Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations

Bimolecular reactions in the plasma membrane, such as receptor dimerization, are a key signaling step for many signaling systems. For receptors to dimerize, they must first diffuse until a collision happens, upon which a dimerization reaction may occur. Therefore, study of the dynamics of cell signaling on the membrane may require the use of a spatial modeling framework. Despite the availability of spatial simulation methods, e.g., stochastic spatial Monte Carlo (MC) simulation and partial differential equation (PDE) based approaches, many biological models invoke well-mixed assumptions without completely evaluating the importance of spatial organization. Whether one is to utilize a spatial or non-spatial simulation framework is therefore an important decision. In order to evaluate the importance of spatial effects a priori, i.e., without performing simulations, we have assessed the applicability of a dimensionless number, known as second Damköhler number (Da), defined here as the ratio of time scales of collision and reaction, for 2-dimensional bimolecular reactions. Our study shows that dimerization reactions in the plasma membrane with Da ∼> 0.1 (tested in the receptor density range of 10²–10⁵/μm²) require spatial modeling. We also evaluated the effective reaction rate constants of MC and simple deterministic PDEs. Our simulations show that the effective reaction rate constant decreases with time due to time dependent changes in the spatial distribution of receptors. As a result, the effective reaction rate constant of simple PDEs can differ from that of MC by up to two orders of magnitude. Furthermore, we show that the fluctuations in the number of copies of signaling proteins (noise) may also depend on the diffusion properties of the system. Finally, we used the spatial MC model to explore the effect of plasma membrane heterogeneities, such as receptor localization and reduced diffusivity, on the dimerization rate. Interestingly, our simulations show that localization of epidermal growth factor receptor (EGFR) can cause the diffusion limited dimerization rate to be up to two orders of magnitude higher at higher average receptor densities reported for cancer cells, as compared to a normal cell.     

A molecular membrane model of sperm capacitation and the acrosome reaction of mammalian spermatozoa

The abundance of data pertaining to the metabolism of lipids in relation to mammalian fertilization has warranted an effort to assemble a molecular membrane model for the comprehensive visualization of the biochemical events involved in sperm capacitation and the acrosome reaction. Derived both from earlier models as well as from current concepts, our membrane model depicts a lipid bilayer assembly of space-filling molecular models of sterols and phospholipids in dynamic equilibrium with peripheral and integral membrane proteins. A novel feature is the possibility of visualizing individual lipid molecules such as phosphatidylcholine, phosphatidylethanolamine, lysophospholipids, fatty acids, and free or esterified cholesterol. The model illustrates enzymatic reactions which are believed to regulate the permeability and integrity of the plasma membrane overlying the acrosome during interactions between the male gamete and capacitation factors present in fluids of the female genital tract. The use of radioactive lipids as molecular probes for monitoring the metabolism of cholesterol and phosphatidylcholine revealed the presence of (1) steroid sulfatase in hamster cumulus cells, (2) lecithin: cholesterol acyltransferase in human follicular fluid, (3) phospholipase A₂, and (4) lysophospholipase in human spermatozoa. These enzymatic reactions can be integrated into a pathway that provides a link between the concepts of lysophospholipid accumulation in the sperm membranes and alteration of the cholesterol/phospholipid ratio as factors involved in the preparation of the membranes for the acrosome reaction. Capacitation is viewed as a reversible phenomenon which, upon completion, results in a decrease in negative surface charge, an efflux of membrane cholesterol, and an influx of calcium between the plasma and outer acrosomal membranes. Triggered by the entry of calcium, the acrosome reaction involves phospholipase A₂ activation followed by a transient accumulation of unsaturated fatty acids and lysophospholipids implicated in membrane fusion which occurs during the formation of membrane vesicles in spermatozoa undergoing the acrosome reaction.     

Maturation of mammalian spermatozoa: modifications of the acrosome and plasma membrane leading to fertilization

The mammalian spermatozoon is a terminally differentiated cell. Its surface is covered by a continuous plasma membrane that is divided into distinct domains in which functional molecules are distributed. The acrosome is an internal organelle located at the anterior head and contains hydrolytic enzymes. The anterior acrosome participates in the acrosome reaction, which is an indispensable event during fertilization. These surface domains and the acrosome are formed during spermiogenesis, during which associated molecules are transported and organized. Many of the molecules thus arranged are functionally immature but gradually become mature during epididymal maturation. Some of them are further altered and redistributed during the fertilization process and play various roles. Here, the sequential changes in the acrosome and plasma membrane during spermatozoan maturation are reviewed, particular attention being paid to molecules derived from the testis.     

