Hugo A. L. Filipe

How To Tackle the Issues in Free Energy Simulations of Long Amphiphiles Interacting with Lipid Membranes: Convergence and Local Membrane Deformations

One of the great challenges in membrane biophysics is to find a means to foster the transport of drugs across complex membrane structures. In this spirit, we elucidate methodological challenges associated with free energy computations of complex chainlike molecules across lipid membranes. As an appropriate standard molecule to this end, we consider 7-nitrobenz-2-oxa-1,3-diazol-4-yl-labeled fatty amine, NBD-Cn, which is here dealt with as a homologous series with varying chain lengths. We found the membrane-water interface region to be highly sensitive to details in free energy computations. Despite considerable simulation times, we observed substantial hysteresis, the cause being the small frequency of insertion/desorption events of the amphiphiles alkyl chain in the membrane interface. The hysteresis was most pronounced when the amphiphile was pulled from water to the membrane and compromised the data that were not in line with experiments. The subtleties in umbrella sampling for computing distance along the transition path were also observed to be potential causes of artifacts. With the PGD (pull geometry distance) scheme, in which the distance from the molecule was computed to a reference plane determined by an average over all lipids in the membrane, we found marked deformations in membrane structure when the amphiphile was close to the membrane. The deformations were weaker with the PGC (pull geometry cylinder) method, where the reference plane is chosen based on lipids that are within a cylinder of radius 1.7 nm from the amphiphile. Importantly, the free energy results given by PGC were found to be qualitatively consistent with experimental data, while the PGD results were not. We conclude that with long amphiphiles there is reason for concern with regard to computations of their free energy profiles. The membrane-water interface is the region where the greatest care is warranted.

Interaction of 7-nitrobenz-2-oxa-1,3-diazol-4-yl-labeled fatty amines with 1-palmitoyl, 2-oleoyl-sn-glycero-3-phosphocholine bilayers: a molecular dynamics study.

A complete homologous series of fluorescent 7-nitrobenz-2-oxa-1,3-diazol-4-yl (NBD)-labeled fatty amines of varying alkyl chain length, NBD-C(n), inserted in 1-palmitoyl, 2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers, was studied using atomistic molecular dynamics (MD) simulations. For all amphiphiles, the NBD fluorophore locates near the glycerol backbone/carbonyl region of POPC and establishes stable hydrogen bonding with POPC ester oxygen atoms. Small differences observed in the transverse location of the fluorophore correlate with other calculated parameters and with small discrepancies recently measured in the photophysical properties of the molecules. The longer-chained NBD-C(n) amphiphiles show significant mass density near the bilayer midplane, and the chains of these derivatives interdigitate to some extent the opposite bilayer leaflet. This phenomenon leads to a slower lateral diffusion for the longer-chained derivatives (n > 12). Effects of these amphiphiles on the structure and dynamics of the host lipid were found to be relatively mild, in comparison with acyl-chain-labeled NBD probes. The molecular details obtained by this work allow the rationalization of the nonmonotonic behavior, recently obtained experimentally, for the photophysical parameters of the amphiphiles and the kinetic and thermodynamic parameters for their interaction with the POPC membranes.

Chain length effect on the binding of amphiphiles to serum albumin and to POPC bilayers.

The interaction of small molecules, such as drugs or metabolites, with proteins and biomembranes is of fundamental importance for their bioavailability. The systematic characterization of the binding affinity for structurally related ligands may provide rules that allow its prediction for any other relevant molecule. In this work we have studied a homologous series of fluorescent fatty amines with the fluorescent moiety 7-nitrobenz-2-oxa-1,3-diazol-4-yl covalently bound to the amine group (NBD-C(n); n = 4, 6, 8, 10, 12, 14, and 16) in aqueous solution and associated with BSA or lipid bilayers. We have found a linear dependence with the length of the alkyl chain, up to NBD-C(10), for the Gibbs free energy of partition between the aqueous solution and 1-palmitoyl-2-oleoyl phosphatidylcholine bilayers equal to ΔΔG = -2.5 ± 0.3 kJ/mol per methylene group. Additionally, the amphiphiles interacted efficiently with bovine serum albumin, and it was inhibited by fatty acids indicating that binding occurs to the fatty acids highest affinity binding site. The association of the amphiphiles with BSA and POPC bilayers was performed at different temperatures (15-35 °C) allowing for the calculation of the enthalpic and entropic contributions. A value of ΔH = -15 ± 4 kJ/mol was obtained for all amphiphiles and binding agents. The entropy contribution was always positive and increased with the length of the alkyl chain. The location of the ligand in the biological membrane is also of high relevance, namely because this will determine its effect on biomembrane properties at high ligand concentrations. With this goal, we have measured some photophysical properties of the amphiphiles inserted in POPC bilayers, and we found no significant variation along the series, indicating that the NBD group is located in a region with similar properties regardless of the length of the nonpolar group. An exception was noted for the case of NBD-C(14) whose parameters were somewhat different from the trend observed.

