A stepwise mechanism for the permeation of phloretin through a lipid bilayer

The thermodynamics of interactions between phloretin and a phosphatidylcholine (PC) vesicle membrane are characterized using equilibrium spectrophotometric titration, stopped-flow, and temperature- jump techniques. Binding of phloretin to a PC vesicle membrane is diffusion limited, with an association rate constant greater than 10(8) M-1s-1, and an interfacial activation free energy of less than 2 kcal/mol. Equilibrium binding of phloretin to a vesicle membrane is characterized by a single class of high-affinity (8 micro M), noninteracting sites. Binding is enthalpy driven (delta H = -4.9 kcal/mol) at 23 degrees C. Analysis of amplitudes of kinetic processes shows that 66 +/- 3% of total phloretin binding sites are exposed at the external vesicle surface. The rate of phloretin movement between binding sites located near the external and internal interfaces is proportional to the concentration of un-ionized phloretin, with a rate constant of 5.7 X 10(4) M-1s-1 at 23 degrees C. The rate of this process is limited by a large enthalpic (9 kcal/mol) and entropic (-31 entropy units) barrier. An analysis of the concentration dependence of the rate of transmembrane movement suggests the presence of multiple intramembrane potential barriers. Permeation of phloretin through a lipid bilayer is modeled quantitatively in terms of discrete steps: binding to a membrane surface, translocation across a series of intramembrane barriers, and dissociation from the opposite membrane surface. The permeability coefficient for phloretin is calculated as 1.9 X 10(-3) cm/s on the basis of the model presented. Structure- function relationships are examined for a number of phloretin analogues.     

Effective lattice behavior of fluorescence energy transfer at lamellar macromolecular interfaces.

Fluorescence energy transfer between donors and acceptors confined to macromolecular interfaces is considered. In particular, we discuss two theoretical models for the ensemble-average fluorescence intensity decay of the donor when both fluorophores are incorporated into a planar (e.g., lamellar) interface. The first model is based on a continuous distribution of donor and acceptor molecules on a two-dimensional surface, whereas the other assumes a discrete distribution of fluorophores along the nodes of a two-dimensional square lattice. Results for the discrete model show that the fluorescence intensity kinetics of a donor depends strongly on the geometry of the molecular distribution (i.e., the lattice constant) and the photophysics of fluorophores (i.e., critical radius of the energy transfer). Furthermore, a "discrete molecular distribution" might manifest itself in the experimental data as an increase in the apparent dimensionality of the energy transfer with increasing acceptor concentration. Altogether, the experimental and theoretical underpinnings indicate the enormous potential of using fluorescence energy-transfer kinetics for revealing structural features of molecular ensembles (i.e., geometry, shape) based on a single experimental measurement. However, further understanding the effects of restricted geometries on the fluorescence energy transfer is required to take full advantage of this information. Basic theoretical considerations to that end are provided.     

A tethered adhesive particle model of two-dimensional elasticity and its application to the erythrocyte membrane.

A new model of two-dimensional elasticity with application to the erythrocyte membrane is proposed. The system consists of a planar array of self-adhesive particles attached to nearest neighbors with flexible tethers. Stretching from the equilibrium dimension is resisted because force is required to dissociate the particle clusters and to decrease the distribution entropy. Release of the external force is accompanied by a contraction as thermal diffusion randomizes the particles and allows interparticle attachments to form again. Analysis of membrane thermodynamics and mechanics under the two-state particle assumption results in a shear softening stress-strain relation. The shear modulus is found proportional to the square root of the surface density of particles, the interparticle adhesive energy, and is inversely proportional to the tether length. Applied to the erythrocyte membrane under the assumption that band 3 tetramer represents the particle and spectrin the tether, the shear modulus predicted corresponds to the measured value when the interparticle adhesive energy is approximately 4.0-5.9 kT, where kT is the Boltzmann constant multiplied by the temperature. This model suggests a mechanism wherein erythrocyte membrane deformability depends on integral protein homomultimeric interactions and can be modulated from the external surface.     

