Horizontal Magnetic Tweezers to Directly Measure the Force-Velocity Relationship for Multiple Kinesin Motors.

Transport of intracellular cargo along cytoskeletal filaments is often achieved by the concerted action of multiple motor molecules. While single-molecule studies have provided profound insight into the mechano-chemical principles and force generation of individual motors, studies on multi-motor systems are less advanced. Here, a horizontal magnetic-tweezers setup is applied, capable of producing up to 150 pN of horizontal force onto 2.8 µm superparamagnetic beads, to motor-propelled cytoskeletal filaments. It is found that kinesin-1 driven microtubules decorated with individual beads display frequent transitions in their gliding velocities which we attribute to dynamic changes in the number of engaged motors. Applying defined temporal force-ramps the force-velocity relationship is directly measured for multi-motor transport. It is found that the stall forces of individual motors are approximately additive and collective backward motion of the transport system under super-stall forces is observed. The magnetic-tweezers apparatus is expected to be readily applicable to a wide range of molecular and cellular motility assays.

On the role of cell surface associated, mucin-like glycoproteins in the pennate diatom Craspedostauros australis (Bacillariophyceae).

Diatoms are single-celled microalgae with silica-based cell walls (frustules) that are abundantly present in aquatic habitats, and form the basis of the food chain in many ecosystems. Many benthic diatoms have the remarkable ability to glide on all natural or man-made underwater surfaces using a carbohydrate- and protein-based adhesive to generate traction. Previously, three glycoproteins, termed FACs (Frustule Associated Components), have been identified from the common fouling diatom Craspedostauros australis and were implicated in surface adhesion through inhibition studies with a glycan-specific antibody. The polypeptide sequences of FACs remained unknown, and it was unresolved whether the FAC glycoproteins are indeed involved in adhesion, or whether this is achieved by different components sharing the same glycan epitope with FACs. Here we have determined the polypeptide sequences of FACs using peptide mapping by LC-MS/MS. Unexpectedly, FACs share the same polypeptide backbone (termed CaFAP1), which has a domain structure of alternating Cys-rich and Pro-Thr/Ser-rich regions reminiscent of the gel-forming mucins. By developing a genetic transformation system for C. australis, we were able to directly investigate the function of CaFAP1-based glycoproteins in vivo. GFP-tagging of CaFAP1 revealed that it constitutes a coat around all parts of the frustule and is not an integral component of the adhesive. CaFAP1-GFP producing transformants exhibited the same properties as wild type cells regarding surface adhesion and motility speed. Our results demonstrate that FAC glycoproteins are not involved in adhesion and motility, but might rather act as a lubricant to prevent fouling of the diatom surface.

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.

Multivalent electrostatic microtubule interactions of synthetic peptides are sufficient to mimic advanced MAP-like behavior.

Microtubule-associated proteins (MAPs) are a functionally highly diverse class of proteins that help to adjust the shape and function of the microtubule cytoskeleton in space and time. For this purpose, MAPs structurally support microtubules, modulate their dynamic instability, or regulate the activity of associated molecular motors. The microtubule-binding domains of MAPs are structurally divergent, but often depend on electrostatic interactions with the negatively charged surface of the microtubule. This suggests that the surface exposure of positive charges rather than a certain structural fold is sufficient for a protein to associate with microtubules. Consistently, positively charged artificial objects have been shown to associate with microtubules and to diffuse along their lattice. Natural MAPs, however, show a more sophisticated functionality beyond lattice-diffusion. Here, we asked whether basic electrostatic interactions are sufficient to also support advanced MAP functionality. To test this hypothesis, we studied simple positively charged peptide sequences for the occurrence of typical MAP-like behavior. We found that a multivalent peptide construct featuring four lysine-alanine heptarepeats (starPEG-(KA7)4)-but not its monovalent KA7-subunits-show advanced, biologically relevant MAP-like behavior: starPEG-(KA7)4 binds microtubules in the low nanomolar range, diffuses along their lattice with the ability to switch between intersecting microtubules, and tracks depolymerizing microtubule ends. Further, starPEG-(KA7)4 promotes microtubule nucleation and growth, mediates depolymerization coupled pulling at plus ends, and bundles microtubules without significantly interfering with other proteins on the microtubule lattice (as exemplified by the motor kinesin-1). Our results show that positive charges and multivalency are sufficient to mimic advanced MAP-like behavior.

Curvature regulation of the ciliary beat through axonemal twist.