Beyond Overton's rule: quantitative modeling of passive permeation through tight cell monolayers.

One of the great challenges in pharmacokinetics is to find a means to optimize the transport across cell barriers. In this work, permeation across a cell monolayer, such as the tight endothelia in the blood-brain barrier, was modeled using a homologous series of amphipatic molecules, 7-nitrobenz-2-oxa-1,3-diazol-4-yl (NBD)-labeled alkyl chain amphiphiles (NBD-Cn, n = 2 to 16), to obtain rules that relate permeant structure to permeability. The amphiphile enters the system from the serum, equilibrated with serum albumin and lipoproteins, and its sequestration by serum components, interaction with the endothelium, and accumulation in the tissue is followed over time. The dependence of the permeability coefficient on the number of carbons of the amphiphiles alkyl chain has a parabolic-like shape. After a threshold value, an increase in the hydrophobicity of the amphiphile, along the homologous series, results in a decrease in the characteristic rate of permeation to the tissue. A sensitivity analysis was performed, and the rate limiting steps for permeation of each amphiphile were identified. Sequestration in the serum and rate of interaction with the endothelium, particularly the rate of desorption, were found to be the determinant processes for some amphiphiles, while for others translocation was the rate limiting step. Additionally, for some amphiphiles a single rate limiting step could not be identified, with several steps contributing significantly to the overall permeation. Finally, we derived analytical equations that adequately describe the rate of amphiphile accumulation in the tissue for the cases where permeation is controlled by a single rate limiting step.

HOMEOSTASIS OF FREE CHOLESTEROL IN THE BLOOD - A PRELIMINARY EVALUATION AND MODELING OF ITS PASSIVE TRANSPORT

The rate of noncatalyzed transfer of cholesterol (Chol) among lipoproteins and cells in the blood is of fundamental importance as a baseline to assess the role of active transport mechanisms, but remains unknown. Here we address this gap by characterizing the association of the Chol analog, ergosta-5,7,9(11),22-tetraen-3β-ol (DHE), with the lipoproteins VLDL, LDL, HDL2, and HDL3. Combining these results with data for the association of DHE with liposomes, we elaborated a kinetic model for the noncatalyzed exchange of free Chol among blood compartments. The computational results are in good agreement with experimental values. The small deviations are explained by the nonequilibrium distribution of unesterified Chol in vivo, due to esterification and entry of new unesterified Chol, and eventual effects introduced by incubations at low temperatures. The kinetic profile of the homeostasis of unesterified Chol in the blood predicted by the model developed in this work is in good agreement with the observations in vivo, highlighting the importance of passive processes.

Synthesis and characterization of a lipidic alpha amino acid: solubility and interaction with serum albumin and lipid bilayers.

The lipidic α-amino acid with 11 carbons in the alkyl lateral chain (α-aminotridecanoic acid) was synthesized via multicomponent hydroformylation/Strecker reaction, which is a greener synthetic approach to promote this transformation relative to previously described methods. Its solubility and aggregation behavior in aqueous solutions was characterized, as well as the interaction with lipid bilayers. Lipidic amino acids are very promising molecules in the development of prodrugs with increased bioavailability due to the presence of the two polar functional groups and nonpolar alkyl chain. They are also biocompatible surfactants that may be used in the food and pharmaceutical industry. In this work we have conjugated the lipidic amino acid with a fluorescent polar group (7-nitrobenz-2-oxa-1,3-diazol-4-yl), to mimic drug conjugates, and its association with serum proteins and lipid bilayers was characterized. The results obtained indicate that conjugates of polar molecules with lipidic α-amino acid, via covalent attachment to the amine group, have a relatively high solubility in aqueous solutions due to their negative global charge. They bind to serum albumin with intermediate affinity and show a very high partition coefficient into lipid bilayers in the liquid-disordered state. The attachment of the polar group to the lipidic amino acid increased strongly the aqueous solubility of the amphiphile, although the partition coefficient into lipid membranes was not significantly reduced. Conjugation of polar drugs with lipidic amino acids is therefore an efficient approach to increase their affinity for biomembranes.

