Model biomolecular condensates have heterogeneous structure quantitatively dependent on the interaction profile of their constituent macromolecules.

Biomolecular condensates play numerous roles in cells by selectively concentrating client proteins while excluding others. These functions are likely to be sensitive to the spatial organization of the scaffold proteins forming the condensate. We use coarse-grained molecular simulations to show that model intrinsically-disordered proteins phase separate into a heterogeneous, structured fluid characterized by a well-defined length scale. The proteins are modelled as semi-flexible polymers with punctate, multifunctional binding sites in good solvent conditions. Their dense phase is highly solvated with a spatial structure that is more sensitive to the separation of the binding sites than their affinity. We introduce graph theoretic measures to quantify their heterogeneity, and find that it increases with increasing binding site number, and exhibits multi-timescale dynamics. The model proteins also swell on passing from the dilute solution to the dense phase. The simulations predict that the structure of the dense phase is modulated by the location and affinity of binding sites distant from the termini of the proteins, while sites near the termini more strongly affect its phase behaviour. The relations uncovered between the arrangement of weak interaction sites on disordered proteins and the material properties of their dense phase can be experimentally tested to give insight into the biophysical properties, pathological effects, and rational design of biomolecular condensates.

Fluctuations and conformational stability of a membrane patch with curvature inducing inclusions.

Membranes with curvature inducing inclusions display a range of cooperative phenomena, which can be linked to biomembrane function, e.g. membrane tubulation, vesiculation, softening and spontaneous tension. We investigate how these phenomena are related for a fluctuating, framed membrane through analysis of a descretized membrane model by Monte Carlo simulation techniques. The membrane model is based on a dynamically triangulated surface equipped with non-interacting, up-down symmetry breaking inclusions where only terms coupled linearly to mean-curvature are maintained. We show that the lateral configurational entropy plays a key role for the mechanical properties of the semi-flexible membrane, e.g. a pronounced softening at intermediate inclusion coverages of the membrane and generation of membrane tension. Tensionless framed membranes will remain quasi-flat up to some threshold coverage, where a shape instability occurs with formation of pearling or tubular membranes, which below full coverage is associated with segregation of inclusions between the curved and flat membrane geometries. For inclusions with preference for highly curved membranes the instability appears at dilute inclusion coverages and is accompanied by strong configurational fluctuations.

The tension of framed membranes from computer simulations.

We have analyzed the behavior of a randomly triangulated, self-avoiding surface model of a flexible, fluid membrane subject to a circular boundary by Wang-Landau Monte Carlo computer simulation techniques. The dependence of the canonical free energy and frame tension on the frame area is obtained for flexible membranes. It is shown that for low bending rigidities the framed membrane is only stable above a threshold tension, suggesting a discontinuous transition from the collapsed (branched polymer) state to a finite tension extended state. In a tension range above this threshold tension the membranes display power-law characteristics for the equation of state, while higher tension levels includes both an extended linear (elastic) as well as a highly non-linear stretching regime. For semi-flexible membranes a transition from extended to buckled conformations takes place at negative frame tensions. Our analysis indicates that at zero frame tension the crumpling transition of fluid membranes show characteristics of both critical behavior and a discontinuous transition at low bending rigidities.

Spatial distribution and activity of Na(+)/K(+)-ATPase in lipid bilayer membranes with phase boundaries.

We have reconstituted functional Na(+)/K(+)-ATPase (NKA) into giant unilamellar vesicles (GUVs) of well-defined binary and ternary lipid composition including cholesterol. The activity of the membrane system can be turned on and off by ATP. The hydrolytic activity of NKA is found to depend on membrane phase, and the water relaxation in the membrane on the presence of NKA. By collapsing and fixating the GUVs onto a solid support and using high-resolution atomic-force microscopy (AFM) imaging we determine the protein orientation and spatial distribution at the single-molecule level and find that NKA is preferentially located at lo/ld interfaces in two-phase GUVs and homogeneously distributed in single-phase GUVs. When turned active, the membrane is found to unbind from the support suggesting that the protein function leads to softening of the membrane.

