A theoretical analysis for the effect of focal contact formation on cell-substrate attachment strength.

For many cell types, growth, differentiation, and motility are dependent on receptor-mediated adhesion to ligand-coated surfaces. Focal contacts are strong, specialized, adhesive connections between cell and substrate in which receptors aggregate and connect extracellular ligand to intracellular cytoskeletal molecules. In this paper, we present a mathematical model to examine how focal contact formation affects cellular adhesive strength. To calculate adhesive strength with and without focal contacts, we use a one-dimensional tape peeling analysis to determine the critical tension necessary to peel the membrane. Receptor-ligand bonds are modeled as adhesive springs. In the absence of focal contacts, we derive analytic expressions for the critical tension at low and high ligand densities and show how membrane morphology affects adhesion. Then, focal contacts are modeled as cytoplasmic nucleation centers which bind adhesion receptors. The extent of adhesive strengthening upon focal contact formation depends on the elastic rigidity of the cytoskeletal connections, which determines the structural integrity of the focal contact itself. We consider two limits to this elasticity, very weak and rigid. Rigid cytoskeletal connections give much greater attachment strengths. The dependence of attachment strength on measurable model parameters is quite different in these two limits, which suggests focal contact structure might be deduced from properly performed adhesion experiments. Finally, we compare our model to the adhesive strengthening response reported for glioma cell adhesion to fibronectin (Lotz et al., 1989. J. Cell Biol. 109:1795-1805). Our model successfully predicts the observed detachment forces at 4 degrees C and yields values for the number of fibronectin receptors per glioma cell and the density of cytoskeletal connection molecules (talin) involved in receptor clusters which are consistent with measurements for other cell types. Comparison of the model with data at 37 degrees C suggests that while cytoskeletal cross-linking and clustering of fibronectin receptors significantly increases adhesion strength, specific glioma cell-substratum attachment sites possess little mechanical rigidity and detach through a peeling mechanism, consistent with the view that these sites of < or = 15 nm cell-substrate separation are precursors to fully formed, elastically rigid focal contacts.     

Dissection properties of the human aortic media: an experimental study

Aortic dissection occurs frequently and is clinically challenging; the underlying mechanics remain unclear. The present study investigates the dissection properties of the media of 15 human abdominal aortas (AAs) by means of direct tension tests (n=8) and peeling tests (n=12). The direct tension test demonstrates the strength of the media in the radial direction, while the peeling test allows a steady-state investigation of the dissection propagation. To explore the development of irreversible microscopic changes during medial dissection, histological images (n=8) from four AAs at different peeling stages are prepared and analyzed. Direct tension tests of coin-shaped medial specimens result in a radial failure stress of 140.1+/-15.9 kPa (mean+/-SD, n=8). Peeling tests of rectangular-shaped medial strips along the circumferential and axial directions provide peeling force/width ratios of 22.9+/-2.9 mN/mm (n=5) and 34.8+/-15.5 mN/mm (n=7); the related dissection energies per reference area are 5.1+/-0.6 mJ/cm(2) and 7.6+/-2.7 mJ/cm(2), respectively. Although student's t-tests indicate that force/width values of both experimental tests are not significantly different (alpha=0.05, p=0.125), the strikingly higher resisting force/width obtained for the axial peeling tests is perhaps indicative of anisotropic dissection properties of the human aortic media. Peeling in the axial direction of the aorta generates a remarkably "rougher" dissection surface with respect to the surface generated by peeling in the circumferential direction. Histological analysis of the stressed specimens reveals that tissue damage spreads over approximately six to seven elastic laminae, which is about 15-18% of the thickness of the abdominal aortic media, which forms a pronounced cohesive zone at the dissection front.     

