Protein diffusion on charged membranes: a dynamic mean-field model describes time evolution and lipid reorganization

As charged macromolecules adsorb and diffuse on cell membranes in a large variety of cell signaling processes, they can attract or repel oppositely charged lipids. This results in lateral membrane rearrangement and affects the dynamics of protein function. To address such processes quantitatively we introduce a dynamic mean-field scheme that allows self-consistent calculations of the equilibrium state of membrane-protein complexes after such lateral reorganization of the membrane components, and serves to probe kinetic details of the process. Applicable to membranes with heterogeneous compositions containing several types of lipids, this comprehensive method accounts for mobile salt ions and charged macromolecules in three dimensions, as well as for lateral demixing of charged and net-neutral lipids in the membrane plane. In our model, the mobility of membrane components is governed by the diffusion-like Cahn-Hilliard equation, while the local electrochemical potential is based on nonlinear Poisson-Boltzmann theory. We illustrate the method by applying it to the adsorption of the anionic polypeptide poly-Lysine on negatively charged lipid membranes composed of binary mixtures of neutral and monovalent lipids, or onto ternary mixtures of neutral, monovalent, and multivalent lipids. Consistent with previous calculations and experiments, our results show that at steady-state multivalent lipids (such as PIP₂), but not monovalent lipid (such as phosphatidylserine), will segregate near the adsorbing macromolecules. To address the corresponding diffusion of the adsorbing protein in the membrane plane, we couple lipid mobility with the propagation of the adsorbing protein through a dynamic Monte Carlo scheme. We find that due to their higher mobility dictated by the electrochemical potential, multivalent lipids such as PIP₂ more quickly segregate near oppositely charged proteins than do monovalent lipids, even though their diffusion constants may be similar. The segregation, in turn, slows protein diffusion, as lipids introduce an effective drag on the motion of the adsorbate. In contrast, monovalent lipids such as phosphatidylserine only weakly segregate, and the diffusions of protein and lipid remain largely uncorrelated.     

Effect of polyelectrolyte adsorption on lateral distribution and dynamics of anionic lipids: a Monte Carlo study of a coarse-grain model

We employ Monte Carlo simulations to investigate the interaction between an adsorbing linear flexible cationic polyelectrolyte and a ternary mixed fluid membrane containing neutral (phosphatidylcholine, PC), monovalent (phosphatidylserine, PS), and multivalent (phosphatidylinositol, PIP₂) anionic lipids. We systematically explore the influences of polyelectrolyte chain length, polyelectrolyte charge density, polyelectrolyte total charge amount, and salt solution ionic strength on the static and dynamic properties of different anionic lipid species. Our results show that the multivalent PIP₂ lipids dominate the polyelectrolyte–membrane interaction and competitively inhibit polyelectrolyte–PS binding. When the total charge amount of the polyelectrolyte is less than that of the local oppositely charged PIP₂ lipids, the polyelectrolyte can drag the bound multivalent lipids to diffuse on the membrane, but cannot interact with the PS lipids. Under this condition, the diffusion behaviors of the polyelectrolyte closely follow the prediction of the Rouse model, and the polyelectrolyte chain properties determine the adsorption amount, concentration gradients, and hierarchical mobility of the bound PIP₂ lipids. However, when the total charge amount of the polyelectrolyte is larger than that of the local PIP₂ lipids, the polyelectrolyte further binds the PS lipids around the polyelectrolyte–PIP₂ complex to achieve local electrical neutrality. In this condition, parts of the polyelectrolyte desorb from the membrane and show faster mobility, and the bound PS presents much faster mobility than the segregated PIP₂. This work provides an explanation for heterogeneity formation in different anionic lipids induced by polyelectrolyte adsorption.     

The "electrostatic-switch" mechanism: Monte Carlo study of MARCKS-membrane interaction

The binding of the myristoylated alanine-rich C kinase substrate (MARCKS) to mixed, fluid, phospholipid membranes is modeled with a recently developed Monte Carlo simulation scheme. The central domain of MARCKS is both basic (ζ = +13) and hydrophobic (five Phe residues), and is flanked with two long chains, one ending with the myristoylated N-terminus. This natively unfolded protein is modeled as a flexible chain of “beads” representing the amino acid residues. The membranes contain neutral (ζ = 0), monovalent (ζ = −1), and tetravalent (ζ = −4) lipids, all of which are laterally mobile. MARCKS-membrane interaction is modeled by Debye-Hückel electrostatic potentials and semiempirical hydrophobic energies. In agreement with experiment, we find that membrane binding is mediated by electrostatic attraction of the basic domain to acidic lipids and membrane penetration of its hydrophobic moieties. The binding is opposed by configurational entropy losses and electrostatic membrane repulsion of the two long chains, and by lipid demixing upon adsorption. The simulations provide a physical model for how membrane-adsorbed MARCKS attracts several PIP₂ lipids (ζ = −4) to its vicinity, and how phosphorylation of the central domain (ζ = +13 to ζ = +7) triggers an “electrostatic switch”, which weakens both the membrane interaction and PIP₂ sequestration. This scheme captures the essence of “discreteness of charge” at membrane surfaces and can examine the formation of membrane-mediated multicomponent macromolecular complexes that function in many cellular processes.     

