Jure Derganc

Curvature-driven lateral segregation of membrane constituents in Golgi cisternae

Lateral segregation of mobile membrane constituents (e.g. lipids, proteins or membrane domains) into the regions of their preferred curvature relaxes stresses in the membrane. The equilibrium distribution of the constituents in the membrane is thus a balance between the gains in the membrane elastic energy and the segregation-induced loss of entropy. The membrane in the Golgi cisternae is particularly susceptible to the curvature-driven segregation because it possesses two very different curvatures-the highly curved membrane in the cisternal rims and the flat membrane in the cisternal sides. In this work, we calculate the extent of lateral segregation in the Golgi cisternae in the case where the segregation is driven by the Helfrich bending energy. It is assumed that the membrane bending constant and spontaneous curvature depend on the local membrane composition. A simple analytical expression for the extent of the lateral segregation is derived. The results show that the segregation depends on the ratio between the bending constant and the thermal energy, the difference of the preferred curvatures of the constituents and the sizes of the constituents. Applying the model to a typical Golgi cisterna, it was found that entropy can effectively limit the extent of the curvature-driven lateral segregation.

Stability Analysis of Micropipette Aspiration of Neutrophils

During micropipette aspiration, neutrophil leukocytes exhibit a liquid-drop behavior, i.e., if a neutrophil is aspirated by a pressure larger than a certain threshold pressure, it flows continuously into the pipette. The point of the largest aspiration pressure at which the neutrophil can still be held in a stable equilibrium is called the critical point of aspiration. Here, we present a theoretical analysis of the equilibrium behavior and stability of a neutrophil during micropipette aspiration with the aim to rigorously characterize the critical point. We take the energy minimization approach, in which the critical point is well defined as the point of the stability breakdown. We use the basic liquid-drop model of neutrophil rheology extended by considering also the neutrophil elastic area expansivity. Our analysis predicts that the behavior at large pipette radii or small elastic area expansivity is close to the one predicted by the basic liquid-drop model, where the critical point is attained slightly before the projection length reaches the pipette radius. The effect of elastic area expansivity is qualitatively different at smaller pipette radii, where our analysis predicts that the critical point is attained at the projection lengths that may significantly exceed the pipette radius.

Equilibrium Shapes of Erythrocytes in Rouleau Formation

A well known physiological property of erythrocytes is that they can aggregate and form a rouleau. We present a theoretical analysis of erythrocyte shapes in a long rouleau composed of cells with identical sizes. The study is based on the area difference elasticity model of lipid membranes, and takes into consideration the adhesion of curved axisymmetric membranes. The analysis predicts that the erythrocytes in the rouleau can have either a discoid or a cup-like shape. These shapes are analogous to the discoid and stomatocyte shapes of free erythrocytes. The transitions between the discoid and cup-like shapes in the rouleau are characterized. The occurrence of these transitions depends on three model parameters: the cell relative volume, the preferred difference between the areas of the membrane bilayer leaflets, and the strength of the adhesion between the membranes. The cup-like shapes are favored at small relative volumes and small preferred area differences, and the discoid shapes are favored at large values of these parameters. Increased adhesion strength enlarges the contact area between the cells, flattens the cells, and consequently promotes the discoid shapes.

Physical Factors that Affect the Number and Size of Golgi Cisternae

Despite continual membrane reorganization in the Golgi complex, the number of cisternae in a Golgi stack is a stable parameter. The cisternal number is conserved within any given cell line and also after Golgi reassembly, e.g. following brefeldin‐A‐induced disruption. However, the factors that determine the cisternal number in a single Golgi stack remain to be fully determined. We propose a simple mechanical model of the Golgi stack and present a theoretical analysis of different physical factors that may affect the number of cisternae in a Golgi stack. The model takes into account the Golgi membrane bending elasticity, which is related to the membrane curvature, and the adhesion, which holds the cisternae together. The analysis shows that the equilibrium configuration of the Golgi stack can be regarded as a balance between these two effects – the adhesion, which tends to increase the number of cisternae, is opposed by the membrane resistance to bending, which does not favor highly curved cisternal rims. The adhesion strength that is needed to hold together a typical stack is calculated. In addition, the model is used to analyze changes in the cisternal numbers as a controlled traffic wave enters a Golgi stack and increases the amount of the membrane in that stack.