Assessment of potential stimuli for mechano-dependent gating of MscL: effects of pressure, tension, and lipid headgroups

MscL is a mechanosensitive channel of large conductance that serves as an "emergency relief valve", protecting bacteria from acute hypoosmotic stress. Although it is well-accepted that the MscL protein and an adequate membrane matrix are necessary and sufficient for the function of this channel, the exact role of the membrane has yet to be elucidated. Here, we address the role of the membrane matrix through in vitro reconstitution of the MscL protein in defined lipid bilayers. We have applied Laplace's law to visualized membrane patches where we can measure patch curvature as described in previous studies. Here, by comparing patches with different curvatures, we demonstrate that the MscL channel senses tension within the membrane and that the pressure across it plays no detectable role as a stimulus. In addition, gating only occurs when the smallest radius of curvature is nearly achieved, suggesting that the lateral tension rather than membrane curvature is the important biophysical parameter. Finally, we have examined the contribution of specific headgroups by measuring their effect on the membrane tension required to gate the channel. We have found that the addition of neither anionic nor endogenous lipids to a non-native membrane effected a leftward shift in the activation curve. In fact, the major endogenous lipid of the Escherichia coli membrane, phosphatidylethanolamine, led to a channel activity at a higher tension threshold, suggesting that this lipid effects altered activity through changes in the biophysical properties of the membrane, rather than through an MscL-specific interaction.     

Genetic variation within and among patches of the clonal species, Vaccinium stamineum L

Once thought to be dominated by a few genets, clonal plant populations can contain high levels of genetic diversity. Sexual reproduction and vegetative growth strategy affect the amount and distribution of genetic diversity within clonal plant populations. We determined the scale of genetic diversity in a population of Vaccinium stamineum, a clonal shrub that forms discrete patches. Using the random amplified polymorphic DNA (RAPD) technique, we surveyed the genetic diversity of V. stamineum within and among patches from a 1-ha site. We found 67 unique RAPD profiles among the 99 sampled individuals from 22 patches. In two patches, all the sampled individuals had the same RAPD profile. In seven patches, every individual sampled had a different RAPD profile. The remaining patches showed mixed RAPD profiles which suggested both clonal and sexual reproduction. Each unique RAPD profile was restricted to one patch (with one exception), which suggests that clonal growth occurs at the patch scale. High levels of genetic variation within some patches may be explained by somatic mutation; however, seedling recruitment is a more likely explanation.     

The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Biological adhesion is frequently mediated by specific membrane proteins (adhesion molecules). Starting with the notion of adhesion molecules, we present a simple model of the physics of membrane-to-surface attachment and detachment. This model consists of coupling the equations for deformation of an elastic membrane with equations for the chemical kinetics of the adhesion molecules. We propose a set of constitutive laws relating bond stress to bond strain and also relating the chemical rate constants of the adhesion molecules to bond strain. We derive an exact formula for the critical tension. We also describe a fast and accurate finite difference algorithm for generating numerical solutions of our model. Using this algorithm, we are able to compute the transient behaviour during the initial phases of adhesion and detachment as well as the steady-state geometry of adhesion and the velocity of the contact. An unexpected consequence of our model is the predicted occurrence of states in which adhesion cannot be reversed by application of tension. Such states occur only if the adhesion molecules have certain constitutive properties (catch-bonds). We discuss the rational for such catch-bonds and their possible biological significance. Finally, by analysis of numerical solutions, we derive an accurate and general expression for the steady-state velocity of attachment and detachment. As applications of the theory, we discuss data on the rolling velocity of granulocytes in post-capillary venules and data on lectin-mediated adhesion of red cells.     

The breakdown of cell membranes by electrical and mechanical stress.

We attempted to determine whether mechanical tension and electrical stress couple to cause membrane breakdown in cells. Using cell-attached patches from HEK293 cells, we estimated the mechanically produced tension from the applied pressure and geometry of the patch. Voltage pulses of increasing amplitude were applied until we observed a sudden increase in conductance and capacitance. For pulses of 50 micros duration, breakdown required >0.5 V and was dependent on the tension. For pulses of 50-100 ms duration, breakdown required 0.2-0.4 V and was independent of tension. Apparently two physically different processes can lead to membrane breakdown. We could explain the response to the short, high-voltage pulses if breakdown occurred in the lipid bilayer. The critical electromechanical energy per unit area for breakdown by short pulses was approximately 4 dyne/cm, in agreement with earlier results on bilayers. Our data suggest that, at least in a patch, the bilayer may hold a significant fraction (approximately 40%) of the mean tension. To be compatible with the large, nonlytic area changes of patches, the bilayer appears to be pulled toward the pipette tip, perhaps by hydrophobic forces wetting membrane proteins bound to the glass. Although breakdown voltages for long pulses were in agreement with earlier work on algae, the mechanism(s) for this breakdown remain unclear.     