Membrane Tubulation in Lipid Vesicles Triggered by the Local Application of Calcium Ions.

Experimental and theoretical studies on ion-lipid interactions predict that binding of calcium ions to cell membranes leads to macroscopic mechanical effects and membrane remodeling. Herein, we provide experimental evidence that a point source of Ca2+ acting upon a negatively charged membrane generates spontaneous curvature and triggers the formation of tubular protrusions that point away from the ion source. This behavior is rationalized by strong binding of the divalent cations to the surface of the charged bilayer, which effectively neutralizes the surface charge density of outer leaflet of the bilayer. The mismatch in the surface charge density of the two leaflets leads to nonzero spontaneous curvature. We probe this mismatch through the use of molecular dynamics simulations and validate that calcium ion binding to a lipid membrane is sufficient to generate inward spontaneous curvature, bending the membrane. Additionally, we demonstrate that the formed tubular protrusions can be translated along the vesicle surface in a controlled manner by repositioning the site of localized Ca2+ exposure. The findings demonstrate lipid membrane remodeling in response to local chemical gradients and offer potential insights into the cell membrane behavior under conditions of varying calcium ion concentrations.

Preparing giant unilamellar vesicles (GUVs) of complex lipid mixtures on demand: Mixing small unilamellar vesicles of compositionally heterogeneous mixtures.

Giant unilamellar vesicles (GUVs) are simple model membrane systems of cell-size, which are instrumental to study the function of more complex biological membranes involving heterogeneities in lipid composition, shape, mechanical properties, and chemical properties. We have devised a method that makes it possible to prepare a uniform sample of ternary GUVs of a prescribed composition and heterogeneity by mixing different populations of small unilamellar vesicles (SUVs). The validity of the protocol has been demonstrated by applying it to ternary lipid mixture of DOPC, DPPC, and cholesterol by mixing small unilamellar vesicles (SUVs) of two different populations and with different lipid compositions. The compositional homogeneity among GUVs resulting from SUV mixing is quantified by measuring the area fraction of the liquid ordered-liquid disordered phases in giant vesicles and is found to be comparable to that in GUVs of the prescribed composition produced from hydration of dried lipids mixed in organic solvent. Our method opens up the possibility to quickly increase and manipulate the complexity of GUV membranes in a controlled manner at physiological buffer and temperature conditions. The new protocol will permit quantitative biophysical studies of a whole new class of well-defined model membrane systems of a complexity that resembles biological membranes with rafts.

Fluid domain patterns in free-standing membranes captured on a solid support.

We devise a methodology to fixate and image dynamic fluid domain patterns of giant unilamellar vesicles (GUVs) at sub-optical length scales. Individual GUVs are rapidly transferred to a solid support forming planar bilayer patches. These are taken to represent a fixated state of the free standing membrane, where lateral domain structures are kinetically trapped. High-resolution images of domain patterns in the liquid-ordered (lo) and liquid-disordered (ld) co-existence region in the phase-diagram of ternary lipid mixtures are revealed by atomic force microscopy (AFM) scans of the patches. Macroscopic phase separation as known from fluorescence images is found, but with superimposed fluctuations in the form of nanoscale domains of the lo and ld phases. The size of the fluctuating domains increases as the composition approaches the critical point, but with the enhanced spatial resolution, such fluctuations are detected even deep in the coexistence region. Agreement between the area-fraction of domains in GUVs and the patches respectively, supports the assumption that the thermodynamic state of the membrane remains stable. The approach is not limited to specific lipid compositions, but could potentially help uncover lateral structures in highly complex membranes.

Organelle morphogenesis by active membrane remodeling.

