Mechanism of membrane nanotube formation by molecular motors

Phospholipid Membranes as Chemically and Functionally Tunable Materials

The sheet-like lipid bilayer is the fundamental structural component of all cell membranes. Its building blocks are phospholipids and cholesterol. Their amphiphilic structure spontaneously leads to the formation of a bilayer in aqueous environment. Lipids are not just structural elements. Individual lipid species, the lipid membrane structure, and lipid dynamics influence and regulate membrane protein function. An exciting field is emerging where the membrane-associated material properties of different bilayer systems are used in designing innovative solutions for widespread applications across various fields, such as the food industry, cosmetics, nano- and biomedicine, drug storage and delivery, biotechnology, nano- and biosensors, and computing. Here, the authors summarize what is known about how lipids determine the properties and functions of biological membranes and how this has been or can be translated into innovative applications. Based on recent progress in the understanding of membrane structure, dynamics, and physical properties, a perspective is provided on how membrane-controlled regulation of protein functions can extend current applications and even offer new applications.

Membrane Proteins and Membrane Curvature: Mutual Interactions and a Perspective on Disease Treatments

The pathogenesis of various diseases often involves an intricate interplay between membrane proteins and membrane curvature. Understanding the underlying mechanisms of this interaction could offer novel perspectives on disease treatment. In this review, we provide an introduction to membrane curvature and its association with membrane proteins. Furthermore, we delve into the impact and potential implications of this interaction in the context of disease treatment. Lastly, we discuss the prospects and challenges associated with harnessing these interactions for effective disease management, aiming to provide fresh insights into therapeutic strategies.

Spontaneous formation and growth kinetics of lipid nanotubules induced by passive nanoparticles

Lipid nanotubules (LNTs) are conduits that form on the membranes of cells and organelles, and they are ubiquitous in all forms of life from archaea and bacteria to plants and mammals. The formation, shape and dynamics of these LNTs are critical for cellular functions, supporting the transport of myriad cellular cargoes as well as communication within and between cells, and they are also widely believed to be responsible for exploitation of host cells by pathogens for the spread of infection and diseases. In vitro kinetic control of LNT formation can considerably enhance the scope of utilization of these structures for disease control and therapy. Here we report a new paradigm for spontaneous lipid nanotubulation, capturing the dynamical regimes of growth, stabilization and retraction of the tubes through the binding of synthetic nanoparticles on supported lipid bilayers (SLBs). The tubulation is determined by the spontaneous binding-unbinding of nanoparticles on the LNTs. The presented methodology could be used to rectify malfunctioning cellular tubules or to prevent the pathogenic spread of diseases through inhibition of cell-to-cell nanotubule formation.

Actomyosin-Assisted Pulling of Lipid Nanotubes from Lipid Vesicles and Cells

Molecular motors are pivotal for intracellular transport as well as cell motility and have great potential to be put to use outside cells. Here, we exploit engineered motor proteins in combination with self-assembly of actin filaments to actively pull lipid nanotubes from giant unilamellar vesicles (GUVs). In particular, actin filaments are bound to the outer GUV membrane and the GUVs are seeded on a heavy meromyosin-coated substrate. Upon addition of ATP, hollow lipid nanotubes with a length of tens of micrometer are pulled from single GUVs due to the motor activity. We employ the same mechanism to pull lipid nanotubes from different types of cells. We find that the length and number of nanotubes critically depends on the cell type, whereby suspension cells form bigger networks than adherent cells. This suggests that molecular machines can be used to exert forces on living cells to probe membrane-to-cortex attachment.

Light-inducible deformation of mitochondria in live cells

Mitochondria, the powerhouse of the cell, are dynamic organelles that undergo constant morphological changes. Increasing evidence indicates that mitochondria morphologies and functions can be modulated by mechanical cues. However, the mechano-sensing and -responding properties of mitochondria and the relation between mitochondrial morphologies and functions are unclear due to the lack of methods to precisely exert mechano-stimulation on and deform mitochondria inside live cells. Here, we present an optogenetic approach that uses light to induce deformation of mitochondria by recruiting molecular motors to the outer mitochondrial membrane via light-activated protein-protein hetero-dimerization. Mechanical forces generated by motor proteins distort the outer membrane, during which the inner mitochondrial membrane can also be deformed. Moreover, this optical method can achieve subcellular spatial precision and be combined with different optical dimerizers and molecular motors. This method presents a mitochondria-specific mechano-stimulator for studying mitochondria mechanobiology and the interplay between mitochondria shapes and functions.