Lipid demixing and protein-protein interactions in the adsorption of charged proteins on mixed membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.     

Colloid adsorption onto responsive membranes

The adsorption of colloids of varying sizes and charges onto a surface that carries both negative and positive charges, representing a membrane, has been investigated using a simple model employing Monte Carlo simulations. The membrane is made of positive and negative charges (headgroups) that are allowed to move along the membrane, simulating the translational diffusion of the lipids, and are also allowed to protrude into the solution, giving rise to a fluid and soft membrane. When an uncharged colloid is placed in the vicinity of the membrane, a short-range repulsion between the colloid and the membrane is observed and the membrane will deflect to avoid coming into contact with the colloid. When the colloid is charged, the membrane response is twofold: the headgroups of the membrane move toward the colloid, as if to partly embrace it, and the positive headgroups of the membrane approach the oppositely charged colloid, inducing the demixing of the membrane lipids (polarization). The presence of protrusions enhances the polarization of the membrane. Potential of mean force calculations show that protrusions give rise to a more long-range attractive colloid-membrane potential which has a smaller magnitude at short separations.     

Near-Critical Fluctuations and Cytoskeleton-Assisted Phase Separation Lead to Subdiffusion in Cell Membranes

We address the relationship between membrane microheterogeneity and anomalous subdiffusion in cell membranes by carrying out Monte Carlo simulations of two-component lipid membranes. We find that near-critical fluctuations in the membrane lead to transient subdiffusion, while membrane-cytoskeleton interaction strongly affects phase separation, enhances subdiffusion, and eventually leads to hop diffusion of lipids. Thus, we present a minimum realistic model for membrane rafts showing the features of both microscopic phase separation and subdiffusion.     

Interaction of insulin receptors with lipid bilayers and specific and nonspecific binding of insulin to supported membranes

In the first part, we study the interaction of the insulin receptor with model membranes of dimyristoylphosphatidylcholine (DMPC) by various techniques, including calorimetry, densitometry, static light scattering, and electron microscopy. By analyzing the pronounced depression of the lipid chain melting transition in terms of the Van Laar-Hildebrand theory of regular dilute solutions, an (exothermic) interaction energy of Wp = 2000 kJ.mol-1 is found for the receptor and of WL = 0.6 kJ.mol-1 for the lipid. This is interpreted in terms of an adsorption of the 2 hydrophilic head groups of the receptor to the membrane surface so that 1 protein interacts with about 2000 lipids. This number is verified by freeze-fracture electron microscopy. Binding of insulin induces a remarkable decoupling of the receptor head group from the membrane, pointing to a pronounced conformational change. In the second part, we introduce a simple fluorescence technique by which adsorption isotherms of water-soluble and fluorescent-labeled substrates, such as insulin, to membranes may be determined. It is based on the selective evanescent field excitation of ligands adsorbed to supported planar bilayers on argon-sputtered glass plates. These are deposited by the monolayer transfer technique or by vesicle condensation. The reconstituted receptor exhibits a weak (binding constant Kw = 3 X 10(9) L.M-1) and a strong (binding constant Ks greater than 10(10) L.M-1) binding site. Insulin exhibits a weak but remarkable nonspecific binding to bilayers of pure DMPC and DMPC containing 20% positively charged lipid and a strong binding to DMPC containing negatively charged lipids such as phosphatidylserine or ganglioside (GT1b).(ABSTRACT TRUNCATED AT 250 WORDS)     

Ion-binding properties of calbindin D9k: a Monte Carlo simulation study

Monte Carlo simulations are used to calculate the binding constant of two Ca2+ ions to the protein bovine calbindin D9k. The change in binding constant with respect to mutation of charged amino acids, presence of various electrolytes, protein concentration, solution pH, and competitive binding of monovalent ions is investigated. Each of these factors may have a large influence on the binding constant. The simulations are performed in a dielectric continuum model, the so-called primitive model of electrolyte theory, with a fixed protein structure and a uniform dielectric permittivity. The calculated binding constants are in excellent agreement with experimental data and describe changes in the binding constant over six orders of magnitude.     

