Topology recapitulates morphogenesis of neuronal dendrites.

Branching allows neurons to make synaptic contacts with large numbers of other neurons, facilitating the high connectivity of nervous systems. Neuronal arbors have geometric properties such as branch lengths and diameters that are optimal in that they maximize signaling speeds while minimizing construction costs. In this work, we asked whether neuronal arbors have topological properties that may also optimize their growth or function. We discovered that for a wide range of invertebrate and vertebrate neurons the distributions of their subtree sizes follow power laws, implying that they are scale invariant. The power-law exponent distinguishes different neuronal cell types. Postsynaptic spines and branchlets perturb scale invariance. Through simulations, we show that the subtree-size distribution depends on the symmetry of the branching rules governing arbor growth and that optimal morphologies are scale invariant. Thus, the subtree-size distribution is a topological property that recapitulates the functional morphology of dendrites.

A kinesin-1 adaptor complex controls bimodal slow axonal transport of spectrin in Caenorhabditis elegans.

An actin-spectrin lattice, the membrane periodic skeleton (MPS), protects axons from breakage. MPS integrity relies on spectrin delivery via slow axonal transport, a process that remains poorly understood. We designed a probe to visualize endogenous spectrin dynamics at single-axon resolution in vivo. Surprisingly, spectrin transport is bimodal, comprising fast runs and movements that are 100-fold slower than previously reported. Modeling and genetic analysis suggest that the two rates are independent, yet both require kinesin-1 and the coiled-coil proteins UNC-76/FEZ1 and UNC-69/SCOC, which we identify as spectrin-kinesin adaptors. Knockdown of either protein led to disrupted spectrin motility and reduced distal MPS, and UNC-76 overexpression instructed excessive transport of spectrin. Artificially linking spectrin to kinesin-1 drove robust motility but inefficient MPS assembly, whereas impairing MPS assembly led to excessive spectrin transport, suggesting a balance between transport and assembly. These results provide insight into slow axonal transport and MPS integrity.

Herding of proteins by the ends of shrinking polymers.

The control of biopolymer length is mediated by proteins that localize to polymer ends and regulate polymerization dynamics. Several mechanisms have been proposed to achieve end localization. Here, we propose a novel mechanism by which a protein that binds to a shrinking polymer and slows its shrinkage will be spontaneously enriched at the shrinking end through a "herding" effect. We formalize this process using both lattice-gas and continuum descriptions, and we present experimental evidence that the microtubule regulator spastin employs this mechanism. Our findings extend to more general problems involving diffusion within shrinking domains.

Cilia function as calcium-mediated mechanosensors that instruct left-right asymmetry.

The breaking of bilateral symmetry in most vertebrates is critically dependent upon the motile cilia of the embryonic left-right organizer (LRO), which generate a directional fluid flow; however, it remains unclear how this flow is sensed. Here, we demonstrated that immotile LRO cilia are mechanosensors for shear force using a methodological pipeline that combines optical tweezers, light sheet microscopy, and deep learning to permit in vivo analyses in zebrafish. Mechanical manipulation of immotile LRO cilia activated intraciliary calcium transients that required the cation channel Polycystin-2. Furthermore, mechanical force applied to LRO cilia was sufficient to rescue and reverse cardiac situs in zebrafish that lack motile cilia. Thus, LRO cilia are mechanosensitive cellular levers that convert biomechanical forces into calcium signals to instruct left-right asymmetry.

Dynamic microtubules slow down during their shrinkage phase.

Microtubules are dynamic polymers that undergo stochastic transitions between growing and shrinking phases. The structural and chemical properties of these phases remain poorly understood. The transition from growth to shrinkage, termed catastrophe, is not a first-order reaction but rather a multistep process whose frequency increases with the growth time: the microtubule ages as the older microtubule tip becomes more unstable. Aging shows that the growing phase is not a single state but comprises several substates of increasing instability. To investigate whether the shrinking phase is also multistate, we characterized the kinetics of microtubule shrinkage following catastrophe using an in vitro reconstitution assay with purified tubulins. We found that the shrinkage speed is highly variable across microtubules and that the shrinkage speed of individual microtubules slows down over time by as much as several fold. The shrinkage slowdown was observed in both fluorescently labeled and unlabeled microtubules as well as in microtubules polymerized from tubulin purified from different species, suggesting that the shrinkage slowdown is a general property of microtubules. These results indicate that microtubule shrinkage, like catastrophe, is time dependent and that the shrinking microtubule tip passes through a succession of states of increasing stability. We hypothesize that the shrinkage slowdown is due to destabilizing events that took place during growth, which led to multistep catastrophe. This suggests that the aging associated with growth is also manifested during shrinkage, with the older, more unstable growing tip being associated with a faster depolymerizing shrinking tip.