Clustering, mobility, and triggering activity of small oligomers of immunoglobulin E on rat basophilic leukemia cells

We have recently shown that small oligomers of IgE bound to univalent receptors for IgE on the surface of rat basophilic leukemia cells induce extensive aggregation of the receptors at 4 degrees C into patches resolvable by fluorescence microscopy and that this does not occur with monomeric IgE (Menon, A. K., D. Holowka, and B. Baird, 1984, J. Cell Biol. 98:577-583). Here we use fluorescence photobleaching recovery measurements to show that receptor oligomerization by this means is accompanied by a dramatic reduction of receptor lateral mobility, and that this immobilization occurs even when the clustering is not microscopically detectable. Furthermore, the degree of immobility induced by a particular oligomer fraction from a gel filtration column correlates positively with its ability to trigger cellular degranulation, whereas receptors labeled with monomeric IgE have no triggering activity and exhibit typical membrane protein mobility. The slow, large-scale oligomer-induced clustering appears to be a long term consequence of earlier selective interactions that result in receptor immobilization, and this highly clustered state provides a competent, noninhibitory triggering signal resulting in cellular degranulation upon warming to 37 degrees C. We conclude that even limited clustering of IgE receptors on rat basophilic leukemia cells induces interactions with other cellular components that constrain receptor mobility and eventually cause massive coalescence of the clusters. These primary selective interactions occurring at the level of receptor oligomers or small clusters of oligomers that result in immobilization may play a role in triggering cellular degranulation.     

Area-dependent migration by ringlet butterflies generates a mixture of patchy population and metapopulation attributes

Interpretation of spatially structured population systems is critically dependent on levels of migration between habitat patches. If there is considerable movement, with each individual visiting several patches, there is one ”patchy population”; if there is intermediate movement, with most individuals staying within their natal patch, there is a metapopulation; and if (virtually) no movement occurs, then the populations are separate (Harrison 1991, 1994). These population types actually represent points along a continuum of much to no mobility in relation to patch structure. Therefore, interpretation of the effects of spatial structure on the dynamics of a population system must be accompanied by information on mobility. We use empirical data on movements by ringlet butterflies, Aphantopus hyperantus, to investigate two key issues that need to be resolved in spatially-structured population systems. First, do local habitat patches contain largely independent local populations (the unit of a metapopulation), or merely aggregations of adult butterflies (as in patchy populations)? Second, what are the effects of patch area on migration in and out of the patches, since patch area varies considerably within most real population systems, and because human landscape modification usually results in changes in habitat patch sizes? Mark-release-recapture (MRR) data from two spatially structured study systems showed that 63% and 79% of recaptures remained in the same patch, and thus it seems reasonable to call both systems metapopulations, with some capacity for separate local dynamics to take place in different local patches. Per capita immigration and emigration rates declined with increasing patch area, while the resident fraction increased. Actual numbers of emigrants either stayed the same or increased with area. The effect of patch area on movement of individuals in the system are exactly what we would have expected if A. hyperantus were responding to habitat geometry. Large patches acted as local populations (metapopulation units) and small patches simply as locations with aggregations (units of patchy populations), all within 0.5 km². Perhaps not unusually, our study system appears to contain a mixture of metapopulation and patchy-population attributes.     