PI(3,4)P2-mediated membrane tubulation promotes integrin trafficking and invasive cell migration

Invadopodia are integrin-mediated adhesions with abundant PI(3,4)P₂ However, the functional role of PI(3,4)P₂ in adhesion signaling remains unclear. Here, we find that the PI(3,4)P₂ biogenesis regulates the integrin endocytosis at invadopodia. PI(3,4)P₂ is locally produced by PIK3CA and SHIP2 and is concentrated at the trailing edge of the invadopodium arc. The PI(3,4)P₂-rich compartment locally forms small puncta (membrane buds) in a SNX9-dependent manner, recruits dynein activator Hook1 through AKTIP, and rearranges into micrometer-long tubular invaginations (membrane tubes). The uncurving membrane tube extends rapidly, follows the retrograde movement of dynein along microtubule tracks, and disconnects from the plasma membrane. Activated integrin-beta3 is locally internalized through the pathway of PI(3,4)P₂-mediated membrane invagination and is then actively recycled. Blockages of PI3K, SHIP2, and SNX9 suppress integrin-beta3 endocytosis, delay adhesion turnover, and impede transwell invasion of MEF-Src and MDA-MB-231 cells. Thus, the production of PI(3,4)P₂ promotes invasive cell migration by stimulating the trafficking of integrin receptor at the invadopodium.

Biological lipid nanotubes and their potential role in evolution

The membrane of cells and organelles are highly deformable fluid interfaces, and can take on a multitude of shapes. One distinctive and particularly interesting property of biological membranes is their ability to from long and uniform nanotubes. These nanoconduits are surprisingly omnipresent in all domains of life, from archaea, bacteria, to plants and mammals. Some of these tubes have been known for a century, while others were only recently discovered. Their designations are different in different branches of biology, e.g. they are called stromule in plants and tunneling nanotubes in mammals. The mechanical transformation of flat membranes to tubes involves typically a combination of membrane anchoring and external forces, leading to a pulling action that results in very rapid membrane nanotube formation - micrometer long tubes can form in a matter of seconds. Their radius is set by a mechanical balance of tension and bending forces. There also exists a large class of membrane nanotubes that form due to curvature inducing molecules. It seems plausible that nanotube formation and functionality in plants and animals may have been inherited from their bacterial ancestors during endosymbiotic evolution. Here we attempt to connect observations of nanotubes in different branches of biology, and outline their similarities and differences with the aim of providing a perspective on their joint functions and evolutionary origin.

Multicomponent and Multiphase Lipid Nanotubes Formed by Gliding Microtubule-Kinesin Motility and Phase-Separated Giant Unilamellar Vesicles

Cytoskeletal filaments and motor proteins are critical components in the transport and reorganization of membrane-based organelles in eukaryotic cells. Previous studies have recapitulated the microtubule-kinesin transport system in vitro to dynamically assemble large-scale nanotube networks from multilamellar liposomes and polymersomes. Moving toward more biologically relevant systems, the present work examines whether lipid nanotube (LNT) networks can be generated from giant unilamellar vesicles (GUVs) and subsequently characterizes how the lipid composition may be tuned to alter the dynamics, structure, and fluidity of networks. Here, we describe a two-step process in which microtubule motility (i) drives the transport and aggregation of GUVs to form structures with a decreased energy barrier for LNT formation and (ii) extrudes LNTs without destroying parent GUVs, allowing for the formation of large LNT networks. We further show that the lipid composition of the GUV influences formation and morphology of the extruded LNTs and associated networks. For example, LNTs formed from phase-separated GUVs (e.g., liquid-solid phase-separated and coexisting liquid-ordered and liquid-disordered phase-separated) display morphologies related to the specific phase behavior reflective of the parent GUVs. Overall, the ability to form nanotubes from compositionally complex vesicles opens the door to generating lipid networks that more closely mimic the structure and function of those found in cellular systems.