Cilia and flagella are hairlike organelles that propel cells through fluid. The active motion of the axoneme, the motile structure inside cilia and flagella, is powered by molecular motors of the axonemal dynein family. These motors generate forces and torques that slide and bend the microtubule doublets within the axoneme. To create regular waveforms, the activities of the dyneins must be coordinated. It is thought that coordination is mediated by stresses due to radial, transverse, or sliding deformations, and which build up within the moving axoneme and feed back on dynein activity. However, which particular components of the stress regulate the motors to produce the observed waveforms of the many different types of flagella remains an open question. To address this question, we describe the axoneme as a three-dimensional bundle of filaments and characterize its mechanics. We show that regulation of the motors by radial and transverse stresses can lead to a coordinated flagellar motion only in the presence of twist. We show that twist, which could arise from torque produced by the dyneins, couples curvature to transverse and radial stresses. We calculate emergent beating patterns in twisted axonemes resulting from regulation by transverse stresses. The resulting waveforms are similar to those observed in flagella of Chlamydomonas and sperm. Due to the twist, the waveform has nonplanar components, which result in swimming trajectories such as twisted ribbons and helices, which agree with observations.

Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella.

Cilia and flagella are model systems for studying how mechanical forces control morphology. The periodic bending motion of cilia and flagella is thought to arise from mechanical feedback: dynein motors generate sliding forces that bend the flagellum, and bending leads to deformations and stresses, which feed back and regulate the motors. Three alternative feedback mechanisms have been proposed: regulation by the sliding forces, regulation by the curvature of the flagellum, and regulation by the normal forces that deform the cross-section of the flagellum. In this work, we combined theoretical and experimental approaches to show that the curvature control mechanism is the one that accords best with the bending waveforms of Chlamydomonas flagella. We make the surprising prediction that the motors respond to the time derivative of curvature, rather than curvature itself, hinting at an adaptation mechanism controlling the flagellar beat.

Independent Control of the Static and Dynamic Components of the Chlamydomonas Flagellar Beat.

When the green alga Chlamydomonas reinhardtii swims, it uses the breaststroke beat of its two flagella to pull itself forward [1]. The flagellar waveform can be decomposed into a static component, corresponding to an asymmetric time-averaged shape, and a dynamic component, corresponding to the time-varying wave [2]. Extreme lightening conditions photoshock the cell, converting the breaststroke beat into a symmetric sperm-like beat, which causes a reversal of the direction of swimming [3]. Waveform conversion is achieved by a reduction in magnitude of the static component, whereas the dynamic component remains unchanged [2]. The coupling between static and dynamic components, however, is poorly understood, and it is not known whether the static component requires the dynamic component or whether it can exist independently. We used isolated and reactivated axonemes [4] to investigate the relation between the two beat components. We discovered that, when reactivated in the presence of low ATP concentrations, axonemes displayed the static beat component in absence of the dynamic component. Furthermore, we found that the amplitudes of the two components depend on ATP in qualitatively different ways. These results show that the decomposition into static and dynamic components is not just a mathematical concept but that the two components can independently control different aspects of cell motility: the static component controls swimming direction, whereas the dynamic component provides propulsion.

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets.

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy.

Broken detailed balance at mesoscopic scales in active biological systems.

Systems in thermodynamic equilibrium are not only characterized by time-independent macroscopic properties, but also satisfy the principle of detailed balance in the transitions between microscopic configurations. Living systems function out of equilibrium and are characterized by directed fluxes through chemical states, which violate detailed balance at the molecular scale. Here we introduce a method to probe for broken detailed balance and demonstrate how such nonequilibrium dynamics are manifest at the mesosopic scale. The periodic beating of an isolated flagellum from Chlamydomonas reinhardtii exhibits probability flux in the phase space of shapes. With a model, we show how the breaking of detailed balance can also be quantified in stationary, nonequilibrium stochastic systems in the absence of periodic motion. We further demonstrate such broken detailed balance in the nonperiodic fluctuations of primary cilia of epithelial cells. Our analysis provides a general tool to identify nonequilibrium dynamics in cells and tissues.

Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga.

The unicellular green alga Chlamydomonas swims with two flagella that can synchronize their beat. Synchronized beating is required to swim both fast and straight. A long-standing hypothesis proposes that synchronization of flagella results from hydrodynamic coupling, but the details are not understood. Here, we present realistic hydrodynamic computations and high-speed tracking experiments of swimming cells that show how a perturbation from the synchronized state causes rotational motion of the cell body. This rotation feeds back on the flagellar dynamics via hydrodynamic friction forces and rapidly restores the synchronized state in our theory. We calculate that this "cell-body rocking" provides the dominant contribution to synchronization in swimming cells, whereas direct hydrodynamic interactions between the flagella contribute negligibly. We experimentally confirmed the two-way coupling between flagellar beating and cell-body rocking predicted by our theory.