Analysis of local order in the spatial distribution of cell surface molecular assemblies

Mathematical Modeling of Virus-Mediated Syncytia Formation: Past Successes and Future Directions

Many viruses have the ability to cause cells to fuse into large multi-nucleated cells, known as syncytia. While the existence of syncytia has long been known and its importance in helping spread viral infection within a host has been understood, few mathematical models have incorporated syncytia formation or examined its role in viral dynamics. This review examines mathematical models that have incorporated virus-mediated cell fusion and the insights they have provided on how syncytia can change the time course of an infection. While the modeling efforts are limited, they show promise in helping us understand the consequences of syncytia formation if future modeling efforts can be coupled with appropriate experimental efforts to help validate the models.

Fluctuations and membrane heterogeneity

Biological membranes contain many specialized domains, ranging from tens of nanometers to several microns in size and characterized by different concentrations and compositions of protein. Because these domains influence membrane function, considerable attention has focused on understanding their origin. Here it is shown that number fluctuations and nonspecific interprotein interactions can lead to considerable heterogeneity in the distribution of membrane proteins, and to an associated submicron-scale domain structure. Number fluctuations were analyzed by modeling the membrane as a two-dimensional fluid containing interacting protein solutes. The characteristic size and lifetime of a domain in which one would expect to observe a fluctuation of specified magnitude was calculated; snapshots showing fluctuation-induced heterogeneity were generated by Monte Carlo simulation. Domain size was found to depend on the nature of the interprotein force (e.g., attractive or repulsive) and on the average protein concentration. Domain size was largest at low protein concentrations and in the presence of attractive interprotein forces, and was smallest at high protein concentrations and in the presence of repulsive interprotein forces. Domain lifetime was found to depend on domain size and on the diffusion coefficient of the proteins. In a 'typical' membrane containing 5-nm proteins with diffusion coefficient 10(-10) cm(2)/s at a density of 1000 proteins/microm(2), a 30% fluctuation will yield domains characterized by a 2-fold difference in local concentration; these domains persist over a distance of about 100 nm and have a lifetime of about 0.25 s. These results can be used to analyze the domain structure commonly observed in electron micrographs, and have implications for both number fluctuation and Monte Carlo studies of the distribution and dynamics of membrane proteins.

Effects of retinyl acetate on surface morphology and intramembrane particle distribution in the plasma membrane of 10T1/2 cells

Scanning electron microscopy and freeze fracture electron microscopy were used to characterize membrane ultrastructural differences between parental, C3H/10T1/2, and carcinogen-initiated, INIT C3H/10T1/2, cells and treatments with retinyl acetate. The intramembranous particle distribution on the E-face was detected and quantitated by the methods of automated image analysis to obtain statistically meaningful numerical characteristics of intramembranous particle size and density. Subtle differences were found when no differences were apparent by light microscopy or by scanning electron microscopy. Initial retinyl acetate treatment caused a significant increase of the intramembranous particle size in parental cells. Intramembranous particle density increased for retinyl acetate treatment in parental and INIT cells and in INIT cells previously maintained but withheld from retinyl acetate. Intramembranous particle distribution analysis includes the interparticle distance of nearest neighbors and the randomness of the distribution by the differential density distribution function, which compares the observed sample to Poisson modified for particle size. These measures show that the three cell groups that have been treated with retinyl acetate have a more even distribution of intramembranous particles than was found for untreated parental cells. The relationship between the freeze fracture morphology and the biological responses to retinyl acetate treatment is discussed.

Quantitative analysis of intramembranous particles in rapidly frozen 10T1/2 cell monolayers

A simple method for ultrarapid freezing of cell cultures in monolayers was developed. Unfixed and unglycerinated cells were grown on glass substrates. No special treatments of the glass or cells were necessary to facilitate freeze-fracture along the upper plasma membranes. A reliable nonbiased method was developed to detect intramembranous particles (IMP) from the background by totally automatic means using the Cambridge Instruments Quantimet 920 Image Analysis system. Size and density data of IMP from a large number of electron micrographs can be rapidly and objectively quantitated. The automatic determination of locational coordinates for each IMP enables subtle determination of spatial distributional differences by the nearest neighbour function and the differential density distribution function, which are measurements of randomness. Quantitative analysis of the IMP distribution on the fracture face of C3H/10T1/2 mouse embryo fibroblasts upon various drug treatments was demonstrated.

