Numerical Study of Membrane Configurations

We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit in-plane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells). The topological defects are always present on the surfaces with the topology of a sphere. The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy

Modelling how curved active proteins and shear flow pattern cellular shape and motility

Cell spreading and motility on an adhesive substrate are driven by the active physical forces generated by the actin cytoskeleton. We have recently shown that coupling curved membrane complexes to protrusive forces, exerted by the actin polymerization that they recruit, provides a mechanism that can give rise to spontaneous membrane shapes and patterns. In the presence of an adhesive substrate, this model was shown to give rise to an emergent motile phenotype, resembling a motile cell. Here, we utilize this “minimal-cell” model to explore the impact of external shear flow on the cell shape and migration on a uniform adhesive flat substrate. We find that in the presence of shear the motile cell reorients such that its leading edge, where the curved active proteins aggregate, faces the shear flow. The flow-facing configuration is found to minimize the adhesion energy by allowing the cell to spread more efficiently over the substrate. For the non-motile vesicle shapes, we find that they mostly slide and roll with the shear flow. We compare these theoretical results with experimental observations, and suggest that the tendency of many cell types to move against the flow may arise from the very general, and non-cell-type-specific mechanism predicted by our model

Morphological alterations of T24 cells on flat and nanotubular TiO2 surfaces

Aim To investigate morphological alterations of malignant cancer cells (T24) of urothelial origin seeded on flat titanium (Ti) and nanotubular titanium dioxide (TiO2) nanostructures. Methods Using anodization method, TiO2 surfaces composed of vertically aligned nanotubes of 50-100 nm diameters were produced. The flat Ti surface was used as a reference. The alteration in the morphology of cancer cells was evaluated using scanning electron microscopy (SEM). A computational model, based on the theory of membrane elasticity, was constructed to shed light on the biophysical mechanisms responsible for the observed changes in the contact area of adhesion. Results Large diameter TiO2 nanotubes exhibited a significantly smaller contact area of adhesion (P < 0.0001) and had more membrane protrusions (eg, microvilli and intercellular membrane nanotubes) than on flat Ti surface. Numerical membrane dynamics simulations revealed that the low adhesion energy per unit area would hinder the cell spreading on the large diameter TiO2 nanotubular surface, thus explaining the small contact area. Conclusion The reduction in the cell contact area in the case of large diameter TiO2 nanotube surface, which does not enable formation of the large enough number of the focal adhesion points, prevents spreading of urothelial cells

SPECTRAL ANALYSIS OF THERMALLY FLUCTUATING MEMBRANES USING PHASE-CONTRAST MICROSCOPY AND MONTE-CARLO COMPUTER SIMULATIONS