Artificial Cell Membranes Interfaced with Optical Tweezers: A Versatile Microfluidics Platform for Nanomanipulation and Mechanical Characterization

Cell lipid membranes are the site of vital biological processes, such as motility, trafficking, and sensing, many of which involve mechanical forces. Elucidating the interplay between such bioprocesses and mechanical forces requires the use of tools that apply and measure piconewton-level forces, e.g., optical tweezers. Here, we introduce the combination of optical tweezers with free-standing lipid bilayers, which are fully accessible on both sides of the membrane. In the vicinity of the lipid bilayer, optical trapping would normally be impossible due to optical distortions caused by pockets of the solvent trapped within the membrane. We solve this by drastically reducing the size of these pockets via tuning of the solvent and flow cell material. In the resulting flow cells, lipid nanotubes are straightforwardly pushed or pulled and reach lengths above half a millimeter. Moreover, the controlled pushing of a lipid nanotube with an optically trapped bead provides an accurate and direct measurement of important mechanical properties. In particular, we measure the membrane tension of a free-standing membrane composed of a mixture of dioleoylphosphatidylcholine (DOPC) and dipalmitoylphosphatidylcholine (DPPC) to be 4.6 × 10^-6 N/m. We demonstrate the potential of the platform for biophysical studies by inserting the cell-penetrating trans-activator of transcription (TAT) peptide in the lipid membrane. The interactions between the TAT peptide and the membrane are found to decrease the value of the membrane tension to 2.1 × 10^-6 N/m. This method is also fully compatible with electrophysiological measurements and presents new possibilities for the study of membrane mechanics and the creation of artificial lipid tube networks of great importance in intra- and intercellular communication.

Reconstitution reveals how myosin-VI self-organises to generate a dynamic mechanism of membrane sculpting

One enigma in biology is the generation, sensing and maintenance of membrane curvature. Curvature-mediating proteins have been shown to induce specific membrane shapes by direct insertion and nanoscopic scaffolding, while the cytoskeletal motors exert forces indirectly through microtubule and actin networks. It remains unclear, whether the manifold direct motorprotein-lipid interactions themselves constitute another fundamental route to remodel the membrane shape. Here we show, combining super-resolution-fluorescence microscopy and membrane-reshaping nanoparticles, that curvature-dependent lipid interactions of myosin-VI on its own, remarkably remodel the membrane geometry into dynamic spatial patterns on the nano- to micrometer scale. We propose a quantitative theoretical model that explains this dynamic membrane sculpting mechanism. The emerging route of motorprotein-lipid interactions reshaping membrane morphology by a mechanism of feedback and instability opens up hitherto unexplored avenues of membrane remodelling and links cytoskeletal motors to early events in the sequence of membrane sculpting in eukaryotic cell biology.

Neck linker docking is critical for Kinesin-1 force generation in cells but at a cost to motor speed and processivity

Kinesin force generation involves ATP-induced docking of the neck linker (NL) along the motor core. However, the roles of the proposed steps of NL docking, cover-neck bundle (CNB) and asparagine latch (N-latch) formation, during force generation are unclear. Furthermore, the necessity of NL docking for transport of membrane-bound cargo in cells has not been tested. We generated kinesin-1 motors impaired in CNB and/or N-latch formation based on molecular dynamics simulations. The mutant motors displayed reduced force output and inability to stall in optical trap assays but exhibited increased speeds, run lengths, and landing rates under unloaded conditions. NL docking thus enhances force production but at a cost to speed and processivity. In cells, teams of mutant motors were hindered in their ability to drive transport of Golgi elements (high-load cargo) but not peroxisomes (low-load cargo). These results demonstrate that the NL serves as a mechanical element for kinesin-1 transport under physiological conditions.

Membrane nanotube pearling restricted by confined polymers

Increasing evidence showed that membrane nanotubes readily undergo pearling in response to external stimuli, while long tubular membrane structures have been observed connecting cells and functioning as channels for intercellular transport, raising a fundamental question of how the stability of membrane nanotubes is maintained in the cellular environment. Here, combining dissipative particle dynamics simulations, free energy calculations, and a force analysis, we propose and demonstrate that nanotube pearling can be restricted by confined polymers, which can be DNA and protein chains transported through the nanotubes, or actin filaments participating in tube formation and elongation. Thermodynamically, nanotube pearling releases the membrane surface energy, but costs bending energies of both the membrane and the confined polymers. Following the mechanism, the pearling of nanotubes confining longer and stiffer polymers is more difficult as it costs larger polymer bending energies. In dynamics, nanotube pearling occurs by repelling polymers from the region of nanotube shrinking to that of swelling. Shorter polymers can be readily repelled owing to the unbalanced force exerted by the shrinking tube region, whereas longer polymers tend to be trapped at the shrinking region to retard the nanotube pearling. Besides the low surface tension maintained by lipid reservoirs kept in living cells, our results supplement the explanation for the stability of membrane nanotubes, and open up a new avenue to manipulate the shape deformation of tubular membrane structures for study of many biological processes.