Transmembrane interactions and the mechanisms of transport of proteins across membranes

We have made observations, by double fluorescence staining of the same cell, of the distributions of surface receptors, and of intracellular actin and myosin, on cultured normal fibroblasts and other flat cells, and on lymphocytes and other rounded cells. The binding of multivalent ligands (a lectin or specific antibodies) to a cell surface receptor on flat cells clusters the cell receptors into small patches, which line up directly over the actin- and myosin-containing stress fibers inside the cell. Similar ligands binding to rounded cells can cause their surface receptors to be collected into caps on the surface, and these caps are invariably found to be associated with concentrations of actin and myosin under the capped membrane. Although these ligand-induced surface phenomena appear to be different on flat and rounded cells, we propose that in both cases clusters of receptors become linked across the membrane to actin- and myosin-containing structures. In flat cells these structures are very long stress fibers; therefore, when clusters of receptors become linked to these fibers, the clusters are immobilized. In round cells, membrane-associated actin- and myosin-containing structures are apparently much less extensive than in flat cells; therefore, clusters of receptors linked to these structures are still mobile in the plane of the membrane. We suggest that in this case the clusters are then actively collected into a cap by an analogue of the muscle sliding filament mechanism. To explain the transmembrane linkage, we propose that actin is associated with the plasma membrane as a peripheral protein which is directly or indirectly bound to an integral protein (or proteins) X of the membrane. Individual molecules of any receptor are not bound to X, but after they are specifically clustered into patches, a patch of receptors then becomes bound to S and hence to actin/myosin. Patching and capping of specific receptors on rounded cells is often accompanied by a specific endocytosis of the ligand-receptor complexes. This represents one common transport mechanism of a protein (the ligand) across the plasma membrane. The possibility is discussed that this type of endocytosis is mediated by a transmembrane linkage of the clustered receptor to actin/myosin. Another mechanism of endocytosis involves the “coated pit” structures that are observed by electron microscopy of plasma membranes. The possible relationships between an actin/myosin and a coated pit mechanism of endocytosis are explored.     

Distribution of substance P receptors on murine spleen and Peyer's patch T and B cells

Previous studies have demonstrated that the sensory neuropeptide substance P (SP) can modulate immune responses in vitro. Work from this laboratory has shown that SP enhances immunoglobulin synthesis by murine splenic and Peyer's patch lymphocytes stimulated with concanavalin A. One mechanism underlying these effects is the binding of SP to specific receptors on lymphocytes. We examined the distribution of SP receptors on murine T and B lymphocytes and their subsets by one and two color fluorescence-activated cell sorter analysis. The specificity and nature of binding was examined using radiolabeled SP, and competitive inhibition experiments were performed with cold SP. In cytofluorimetry experiments, both T and B lymphocytes from Peyer's patches and spleen were bound to SP, with those from Peyer's patches having a higher proportion than lymphocytes from the spleen. The majority of T cells from both organs bound SP with binding being evenly distributed between Lyt-1+ and Lyt-2+ cells. Similarly, the majority of B lymphocytes from spleen and Peyer's patches showed SP binding. There were no significant isotype-specific differences within any organ. Studies using 125I-labeled SP showed specific binding to all lymphocyte subpopulations examined. SP receptors were fewer in number on cells isolated from spleen than on cells from Peyer's patches although the dissociation constants were similar for all populations examined. These studies demonstrated that SP receptors are present both on murine T and B lymphocytes from Peyer's patches and spleen. There is no evidence for differential SP receptor expression on distinct lymphocyte subsets in spleen or Peyer's patches.     

Focal contact assembly through cytoskeletal polymerization: steady state analysis

For many cell types, initial receptor-mediated attachment to a ligand-coated surface is followed by the formation of focal contacts - strong, specialized, discrete adhesive connections between cell and substrate in which receptors are clustered and simultaneously linked to extracellular ligand and cytoskeletal proteins. Since adhesion affects many aspects of cellular physiology including growth, differentiation, and motility, understanding the biochemical factors which regulate focal contact assembly should enhance our understanding of these phenomena. In this paper, we present a mathematical model to examine how receptor-ligand, receptor-cytoskeleton, and cytoskeleton-cytoskeleton interactions affect the formation of receptor clusters which serve as precursors to mature focal contacts. Receptor clustering is presumed to occur through self-recognition of cytoskeletal elements which induce the polymerization of ligand-receptor-cytoskeleton complexes. Polymerization only occurs when the ligand density is above a critical value and a decrease in the receptor-ligand affinity shifts the critical ligand density to higher values. While cytoskeletal protein expression and receptor-cytoskeleton affinity influence the concentration of monomeric complexes, the formation of polymeric ligand-receptor-cytoskeleton aggregates is most sensitive to changes in the self-association affinity between cytoskeletal proteins. We find that a 100-fold enhancement in the affinity between cytoskeletal elements can produce a substantial increase in the total fraction of adhesion receptors associated with focal contact precursors (from 5% to over 90%). Our results suggest that under physiological conditions, cellular control of focal contact assembly most likely occurs through modulation of specific cytoskeletal proteins to solidify cytoskeleton-cytoskeleton connections within precursor focal contact structures.     