Intracellular organelles are subject to a steady flux of lipids and proteins through active, energy consuming transport processes. Active fission and fusion are promoted by GTPases, e.g., Arf-Coatamer and the Rab-Snare complexes, which both sense and generate local membrane curvature. Here we investigate, through Dynamical Triangulation Monte Carlo simulations, the role that these active processes play in determining the morphology and composition segregation in closed membranes. We find that the steady state shapes obtained as a result of such active processes, bear a striking resemblance to the ramified morphologies of organelles in vivo, pointing to the relevance of nonequilibrium fission-fusion in organelle morphogenesis.

The effects of globotriaosylceramide tail saturation level on bilayer phases.

Globotriaosylceramide (Gb3) is a glycosphingolipid present in the plasma membrane that is the natural receptor of the bacterial Shiga toxin. The unsaturation level of Gb3 acyl chains has a drastic impact on lipid bilayer properties and phase behaviour, and on many Gb3-related cellular processes. For example: the Shiga toxin B subunit forms tubular invaginations in the presence of Gb3 with an unsaturated acyl chain (U-Gb3), while in the presence of Gb3 with a saturated acyl chain (S-Gb3) such invagination does not occur. We have used all-atom molecular dynamics simulations to investigate the effects of the Gb3 concentration and its acyl chain saturation on the phase behaviour of a mixed bilayer of dioleoylphosphatidylcholine and Gb3. The simulation results show that: (1) the Gb3 acyl chains (longer tails) from one leaflet interdigitate into the opposing leaflet and lead to significant bilayer rigidification and immobilisation of the lipid tails. S-Gb3 can form a highly ordered, relatively immobile phase which is resistant to bending while these changes for U-Gb3 are not significant. (2) At low concentrations of Gb3, U-Gb3 and S-Gb3 have a similar impact on the bilayer reminiscent of the effect of sphingomyelin lipids and (3) At higher Gb3 concentrations, U-Gb3 mixes better with dioleoylphosphatidylcholine than S-Gb3. Our simulations also provide the first molecular level structural model of Gb3 in membranes.

Curvature inducing macroion condensation driven shape changes of fluid vesicles.

We study the effect of curvature inducing macroion condensation on the shapes of charged deformable fluid interfaces using dynamically triangulated Monte Carlo simulations. In the weak electrostatic coupling regime, surface charges are weakly screened and the conformations of a vesicle, with fixed spherical topology, depend on the charge-charge interaction on the surface. While in the strong coupling regime, condensation driven curvature induction plays a dominant role in determining the conformations of these surfaces. Condensation itself is observed to be dependent on the induced curvature, with larger induced curvatures favoring increased condensation. We show that both curvature generation and curvature sensing, induced by the interplay of electrostatics and curvature energy, contribute to determination of the vesicle configurations.

Intrinsic reaction-cycle time scale of Na+,K+-ATPase manifests itself in the lipid-protein interactions of nonequilibrium membranes.

Interaction between integral membrane proteins and the lipid-bilayer component of biological membranes is expected to mutually influence the proteins and the membrane. We present quantitative evidence of a manifestation of the lipid-protein interactions in liposomal membranes, reconstituted with actively pumping Na(+),K(+)-ATPase, in terms of nonequilibrium shape fluctuations that contain a relaxation time, τ, which is robust and independent of the specific fluctuation modes of the membrane. In the case of pumping Na(+)-ions, analysis of the flicker-noise temporal correlation spectrum of the liposomes leads to τ ~/= 0.5 s, comparing favorably with an intrinsic reaction-cycle time of about 0.4 s from enzymology.

Buffers affect the bending rigidity of model lipid membranes.

In biophysical and biochemical studies of lipid bilayers the influence of the used buffer is often ignored or assumed to be negligible on membrane structure, elasticity, or physical properties. However, we here present experimental evidence, through bending rigidity measurements performed on giant vesicles, of a more complex behavior, where the buffering molecules may considerably affect the bending rigidity of phosphatidylcholine bilayers. Furthermore, a synergistic effect on the bending modulus is observed in the presence of both salt and buffer molecules, which serves as a warning to experimentalists in the data interpretation of their studies, since typical lipid bilayer studies contain buffer and ion molecules.