Mechanics of cellular packing of nanorods with finite and non-uniform diameters

To understand the mechanics of cellular/intracellular packing of one-dimensional nanomaterials, we performed theoretical analysis and molecular dynamics simulations to investigate how the morphology and mechanical behaviors of a lipid vesicle are regulated by encapsulated rigid nanorods of finite and non-uniform diameters, including a cylindrical rod, a rod with widened ends, a cone-shaped rod, and a screwdriver-shaped rod. As the rod length increases, the vesicle evolves from a sphere into different shapes, such as a lemon, a conga drum, a cherry, a bowling pin, or a tubular shape for long and thick rods. The contact between the vesicle protrusion and the rod plays an important role in regulating the vesicle tubulation, membrane tension, and axial contact force on the rod. Our analysis provides a theoretical basis to understand a wide range of experiments on morphological transitions that occur in cellular packing of actin or microtubule bundles, mitotic cell division, and intracellular packing of carbon nanotubes.

Friction Mediates Scission of Tubular Membranes Scaffolded by BAR Proteins

Membrane scission is essential for intracellular trafficking. While BAR domain proteins such as endophilin have been reported in dynamin-independent scission of tubular membrane necks, the cutting mechanism has yet to be deciphered. Here, we combine a theoretical model, in vitro, and in vivo experiments revealing how protein scaffolds may cut tubular membranes. We demonstrate that the protein scaffold bound to the underlying tube creates a frictional barrier for lipid diffusion; tube elongation thus builds local membrane tension until the membrane undergoes scission through lysis. We call this mechanism friction-driven scission (FDS). In cells, motors pull tubes, particularly during endocytosis. Through reconstitution, we show that motors not only can pull out and extend protein-scaffolded tubes but also can cut them by FDS. FDS is generic, operating even in the absence of amphipathic helices in the BAR domain, and could in principle apply to any high-friction protein and membrane assembly.

Vesicle Size Regulates Nanotube Formation in the Cell

Intracellular membrane nanotube formation and its dynamics play important roles for cargo transportation and organelle biogenesis. Regarding the regulation mechanisms, while much attention has been paid on the lipid composition and its associated protein molecules, effects of the vesicle size has not been studied in the cell. Giant unilamellar vesicles (GUVs) are often used for in vitro membrane deformation studies, but they are much larger than most intracellular vesicles and the in vitro studies also lack physiological relevance. Here, we use lysosomes and autolysosomes, whose sizes range between 100 nm and 1 μm, as model systems to study the size effects on nanotube formation both in vivo and in vitro. Single molecule observations indicate that driven by kinesin motors, small vesicles (100–200 nm) are mainly transported along the tracks while a remarkable portion of large vesicles (500–1000 nm) form nanotubes. This size effect is further confirmed by in vitro reconstitution assays on liposomes and purified lysosomes and autolysosomes. We also apply Atomic Force Microscopy (AFM) to measure the initiation force for nanotube formation. These results suggest that the size-dependence may be one of the mechanisms for cells to regulate cellular processes involving membrane-deformation, such as the timing of tubulation-mediated vesicle recycling.

Membrane curvature at a glance

Membrane curvature is an important parameter in defining the morphology of cells, organelles and local membrane subdomains. Transport intermediates have simpler shapes, being either spheres or tubules. The generation and maintenance of curvature is of central importance for maintaining trafficking and cellular functions. It is possible that local shapes in complex membranes could help to define local subregions. In this Cell Science at a Glance article and accompanying poster, we summarize how generating, sensing and maintaining high local membrane curvature is an active process that is mediated and controlled by specialized proteins using general mechanisms: (i) changes in lipid composition and asymmetry, (ii) partitioning of shaped transmembrane domains of integral membrane proteins or protein or domain crowding, (iii) reversible insertion of hydrophobic protein motifs, (iv) nanoscopic scaffolding by oligomerized hydrophilic protein domains and, finally, (v) macroscopic scaffolding by the cytoskeleton with forces generated by polymerization and by molecular motors. We also summarize some of the discoveries about the functions of membrane curvature, where in addition to providing cell or organelle shape, local curvature can affect processes like membrane scission and fusion as well as protein concentration and enzyme activation on membranes.