The effect of patch isolation on reproductive synchrony in the root vole

Both social and environmental cues can synchronise breeding, but are likely to operate at different spatial and temporal scales. Here we test if breeding is synchronised at the patch or the population level in experimental patchy populations of root voles. We found no overall synchronisation neither at the patch nor at the population level. However, at the patch level, breeding was synchronised within patches if the patches were isolated and thus had little exchange of animals with other patches. In accordance with what has been predicted for matrilineally structured populations, we conclude that breeding synchrony is facilitated when social cues are exchanged within stable female groups.     

Cell-cell, cell-substrate adhesion: theoretical and experimental considerations

Cell-cell adhesion plays a fundamental role in tissue and organ development, cell mediated immunity and blood flow. In the present study a micro-mechanical model of specific adhesion is presented. Analytical expressions are derived for the adhesive energy density (gamma) at zero speed of peeling for the cases of immobile (trapped) as well as laterally mobile bonds. It is shown that gamma increases in both cases with the increasing density of bonds and with the binding of affinity of unstressed bonds. In the case of laterally mobile bonds gamma also increases with the extent of peeling. The analytical results are shown to be valid whether or not one takes into account of the bending stiffness of adhering membranes. It is also shown that gamma does not depend on the functional form of bond elasticity. The effect of the speed of peeling on the number density distribution of attached bonds is considered next. Numerical solutions for the energy required to separate conjugated cell pairs are presented. The theoretical predictions are then used to analyze experimental data on red cell aggregation and adhesion between a cytotoxic-T cell and its target cell. The results show that the binding affinity of unstressed bonds and their number density before conjugation can be obtained from data on slow peeling of cell-pairs. The information on the diffusivity of bonds, their stiffness and their rates of attachment and detachment are more difficult to obtain, requiring a set of experiments with increasing rates of separation (conjugation) of cell-pairs.     

A novel patch assembly domain in Num1 mediates dynein anchoring at the cortex during spindle positioning

During mitosis in budding yeast, cortically anchored dynein generates pulling forces on astral microtubules to position the mitotic spindle across the mother-bud neck. The attachment molecule Num1 is required for dynein anchoring at the cell membrane, but how Num1 assembles into stationary cortical patches and interacts with dynein is unknown. We show that an N-terminal Bin/Amphiphysin/Rvs (BAR)-like domain in Num1 mediates the assembly of morphologically distinct patches and its interaction with dynein for spindle translocation into the bud. We name this domain patch assembly domain (PA; residues 1-303), as it was both necessary and sufficient for the formation of functional dynein-anchoring patches when it was attached to a pleckstrin homology domain or a CAAX motif. Distinct point mutations targeting the predicted BAR-like PA domain differentially disrupted patch assembly, dynein anchoring, and mitochondrial attachment functions of Num1. We also show that the PA domain is an elongated dimer and discuss the mechanism by which it drives patch assembly.     

The kinetics of aggregation phenomena. I. Minimal models for patch formation of lymphocyte membranes.

