We study the role of a biomimetic actin network during the application of electric pulses that induce electroporation or electropermeabilization, using giant unilamellar vesicles (GUVs) as a model system. The actin cortex, a subjacently attached interconnected network of actin filaments, regulates the shape and mechanical properties of the plasma membrane of mammalian cells, and is a major factor influencing the mechanical response of the cell to external physical cues. We demonstrate that the presence of an actin shell inhibits the formation of macropores in the electroporated GUVs. Additionally, experiments on the uptake of dye molecules after electroporation show that the actin network slows down the resealing process of the permeabilized membrane. We further analyze the stability of the actin network inside the GUVs exposed to high electric pulses. We find disruption of the actin layer that is likely due to the electrophoretic forces acting on the actin filaments during the permeabilization of the GUVs. Our findings on the GUVs containing a biomimetic network provide a step towards understanding the discrepancies between the electroporation mechanism of a living cell and its simplified model of the empty GUV.

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Biological membranes are selective soft barriers that compartmentalize internal structure of a cell into organelles and separate them as a whole from the external environment. Due to their innate feature of being able to undergo constant reshaping, cellular membranes spatially attain diverse shapes ranging from simple spherical vesicles to more peculiar structures like the interconnected network of tubes found in the endoplasmic reticulum. Membranes are not only composed of lipids, but also host an enormous number of inclusions like proteins. Recent studies of biological membranes have revealed that such inclusions play a key role in diverse biological processes through either sensing or inducing perturbations to the membrane shape. In this dissertation, we studied the interplay between the shape of membrane and the spatial organization of attached curvature inducing objects using mathematical tools and numerical simulations in highly curved spherical and cylindrical geometries. First, we investigated the interaction between inclusions of different shapes embedded in/adhered to tubular membranes. Our combined theoretical analysis and numerical simulation results evinced that tubular membranes, in contrast to their planar counterpart, transmit an attractive force between inclusions, stemming from their closed and curved geometry. We then elucidated that collective interaction between proteins results in the formation of line-like and ring-like clusters, depending on the their intrinsic shape (Chapters 2–4). We further showed how curvature sensing crescent-like proteins in high densities can constrict tubular membranes and facilitate their splitting, demonstrating that both the curvature-sensing and curvature-inducing property of proteins are two sides of the same coin. Moreover, we used our simulation results to explain how mitochondorial machinery triggers, facilitates and drives membrane fission in its tubular network to avoid entanglements (Chapter 3). Next, we examined the interaction of spherical proteins adhered to closed vesicles. Our simulation results – supported by recent experimental evidence – revealed membrane curvature as a common physical origin for interactions between any membrane deforming objects, from nanometre-sized proteins to micrometre-sized particles (Chapter 5). Our further simulations unraveled how introducing curvature variation on the surface of a closed vesicle can be exploited by inanimate particles to regulate their pattern formation (Chapter 6). Finally, through theoretical calculations,we analyzed the interplay between the shape of a cell and the rearrangement of attached microtubules (Chapter 7). Our results particularly suggested that the commonly reported parallel structure and bundling of microtubules can be induced by membrane mediated interactions.@en

Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins influence the membrane shape, the membrane shape affects the interactions between the proteins. To study these membrane-mediated interactions on closed and anisotropically curved membranes, we use colloids adhered to ellipsoidal membrane vesicles as a model system. We find that two particles on a closed system always attract each other, and tend to align with the direction of largest curvature. Multiple particles form arcs, or, at large enough numbers, a complete ring surrounding the vesicle in its equatorial plane. The resulting vesicle shape resembles a snowman. Our results indicate that these physical interactions on membranes with anisotropic shapes can be exploited by cells to drive macromolecules to preferred regions of cellular or intracellular membranes, and utilized to initiate dynamic processes such as cell division. The same principle could be used to find the midplane of an artificial vesicle, as a first step towards dividing it into two equal parts.@en

Eukaryotic cells are densely packed with macromolecular complexes and intertwining organelles, continually transported and reshaped. Intriguingly, organelles avoid clashing and entangling with each other in such limited space. Mitochondria form extensive networks constantly remodeled by fission and fusion. Here, we show that mitochondrial fission is triggered by mechanical forces. Mechano-stimulation of mitochondria - via encounter with motile intracellular pathogens, via external pressure applied by an atomic force microscope, or via cell migration across uneven microsurfaces - results in the recruitment of the mitochondrial fission machinery, and subsequent division. We propose that MFF, owing to affinity for narrow mitochondria, acts as a membrane-bound force sensor to recruit the fission machinery to mechanically strained sites. Thus, mitochondria adapt to the environment by sensing and responding to biomechanical cues. Our findings that mechanical triggers can be coupled to biochemical responses in membrane dynamics may explain how organelles orderly cohabit in the crowded cytoplasm.

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Membrane tubes and tubular networks are ubiquitous in living cells. Inclusions like proteins are vital for both the stability and the dynamics of such networks. These inclusions interact via the curvature deformations they impose on the membrane. We analytically study the resulting membrane mediated interactions in strongly curved tubular membranes. We model inclusions as constraints coupled to the curvature tensor of the membrane tube. First, as special test cases, we analyze the interaction between ring- and rod-shaped inclusions. Using Monte Carlo simulations, we further show how pointlike inclusions interact to form linear aggregates. To minimize the curvature energy of the membrane, inclusions self-assemble into either line- or ringlike patterns. Our results show that the global curvature of the membrane strongly affects the interactions between proteins embedded in it, and can lead to the spontaneous formation of biologically relevant structures.

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The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 k_BT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles.

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