Bioinspired membrane-based systems for a physical approach of cell organization and dynamics: usefulness and limitations

Being at the periphery of each cell compartment and enclosing the entire cell while interacting with a large part of cell components, cell membranes participate in most of the cell's vital functions. Biologists have worked for a long time on deciphering how membranes are organized, how they contribute to trafficking, motility, cytokinesis, cell-cell communication, information transport, etc., using top-down approaches and always more advanced techniques. In contrast, physicists have developed bottom-up approaches and minimal model membrane systems of growing complexity in order to build up general models that explain how cell membranes work and how they interact with proteins, e.g. the cytoskeleton. We review the different model membrane systems that are currently available, and how they can help deciphering cell functioning, but also list their limitations. Model membrane systems are also used in synthetic biology and can have potential applications beyond basic research. We discuss the possible synergy between the development of complex in vitro membrane systems in a biological context and for technological applications. Questions that could also be discussed are: what can we still do with synthetic systems, where do we stop building up and which are the alternative solutions?

Dynamic assembly of polymer nanotube networks via kinesin powered microtubule filaments

We describe for the first time how biological nanomotors may be used to actively self-assemble mesoscale networks composed of diblock copolymer nanotubes. The collective force generated by multiple kinesin nanomotors acting on a microtubule filament is large enough to overcome the energy barrier required to extract nanotubes from polymer vesicles comprised of poly(ethylene oxide-b-butadiene) in spite of the higher force requirements relative to extracting nanotubes from lipid vesicles. Nevertheless, large-scale polymer networks were dynamically assembled by the motors. These networks displayed enhanced robustness, persisting more than 24 h post-assembly (compared to 4-5 h for corresponding lipid networks). The transport of materials in and on the polymer membranes differs substantially from the transport on analogous lipid networks. Specifically, our data suggest that polymer mobility in nanotubular structures is considerably different from planar or 3D structures, and is stunted by 1D confinement of the polymer subunits. Moreover, quantum dots adsorbed onto polymer nanotubes are completely immobile, which is related to this 1D confinement effect and is in stark contrast to the highly fluid transport observed on lipid tubules.

Microtubule motors power plasma membrane tubulation in clathrin-independent endocytosis

How the plasma membrane is bent to accommodate clathrin-independent endocytosis remains uncertain. Recent studies suggest Shiga and cholera toxin induce membrane curvature required for their uptake into clathrin-independent carriers by binding and cross-linking multiple copies of their glycosphingolipid receptors on the plasma membrane. But it remains unclear if toxin-induced sphingolipid crosslinking provides sufficient mechanical force for deforming the plasma membrane, or if host cell factors also contribute to this process. To test this, we imaged the uptake of cholera toxin B-subunit into surface-derived tubular invaginations. We found that cholera toxin mutants that bind to only one glycosphingolipid receptor accumulated in tubules, and that toxin binding was entirely dispensable for membrane tubulations to form. Unexpectedly, the driving force for tubule extension was supplied by the combination of microtubules, dynein and dynactin, thus defining a novel mechanism for generating membrane curvature during clathrin-independent endocytosis.

Building endocytic pits without clathrin

How endocytic pits are built in clathrin- and caveolin-independent endocytosis still remains poorly understood. Recent insight suggests that different forms of clathrin-independent endocytosis might involve the actin-driven focusing of membrane constituents, the lectin-glycosphingolipid-dependent construction of endocytic nanoenvironments, and Bin-Amphiphysin-Rvs (BAR) domain proteins serving as scaffolding modules. We discuss the need for different types of internalization processes in the context of diverse cellular functions, the existence of clathrin-independent mechanisms of cargo recruitment and membrane bending from a biological and physical perspective, and finally propose a generic scheme for the formation of clathrin-independent endocytic pits.

Freely drawn single lipid nanotube patterns

LNTs are unique 3D structures made only of safe and abundant biomaterials by self-assembly. The current bottleneck for developing applications using LNTs is the lack of an easy technique to pattern them on substrates. We report a method to free-draw single lipid nanotube (LNT) patterns in any shape on surfaces with 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE) that takes an inverted hexagonal (HII) phase. We used pre-self-assembled LNTs or HII lipid blocks as a lipid reservoir from which new LNTs were pulled by applying a point load with a micromanipulator. The extreme simplicity of our technique originates from the fundamental nature of DOPE lipids that prefer a HII phase, while all the conventional approaches use PC lipids that form a lamellar phase. By adjusting the surface properties with polyelectrolyte multilayers, the created single LNT objects are able to remain adhered to the surface for over a week. Importantly, it could be shown that two vesicles loaded with caged fluorescent molecules were able to fuse well with a LNT, enabling diffusive transport of uncaged fluorescent molecules from one vesicle to the other.

Nature's lessons in design: nanomachines to scaffold, remodel and shape membrane compartments

Our understanding of the membrane sculpting capabilities of proteins from experimental model systems could be used to construct functional compartmentalised architectures for the engineering of synthetic cells.