Numerous biological processes involve the assembly of one or more monomers into aggregates or networks of interconnected units. In this paper we present the initial aspects of a mathematical theory for network formation on lymphocyte membranes. We assume the fluid mosaic membrane model is valid, that a lymphocyte possesses a homogeneous set of mobile but membrane bound receptors and that these receptors can form bimolecular complexes with antigen. We show that these complexes tend to aggregate and derive expressions for their size distribution as a function of time, antigen valence and concentration, and antigenreceptor affinity.At early times, the mass of the system (receptors plus antigen) is in very small aggregates. However under appropriate conditions, a critical time is reached at which they coalesce in such a way that the mass shifts, becoming concentrated predominantly in large aggregates. We assume that this coalescence (“patch” formation) is a necessary condition for lymphocyte triggering and briefly pursue the consequences.It is shown that the time required for patch formation is a sensitive function of affinity (K), antigen valence and antigen concentration (C), and that if KC is either too high or too low patch formation will not be possible. Moreover within the range of binding constants which can lead to patching, there will be an optimum value which leads to the fastest rate of triggering, and this optimum shifts to higher affinity as the concentration of free antigen surrounding the cell decreases. For optimum KC values we estimate times typically of the order of (10–100) seconds for patch formation. The theory also suggests that if antigen valence is too low, triggering will not be possible within times of interest, without introducing other factors. It thus leads naturally to a requirement for auxiliary cells which would tend to present low valence antigens in such a way that the B lymphocytes see an effective, increased valence. The theory, although primitive, thus meets some minimal requirements in that it distinguishes binding reactions from triggering reactions, makes predictions consistent with observations on affinity maturation and the nonresponsiveness to high doses and low doses of antigen, and suggests the need for helper cells (or their products) in order for low valence antigens to be effective in lymphocyte triggering.     

Receptor aggregation by intermembrane interactions: a Monte Carlo study

The lateral organization of receptors on cell surfaces is critically important to their function; many receptors transmit transmembrane signals when redistributed into clusters, while the response of others is potentiated by their aggregation. Cell-cell contact can play a crucial role in receptor aggregation, even when the bonds between receptors on one cell and ligands on the other are monovalent. Monte Carlo simulations on a two-membrane model were carried out to determine whether weak enthalpic interactions among receptors in one membrane, and among ligands in another, can work synergistically to give large-scale clustering when the two membranes are brought into contact. The simulations give support to such a clustering mechanism. In addition, because clustering is a cooperative process akin to a phase separation, individual receptors and ligands may undergo repeated binding and unbinding while in a clustered "phase," and a single ligand could interact with multiple different receptor partners. The results suggest a resolution of the dichotomy between serial triggering and aggregation models of T cell activation.     

Serotonin 5-HT2C receptor homodimer biogenesis in the endoplasmic reticulum: real-time visualization with confocal fluorescence resonance energy transfer

Dimerization is a common property of G-protein-coupled receptors (GPCR). While the formation of GPCR dimers/oligomers has been reported to play important roles in regulating receptor expression, ligand binding, and second messenger activation, less is known about how and where GPCR dimerization occurs. The present study was performed to identify the precise cellular compartment in which class A GPCR dimer/oligomer biogenesis occurs. We addressed this issue using confocal microscopy and fluorescence resonance energy transfer (FRET) to monitor GPCR proximity within discrete intracellular compartments of intact living cells. Time-lapse confocal imaging was used to follow CFP- and YFP-tagged serotonin 5-HT2C receptors during biosynthesis in the endoplasmic reticulum (ER), trafficking through the Golgi apparatus and subsequent expression on the plasma membrane. Real-time monitoring of FRET between CFP- and YFP-tagged 5-HT2C receptors was performed by acceptor photobleaching within discrete regions of the ER, Golgi, and plasma membrane. The FRET signal was dependent on the ratio of CFP- to YFP-tagged 5-HT2C receptors expressed in each region and was independent of receptor expression level, as predicted for proteins in a non-random, clustered distribution. FRET efficiencies measured in the ER, Golgi, and plasma membrane were similar. These experiments provide direct evidence for homodimerization/oligomerization of class A GPCR in the ER and Golgi of intact living cells, and suggest that dimer/oligomer formation is a naturally occurring step in 5-HT2C receptor maturation and processing.     