Quantitative assessment of methods used to obtain rate constants from molecular dynamics simulations – translocation of cholesterol across lipid bilayers

Accurately calculating rate constants of macroscopic chemical processes from molecular dynamics simulations is a long-sought but elusive goal. The problem is particularly relevant for processes occurring in biological systems, as is the case for ligand-protein and ligand-membrane interactions. Several formalisms to determine rate constants from easily accessible free-energy profiles [Δ Go( z)] of a molecule along a coordinate of interest have been proposed. However, their applicability for molecular interactions in condensed media has not been critically evaluated or validated. This work presents such evaluation and validation and introduces improved methodology. As a case study, we have characterized quantitatively the rate of translocation of cholesterol across 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine bilayers. Translocation across lipid bilayers is the rate-limiting step in the permeation of most drugs through biomembranes. We use coarse-grained molecular dynamics simulations and different kinetic formalisms to calculate this rate constant. A self-consistent test of the applicability of various available formalisms is provided by comparing their predictions with the translocation rates obtained from actual events observed in long unrestrained simulations. To this effect, a novel procedure was used to obtain the effective rate constant, based on an analysis of time intervals between transitions among different states along the reaction coordinate. While most tested formalisms lead to results in reasonable agreement (within a factor of 5) with this effective rate constant, the most adequate one is based on the explicit relaxation frequencies from the transition state in the forward and backward directions along the reaction coordinate.

Interaction of Amphiphilic Molecules with Lipid Bilayers: Kinetics of Insertion, Desorption and Translocation

Passive transport across lipid bilayers is a significant, if not dominant, route for the permeation of biologically active amphiphiles through cell membranes. Often, the quantitative description of the rate of permeation is based on a single kinetic parameter, the permeability coefficient. However, the nature of the interactions between amphiphilic molecules and lipid bilayers is complex and involves different steps (insertion, translocation and desorption), which affect both the extent of partition and the rate of permeation. Quantitative knowledge of the rate constants associated with each individual step is required for proper understanding of the whole process, and certainly useful in prediction of the ability of new drug compounds to access the interior of their cell targets. This chapter reviews the formalisms applicable to the kinetics of interaction of small solutes with lipid bilayers. Several important limiting cases, corresponding to different ranges of aqueous solubility and membrane partition, are considered, and selected examples of applications of fluorescence spectroscopy to quantitative description of solute/bilayer interaction are presented. We also address the state of the art regarding methods for calculation of rate constants of solute/lipid interaction and permeability coefficients from molecular dynamics simulations. These methods rely on accurate computation of free energy profiles of solutes across lipid bilayers, and strategies to this purpose, namely employing enhanced sampling of improbable states with the so-called umbrella sampling method, are discussed.

New Method for the Measurement of Binding Constants for Amphiphiles with a Very Small Solubility in Aqueous Media

The aqueous solubility of the monomeric form of most amphiphiles is relatively small and above a certain concentration, the critical aggregation concentration (CAC), they tend to form aggregates where the contact between their non-polar moieties and water is minimized. The affinity of the amphiphiles to hydrophobic environments, such as proteins or lipid bilayers, may be obtained by equilibrium titration with the binding agent but its correct evaluation requires the use of amphiphile concentrations below their CAC which, at times, can be extremely low.In this work we develop a method where the partition of amphiphiles between water and lipid bilayers may be accurately measured for amphiphiles with a CAC in the sub-nanomolar range. The method is based on the physical separation of the bound and free amphiphile using size exclusion chromatography and quantification of the bound amphiphile by HPLC. The high sensitivity of the method relies on an efficient increase in the concentration of the amphiphile by a minimum factor of 25 at the HPLC column, by injection of a very large volume coming from the size exclusion column and, for fluorescent amphiphiles, on the quantification in a solvent where it shows a very high fluorescent quantum yield.The equilibrium partition is performed at the required temperature and the physical separation between both fractions of amphiphile is performed at low temperature to guaranty that the equilibrium is not displaced. The method was implemented for the fluorescent amphiphile NBD-C16 for which the desorption from POPC lipid bilayers is a very slow process (k-=7.4×10−5 s−1 at 4°C (Cardoso, R., Master Thesis, Coimbra 2008)) conducing to less than 5% deviation from equilibrium during the 10 min required for separation of the two amphiphile fractions.