Side-chain conformational entropy at protein-protein interfaces

Protein-protein interactions are the key to many biological processes. How proteins selectively and correctly associate with their required protein partner(s) is still unclear. Previous studies of this "protein-docking problem" have found that shape complementarity is a major determinant of interaction, but the detailed balance of energy contributions to association remains unclear. This study estimates side-chain conformational entropy (per unit solvent accessible area) for various protein surface regions, using a self-consistent mean field calculation of rotamer probabilities. Interfacial surface regions were less flexible than the rest of the protein surface for calculations with monomers extracted from homodimer datasets in 21 of 25 cases, and in 8 of 9 for the large protomer from heterodimer datasets. In surface patch analysis, based on side-chain conformational entropy, 68% of true interfaces were ranked top for the homodimer set and 66% for the large protomer/heterodimer set. The results indicate that addition of a side-chain entropic term could significantly improve empirical calculations of protein-protein association.     

Model for transformations of the clathrin lattice in the coated vesicle pathway

Transport of receptors by the coated vesicle pathway entails assembly of clathrin triskelions into a lattice in conjunction with receptors in a membrane. The processes by which the receptors are concentrated, the lattice is assembled, transformed into a cage during vesiculation, and subsequently removed from pinched off vesicles are not understood in regard to mechanism, energetics or control. Tubulin and actin assembly are looked to for analogies applicable to clathrin. The present model supposes that clathrin assembly is energy linked and can be described by kinetic equations of the same general form as those for treadmilling in linear polymers. The coat lattice assembles in a steady state involving the degradation of a high energy form of the clathrin triskelions. Diffuse endocytosis receptors are assumed to be associated with individual triskelions and to be able to trigger clustering and coated pit formation by influencing the assembly kinetics of the bound triskelions. A generalization of the treadmilling scheme is proposed by which the kinetic parameters associated with clathrin polymerization can shift simultaneously for an entire lattice to favor alternatively net assembly or disassembly. This shift is effected by a coordinated conversion of the lattice bound receptors. The conversion of the receptors in turn depends on some global property of the membrane compartments (arguably pH, calcium concentration or transmembrane voltage) which is likely to change as a consequence of vesiculation. Thereby, lattice disassembly can be coordinated with the topological conversion from coated pit to coated vesicle.     

Dynamin GTPase,a force-generating molecular switch

Dynamin is a GTPase that regulates late events in clathrin-coated vesicle formation. Our current working model suggests that dynamin is targeted to coated pits in its unoccupied or GDP-bound form, where it is initially distributed uniformly throughout the clathrin lattice. GTP/GDP exchange triggers its release from these sites and its assembly into short helices that encircle the necks of invaginated coated pits like a collar. GTP hydrolysis, which is required for vesicle detachment, presumably induces a concerted conformation change, tightening the collar. Unlike most of its GTPase cousins that serve as molecular switches, dynamin has a low affinity for GTP, a very high intrinsic rate of GTP hydrolysis and functions as a homo-oligomer. A concerted conformational change resulting from coordinated GTP hydrolysis by the dynamin oligomer might be sufficient to generate force. In this case, dynamin would be the first GTPase identified that acts as a structural protein with mechano-chemical function.     

Role of coated vesicles, microfilaments, and calmodulin in receptor- mediated endocytosis by cultured B lymphoblastoid cells

Cell surface receptor IgM molecules of cultured human lymlphoblastoid cells (WiL2) patch and redistribute into a cap over the Golgi region of the cell after treatment with multivalent anti-IgM antibodies. During and after the redistribution, ligand-receptor clusters are endocytosed into coated pits and coated vesicles. Morphometric analysis of the distribution of ferritin-labeled ligand at EM resolution reveals the following sequence of events in the endocytosis of cell surface IgM: (a) binding of the multivalent ligand in a diffuse cell surface distribution, (b) clustering of the ligand-receptor complexes, (c) recruitment of clathrin coats to the cytoplasmic surface of the cell membrane opposite ligand-receptor clusters, (d) assembly and (e) internalization of coated vesicles, and (f) delivery of label into a large vesicular compartment, presumably partly lysosomal. Most of the labeled ligand enters this pathway. The recruitment of clathrin coats to the membrane opposite ligand-receptor clusters is sensitive to the calmodulin-directed drug Stelazine (trifluoperazine dihydrochloride). In addition, Stelazine inhibits an alternate pathway of endocytosis that does not involve coated vesicle formation. The actin-directed drug dihydrocytochalasin B has no effect on the recruitment of clathrin to the ligand-receptor clusters and the formation of coated pits and little effect on the alternate pathway, but this drug does interfere with subsequent coated vesicle formation and it inhibits capping. Cortical microfilaments that decorate with heavy meromyosin with constant polarity are observed in association with the coated regions of the plasma membrane and with coated vesicles. SDS-polyacrylamide gel electrophoresis analysis of a coated vesicle preparation isolated from WiL2 cells demonstrates that the major polypeptides in the fraction are a 175-kdalton component that comigrates with calf brain clathrin, a 42- kdalton component that comigrates with rabbit muscle actin and a 18.5- kdalton minor component that comigrates with calmodulin as well as 110- , 70-, 55-, 36-, 30-, and 17-kdalton components. These results clarify the pathways of endocytosis in this cell and suggest functional roles for calmodulin, especially in the formation of clathrin-coated pits, and for actin microfilaments in coated vesicle formation and in capping.     