Use of cyclodextrins to manipulate plasma membrane cholesterol content: evidence, misconceptions and control strategies

The physiological importance of cholesterol in the cell plasma membrane has attracted increased attention in recent years. Consequently, the use of methods of controlled manipulation of membrane cholesterol content has also increased sharply, especially as a method of studying putative cholesterol-enriched cell membrane domains (rafts). The most common means of modifying the cholesterol content of cell membranes is the incubation of cells or model membranes with cyclodextrins, a family of compounds, which, due to the presence of relatively hydrophobic cavity, can be used to extract cholesterol from cell membranes. However, the mechanism of this activity of cyclodextrins is not completely established. Moreover, under conditions commonly used for cholesterol extraction, cyclodextrins may remove cholesterol from both raft and non-raft domains of the membrane as well as alter the distribution of cholesterol between plasma and intracellular membranes. In addition, other hydrophobic molecules such as phospholipids may also be extracted from the membranes by cyclodextrins. We review the evidence for the specific and non-specific effects of cyclodextrins and what is known about the mechanisms for cyclodextrin-induced cholesterol and phospholipid extraction. Finally, we discuss useful control strategies that may help to verify that the observed effects are due specifically to cyclodextrin-induced changes in cellular cholesterol.     

The collisional limit: an important consideration for membrane-associated enzymes and receptors

Because of the proximity of many bound receptors or enzymes, a membrane surface may become uniformly reactive so that every collision between a ligand and the membrane particle results in a binding or catalytic event. At this limit (the collisional limit), the reaction rate depends on membrane particle (cell) concentration and is independent of receptor concentration. Many receptor systems display properties that satisfy the requirements of a collisionally limited reaction. These include the presence of many receptors per cell. The filling of only a few of these receptors often generates the maximum cellular response, and the remaining receptors have been referred to as spare receptors. However, many receptors are needed to produce the collisional limit, and spare receptors may represent nature's evolution toward a reaction that provides the maximum rate as well as the maximum sensitivity to a ligand. Since receptors or enzymes provided on small membrane fragments will not function at the collisional limit, properties of reconstituted enzymes or receptors may not be extrapolated to the physiological situation. The use of normal bimolecular kinetic or equilibrium equations is inappropriate for reactions limited by collision and can give unusual results that lead to inappropriate conclusions. Determination of whether the collisional limit applies to a membrane-bound system is important for understanding its properties and those of the physiological circumstance.     

Role of GM3-enriched microdomains in signal transduction regulation in T lymphocytes

Gangliosides, sialic acid containing glycosphigolipids, are ubiquitous constituents of cell plasma membranes. Each cell type shows a peculiar ganglioside expression pattern. In human T lymphocytes monosialoganglioside GM3 represents the main ganglioside constituent of cell plasma membrane where it is concentrated in glycosphingolipid-enriched microdomains (GEM). The presence of tyrosine kinase receptors, mono- (Ras, Rap) and heterotrimeric G proteins, Src-like tyrosine kinases (lck, lyn, fyn), PKC isozymes, glycosylphosphatidylinositol (GPI)-anchored proteins and, after T cell activation, the Syk-family kinase Zap-70, prompts these portions of the plasma membrane to be considered as "glycosignaling domains." In particular, during T cell activation and/or other dynamic functions of the cell, such as apoptosis, key signaling molecules are recruited to these microdomains, where they strictly interact with GM3. The association of transducer proteins with GM3 in microdomains suggests that this ganglioside is the main marker of GEM in human lymphocytes and is a component of a cell plasma membrane multimolecular signaling complex involved in cell-cell interaction, signal transduction, and cell activation.     