Lipophilic contaminants influence cold tolerance of invertebrates through changes in cell membrane fluidity.

Contaminants taken up by living organisms in the environment as a result of anthropogenic contamination can reduce the tolerance of natural stressors, e.g., low temperatures, but the physiological mechanisms behind these interactions of effects are poorly understood. The tolerance to low temperatures of organisms that cannot regulate their body temperature (ectotherms) depends on their ability to increase the fluidity of their cellular membranes at low temperatures. Our study shows that contaminants accumulating in lipids of organisms alter the physical state of their membranes simply by being present. Contaminants of varying chemical structures can alter the membrane fluidity in either direction and correspondingly modulate the cold tolerance of intact animals.

Mesoscale simulation of biomembranes with FreeDTS.

We present FreeDTS software for performing computational research on biomembranes at the mesoscale. In this software, a membrane is represented by a dynamically triangulated surface equipped with vertex-based inclusions to integrate the effects of integral and peripheral membrane proteins. Several algorithms are included in the software to simulate complex membranes at different conditions such as framed membranes with constant tension, vesicles and high-genus membranes with various fixed volumes or constant pressure differences and applying external forces to membrane regions. Furthermore, the software allows the user to turn off the shape evolution of the membrane and focus solely on the organization of proteins. As a result, we can take realistic membrane shapes obtained from, for example, cryo-electron tomography and backmap them into a finer simulation model. In addition to many biomembrane applications, this software brings us a step closer to simulating realistic biomembranes with molecular resolution. Here we provide several interesting showcases of the power of the software but leave a wide range of potential applications for interested users.

Bottom-up approach to explore alpha-amylase assisted membrane remodelling.

Soluble alpha-amylases play an important role in the catabolism of polysaccharides. In this work, we show that the malt α -amylase can interact with the lipid membrane and further alter its mechanical properties. Vesicle fluctuation spectroscopy is used for quantitative measurement of the membrane bending rigidity of phosphatidylcholines lipid vesicles from the shape fluctuation based on the whole contour of Giant Unilamellar Vesicles (GUVs). The bending rigidity of the 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipid vesicles in water increases significantly with the presence of 0.14 micromolar alpha-amylase (AA) in the exterior solution. It appears that the enzyme present in the external solution interacts with the outer layer of the bilayer membrane, leading to an asymmetry of the solution on either side of the bilayer membrane and altering its elasticity. At AA concentration of 1.5 micromolars and above, changes in the morphology of the GUV membrane are observed. The interaction between AA in the external solution and the external leaflet causes the bilayer membrane to curve spontaneously, leading to the formation of outbuds, giving a positive spontaneous curvature of C0 ≤ 0.05 µm-1 at ≈ 1 mg / ml of the AA concentration. We validate and characterize its concentration-dependent role in stabilizing the membrane curvature. Our findings indicate that the involvement of the enzyme, depending on the concentration, can have a considerable effect on the mechanical characteristics of the membrane.

Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation.

The shapes of cell membranes are largely regulated by membrane-associated, curvature-active proteins. Herein, we use a numerical model of the membrane, recently developed by us, with elongated membrane inclusions possessing spontaneous directional curvatures that could be different along, and perpendicular to, the membrane's long axis. We show that, due to membrane-mediated interactions, these curvature-inducing membrane-nematogens can aggregate spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these protein lattices. Furthermore, the elastic properties of the tubes, such as their compressional stiffness and persistence length, are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes.

Linking membrane physical properties and low temperature tolerance in arthropods.