Chemical Sensors for Solvent Vapors: Enthalpic and Entropic Contributions to Host-Guest Interactions

Chemical sensors, based on the mass-sensitive quartz micro balance (QMB) or the surface acoustic wave device (SAW), that are coated with thin cyclophane layers allow the detection of harmful organic vapors. The sensor signal of these supramolecular analyte-receptors can be predicted by a method that uses estimated free energies of the host-guest complex formation. From MM3 force field calculations, the reaction enthalpies (H° of host-guest interaction between the macrocycle and the analyte can be calculated, whereas the entropy changes are taken from condensation data. The validity of this condensation model is proven by an excellent linear correlation of the logarithm of the experimental equilibrium constant with the estimated Gibbs energy DG°. In this way promising sensor materials can be selected, even before they are synthesized.     

Influence of thermally driven surface undulations on tethers formed from bilayer membranes

Tether formation is a powerful method to study the mechanical properties of soft lipid bilayer membranes. The force required to maintain a tether at a given length depends upon both membrane elastic properties and tension. In this report, we develop a theoretical analysis that considers the contribution of thermally driven surface undulations and the corresponding entropically driven tensions on the conformation of tethers formed from unaspirated lipid vesicles. In this model, thermal undulations of the vesicle surface provide the excess area required for tether formation. Energy minimization demonstrates the dependence of equilibrium tether conformation on membrane tension and provides an analytical relationship between tether force and radius. If the contributions of nonlocal bending are not considered, an analytical relationship between tether force and length can also be obtained. The predictions of the model are compared to recently reported experimental data, and a value for the initial vesicle tension is obtained. Since most analyses of tether formation from cells and unaspirated vesicles neglect the contributions of nonlocal bending, the appropriateness of this assumption is analyzed. The effect of surface microvesiculations on the tether force-length relation is also considered.     

Clathrin-associated adaptor proteins - putting it all together

Adaptors are multifunctional linker proteins that, as a coated vesicle assembles, tether the clathrin lattice to the underlying membrane bud site. Each adaptor is composed of four distinct protein submits, but how these assemble into the functional complex is not clear. Here, some features of the protein sequences are discussed in an attempt to develop a speculative, low-resolution structural model of possible subunit interactions.     

Mathematical modelling of the formation of coated vesicles. A theoretical geometrical approach.

The mechanism by which flat hexagonal lattices of clathrin trimers transform into pentagonal/hexagonal spheres remains a mystery. In light of the geometrical nature of this process we have pursued a mathematical approach to the question. Through the geometrical analysis of flat hexagonal lattices we have discovered three possible forms of transformation to introduce curvature into the centre of the lattice: hub-centre transformation; hub-edge transformation; fringe transformation. Hub-edge and fringe transformations are used first to close the lattice while introducing localized curvature at the edges of the lattice. Hub-centre transformation is used after closure to relax the severely localized curvature generated during closure. This scheme not only maximizes the size of the coated vesicle generated, but also minimizes the number of transformations, thus minimizing the energy expended.     

Depletion effect and biomembrane budding

Depletion effects are well known to lead to phase separation in microsystems consisting of large and small particles with short-range repulsive interactions that act over macromolecular length scales. The equilibrium mechanics between an enveloped colloidal particle and a biomembrane caused by entropy is investigated by using a continuum model. We show that the favorable contact energy stems from entropy, which is sufficient to drive engulfment of the colloidal particle, and deformation of the biomembrane determines the resistance to the engulfment of the colloidal particle. The engulfment process depends on the ratio of the radii of the larger particle and smaller particles and the bending rigidity. The results show insights into the effects of depletion on biomembrane budding and nanoparticle transportation by a vesicle.     