Use of cyclodextrins to manipulate plasma membrane cholesterol content: Evidence, misconceptions and control strategies

The physiological importance of cholesterol in the cell plasma membrane has attracted increased attention in recent years. Consequently, the use of methods of controlled manipulation of membrane cholesterol content has also increased sharply, especially as a method of studying putative cholesterol-enriched cell membrane domains (rafts). The most common means of modifying the cholesterol content of cell membranes is the incubation of cells or model membranes with cyclodextrins, a family of compounds, which, due to the presence of relatively hydrophobic cavity, can be used to extract cholesterol from cell membranes. However, the mechanism of this activity of cyclodextrins is not completely established. Moreover, under conditions commonly used for cholesterol extraction, cyclodextrins may remove cholesterol from both raft and non-raft domains of the membrane as well as alter the distribution of cholesterol between plasma and intracellular membranes. In addition, other hydrophobic molecules such as phospholipids may also be extracted from the membranes by cyclodextrins. We review the evidence for the specific and non-specific effects of cyclodextrins and what is known about the mechanisms for cyclodextrin-induced cholesterol and phospholipid extraction. Finally, we discuss useful control strategies that may help to verify that the observed effects are due specifically to cyclodextrin-induced changes in cellular cholesterol.     

Calculation of diffusion-limited kinetics for the reactions in collision coupling and receptor cross-linking

Both enzyme (e.g., G-protein) activation via a collision coupling model and the formation of cross-linked receptors by a multivalent ligand involve reactions between two molecules diffusing in the plasma membrane. The diffusion of these molecules is thought to play a critical role in these two early signal transduction events. In reduced dimensions, however, diffusion is not an effective mixing mechanism; consequently, zones in which the concentration of particular molecules (e.g., enzymes, receptors) becomes depleted or enriched may form. To examine the formation of these depletion/ accumulation zones and their effect on reaction rates and ultimately the cellular response, Monte Carlo techniques are used to simulate the reaction and diffusion of molecules in the plasma membrane. The effective reaction rate at steady state is determined in terms of the physical properties of the tissue and ligand for both enzyme activation via collision coupling and the generation of cross-linked receptors. The diffusion-limited reaction rate constant is shown to scale with the mean square displacement of a receptor-ligand complex. The rate constants determined in the simulation are compared with other theoretical predictions as well as experimental data.     

Capacitation and the acrosome reaction in equine sperm.

During sexual reproduction, the sperm and oocyte must fuse before the production of a diploid zygote can proceed. In mammals such as equids, fusion depends critically on complex changes in the plasma membrane of the sperm and, not surprisingly, this membrane differs markedly from that of somatic cells. After leaving the testes, sperm cease to synthesize plasma membrane lipids or proteins, and vesicle-mediated transport stops. When the sperm reaches the female reproductive tract, it is activated by so-called capacitation factors that initiate a delicate reorientation and modification of molecules within the plasma membrane. These surface changes enable the sperm to bind to the extracellular matrix of the egg (zona pellucida ZP) and the zona then primes the sperm to initiate the acrosome reaction, an exocytotic event required for the sperm to penetrate the zona. This paper will review the processes that occur at the sperm plasma membrane before and during successful penetration of the equine ZP. It is noted that while several methods have been described for detecting changes that occur during capacitation and the acrosome reaction in bovine and porcine sperm, relatively little has been documented for equine sperm. Special attention will therefore be dedicated to recent attempts to develop and implement new assays for the detection of the capacitation status of live, acrosome-intact and motile equine sperm.     

The second cell membrane: the basal lamina and the tissue cell theory of metazoa.