The ultrastructure of patch-clamped membranes: a study using high voltage electron microscopy

We have developed techniques for studying patch-clamped membranes inside glass pipettes using high voltage electron microscopy (HVEM). To preserve the patch structure with the least possible distortion, we rapidly froze and freeze dried the pipette tip. The pipette is transparent for more than 50 microns from the tip. HVEM images of patches confirm light microscopy observations that the patch is not a bare bilayer, but a membrane-covered bleb of cytoplasm that may include organelles and cytoskeleton. The membrane that spans the pipette is commonly tens of micrometers from the tip of the pipette and occasionally as far as 100 microns. The structure of patches taken from a single cell type is variable but there are consistent differences between patches made from different cell types. With suction applied to the pipette before seal formation, we have seen in the light microscope vesicles swept from the plasmalemma up the pipette. These vesicles are visible in electron micrographs, particularly those made from chick cardiac muscle. Colloidal gold labeling of the patch permitted identification of lectin-binding sites and acetylcholine receptors. In young cultures of Xenopus myocytes, the receptors were diffuse. In 1-wk-old cultures, the receptors formed densely packed arrays. The patch pipette can serve, not only as a recording device, but as a tool for sampling discrete regions of the cell surface. Because the pipette has a constant path length for axial rotation, it is a unique specimen holder for microtomography. We have made preliminary tomographic reconstructions of a patch from Xenopus oocyte.     

Agent-based model approach to optimal foraging in heterogeneous landscapes: effects of patch clumpiness

Optimal foraging theory concerns animal behavior in landscapes where food is concentrated in patches. The efficiency of foraging is an effect of both the animal behavior and the geometry of the landscape; furthermore, the landscape is itself affected by the foraging of animals. We investigated the effect of landscape heterogeneity on the efficiency of an optimal forager. The particular aspect of heterogeneity we considered was "clumpiness"– the degree to which food resource patches are clustered together. The starting point for our study was the framework of the Mean Value Theorem (MVT) by Charnov. Since MVT is not spatially explicit, and thus not apt to investigate effects of clumpiness, we built an agent-based (or individual-based) model for animal movement in discrete landscapes extending the MVT. We also constructed a model for generating landscapes where the clumpiness of patches can be easily controlled, or "tuned", by an input parameter. We evaluated the agent based model by comparing the results with what the MTV would give, i.e. if the spatial effects were removed. The MVT matched the simulations best on landscapes with random patch configuration and high food recovery rates. As for our main question about the effects of clumpiness, we found that, when landscapes were highly productive (rapid food replenishment), foraging efficiency was greatest in clumped landscapes. In less productive landscapes, however, foraging efficiency was lowest in landscapes with a clumped patch distribution.     

Morphology of cell-substratum adhesion

Many cell types modulate growth, differentiation, and motility through changes in cell substrate adhesion, including regulation of focal contact formation. Clustering of cell surface adhesion receptors is an essential early step in the development of focal contacts, and thus may influence cell physiology. In this paper, we present a theoretical framework to examine how cell surface chemistry affects receptor clustering. Our one-dimensional tape-peeling model couples the equations of mechanical equilibrium for a cell membrane with kinetic receptor-ligand binding relations. We considered two distinct model scenarios: Adhesion mediated by multiple receptor-ligand interactions of different length and specific binding of a single receptor type occurs in the presence of van der Waals attraction and nonspecific repulsion. In each case, nonuniform (wave-like) membrane morphologies are observed in certain parameter ranges that support the clustering of adhesion receptors. The formation of these morphologies is described in terms of a balance of membrane stresses; when cell-surface potential as a function of separation distance is symmetric between two potential energy minima, nonuniform morphologies are obtained. Increases in the chemical binding energy between receptor and ligand (e.g., increases in ligand density) or decreases in the membrane rigidity result in smaller wavelengths for nonuniform interfaces. Additionally, we show wave-like geometries appear only when the mechanical compliance of receptor-ligand bonds is within an intermediate range, and examine how the mobility of “repellers”—glycocalyx molecules that exert a nonspecific repulsive force—influences membrane morphology. We find fully mobile repellers always redistribute to prevent nonuniform morphologies.