A Monte Carlo simulation study of protein-induced heat capacity changes and lipid-induced protein clustering.

Monte Carlo simulations were used to describe the interaction of peripheral and integral proteins with lipids in terms of heat capacity profiles and protein distribution. The simulations were based on a two-state model for the lipid, representing the lipid state as being either gel or fluid. The interaction between neighboring lipids has been taken into account through an unlike nearest neighbor free energy term delta omega, which is a measure of the cooperativity of the lipid transition. Lipid/protein interaction was considered using the experimental observation that the transition midpoints of lipid membranes are shifted upon protein binding, a thermodynamic consequence of different binding constants of protein with fluid or gel lipids. The difference of the binding free energies was used as an additional parameter to describe lipid-protein interaction. The heat capacity profiles of lipid/protein complexes could be well described for both peripheral and integral proteins. Binding of proteins results in a shift and an asymmetric broadening of the melting profile. The model results in a coexistence of gel and fluid lipid domains in the proximity of the thermotropic transition. As a consequence, bound peripheral proteins aggregate in the temperature range of the lipid transition. Integral proteins induce calorimetric melting curves that are qualitatively different from that of peripheral proteins and aggregate in either gel or liquid crystalline lipid phase. The results presented here are in good agreement with calorimetric experiments on lipid-protein complexes and have implementations for the functional control of proteins.     

Increased concentration of polyvalent phospholipids in the adsorption domain of a charged protein

We studied the adsorption of a charged protein onto an oppositely charged membrane, composed of mobile phospholipids of differing valence, using a statistical-thermodynamical approach. A two-block model was employed, one block corresponding to the protein-affected region on the membrane, referred to as the adsorption domain, and the other to the unaffected remainder of the membrane. We calculated the protein-induced lipid rearrangement in the adsorption domain as arising from the interplay between the electrostatic interactions in the system and the mixing entropy of the lipids. Equating the electrochemical potentials of the lipids in the two blocks yields an expression for the relations among the various lipid fractions in the adsorption domain, indicating a sensitive dependence of lipid fraction on valence. This expression is a result of the two-block picture but does not depend on further details of the protein-membrane interaction. We subsequently calculated the lipid fractions themselves using the Poisson-Boltzmann theory. We examined the dependence of lipid enrichment, i.e., the ratio between the lipid fractions inside and outside the adsorption domain, on various parameters such as ionic strength and lipid valence. Maximum enrichment was found for lipid valence in the range between -3 and -4 in physiological conditions. Our results are in qualitative agreement with recent experimental studies on the interactions between peptides having a domain of basic residues and membranes containing a small fraction of the polyvalent phosphatidylinositol 4,5-bisphosphate (PIP2). This study provides theoretical support for the suggestion that proteins adsorbed onto membranes through a cluster of basic residues may sequester PIP2 and other polyvalent lipids.     

Correlation between acetylcholine receptor function and structural properties of membranes

Protein-lipid interactions were studied by using Torpedo californica acetylcholine receptor (AChR) as a model system by reconstituting purified AChR into membranes containing various synthetic lipids and native lipids. AChR function was determined by measuring two activities at 4 degrees C: (1) low to high agonist affinity-state transition of AChR in the presence of an agonist (carbamylcholine) in either membrane fragments or sealed vesicles and (2) ion-gating activity of AChR-containing vesicles in response to carbamylcholine. Sixteen samples were examined, each containing different lipid compositions including phosphatidylcholine, cholesterol, phosphatidic acid, phosphatidylethanolamine, asolectin, neutral lipid depleted asolectin, native lipids, and cholesterol-depleted native lipids. Phosphatidylcholines with different configurations of fatty acyl chains were used. The dynamic structures of these membranes were probed by incorporating spin-labeled fatty acid into AChR-containing vesicles and measuring the order parameters. It was found that both aspects of AChR function were highly dependent on the lipid environment even though carbamylcholine binding itself was not affected. An appropriate membrane fluidity was necessarily required to allow the interconversion between the low and high affinity states of AChR. An optimal fluidity hypothesis is proposed to account for the conformational transition properties of membrane proteins. In addition, the conformational change was only a necessary, but not sufficient, condition for the AChR-mediated ion flux activity. Among membranes in which AChR manifested the affinity-state transition, only those containing both cholesterol and negatively charged phospholipids (such as phosphatidic acid) retained the ion-gating activity.     