Membrane bending by protein crowding is affected by protein lateral confinement

Crowding of asymmetrically-distributed membrane proteins has been recently recognized as an important factor in remodeling of biological membranes, for example during transport vesicle formation. In this paper, we theoretically analyze the effect of protein crowding on membrane bending and examine its dependence on protein size, shape, transmembrane asymmetry and lateral confinement. We consider three scenarios of protein lateral organization, which are highly relevant for cellular membranes in general: freely diffusing membrane proteins without lateral confinement, the presence of a diffusion barrier and interactions with a vesicular coat. We show that protein crowding affects vesicle formation even if the proteins are distributed symmetrically across the membrane and that this effect depends significantly on lateral confinement. The largest crowding effect is predicted for the proteins that are confined to the forming vesicle by a diffusion barrier. We calculate the bending properties of a crowded membrane and find that its spontaneous curvature depends primarily on the degree of transmembrane asymmetry, and its effective bending modulus on the type of lateral confinement. Using the example of COPII vesicle formation from the endoplasmic reticulum, we analyze the energetic cost of vesicle formation. The results provide a novel insight into the effects of lateral and transmembrane organization of membrane proteins, and can guide data interpretation and future experimental approaches.

Equilibrium mechanics of monolayered epithelium

In order to fully understand the epithelial mechanics it is essential to integrate different levels of epithelial organization. In this work, we propose a theoretical approach for connecting the macroscopic mechanical properties of a monolayered epithelium to the mechanical properties at the cellular level. The analysis is based on the established mechanical models-at the macroscopic scale the epithelium is described within the mechanics of thin layers, while the cellular level is modeled in terms of the cellular surface (cortical) tension and the intercellular adhesion. The macroscopic elastic energy of the epithelium is linked to the energy of an average epithelial cell. The epithelial equilibrium state is determined by energy minimization and the macroscopic elastic moduli are calculated from deformations around the equilibrium. The results indicate that the epithelial equilibrium state is defined by the ratio between the adhesion strength and the cellular surface tension. The lower and the upper bounds for this ratio are estimated. If the ratio is small, the epithelium is cuboidal, if it is large, the epithelium becomes columnar. Importantly, it is found that the cellular cortical tension and the intercellular adhesion alone cannot produce the flattened squamous epithelium. Any difference in the surface tension between the apical and basal cellular sides bends the epithelium towards the side with the larger surface tension. Interestingly, the analysis shows that the epithelial area expansivity modulus and the shear modulus depend only on the cellular surface tension and not on the intercellular adhesion. The results are presented in a general analytical form, and are thus applicable to a variety of monolayered epithelia, without relying on the specifics of numerical finite-element methods. In addition, by using the standard theoretical tools for multi-laminar systems, the results can be applied to epithelia consisting of layers with different mechanical properties.

Shapes of Discoid Intracellular Compartments with Small Relative Volumes

A prominent feature of many intracellular compartments is a large membrane surface area relative to their luminal volume, i.e., the small relative volume. In this study we present a theoretical analysis of discoid membrane compartments with a small relative volume and then compare the theoretical results to quantitative morphological assessment of fusiform vesicles in urinary bladder umbrella cells. Specifically, we employ three established extensions of the standard approach to lipid membrane shape calculation and determine the shapes that could be expected according to three scenarios of membrane shaping: membrane adhesion in the central discoid part, curvature driven lateral segregation of membrane constituents, and existence of stiffer membrane regions, e.g., support by protein scaffolds. The main characteristics of each scenario are analyzed. The results indicate that even though all three scenarios can lead to similar shapes, there are values of model parameters that yield qualitatively distinctive shapes. Consequently, a distinctive shape of an intracellular compartment may reveal its membrane shaping mechanism and the membrane structure. The observed shapes of fusiform vesicles fall into two qualitatively different classes, yet they are all consistent with the theoretical results and the current understanding of their structure and function.