Membrane, tanke lonice med dvema področjema, so lahko podvržene termičnim fluktuacijam. Pomemben primer tankih mejnih plasti v naravi so membrane v bioloških celicah. Celice različnih velikosti, oblik in funkcij so osnovni sestavni deli bioloških sistemov. Kljub raznolikosti celic, ki jih najdemo v bioloških sistemih, so osnovni gradniki in njihova kemijska sestava večine celic enaki. Lastnosti bioloških membran, ki obdajajo celice ali njene organele, se precej razlikujejo od lastnosti makroskopskih objektov, ki smo jih vajeni iz vsakodnevnega življenja. Na primer, lipidna dvojna plast, osnova bioloških membran, je tako mehka na upogib, da lahko že termično gibanje okolne raztopine pri sobni temperaturi povzroča spremembe oblike membrane. S spektralno analizo takšnih terminih fluktuacij biološke membrane je mogoče neinvazivno določati njene mehanske lastnosti. Migetanje (utripanje) rdečih krvnih celic je zaznal že Browicz v poznem 19. stoletju z uporabo optičnega mikroskopa. Danes lahko fluktuacije lipidne dvojne plasti opazujemo z izboljšanim faznokontrastnim mikroskopom ter s spektralno analizo teh fluktuacij neinvazivno merimo nekatere ključne lastnosti bioloških celic. V doktorski disertaciji smo izdelali merilni sistem za analizo termičnih fluktuacij bioloških membran s faznokontrastnim mikroskopom. Končni cilj tega razvoja je celostno računalniško krmiljeno eksperimentalno okolje primerno za raziskovalce s področja bioloških znanosti. V doktorskem delu smo predstavili tudi posodobljen in izboljšan računalniki program za simulacije Monte Carlo z naključnimi trikotniškimi mrežami, s katerimi je mogoče modelirati termine fluktuacije bioloških membran. S simulacijami Monte-Carlo smo preverili nekatere predpostavke teoretičnega modela za določanje elastinih lastnosti bioloških membran z analizo njihovih terminih fluktuacij. Teoretični model Milnerja in Safrana za določanje elastinih lastnosti bioloških membran z analizo njihovih terminih fluktuacij temelji na znanem Helfrichovem modelu membrane in vsebuje tudi implicitno predpostavko, da pri terminih fluktuacijah lipidne dvojne plasti nihanji upogiba in natega membrane nista sklopljeni in lahko uporabimo približek povprečnega polja. Veljavnost zgornje predpostavke nameravamo preveriti z numerinim modelom. S simulacijami Monte Carlo z naključnimi trikotniškimi mrežami lahko modeliramo biološke membrane v njihovem termodinamičnem ravnovesju in stohastični Metropolis Hastingsov algoritem nam omogoča analizo njihovih termičnih fluktuacij. Čeprav nam tudi nekateri drugih numerični modeli membrane nudijo primerno časovno zahtevnost za obravnavo celotne celice oziroma lipidnega mehurka, so pri simulacijah Monte Carlo z naključnimi trikotniškimi mrežami elastine konstante membrane (npr. upogibna konstanta) sestavni del samega modela. Čas izvajanja simulacij Monte Carlo z naključnimi trikotniškimi mrežamise povečuje z večanjem simuliranega sistema. Časovna zahtevnost simulacije narašča s kvadratom števila vozlišče naključne trikotniške mreže, če upoštevamo interakcije dolgega dosega med vozlišči, kot so na primer elektrostatične sile med naelektrenimi delci membrane. Ker število vozlišče še dodatno narašča s kvadratom radija celice, simulacijski čas torej narašča s četrto potenco premera celice. S skaliranjem sistema lahko delno rešimo problem časovne zahtevnosti, če lahko majhne površine membrane, ki jo sestavlja množica elementov (molekul) opišemo z enim vozliščem v trikotniški mreži. Dodatno pohitritev simulacij lahko dosežemo s paralelizacijo simulacijskega algoritma in tako izkoristimo prednosti, ki jih nudijo novodobne večjedrne in večnitne procesorske arhitekture. Raziskali smo možnosti paralelizacije naših simulacij z naključnimi trikotniškimi mrežami s pomočjo različnih paralelizacijskih pristopov. Sistemi, ki temeljijo na metodah merjenja s faznokontrastnim mikroskopom, reflektivno interferenčnim in s fluorescentno interferenčnim mikroskopom so primeri merilnih sistemov, ki omogočajo neinvazivno določitev elastičnih lastnosti membran. Sistem je sestavljen iz faznokontrastnega mikroskopa, stroboskopske osvetlitve in kamere povezane z računalnikom. Kamera in stroboskopska osvetlitev morata biti ustrezno sinhronizirana, da lahko natančno zabeležimo obliko membrane v danem času. Stroboskop kratkotrajno osvetli vzorec znotraj posameznega zajema slike in tako odpravi problem neostre slike zaradi hitrih fluktuacij, ki bi sliko zameglile, če bi dopustili daljši čas osvetlitve med integracijskim časom kamere. Stroboskop lahko pri razelektritvi skozi stroboskopsko luč povzroči mehanske tresljaje celotnega mikroskopa in s tem tudi merjenca. Tresljaji pozročajo neželjene premike in deformacije membran, hkrati pa pripomorejo k manjši ločljivosti zaznave robov. Prednost izvedenega merilnega sistema je v popolni avtomatizaciji meritev in izboljšanem sistemu za osvetlitev vzorca.Membranes, thin barriers between compartments, can uctuate. An important example in nature are membranes of biological cells. Cells, these building blocks of biological systems, have diverse capabilities and shapes. However, the basic structural elements and their chemical composition of most cells are the same. Fluid sheets (membranes) enclose the cell and its compartments, while networks of fillaments, if present, maintain the cell\u27s shape and help organize its contents. These structural elements can have quite di_erent mechanical properties than macroscopic objects of our everyday life. For example, they are very soft solely thermal uctuations at room temperature can generate gentle undulations of membranes.Flickering" of red blood cells was already recorded in the late 19th century by Browicz using the light microscope. Today, with phase-contrast microscopy, non-invasive spectral analysis of those thermal uctuations of biological membranes can provide useful information of the membrane properties.Theoretical model for determining elastic properties of biological membranes with analysis of thermal uctuations by Milner and Safran is based on Helfrich model of membrane and includes also an implicit assumption that in the thermal uctuations of phospholipid bilayers, the shape uctuation modes are not correlated with the lateral stretching modes and that the mean-field approximation can be used. Using Randomly triangulated surfaces, we can simulate biological membrane systems in their thermodynamical equilibrium, where the stochastic Metropolis-Hastings algorithm allows us to sample their thermal uctuations. In this thesis, the coarse-grained model of the membrane is implemented in the program written in C programming language, where the membrane is represented by randomly triangulated network. The model takes into account the assumptions by Milner and Safran. The output of the simulator is the bending sti_ness of the membrane Kc which can be compared with the input bending stiffness , to verify if the numerical simulations are in accordance with the theoretical predictions of Milner and Safran. The randomly triangulated surfaces Monte-Carlo simulations can become time consuming for large systems, therefore some sort of parallelization is needed to harvest the capabilities of modern computers. Two approaches were made and compared. The problem proved to be embarrassingly parallelizable and we measured near theoretical max. speedup of the simulations by running multiple instances of the simulators and combining their statistics. Systems based on method of measurement of thermal uctuations with phase-contrast microscopy, interference contrast microscopy and uorescent-interference contrast microscopyare examples of non-invasive determination of the elastic properties of membranes. Our system is based on phase-contrast microscope and illumination apparatus presented in and, including image analysis described in. It basically consists of a phase-contrast microscope, a stroboscopic lighting system and a camera, connected to a computer. The camera and the lighting system was synchronized to allow a precise, blur-less registration of the membrane shape at the given moment, which is then analysed using user friendly software on the computer. The results of the simulations con_rmed the assumptions of Milner and Safran. The measurements of the simulations were behaving accordingly to the prediction of the equation of Milner and Safran, thus we concluded that the numerical simulations of nearly spherical vesicles modelled with triangulated networks can be used to determine the bending sti_- ness. Depending on the resolution of the simulations (the density of the mesh) the di_erence between input and measured bending sti_ness can be well below 10%

