator substance P. METHODOLOGY/PRINCIPAL FINDINGS: Experiments of X ray diffraction, video-microscopy of giant vesicles, fluorescence spectroscopy, turbidimetry and calcein leakage from large vesicles are reported. Permeability and toxicity experiments were performed on cultured cells. The peptides showed differences in bilayer thickness perturbations, vesicles aggregation and local bending properties which form lipidic tubular structures. These structures invade the vesicle lumen in the absence of exogenous energy. CONCLUSIONS/SIGNIFICANCE: We showed that the degree of membrane permeabilization with amphipathic peptides is dependent on both peptide size and hydrophobic nature of the residues. We propose a model for peptide-induced membrane perturbations that explains the differences in peptide membrane activities and suggests the existence of a facilitated “physical endocytosis,” which represents a new pathway for peptide cellular internalization