Maintenance of membrane fluidity is of crucial importance in ectotherms experiencing thermal changes. This maintenance has in ectotherms most often been indicated using indirect measures of biochemical changes of phospholipid membranes, which is then assumed to modulate the physico-chemical properties of the membrane. Here, we measure bending rigidity characterizing the membrane flexibility of re-constituted membrane vesicles to provide a more direct link between membrane physical characteristics and low temperature tolerance. Bending rigidity of lipid bilayers was measured in vitro using Giant Unilamellar Vesicles formed from phospholipid extracts of the springtail, Folsomia candida. The bending rigidity of these membranes decreased when exposed to 0.4 vol% ethanol (0.23 mM/L). Springtails exposed to ethanol for 24h significantly increased their cold shock tolerance. Thus, by chemically inducing decreased membrane rigidity, we have shown a direct link between the physico-chemical properties of the membranes and the capacity to tolerate low temperature in a chill-susceptible arthropod.

Macromolecular Crowding Is Surprisingly Unable to Deform the Structure of a Model Biomolecular Condensate.

The crowded interior of a living cell makes performing experiments on simpler in vitro systems attractive. Although these reveal interesting phenomena, their biological relevance can be questionable. A topical example is the phase separation of intrinsically disordered proteins into biomolecular condensates, which is proposed to underlie the membrane-less compartmentalization of many cellular functions. How a cell reliably controls biochemical reactions in compartments open to the compositionally-varying cytoplasm is an important question for understanding cellular homeostasis. Computer simulations are often used to study the phase behavior of model biomolecular condensates, but the number of relevant parameters increases as the number of protein components increases. It is unfeasible to exhaustively simulate such models for all parameter combinations, although interesting phenomena are almost certainly hidden in their high-dimensional parameter space. Here, we have studied the phase behavior of a model biomolecular condensate in the presence of a polymeric crowding agent. We used a novel compute framework to execute dozens of simultaneous simulations spanning the protein/crowder concentration space. We then combined the results into a graphical representation for human interpretation, which provided an efficient way to search the model's high-dimensional parameter space. We found that steric repulsion from the crowder drives a near-critical system across the phase boundary, but the molecular arrangement within the resulting biomolecular condensate is rather insensitive to the crowder concentration and molecular weight. We propose that a cell may use the local cytoplasmic concentration to assist the formation of biomolecular condensates, while relying on the dense phase to reliably provide a stable, structured, fluid milieu for cellular biochemistry despite being open to its changing environment.

Morphometric image analysis of giant vesicles: a new tool for quantitative thermodynamics studies of phase separation in lipid membranes.

We have developed a strategy to determine lengths and orientations of tie lines in the coexistence region of liquid-ordered and liquid-disordered phases of cholesterol containing ternary lipid mixtures. The method combines confocal-fluorescence-microscopy image stacks of giant unilamellar vesicles (GUVs), a dedicated 3D-image analysis, and a quantitative analysis based in equilibrium thermodynamic considerations. This approach was tested in GUVs composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine/1,2-palmitoyl-sn-glycero-3-phosphocholine/cholesterol. In general, our results show a reasonable agreement with previously reported data obtained by other methods. For example, our computed tie lines were found to be nonhorizontal, indicating a difference in cholesterol content in the coexisting phases. This new, to our knowledge, analytical strategy offers a way to further exploit fluorescence-microscopy experiments in GUVs, particularly retrieving quantitative data for the construction of three lipid-component-phase diagrams containing cholesterol.

Mechanics and dynamics of triglyceride-phospholipid model membranes: Implications for cellular properties and function.

We demonstrate here that triolein alters the mechanical properties of phospholipid membranes and induces extraordinary conformational dynamics. Triolein containing membranes exhibit fluctuations up to size range of 100µm and with the help of these are e.g. able to squeeze through narrow passages between neighbouring structures. Triolein-phosphatidylcholine membranes were found to have bending rigidity significantly lower than that of corresponding pure phosphatidylcholine membrane. Moreover, the triolein containing membranes were found to be reluctant to fuse, which is in good accordance with larger lamellar distances observed in the TOPOPC membranes. These findings suggest repulsion between adjacent membranes. We provide a comprehensive discussion on the possible explanations for the observed mechanics and dynamics in the TOPOPC system and on their potential cellular implications.