Controlled growth of filamentous fatty acid vesicles under flow

The earliest forms of cellular life would have required a membrane compartment capable of growth and division. Fatty acid vesicles are an attractive model of protocell membranes, as they can grow into filamentous vesicles that readily divide while retaining their contents. In order to study vesicle growth, we have developed a method for immobilizing multilamellar fatty acid vesicles on modified glass surfaces and inducing filamentous membrane growth under flow. Filament formation strictly depended on the presence of freshly neutralized fatty acid micelles in the flow chamber. Using light microscopy, we observed a strong dependence of initial growth velocity on initial vesicle size, suggesting that new fatty acid molecules were incorporated into the membrane over the entire external surface of the vesicle. We examined the influences of flow rate, fatty acid concentration, and salt concentration on filamentous growth and observed drastic shape changes, including membrane pearling, of preexisting membrane tubules in response to osmotic stress. These results illustrate the versatility of flow studies for exploring the process of fatty acid vesicle growth following exposure to free fatty acids.

Reversible membrane pearling in live cells upon destruction of the actin cortex

Membrane pearling in live cells is observed when the plasma membrane is depleted of its support, the cortical actin network. Upon efficient depolymerization of actin, pearls of variable size are formed, which are connected by nanotubes of ~40 nm diameter. We show that formation of the membrane tubes and their transition into chains of pearls do not require external tension, and that they neither depend on microtubule-based molecular motors nor pressure generated by myosin-II. Pearling thus differs from blebbing. The pearling state is stable as long as actin is prevented from polymerizing. When polymerization is restored, the pearls are retracted into the cell, indicating continuity of the membrane. Our data suggest that the alternation of pearls and strings is an energetically favored state of the unsupported plasma membrane, and that one of the functions of the actin cortex is to prevent the membrane from spontaneously assuming this configuration.

A coupled model of fast axonal transport of organelles and slow axonal transport of tau protein

We have developed a model that accounts for the effect of a non-uniform distribution of tau protein along the axon length on fast axonal transport of intracellular organelles. The tau distribution is simulated by using a slow axonal transport model; the numerically predicted tau distributions along the axon length were validated by comparing them with experimentally measured tau distributions reported in the literature. We then developed a fast axonal transport model for organelles that accounts for the reduction of kinesin attachment rate to microtubules by tau. We investigated organelle transport for two situations: (1) a uniform tau distribution and (2) a non-uniform tau distribution predicted by the slow axonal transport model. We found that non-uniform tau distributions observed in healthy axons (an increase in tau concentration towards the axon tip) result in a significant enhancement of organelle transport towards the synapse compared with the uniform tau distribution with the same average amount of tau. This suggests that tau may play the role of being an enhancer of organelle transport.

Mechanisms shaping cell membranes

Membranes of intracellular organelles are characterized by large curvatures with radii of the order of 10-30nm. While, generally, membrane curvature can be a consequence of any asymmetry between the membrane monolayers, generation of large curvatures requires the action of mechanisms based on specialized proteins. Here we discuss the three most relevant classes of such mechanisms with emphasis on the physical requirements for proteins to be effective in generation of membrane curvature. We provide new quantitative estimates of membrane bending by shallow hydrophobic insertions and compare the efficiency of the insertion mechanism with those of the protein scaffolding and crowding mechanisms.

What tau distribution maximizes fast axonal transport toward the axonal synapse?

This theoretical research is aimed at investigating the question of why tau protein concentration exhibits a proximal-distal increase in healthy axons and a proximal-distal decrease in degenerating axons in Alzheimer's disease. We developed a model of fast axonal transport toward the axon synapse. The model is based on recently published experimental results by Dixit et al. (2008) [1] who reported that the attachment rate of kinesin-1 to MTs is reduced by tau. Cytoplasmic dynein is affected less by tau (dynein is affected at much higher tau concentrations than those that affect kinesin-1). We used the model to investigate the effect of various tau distributions along the axon length on organelle flux toward the axon synapse. We found that a proximal-distal increase in tau concentration leads to a higher organelle flux while a proximal-distal decrease in tau concentration leads to a smaller organelle flux than a uniform tau concentration. We also computed what tau distribution would give the largest organelle flux toward the synapse. We found that in order to maximize organelle flux, the tau concentration has to be at its minimum level in the proximal axon and its maximum level at the distal axon, which is in agreement with the bang-bang principle in optimal control theory.