Trans-Membrane Area Asymmetry Controls the Shape of Cellular Organelles

Membrane organelles often have complicated shapes and differ in their volume, surface area and membrane curvature. The ratio between the surface area of the cytosolic and luminal leaflets (trans-membrane area asymmetry (TAA)) determines the membrane curvature within different sites of the organelle. Thus, the shape of the organelle could be critically dependent on TAA. Here, using mathematical modeling and stereological measurements of TAA during fast transformation of organelle shapes, we present evidence that suggests that when organelle volume and surface area are constant, TAA can regulate transformation of the shape of the Golgi apparatus, endosomal multivesicular bodies, and microvilli of brush borders of kidney epithelial cells. Extraction of membrane curvature by small spheres, such as COPI-dependent vesicles within the Golgi (extraction of positive curvature), or by intraluminal vesicles within endosomes (extraction of negative curvature) controls the shape of these organelles. For instance, Golgi tubulation is critically dependent on the fusion of COPI vesicles with Golgi cisternae, and vice versa, for the extraction of membrane curvature into 50–60 nm vesicles, to induce transformation of Golgi tubules into cisternae. Also, formation of intraluminal ultra-small vesicles after fusion of endosomes allows equilibration of their TAA, volume and surface area. Finally, when microvilli of the brush border are broken into vesicles and microvilli fragments, TAA of these membranes remains the same as TAA of the microvilli. Thus, TAA has a significant role in transformation of organelle shape when other factors remain constant.

Controlled shaping of lipid vesicles in a microfluidic diffusion chamber

Synthetic lipid vesicles represent an important model system for studying membrane processes, which often depend on membrane shape, but controlled shaping of vesicles remains a challenging experimental task. Here, we present a novel method for shaping giant lipid vesicles by independently regulating osmotic conditions and the concentration of membrane-shaping molecules, which intercalate into the membrane and drive membrane bending. The method is based on the microfluidic diffusion chamber, where the solution around the vesicles can be repeatedly exchanged solely by diffusion, without any hydrodynamic flow that could deform the membrane. By using lipopolysaccharide (LPS) as a vesicle shape-modifying molecule, we demonstrate controlled and reversible transformations across three shape classes, from invaginated to evaginated vesicles. We show that extensive shape transformations can lead to shapes that are assumed to comprise narrow membrane necks that hinder equilibration of the membrane and the vesicle interior. All the observed shapes are in good agreement with the predictions of the area-difference-elasticity model applied to the vesicles that were denser than their surrounding solution. Our results validate the microfluidic diffusion chamber as a universal framework for membrane shaping that could also pave the way towards controlled fabrication of synthetic membranes resembling cell-compartments with large surface-to-volume ratios.

Crowd-Sourcing of Membrane Fission

Fission of cellular membranes is ubiquitous and essential for life. Complex protein machineries, such as the dynamin and ESCRT spirals, have evolved to mediate membrane fission during diverse cellular processes, for example, vesicle budding. A new study suggests that non‐specialized membrane‐bound proteins can induce membrane fission through mass action due to protein crowding. Because up to 2/3 of the mass of cellular membranes is contributed by proteins, membrane protein crowding is an important physiological parameter. Considering the complexity of membrane shape transitions during a fission reaction, spatial and temporal variability in protein distribution, and the abundance of intrinsically disordered regions in proteins on an invaginating membrane, protein crowding can have diverse consequences for fission in the cell. The question is, how and to what extent this mechanism combines with the action of dedicated fission machineries.