We suggest that the basal lamina is essentially a second plasma or cell membrane appearing at the next higher level of biological organization; that together with associated cell monolayers it creates a tissue level membrane which is used to form multicellular cells and that collections of these provide the essential structure of metazoa. Thus when the histological structure of multicellular organisms is viewed in a topologically simplified form such organisms appear to be sets of multicellular cells (m-cells) formed by a unit tissue membrane built around the basal lamina. Not only are m-cells in this way structurally isomorphous (homeomorphic) to unit or classical biological cells (u-cells) but the two cellular levels are also functionally isomorphous. This suggests a “General Principle of Hierarchical Isomorphism or Iteration”, i.e. that multicellular evolution recapitulates unicellular evolution. This principle of structural and functional isomorphic mappability of unicellular onto multicellular organisms then governs the organization of matter all the way from molecules to man. Just as cytoplasm precipitates the bimolecular plasma membrane to form u-cells for the purpose of achieving reaction sequestration, in turn, these u-cells precipitate a common basal lamina to form m-cells, the histologist's acini, to produce sequestered “tissue plasms”. Thus, the “generalized acinus” with its basal laminar complex seem to constitute a second level (multicellular) cell and cell membrane, respectively.Four operators, ultimately under genetic control, can generate both u and m-cells from planar configurations of their respective unit membranes therewith providing the essential structure of all cells, tissues, organs and organisms. These are the ply, permeability vector, topological and stratificational operators. They are collected into a set of “organ formulae”. Both the plasma membrane and the basal lamina act as covering membranes and, again, as membranes for subcells so that a complete multicellular organism is a tetrahierarchical cell in which the molecule is the element of the first two cellular domains and the cell is the element of the last two. The analysis identifies a new transport organ group which together with the classical endocrine and exocrine groups comprises nearly the whole of the soft tissue organs. In a major reduction, all these organs are continuously (topologically) transformable into each and into hollow spheres, cells or acini thus greatly simplifying the histology of metazoa. Given this emphasis on cellularization it would seem that life, i.e. the autonomous chemoservo, results from the cooperation of cellularization and replication operations on the catalyzation process. Through cellularization, the lipid bilayer and basal laminar membranes provide the essential catalytic reaction sequestration demanded by chemical reaction theory while through complementary base pairing the DNA double helix provides the essential memory which stores the patterns of the variations of the sequestered reactions.     

Direct evidence for cholesterol crystalline domains in biological membranes: role in human pathobiology

This review will discuss the use of small-angle X-ray diffraction approaches to study the organization of lipids in plasma membranes derived from two distinct mammalian cell types: arterial smooth muscle cells and ocular lens fiber cells. These studies indicate that cholesterol at an elevated concentration can self-associate and form immiscible domains in the plasma membrane, a phenomenon that contributes to both physiologic and pathologic cellular processes, depending on tissue source. In plasma membrane samples isolated from atherosclerotic smooth muscle cells, the formation of sterol-rich domains is associated with loss of normal cell function, including ion transport activity and control of cell replication. Analysis of meridional diffraction patterns from intact and reconstituted plasma membrane samples indicates the presence of an immiscible cholesterol domain with a unit cell periodicity of 34 Å, consistent with a cholesterol monohydrate tail-to-tail bilayer, under disease conditions. These cholesterol domains were observed in smooth muscle cells enriched with cholesterol in vitro as well as from cells obtained ex vivo from an animal model of atherosclerosis. By contrast, well-defined cholesterol domains appear to be essential to the normal physiology of fiber cell plasma membranes of the human ocular lens. The organization of cholesterol into separate domains underlies the role of lens fiber cell plasma membranes in maintaining lens transparency. These domains may also interfere with cataractogenic aggregation of soluble lens proteins at the membrane surface. Taken together, these analyses provide examples of both physiologic and pathologic roles that sterol-rich domains may have in mammalian plasma membranes. These findings support a model of the membrane in which cholesterol aggregates into structurally distinct regions that regulate the function of the cell membrane.     

Apolipoproteins, membrane cholesterol domains, and the regulation of cholesterol efflux.

Published data related to both cell membrane biology and apolipoprotein structure are reviewed and used to formulate a new model describing the mechanisms of cholesterol efflux from cell plasma membrane to high density lipoprotein (HDL) particles. The central premise of this model is the existence of heterogenous domains of cholesterol within plasma membranes. We propose that cholesterol efflux from cell membranes is influenced by three factors: 1) the distribution of cholesterol between cholesterol-rich and cholesterol-poor membrane domains, 2) the diffusion of cholesterol molecules through the extracellular unstirred water layer, and 3) the transient interaction of segments of the amphipathic helix of the HDL apolipoprotein with cholesterol-poor membrane domains resulting in enhanced cholesterol efflux.     