Modeling stochastic kinetics of molecular machines at multiple levels: from molecules to modules

A molecular machine is either a single macromolecule or a macromolecular complex. In spite of the striking superficial similarities between these natural nanomachines and their man-made macroscopic counterparts, there are crucial differences. Molecular machines in a living cell operate stochastically in an isothermal environment far from thermodynamic equilibrium. In this mini-review we present a catalog of the molecular machines and an inventory of the essential toolbox for theoretically modeling these machines. The tool kits include 1), nonequilibrium statistical-physics techniques for modeling machines and machine-driven processes; and 2), statistical-inference methods for reverse engineering a functional machine from the empirical data. The cell is often likened to a microfactory in which the machineries are organized in modular fashion; each module consists of strongly coupled multiple machines, but different modules interact weakly with each other. This microfactory has its own automated supply chain and delivery system. Buoyed by the success achieved in modeling individual molecular machines, we advocate integration of these models in the near future to develop models of functional modules. A system-level description of the cell from the perspective of molecular machinery (the mechanome) is likely to emerge from further integrations that we envisage here.

Cooperative force generation of KIF1A Brownian motors

KIF1A is a kinesin motor protein that can work processively in a monomeric (single-headed) form by using a noise-driven ratchet mechanism. Here, we show that the combination of a passive diffusive state and finite-time kinetics of adenosine triphosphate hydrolysis provides a powerful mechanism of cooperative force generation, implying for instance that ∼10 monomeric KIF1As can team up to become ∼100 times stronger than a single one. Consequently, we propose that KIF1A could outperform conventional (double-headed) kinesin collectively and thus explain its specificity in axonal trafficking. We elucidate the cooperativity mechanism with a lattice model that includes multiparticle transitions.

Protein transport in the connecting cilium of a photoreceptor cell: modeling the effects of bidirectional protein transitions between the diffusion-driven and motor-driven kinetic states

Physics of protein transport through the connecting cilium (CC) of a photoreceptor cell is a long-standing question in cellular biology. There is evidence implicating both molecular motor-driven and diffusion-driven modes of intracellular transport. Based on available experimental clues, this paper develops a new model for intraflagellar transport (IFT) of proteins synthesized in the inner segment and transported through the CC to the outer segment of a photoreceptor cell. The model accounts for the competition between two modes of protein transport: molecular motor-driven transport and diffusion. The obtained solutions made it possible to calculate how the number of protein molecules transported through the CC at a given time depends on their diffusivity. Modeling results were compared with published experimental estimates, and conclusions about possible contributions of diffusion to IFT were made.

A continuous network of lipid nanotubes fabricated from the gliding motility of kinesin powered microtubule filaments

Synthetic interconnected lipid nanotube networks were fabricated on the millimeter scale based on the simple, cooperative interaction between phospholipid vesicles and kinesin-microtubule (MT) transport systems. More specifically, taxol-stabilized MTs, in constant 2D motion via surface absorbed kinesin, extracted and extended lipid nanotube networks from large Lα phase multilamellar liposomes (5-25 μm). Based on the properties of the inverted motility geometry, the total size of these nanofluidic networks was limited by MT surface density, molecular motor energy source (ATP), and total amount and physical properties of lipid source material. Interactions between MTs and extended lipid nanotubes resulted in bifurcation of the nanotubes and ultimately the generation of highly branched networks of fluidically connected nanotubes. The network bifurcation was easily tuned by changing the density of microtubules on the surface to increase or decrease the frequency of branching. The ability of these networks to capture nanomaterials at the membrane surface with high fidelity was subsequently demonstrated using quantum dots as a model system. The diffusive transport of quantum dots was also characterized with respect to using these nanotube networks for mass transport applications.

Numerical investigation of axonal cargo rerouting in a dendrite: a three kinetic state model

The purpose of this paper is to develop a three-kinetic state model to investigate axonal cargo rerouting in a dendrite. It is assumed that axonal cargos are transported by kinesin motors; they can enter dendrites riding on plus-end-out microtubules (MTs). If this happens, cargos are rerouted by dissociating from these MTs and associating with minus-end-out MTs. The same kinesin motors then move axonal cargos out of the dendrite. The model predicts how far axonal cargos can penetrate into the dendrite, concentrations of various populations of axonal cargos, and cargo fluxes.