Predicting the locations of force-generating dyneins in beating cilia and flagella.

Cilia and flagella are slender cylindrical organelles whose bending waves propel cells through fluids and drive fluids across epithelia. The bending waves are generated by dynein motor proteins, ATPases whose force-generating activity changes over time and with position along the axoneme, the motile structure within the cilium. A key question is: where, in an actively beating axoneme, are the force-generating dyneins located? Answering this question is crucial for determining which of the conformational states adopted by the dynein motors generate the forces that bend the axoneme. The question is difficult to answer because the flagellum contains a large number of dyneins in a complex three-dimensional architecture. To circumvent this complexity, we used a molecular-mechanics approach to show how the bending moments produced by single pairs of dynein motors work against elastic and hydrodynamic forces. By integrating the individual motor activities over the length of the axoneme, we predict the locations of the force-generating dyneins in a beating axoneme. The predicted location depends on the beat frequency, the wavelength, and the elastic and hydrodynamic properties of the axoneme. To test these predictions using cryogenic electron microscopy, cilia with shorter wavelengths, such as found in Chlamydomonas, are more suitable than sperm flagella with longer wavelengths because, in the former, the lag between force and curvature is less dependent on the specific mechanical properties and experimental preparation.

The force required to remove tubulin from the microtubule lattice by pulling on its α-tubulin C-terminal tail.

Severing enzymes and molecular motors extract tubulin from the walls of microtubules by exerting mechanical force on subunits buried in the lattice. However, how much force is needed to remove tubulin from microtubules is not known, nor is the pathway by which subunits are removed. Using a site-specific functionalization method, we applied forces to the C-terminus of α-tubulin with an optical tweezer and found that a force of ~30 pN is required to extract tubulin from the microtubule wall. Additionally, we discovered that partial unfolding is an intermediate step in tubulin removal. The unfolding and extraction forces are similar to those generated by AAA-unfoldases. Lastly, we show that three kinesin-1 motor proteins can also extract tubulin from the microtubule lattice. Our results provide the first experimental investigation of how tubulin responds to mechanical forces exerted on its α-tubulin C-terminal tail and have implications for the mechanisms of severing enzymes and microtubule stability.

Dynamic instability of dendrite tips generates the highly branched morphologies of sensory neurons.

The highly ramified arbors of neuronal dendrites provide the substrate for the high connectivity and computational power of the brain. Altered dendritic morphology is associated with neuronal diseases. Many molecules have been shown to play crucial roles in shaping and maintaining dendrite morphology. However, the underlying principles by which molecular interactions generate branched morphologies are not understood. To elucidate these principles, we visualized the growth of dendrites throughout larval development of Drosophila sensory neurons and found that the tips of dendrites undergo dynamic instability, transitioning rapidly and stochastically between growing, shrinking, and paused states. By incorporating these measured dynamics into an agent-based computational model, we showed that the complex and highly variable dendritic morphologies of these cells are a consequence of the stochastic dynamics of their dendrite tips. These principles may generalize to branching of other neuronal cell types, as well as to branching at the subcellular and tissue levels.

Simultaneous Interference Reflection and Total Internal Reflection Fluorescence Microscopy for Imaging Dynamic Microtubules and Associated Proteins.

Several techniques have been employed for the direct visualization of cytoskeletal filaments and their associated proteins. Total-internal-reflection-fluorescence (TIRF) microscopy has a high signal-to-background ratio, but it suffers from photobleaching and photodamage of the fluorescent proteins. Label-free techniques such as interference reflection microscopy (IRM) and interferometric scattering microscopy (iSCAT) circumvent the problem of photobleaching but cannot readily visualize single molecules. This paper presents a protocol for combining IRM with a commercial TIRF microscope for the simultaneous imaging of microtubule-associated proteins (MAPs) and dynamic microtubules in vitro. This protocol allows for high-speed observation of MAPs interacting with dynamic microtubules. This improves on existing two-color TIRF setups by eliminating both the need for microtubule labeling and the need for several additional optical components, such as a second excitation laser. Both channels are imaged on the same camera chip to avoid image registration and frame synchronization problems. This setup is demonstrated by visualizing single kinesin molecules walking on dynamic microtubules.

In Vitro Reconstitution of Microtubule Dynamics and Severing Imaged by Label-Free Interference-Reflection Microscopy.