Quantification of cell surface roughness; a method for studying cell mechanical and adhesive properties

The presence on the surface of nucleated cells of a variety of asperities of different size and shape plays a prominent role in cell-cell and cell-substrate interaction. Also, the organization of these asperities is directly related to cellular cytoskeletal elements. In the present report, we describe a simple and objective method of studying electron micrographs to quantify the roughness of cell contours. Constant-length segments of cell boundaries are compared to reference circular segments with common extremities and enclosing the same area. This procedure was performed with a digitizer connected to a microcomputer, and it was used to analyse model contours or electron micrographs of (i) target tumour cells bound by cytotoxic T lymphocytes and (ii) thymocytes sticking to concanavalin A-coated surfaces. It is shown that this method allows precise quantification of cell deformation in adhesive zones, which may allow absolute evaluation of adhesive stimuli.

Analysis of the irregular planar distribution of proteins in membranes

Methods to characterize the irregular but non-random planar distribution of proteins in biological membranes were investigated. The distribution of the proteins constituting the intramembranous particles (IMP) in human erythrocyte membranes was used as an example. The distribution of IMPs was deliberately altered by experimental means. For real space analyses, the IMP positions in freeze fracture micrograph S were determined by an automatic procedure described. Radial distribution and autocorrelation analysis revealed quantitative differences between experimental groups. These methods are more sensitive than the corresponding optical diffraction or Fourier-Bessel analyses of the same IMP distribution data, due to the inability of the diffraction methods to separate contrast and distribution effects. A method to identify IMPs on a non-uniform background is described.

Lateral distribution of intramembrane particles in Purkinje and granule cells of the rat cerebellar cortex

The lateral distribution of intramembrane protein particles (IMP) in the plasma membrane of Purkinje and granule cells was quantitatively assessed in freeze-fracture replicas of the rat cerebellar cortex. In the plasma membrane of each cell type this technique showed domains with statistically significant differences in the distribution of IMP. The values were highly reproducible between different animals fixed in comparable conditions. This analysis provides an additional parameter (besides the number and size of IMP) in the assessment of neuronal membrane heterogeneity.

A thermodynamic interpretation to formation of clusters at the cell surface

We develop further the original paper by Gershon, concerning the formation of receptor caps at the cell surface. The phenomenon is interpreted in terms of simple thermodynamic factors like boundary tension and supersaturated concentration of membrane components, within the Gibbs free energy change. The hypothesis that the total number of mol receptors is conserved is a sufficient condition to have a minimum of delta G as a function of the radius of the aggregates. We pay particular attention to effects induced by electrostatic interactions among charged receptor molecules. We discuss extensively the simultaneous formation of N aggregates and the role played by either the electrostatic repulsive forces or boundary tension in controlling the size and the number of stable aggregates. Depending on supersaturation of membrane receptors and in the absence of electric charge up to 50% of solute molecules may condense in a cap-like aggregate.

Statistical mechanics of lipid membranes. Protein correlation functions and lipid ordering

An expression is derived for the lipid-mediated intermolecular interaction between protein molecules embedded in a lipid bilayer. It is assumed that protein particles are accommodated by the bilayer, but they distort the lipids in some manner from their equilibrium protein-free configuration. We treat this situation by expanding the free energy density in the plane of the membrane as a Taylor series in some arbitrary parameter and its gradient. Minimization of the total membrane energy for a given particle configuration yields the interparticle interaction energy for that configuration. A test of the model is provided by measurement of the protein-protein pair distribution function from freeze-fracture micrographs of partially aggregated membranes. The measured functions can be simulated by adjustment of two parameters (a) a lipid correlation length that characterizes the distance over which a distortion of the bilayers is transmitted laterally through the bilayer, and (b) a term quantifying the energy of the protein-lipid interaction at the protein-lipid boundary. Correlation lengths obtained by fitting the calculated particle distribution functions to the data are found to be several nanometers. Protein-lipid interaction energies are of the order of a few kT.