Self-inactivation of NADH-oxidase from Mycoplasma cells during reaction

The feasibility of self-inactivation of NADH-oxidase by plasma membranes of Acholeplasma laidlawii cells was investigated. It was demonstrated that the rate of NADH oxidation in a flow reactor upon stirring diminishes with time. This decrease of the reaction rate is not coupled with the presence in the reaction mixture of the reaction products--NAD+ and H2O2, and is irreversible. In the absence of NADH the enzyme activity is unaffected. The data obtained suggest that NADH-oxidase is inactivated in the course of the catalytic reaction. Under the stipulation that the enzyme obtained from plasma membranes of aged (60 hrs of inoculation) cells has identical values of Km and ki but lower values as compared to young cells (24 hrs of inoculation) of Vmax and v0, it is concluded that the decrease of the NADH-oxidase activity upon ageing of cultures is due to the decrease in the amount of active molecules of AND-oxidase in mycoplasm cell plasma membranes.     

PIP5K-dependent production of PIP2 sustains microtubule organization to establish polarized transport in the Drosophila oocyte

The attachment of the cytoskeleton to the plasma membrane is crucial in controlling the polarized transport of cell-fate-determining molecules. Attachment involves adaptor molecules, which have the capacity to bind to both the plasma membrane and elements of the cytoskeleton, such as microtubules and actin filaments. Using the Drosophila oocyte as a model system, we show that the type I phosphatidylinositol 4-phosphate 5-kinase (PIP5K), Skittles, is necessary to sustain the organization of microtubules and actin cytoskeleton required for the asymmetric transport of oskar, bicoid and gurken mRNAs and thereby controls the establishment of cell polarity. We show that Skittles function is crucial to synthesize and maintain phosphatidylinositol 4,5 bisphosphate (PIP2) at the plasma membrane in the oocyte. Reduction of Skittles activity impairs activation at the plasma membrane of Moesin, a member of the ERM family known to link the plasma membrane to the actin-based cytoskeleton. Furthermore, we provide evidence that Skittles, by controlling the localization of Bazooka, Par-1 and Lgl, but not Lkb1, to the cell membrane, regulates PAR polarity proteins and the maintenance of specific cortical domains along the anteroposterior axis.     

Direct evidence for cholesterol crystalline domains in biological membranes: role in human pathobiology

This review will discuss the use of small-angle X-ray diffraction approaches to study the organization of lipids in plasma membranes derived from two distinct mammalian cell types: arterial smooth muscle cells and ocular lens fiber cells. These studies indicate that cholesterol at an elevated concentration can self-associate and form immiscible domains in the plasma membrane, a phenomenon that contributes to both physiologic and pathologic cellular processes, depending on tissue source. In plasma membrane samples isolated from atherosclerotic smooth muscle cells, the formation of sterol-rich domains is associated with loss of normal cell function, including ion transport activity and control of cell replication. Analysis of meridional diffraction patterns from intact and reconstituted plasma membrane samples indicates the presence of an immiscible cholesterol domain with a unit cell periodicity of 34 A, consistent with a cholesterol monohydrate tail-to-tail bilayer, under disease conditions. These cholesterol domains were observed in smooth muscle cells enriched with cholesterol in vitro as well as from cells obtained ex vivo from an animal model of atherosclerosis. By contrast, well-defined cholesterol domains appear to be essential to the normal physiology of fiber cell plasma membranes of the human ocular lens. The organization of cholesterol into separate domains underlies the role of lens fiber cell plasma membranes in maintaining lens transparency. These domains may also interfere with cataractogenic aggregation of soluble lens proteins at the membrane surface. Taken together, these analyses provide examples of both physiologic and pathologic roles that sterol-rich domains may have in mammalian plasma membranes. These findings support a model of the membrane in which cholesterol aggregates into structurally distinct regions that regulate the function of the cell membrane.     