The dynamic architecture of the microtubule cytoskeleton is crucial for cell division, motility and morphogenesis. The dynamic properties of microtubules-growth, shrinkage, nucleation, and severing-are regulated by an arsenal of microtubule-associated proteins (MAPs). The activities of many of these MAPs have been reconstituted in vitro using microscope assays. As an alternative to fluorescence microscopy, interference-reflection microscopy (IRM) has been introduced as an easy-to-use, wide-field imaging technique that allows label-free visualization of microtubules with high contrast and speed. IRM circumvents several problems associated with fluorescence microscopy including the high concentrations of tubulin required for fluorescent labeling, the potential perturbation of function caused by the fluorophores, and the risks of photodamage. IRM can be implemented on a standard epifluorescence microscope at low cost and can be combined with fluorescence techniques like total-internal-reflection-fluorescence (TIRF) microscopy. Here we describe the experimental procedure to image microtubule dynamics and severing using IRM , providing practical tips and guidelines to resolve possible experimental hurdles.

Counting fluorescently labeled proteins in tissues in the spinning-disk microscope using single-molecule calibrations.

Quantification of molecular numbers and concentrations in living cells is critical for testing models of complex biological phenomena. Counting molecules in cells requires estimation of the fluorescence intensity of single molecules, which is generally limited to imaging near cell surfaces, in isolated cells, or where motions are diffusive. To circumvent this difficulty, we have devised a calibration technique for spinning-disk confocal microscopy, commonly used for imaging in tissues, that uses single-step bleaching kinetics to estimate the single-fluorophore intensity. To cross-check our calibrations, we compared the brightness of fluorophores in the SDC microscope to those in the total internal reflection and epifluorescence microscopes. We applied this calibration method to quantify the number of end-binding protein 1 (EB1)-eGFP in the comets of growing microtubule ends and to measure the cytoplasmic concentration of EB1-eGFP in sensory neurons in fly larvae. These measurements allowed us to estimate the dissociation constant of EB1-eGFP from the microtubules as well as the GTP-tubulin cap size. Our results show the unexplored potential of single-molecule imaging using spinning-disk confocal microscopy and provide a straightforward method to count the absolute number of fluorophores in tissues that can be applied to a wide range of biological systems and imaging techniques.

Structures of outer-arm dynein array on microtubule doublet reveal a motor coordination mechanism.

Thousands of outer-arm dyneins (OADs) are arrayed in the axoneme to drive a rhythmic ciliary beat. Coordination among multiple OADs is essential for generating mechanical forces to bend microtubule doublets (MTDs). Using electron microscopy, we determined high-resolution structures of Tetrahymena thermophila OAD arrays bound to MTDs in two different states. OAD preferentially binds to MTD protofilaments with a pattern resembling the native tracks for its distinct microtubule-binding domains. Upon MTD binding, free OADs are induced to adopt a stable parallel conformation, primed for array formation. Extensive tail-to-head (TTH) interactions between OADs are observed, which need to be broken for ATP turnover by the dynein motor. We propose that OADs in an array sequentially hydrolyze ATP to slide the MTDs. ATP hydrolysis in turn relaxes the TTH interfaces to effect free nucleotide cycles of downstream OADs. These findings lead to a model explaining how conformational changes in the axoneme produce coordinated action of dyneins.

The narrowing of dendrite branches across nodes follows a well-defined scaling law.

The systematic variation of diameters in branched networks has tantalized biologists since the discovery of da Vinci's rule for trees. Da Vinci's rule can be formulated as a power law with exponent two: The square of the mother branch's diameter is equal to the sum of the squares of those of the daughters. Power laws, with different exponents, have been proposed for branching in circulatory systems (Murray's law with exponent 3) and in neurons (Rall's law with exponent 3/2). The laws have been derived theoretically, based on optimality arguments, but, for the most part, have not been tested rigorously. Using superresolution methods to measure the diameters of dendrites in highly branched Drosophila class IV sensory neurons, we have found that these types of power laws do not hold. In their place, we have discovered a different diameter-scaling law: The cross-sectional area is proportional to the number of dendrite tips supported by the branch plus a constant, corresponding to a minimum diameter of the terminal dendrites. The area proportionality accords with a requirement for microtubules to transport materials and nutrients for dendrite tip growth. The minimum diameter may be set by the force, on the order of a few piconewtons, required to bend membrane into the highly curved surfaces of terminal dendrites. Because the observed scaling differs from Rall's law, we propose that cell biological constraints, such as intracellular transport and protrusive forces generated by the cytoskeleton, are important in determining the branched morphology of these cells.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells.

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Focal laser stimulation of fly nociceptors activates distinct axonal and dendritic Ca2+ signals.