Cell fusion and intramembrane particle distribution in polyethylene glycol-resistant cells

The distribution of intramembrane particles (IMP) as revealed by freeze-fracture electron microscopy has been analyzed following treatment of mouse L cells and fusion-deficient L cell derivatives with several concentrations of polyethylene glycol (PEG). In cell cultures treated with concentrations of PEG below the critical level for fusion, no aggregation of IMP was observed. When confluent cultures of the parental cells are treated with 50% PEG, greater than 90% of the cells fuse, and cold-induced IMP aggregation is extensive. In contrast, identical treatment of fusion-deficient cell lines shows neither extensive fusion nor IMP redistribution. At higher concentrations of PEG, however, the PEG-resistant cells fuse extensively and IMP aggregation is evident. Thus the decreased ability of the fusion-deficient cells to fuse after treatment with PEG is correlated with the failure of IMP aggregation to occur. A technique for quantifying particle distribution was developed that is practical for the accurate analysis of a large number of micrographs. The variance from the mean number of particles in randomly chosen areas of fixed size was calculated for each cell line at each concentration of PEG. Statistical analysis confirms visual observation of highly aggregated IMP, and allows detection of low levels of aggregation in parental cells that were less extensively fused by exposure to lower concentrations of PEG. When low levels of fusion were induced in fusion-deficient cells, however, no IMP aggregation could be detected.

Pair distribution functions of bacteriorhodopsin and rhodopsin in model bilayers

The pair distribution functions have been measured from freeze-fracture pictures of bacteriorhodopsin and rhodopsin recombinants with diacyl phosphatidylcholines (PC) of various hydrocarbon chain lengths. Pictures were used of samples that had been frozen from above the phase transition temperature of the lipid. Measured functions were compared with those calculated from two model interparticle potential energy functions, (a) a hard-disk repulsion only, and (b) a hard-disk repulsion plus electrostatic repulsion for a point charge buried in the membrane. The measured functions for bacteriorhodopsin di 12:0 PC, di 14:0 PC, and di 16:0 PC recombinants can be simulated using an interparticle hard-disk repulsion only. Bleached rhodopsin di 12:0 PC and di 18:1 trans-PC recombinants, and dark-adapted rhodopsin di 10:0 PC recombinants yield functions that are better simulated by assuming an additional repulsive interaction. The measured functions resemble those calculated using the hard-disk plus electrostatic repulsion model. The picture of dark-adapted rhodopsin in di 18:1 trans-PC frozen from 20 degrees C shows partial aggregation that is apparent in the measured pair distribution function. This attractive interaction persists even at 37 degrees C, where the measured function shows deviations from the hard-disk repulsive model, indicative of an attractive interparticle interaction. Implications of these results are discussed in terms of protein-lipid interactions.

Testing of aggregation measurement techniques for intramembranous particles

Under various physiological and nonphysiological conditions, the intramembranous particles, as seen by freeze-fracture electron microscopy, may be in various degrees of aggregation. To compare various schemes for the measurement of the degree of aggregation, a computer program has been used to generate simulated aggregations. A simple and adequate technique for quantifying the degree of aggregation, which is practical for the electron microscopist, is presented.

Computer assisted analysis of ferritin-insulin receptor sites on adipocytes and the effects of cytochalasin B on groups of insulin receptor sites

A computerized quantitative technique was used to analyze the distribution of ferritininsulin receptor sites on rat adipocytes and the effects of cytochalasin B on groups of receptor sites. Computer analysis of separation distances between receptor sites established that insulin receptor sites on adipocytes did not have a random distribution but have a distinct tendency to exist in groups with a maximum separation distance between particles of 400 A. A peak in the distribution of separation distances occurred at 100-200 A. Cytochalasin B, but not cytochalasin D, treatment of adipocytes resulted in a decrease in the number of large groups of receptor sites and a corresponding increase in single and paired receptor sites without affecting the separation distance between the remaining grouped receptors. This suggested that when cytochalasin B disrupted the bond holding receptor sites together, it caused complete disruption. These observations provided additional information on the ultrastructural characteristics of the insulin receptor. Further application of these techniques to the analysis of insulin receptors may provide the necessary structural correlates to the biochemically observed differences in insulin action in other tissues and diseased states.