Domain formation induced by the adsorption of charged proteins on mixed lipid membranes

Peripheral proteins can trigger the formation of domains in mixed fluid-like lipid membranes. We analyze the mechanism underlying this process for proteins that bind electrostatically onto a flat two-component membrane, composed of charged and neutral lipid species. Of particular interest are membranes in which the hydrocarbon lipid tails tend to segregate owing to nonideal chain mixing, but the (protein-free) lipid membrane is nevertheless stable due to the electrostatic repulsion between the charged lipid headgroups. The adsorption of charged, say basic, proteins onto a membrane containing anionic lipids induces local lipid demixing, whereby charged lipids migrate toward (or away from) the adsorption site, so as to minimize the electrostatic binding free energy. Apart from reducing lipid headgroup repulsion, this process creates a gradient in lipid composition around the adsorption zone, and hence a line energy whose magnitude depends on the protein's size and charge and the extent of lipid chain nonideality. Above a certain critical lipid nonideality, the line energy is large enough to induce domain formation, i.e., protein aggregation and, concomitantly, macroscopic lipid phase separation. We quantitatively analyze the thermodynamic stability of the dressed membrane based on nonlinear Poisson-Boltzmann theory, accounting for both the microscopic characteristics of the proteins and lipid composition modulations at and around the adsorption zone. Spinodal surfaces and critical points of the dressed membranes are calculated for several different model proteins of spherical and disk-like shapes. Among the models studied we find the most substantial protein-induced membrane destabilization for disk-like proteins whose charges are concentrated in the membrane-facing surface. If additional charges reside on the side faces of the proteins, direct protein-protein repulsion diminishes considerably the propensity for domain formation. Generally, a highly charged flat face of a macroion appears most efficient in inducing large compositional gradients, hence a large and unfavorable line energy and consequently lateral macroion aggregation and, concomitantly, macroscopic lipid phase separation.     

Interaction Between Equally Charged Membrane Surfaces Mediated by Positively and Negatively Charged Macro-Ions

In biological systems, charged membrane surfaces are surrounded by charged molecules such as electrolyte ions and proteins. Our recent experiments in the systems of giant phospholipid vesicles indicated that some of the blood plasma proteins (macro-ions) may promote adhesion between equally charged membrane surfaces. In this work, theory was put forward to describe an IgG antibody-mediated attractive interaction between negatively charged membrane surfaces which was observed in experiments on giant phospholipid vesicles with cardiolipin-containing membranes. The attractive interactions between negatively charged membrane surfaces in the presence of negatively and positively charged spherical macro-ions are explained using functional density theory and Monte Carlo simulations. Both, the rigorous solution of the variational problem within the functional density theory and the Monte Carlo simulations show that spatial and orientational ordering of macro-ions may give rise to an attractive interaction between negatively charged membrane surfaces. It is also shown that the distinctive spatial distribution of the charge within the macro-ions (proteins) is essential in this process.     

Membrane Fluctuations Destabilize Clathrin Protein Lattice Order

We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.     

Membrane Fluctuations Destabilize Clathrin Protein Lattice Order

We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.     

Interaction of beta-adrenergic agents with the plasma membranes of the myocardium

The initial stage of interaction of beta-adrenomimetics and beta-adrenoblockers with specific membrane binding sites is characterized by different patterns of thermodynamic parameters. Administration of isadrin results in a decrease of entropy and enthalpy, which reflects the primary binding reaction and agonist-specific receptor isomerization to the conformational form activating adenylate cyclase. Anaprilin and alpheprol do not change the receptor conformation and participate only in the primary binding reaction which is marked by a decrease in enthalpy and a rise of entropy in the course of interaction of beta-adrenoblockers with specific membrane binding sites. The different patterns of thermodynamic parameters under the effect of beta-adrenomimetics and beta-adrenoblockers on plasma membranes are explained by the different influence of these substances on the mobility of membrane lipids, i.e. on the viscosity of plasma membranes.     

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.     

Motif-pattern dependence of biomolecular phase separation driven by specific interactions

Eukaryotic cells partition a wide variety of important materials and processes into biomolecular condensates—phase-separated droplets that lack a membrane. In addition to nonspecific electrostatic or hydrophobic interactions, phase separation also depends on specific binding motifs that link together constituent molecules. Nevertheless, few rules have been established for how these ubiquitous specific, saturating, motif-motif interactions drive phase separation. By integrating Monte Carlo simulations of lattice-polymers with mean-field theory, we show that the sequence of heterotypic binding motifs strongly affects a polymer’s ability to phase separate, influencing both phase boundaries and condensate properties (e.g. viscosity and polymer diffusion). We find that sequences with large blocks of single motifs typically form more inter-polymer bonds, which promotes phase separation. Notably, the sequence of binding motifs influences phase separation primarily by determining the conformational entropy of self-bonding by single polymers. This contrasts with systems where the molecular architecture primarily affects the energy of the dense phase, providing a new entropy-based mechanism for the biological control of phase separation.