Drosophila class IV neurons are polymodal nociceptors that detect noxious mechanical, thermal, optical, and chemical stimuli. Escape behaviors in response to attacks by parasitoid wasps are dependent on class IV cells, whose highly branched dendritic arbors form a fine meshwork that is thought to enable detection of the wasp's needle-like ovipositor barb. To understand how mechanical stimuli trigger cellular responses, we used a focused 405-nm laser to create highly localized lesions to probe the precise position needed to evoke responses. By imaging calcium signals in dendrites, axons, and soma in response to stimuli of varying positions, intensities, and spatial profiles, we discovered that there are two distinct nociceptive pathways. Direct stimulation to dendrites (the contact pathway) produces calcium responses in axons, dendrites, and the cell body, whereas stimulation adjacent to the dendrite (the noncontact pathway) produces calcium responses in the axons only. We interpret the noncontact pathway as damage to adjacent cells releasing diffusible molecules that act on the dendrites. Axonal responses have higher sensitivities and shorter latencies. In contrast, dendritic responses have lower sensitivities and longer latencies. Stimulation of finer, distal dendrites leads to smaller responses than stimulation of coarser, proximal dendrites, as expected if the contact response depends on the geometric overlap of the laser profile and the dendrite diameter. Because the axon signals to the central nervous system to trigger escape behaviors, we propose that the density of the dendritic meshwork is high not only to enable direct contact with the ovipositor but also to enable neuronal activation via diffusing signals from damaged surrounding cells. Dendritic contact evokes responses throughout the dendritic arbor, even to regions distant and distal from the stimulus. These dendrite-wide calcium signals may facilitate hyperalgesia or cellular morphological changes after dendritic damage.

Cutting, Amplifying, and Aligning Microtubules with Severing Enzymes.

Microtubule-severing enzymes - katanin, spastin, fidgetin - are related AAA-ATPases that cut microtubules into shorter filaments. These proteins, also called severases, are involved in a wide range of cellular processes including cell division, neuronal development, and tissue morphogenesis. Paradoxically, severases can amplify the microtubule cytoskeleton and not just destroy it. Recent work on spastin and katanin has partially resolved this paradox by showing that these enzymes are strong promoters of microtubule growth. Here, we review recent structural and biophysical advances in understanding the molecular mechanisms of severing and growth promotion that provide insight into how severing enzymes shape microtubule networks.

Purification of Ciliary Tubulin from Chlamydomonas reinhardtii.

Cilia and flagella play essential roles in environmental sensing, cell locomotion, and development. These organelles possess a central microtubule-based structure known as the axoneme, which serves as a scaffold and is crucial for the function of cilia. Despite their key roles, the biochemical and biophysical properties of the ciliary proteins are poorly understood. To address this issue, we have developed a novel method to purify functional tubulins from different parts of the axoneme, namely the central pair and B-tubule. We use the biflagellate green alga Chlamydomonas reinhardtii, a model organism for studying cilia due to the conserved structure of this organelle, availability of genetic tools and a large collection of mutant strains. Our method yields highly purified functional axonemal tubulins in sufficient quantities to be used for in vitro biochemical and biophysical studies, such as microtubule dynamic assays. It takes 7 to 8 days to grow enough cells; the isolation of the flagella and the purification of the axonemal tubulins require an additional two full days.© 2020 Wiley Periodicals LLC. Basic Protocol 1: Growth and harvest of large volume of cell culture Support Protocol: Assembly of homemade concentration apparatus Basic Protocol 2: Isolation of flagella Basic Protocol 3: Tubulin extraction and purification.

Contribution of increasing plasma membrane to the energetic cost of early zebrafish embryogenesis.

How do early embryos allocate the resources stored in the sperm and egg? Recently, we established isothermal calorimetry to measure heat dissipation by living zebra-fish embryos and to estimate the energetics of specific developmental events. During the reductive cleavage divisions, the rate of heat dissipation increases from ∼60 nJ · s-1 at the two-cell stage to ∼90 nJ · s-1 at the 1024-cell stage. Here we ask which cellular process(es) drive this increasing energetic cost. We present evidence that the cost is due to the increase in the total surface area of all the cells of the embryo. First, embryo volume stays constant during the cleavage stage, indicating that the increase is not due to growth. Second, the heat increase is blocked by nocodazole, which inhibits DNA replication, mitosis, and cell division; this suggests some aspect of cell proliferation contributes to these costs. Third, the heat increases in proportion to the total cell surface area rather than total cell number. Fourth, the heat increase falls within the range of the estimated costs of maintaining and assembling plasma membranes and associated proteins. Thus, the increase in total plasma membrane associated with cell proliferation is likely to contribute appreciably to the total energy budget of the embryo.