Structural bases of lectin-carbohydrate affinities: comparison with protein-folding energetics.

We have made a comparative structure based analysis of the thermodynamics of lectin-carbohydrate (L-C) binding and protein folding. Examination of the total change in accessible surface area in those processes revealed a much larger decrease in free energy per unit of area buried in the case of L-C associations. According to our analysis, this larger stabilization of L-C interactions arises from a more favorable enthalpy of burying a unit of polar surface area, and from higher proportions of polar areas. Hydrogen bonds present at 14 L-C interfaces were identified, and their overall characteristics were compared to those reported before for hydrogen bonds in protein structures. Three major factors might explain why polar-polar interactions are stronger in L-C binding than in protein folding: (1) higher surface density of hydrogen bonds; (2) better hydrogen-bonding geometry; (3) larger proportion of hydrogen bonds involving charged groups. Theoretically, the binding entropy can be partitioned into three main contributions: entropy changes due to surface desolvation, entropy losses arising from freezing rotatable bonds, and entropic effects that result from restricting translation and overall rotation motions. These contributions were estimated from structural information and added up to give calculated binding entropies. Good correlation between experimental and calculated values was observed when solvation effects were treated according to a parametrization developed by other authors from protein folding studies. Finally, our structural parametrization gave calculated free energies that deviate from experimental values by 1.1 kcal/mol on the average; this amounts to an uncertainty of one order of magnitude in the binding constant.     

Bilayer Edges Catalyze Supported Lipid Bilayer Formation

Supported lipid bilayers (SLB) are important for the study of membrane-based phenomena and as coatings for biosensors. Nevertheless, there is a fundamental lack of understanding of the process by which they form from vesicles in solution. We report insights into the mechanism of SLB formation by vesicle adsorption using temperature-controlled time-resolved fluorescence microscopy at low vesicle concentrations. First, lipid accumulates on the surface at a constant rate up to ∼0.8 of SLB coverage. Then, as patches of SLB nucleate and spread, the rate of accumulation increases. At a coverage of ∼1.5 × SLB, excess vesicles desorb as SLB patches rapidly coalesce into a continuous SLB. Variable surface fluorescence immediately before SLB patch formation argues against the existence of a critical vesicle density necessary for rupture. The accelerating rate of accumulation and the widespread, abrupt loss of vesicles coincide with the emergence and disappearance of patch edges. We conclude that SLB edges enhance vesicle adhesion to the surface and induce vesicle rupture, thus playing a key role in the formation of continuous SLB.     

Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin

Extensive measurements and analysis of thermodynamic stability and kinetics of urea-induced unfolding and folding of hisactophilin are reported for 5-50 degrees C, at pH 6.7. Under these conditions hisactophilin has moderate thermodynamic stability, and equilibrium and kinetic data are well fit by a two-state transition between the native and the denatured states. Equilibrium and kinetic m values decrease with increasing temperature, and decrease with increasing denaturant concentration. The betaF values at different temperatures and urea concentrations are quite constant, however, at about 0.7. This suggests that the transition state for hisactophilin unfolding is native-like and changes little with changing solution conditions, consistent with a narrow free energy profile for the transition state. The activation enthalpy and entropy of unfolding are unusually low for hisactophilin, as is also the case for the corresponding equilibrium parameters. Conventional Arrhenius and Eyring plots for both folding and unfolding are markedly non-linear, but these plots become linear for constant DeltaG/T contours. The Gibbs free energy changes for structural changes in hisactophilin have a non-linear denaturant dependence that is comparable to non-linearities observed for many other proteins. These non-linearities can be fit for many proteins using a variation of the Tanford model, incorporating empirical quadratic denaturant dependencies for Gibbs free energies of transfer of amino acid constituents from water to urea, and changes in fractional solvent accessible surface area of protein constituents based on the known protein structures. Noteworthy exceptions that are not well fit include amyloidogenic proteins and large proteins, which may form intermediates. The model is easily implemented and should be widely applicable to analysis of urea-induced structural transitions in proteins.     