Numerical study of membrane configurations

We studied biological membranes of spherical topology within the framework of the spontaneous curvature model. Both Monte Carlo simulations and the numerical minimization of the curvature energy were used to obtain the shapes of the vesicles. The shapes of the vesicles and their energy were calculated for different values of the reduced volume. The vesicles which exhibit inplane ordering were also studied. Minimal models have been developed in order to study the orientational ordering in colloids coated with a thin sheet of nematic liquid crystal (nematic shells).The topological defects are always present on the surfaces with the topology of a sphere.The location of the topological defects depends strongly on the curvature of the surface. We studied the nematic ordering and the formation of topological defects on vesicles obtained by the minimization of the spontaneous curvature energy

Investigation of nano- and microdomains formed by ceramide 1 phosphate in lipid bilayers

Abstract Biological membranes are renowned for their intricate complexity, with the formation of membrane domains being pivotal to the successful execution of numerous cellular processes. However, due to their nanoscale characteristics, these domains are often understudied, as the experimental techniques required for quantitative investigation present significant challenges. In this study we employ spot-variation z-scan fluorescence correlation spectroscopy (svzFCS) tailored for artificial lipid vesicles of varying composition and combine this approach with high-resolution imaging. This method has been harnessed to examine the lipid-segregation behavior of distinct types of ceramide-1-phosphate (C1P), a crucial class of signaling molecules, within these membranes. Moreover, we provide a quantitative portrayal of the lipid membranes studied and the domains induced by C1P at both nano and microscales. Given the lack of definitive conclusions from the experimental data obtained, it was supplemented with comprehensive in silico studies—including the analysis of diffusion coefficient via molecular dynamics and domain populations via Monte Carlo simulations. This approach enhanced our insight into the dynamic behavior of these molecules within model lipid membranes, confirming that nano- and microdomains can co-exist in lipid vesicles

On the role of curved membrane nanodomains and passive and active skeleton forces in the determination of cell shape and membrane budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding

Surfactin molecules with a cone-like structure promote the formation of membrane domains with negative spontaneous curvature and induce membrane invaginations

Surfactin uniquely influences lipid bilayer structure by initially inducing membrane invaginations before solubilization. In this study, we exposed DOPC giant vesicles to various surfactin concentrations at different temperatures and observed surfactin-induced membrane invaginations by using differential interference contrast and confocal laser fluorescence microscopy. These invaginations were stable at room temperature but not at higher temperatures. Surfactin molecules induce membrane nanodomains with negative spontaneous curvature and membrane invaginations despite their intrinsic conical shape and intrinsic positive curvature. Considering the experimentally observed capacity of surfactin to fluidize lipid acyl chains and induce partial dehydration of lipid headgroups, we propose that the resulting surfactin-lipid complexes exhibit a net negative spontaneous curvature. We further conducted 3D numerical Monte Carlo (MC) simulations to investigate the behaviour of vesicles containing negative curvature nanodomains within their membrane at varying temperatures. MC simulations demonstrated strong agreement with experimental results, revealing that invaginations are preferentially formed at low temperatures, while being less pronounced at elevated temperatures. Our findings go beyond the expectations of the Israelachvili molecular shape and packing concepts analysis. These concepts do not take into account the influence of specific interactions between neighboring molecules on the inherent shapes of molecules and their arrangement within curved membrane nanodomains. Our work contributes to a more comprehensive understanding of the complex factors governing vesicle morphology and membrane organization and provides insight into the role of detergent-lipid interactions in modulating vesicle morphology