Role of GM3-enriched microdomains in signal transduction regulation in T lymphocytes

Gangliosides, sialic acid containing glycosphigolipids, are ubiquitous constituents of cell plasma membranes. Each cell type shows a peculiar ganglioside expression pattern. In human T lymphocytes monosialoganglioside GM3 represents the main ganglioside constituent of cell plasma membrane where it is concentrated in glycosphingolipid-enriched microdomains (GEM). The presence of tyrosine kinase receptors, mono- (Ras, Rap) and heterotrimeric G proteins, Src-like tyrosine kinases (lck, lyn, fyn), PKC isozymes, glycosylphosphatidylinositol (GPI)-anchored proteins and, after T cell activation, the Syk-family kinase Zap-70, prompts these portions of the plasma membrane to be considered as “glycosignaling domains.” In particular, during T cell activation and/or other dynamic functions of the cell, such as apoptosis, key signaling molecules are recruited to these microdomains, where they strictly interact with GM3. The association of transducer proteins with GM3 in microdomains suggests that this ganglioside is the main marker of GEM in human lymphocytes and is a component of a cell plasma membrane multimolecular signaling complex involved in cell-cell interaction, signal transduction, and cell activation. Published in 2004. This revised version was published online in August 2006 with corrections to the Cover Date.     

Note on oscillations of turbidity in a precipitation reaction system of thyroxine

A model for a precipitation reaction system is presented in which all steps are reversible monomolecular or bimolecular reactions. Under certain conditions, quasi-stable oscillations in turbidity can occur, as has been observed in the precipitation of thyroxine.     

Molecular oxygen (a substrate of the cyclooxygenase reaction) in the kinetic mechanism of the bifunctional enzyme prostaglandin-H-synthase

Prostaglandin-H-synthase is a bifunctional enzyme catalyzing conversion of arachidonic acid into prostaglandin H2 as a result of cyclooxygenase and peroxidase reactions. The dependence of the rate of the cyclooxygenase reaction on oxygen concentration in the absence and in the presence of electron donor was determined. A two-dimensional kinetic scheme accounting for independent proceeding and mutual influence of the cyclooxygenase and peroxidase reactions and also for hierarchy of the rates of these reactions was used as a model. In the context of this model, it was shown that there are irreversible stages in the mechanism of the cyclooxygenase reaction between points of substrate donation (between donation of arachidonic acid and the first oxygen molecule and also between donation of two oxygen molecules).     

Dynamics of raft molecules in the cell and artificial membranes: approaches by pulse EPR spin labeling and single molecule optical microscopy

Lipid rafts in the plasma membrane, domains rich in cholesterol and sphingolipids, have been implicated in a number of important membrane functions. Detergent insolubility has been used to define membrane "rafts" biochemically. However, such an approach does not directly contribute to the understanding of the size and the lifetime of rafts, dynamics of the raft-constituent molecules, and the function of rafts in the membrane in situ. To address these issues, we have developed pulse EPR spin labeling and single molecule tracking optical techniques for studies of rafts in both artificial and cell membranes. In this review, we summarize our results and perspectives obtained by using these methods. We emphasize the importance of clearly distinguishing small/unstable rafts (lifetime shorter than a millisecond) in unstimulated cells and stabilized rafts induced by liganded and oligomerized (GPI-anchored) receptor molecules (core receptor rafts, lifetime over a few minutes). We propose that these stabilized rafts further induce temporal, greater rafts (signaling rafts, lifetime on the order of a second) for signaling by coalescing other small/unstable rafts, including those in the inner leaflet of the membrane, each containing perhaps one molecule of the downstream effector molecules. At variance with the general view, we emphasize the importance of cholesterol segregation from the liquid-crystalline unsaturated bulk-phase membrane for formation of the rafts, rather than the affinity of cholesterol and saturated alkyl chains. In the binary mixture of cholesterol and an unsaturated phospholipid, cholesterol is segregated out from the bulk unsaturated liquid-crystalline phase, forming cholesterol-enriched domains or clustered cholesterol domains, probably due to the lateral nonconformability between the rigid planar transfused ring structure of cholesterol and the rigid bend of the unsaturated alkyl chain at C9-C10. However, such cholesterol-rich domains are small, perhaps consisting of only several cholesterol molecules, and are short-lived, on the order of 1-100 ns. We speculate that these cholesterol-enriched domains may be stabilized by the presence of saturated alkyl chains of sphingomyelin or glycosphingolipids, and also by clustered raft proteins. In the influenza viral membrane, one of the simplest forms of a biological membrane, the lifetime of a protein and cholesterol-rich domain was evaluated to be on the order of 100 micro, again showing the short lifetime of rafts in an unstimulated state. Finally, we propose a thermal Lego model for rafts as the basic building blocks for signaling pathways in the plasma membrane.