Vesicle formation in the Golgi apparatus

In this paper we examine the mechanics of vesicle budding from the Golgi apparatus. We propose a model for this process based on the notion that molecular surfactants can release the elastic energy stored in the lipid bilayer. The same physical process may drive other vesiculation processes, including coated vesicle formation and budding of enveloped viruses from the plasma membrane.     

Kinetics and thermodynamics of isothermal seed germination.

We have been successful in building a mathematical model that fits both the germination rate and the total number of seeds that germinate as a function of time. This mathematical model is the same autocatalytic reaction model that describes biochemical reactions in which enzymes play an important role. The model gives values for the initial concentration of two enzymes. From these initial enzyme concentrations an equilibrium constant is calculated and the thermodynamic model gives the change in enthalpy, entropy, free energy and the activation energy. A plot of the natural logarithm of the equilibrium constant as a function of the reciprocal of the absolute temperature gives two straight lines. The change of enthalpy for the process below 33 °C differs considerably to the change above 33 °C. The free energy as a function of the absolute temperature gives a straight line from which the change in entropy is calculated. The activation energy is determined from the slope of the natural logarithm of the rate constant as a function of the reciprocal of the absolute temperature.     

Minimal Mesoscale Model for Protein-Mediated Vesiculation in Clathrin-Dependent Endocytosis

In eukaryotic cells, the internalization of extracellular cargo via the endocytic machinery is an important regulatory process required for many essential cellular functions. The role of cooperative protein-protein and protein-membrane interactions in the ubiquitous endocytic pathway in mammalian cells, namely the clathrin-dependent endocytosis, remains unresolved. We employ the Helfrich membrane Hamiltonian together with surface evolution methodology to address how the shapes and energetics of vesicular-bud formation in a planar membrane are stabilized by presence of the clathrin-coat assembly. Our results identify a unique dual role for the tubulating protein epsin: multiple epsins localized spatially and orientationally collectively play the role of a curvature inducing capsid; in addition, epsin serves the role of an adapter in binding the clathrin coat to the membrane. Our results also suggest an important role for the clathrin lattice, namely in the spatial- and orientational-templating of epsins. We suggest that there exists a critical size of the coat above which a vesicular bud with a constricted neck resembling a mature vesicle is stabilized. Based on the observed strong dependence of the vesicle diameter on the bending rigidity, we suggest that the variability in bending stiffness due to variations in membrane composition with cell type can explain the experimentally observed variability on the size of clathrin-coated vesicles, which typically range 50–100 nm. Our model also provides estimates for the number of epsins involved in stabilizing a coated vesicle, and without any direct fitting reproduces the experimentally observed shapes of vesicular intermediates as well as their probability distributions quantitatively, in wildtype as well as CLAP IgG injected neuronal cell experiments. We have presented a minimal mesoscale model which quantitatively explains several experimental observations on the process of vesicle nucleation induced by the clathrin-coated assembly prior to vesicle scission in clathrin dependent endocytosis.     

Modeling the effects of mutations on the denatured states of proteins.

We develop a model for the reversible denaturation of proteins and for the effects of single-site mutations on the denatured states. The model is based on short chains of sequences of H (hydrophobic) and P (other) monomers configured as self-avoiding walks on the two-dimensional square lattice. The N (native) state is defined as the unique conformation of lowest contact energy, whereas the D (denatured) state is defined as the collection of all other conformations. With this model we are able to determine the exact partition function, and thus the exact native-denatured equilibrium for various solvent conditions, using the computer to exhaustively enumerate every possible configuration. Previous studies confirm that this model shows many aspects of protein-like behavior. The present study attempts to model how the denatured state (1) depends on the amino acid sequence, and (2) is changed by single-site mutations. The model accounts for two puzzling experimental results: (1) the replacement of a polar residue by a hydrophobic amino acid on the surface of a protein can destabilize a native protein, and (2) the "denaturant slope," m = partial delta G/partial c (where c is the concentration of denaturant--urea, guanidine hydrochloride), can sometimes change by as much as 30% due to a single mutation. The principal conclusion of the present study is that, under strong folding conditions, the denatured conformations that are in equilibrium with the native state are not open random configurations. Instead, they are an ensemble of highly compact conformations with a distribution that depends on the residue sequence and that can be substantially altered by single mutations. Most importantly, we conclude that mutations can exert their dominant effects on protein stability by changing the entropy of folding.