Modeling of Transient Transport of Soluble Proteins in the Connecting Cilium of a Photoreceptor Cell

A minimal mathematical model describing mass transport in the connecting cilium (CC) of a photoreceptor cell in response to a suddenly increased protein concentration at the base of the CC is developed. Dimensionless governing equations and dimensionless parameters are identified. Analytical solutions are obtained for concentrations of free (diffusion-driven) and motor-driven proteins. The obtained solutions make it possible to predict mass transfer in the CC as a function of two dimensionless transport parameters involved in the model: the diffusivity of free soluble proteins and the transition rate from the diffusion-driven to the motor-driven state. Sensitivities of the obtained solutions to these two parameters are discussed.

Molecular structure of membrane tethers

Membrane tethers are nanotubes formed by a lipid bilayer. They play important functional roles in cell biology and provide an experimental window on lipid properties. Tethers have been studied extensively in experiments and described by theoretical models, but their molecular structure remains unknown due to their small diameters and dynamic nature. We used molecular dynamics simulations to obtain molecular-level insight into tether formation. Tethers were pulled from single-component lipid bilayers by application of an external force to a lipid patch along the bilayer normal or by lateral compression of a confined bilayer. Tether development under external force proceeded by viscoelastic protrusion followed by viscous lipid flow. Weak forces below a threshold value produced only a protrusion. Larger forces led to a crossover to tether elongation, which was linear at a constant force. Under lateral compression, tethers formed from undulations of unrestrained bilayer area. We characterized in detail the tether structure and its formation process, and obtained the material properties of the membrane. To our knowledge, these results provide the first molecular view of membrane tethers.

Studying in vitro membrane curvature recognition by proteins and its role in vesicular trafficking

In recent years, the interest for proteins that exert key functions in vesicular trafficking through their ability to sense or induce positive membrane curvature has expanded. In this chapter, we first present simple protocols to determine whether a protein targets positively curved membranes with liposomes of well-defined size. Next we describe more sophisticated approaches based on the controlled deformation of giant liposomes. These approaches allow visualization and quantification of protein binding to membrane regions of high curvature by real-time fluorescence microscopy. Last we describe several functional assays to measure how membrane curvature controls the activation state of Arf1 via ArfGAP1 or the asymmetric tethering between flat and curved membranes via the golgin GMAP-210.

Colocalization of serum amyloid a with microtubules in human coronary artery endothelial cells

Serum amyloid A (SAA) acts as a major acute phase protein and represents a sensitive and accurate marker of inflammation. Besides its hepatic origin, as the main source of serum SAA, this protein is also produced extrahepatically. The mRNA levels of SAA become significantly elevated following proinflammatory stimuli, as well as, are induced through their own positive feedback in human primary coronary artery endothelial cells. However, the intracellular functions of SAA are so far unknown. Colocalization of SAA with cytoskeletal filaments has previously been proposed, so we analyzed the colocalization of SAA with all three cytoskeletal elements: actin filaments, vimentin filaments, and microtubules. Immunofluorescent double-labeling analyses confirmed by PLA method revealed a strict colocalization of SAA with microtubules and a very infrequent attachment to vimentin while the distribution of actin filaments appeared clearly separated from SAA staining. Also, no significant colocalization was found between SAA and endomembranes labeled with the fluorescent lipid stain DiO₆. However, SAA appears to be located also unbound in the cytosol, as well as inside the nucleus and within nanotubes extending from the cells or bridging neighboring cells. These different locations of SAA in endothelial cells strongly indicate multiple potential functions of this protein.

Analytical expressions for the shape of axisymmetric membranes with multiple domains

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.

Cooperativity of self-organized Brownian motors pulling on soft cargoes

We study the cooperative dynamics of Brownian motors moving along a one-dimensional track when an external load is applied to the leading motor, mimicking molecular motors pulling on membrane-bound cargoes in intracellular traffic. Due to the asymmetric loading, self-organized motor clusters form spontaneously. We model the motors with a two-state noise-driven ratchet formulation and study analytically and numerically the collective velocity-force and efficiency-force curves resulting from mutual interactions, mostly hard-core repulsion and weak (nonbinding) attraction. We analyze different parameter regimes including the limits of weak noise, mean-field behavior, rigid coupling, and large numbers of motors, for the different interactions. We present a general framework to classify and quantify cooperativity. We show that asymmetric loading leads generically to enhanced cooperativity beyond the simple superposition of the effects of individual motors. For weakly attracting interactions, the cooperativity is mostly enhanced, including highly coordinated motion of motors and complex nonmonotonic velocity-force curves, leading to self-regulated clusters. The dynamical scenario is enriched by resonances associated to commensurability of different length scales. Large clusters exhibit synchronized dynamics and bidirectional motion. Biological implications are discussed.