Flagellum-driven cargoes: Influence of cargo size and the flagellum-cargo attachment geometry.

The beating of cilia and flagella, which relies on an efficient conversion of energy from ATP-hydrolysis into mechanical work, offers a promising way to propel synthetic cargoes. Recent experimental realizations of such micro-swimmers, in which micron-sized beads are propelled by isolated and demembranated flagella from the green algae Chlamydomonas reinhardtii (C. reinhardtii), revealed a variety of propulsion modes, depending in particular on the calcium concentration. Here, we investigate theoretically and numerically the propulsion of a bead as a function of the flagellar waveform and the attachment geometries between the bead and the flagellum. To this end, we take advantage of the low Reynolds number of the fluid flows generated by the micro-swimmer, which allows us to neglect fluid inertia. By describing the flagellar waveform as a superposition of a static component and a propagating wave, and using resistive-force theory, we show that the asymmetric sideways attachment of the flagellum to the bead makes a contribution to the rotational velocity of the micro-swimmer that is comparable to the contribution caused by the static component of the flagellar waveform. Remarkably, our analysis reveals the existence of a counter-intuitive propulsion regime in which an increase in the size of the cargo, and hence its drag, leads to an increase in some components of the velocity of the bead. Finally, we discuss the relevance of the uncovered mechanisms for the fabrication of synthetic, bio-actuated medical micro-robots for targeted drug delivery.

Propagation of a multi-vortex beam: far-field diffraction of a Gaussian beam from a multi-fork phase grating.

In this work, the far-field propagation of multi-vortex beams is investigated. We consider diffraction of a Gaussian wave from a spatial light modulator (SLM) in which a multi-fork grating is implemented on it at the waist plane of the Gaussian wave. In the first-order diffraction pattern a multi-vortex beam is produced, and we consider its evolution under propagation when different multi-fork gratings are implemented on the SLM. We consider two different schemes for the phase singularities of the implemented grating. A topological charge (TC) equal to l1 is considered at the center of the grating, and four similar phase singularities all having a TC equal to l2=l14 (or l2=-l14) are located on the corners of a square where the l1 singularity is located on the square center. Some cases with different values of l1, and consequently l2, are investigated. Experimental and simulation results show that if signs of the TCs at the corners and center of the square are the same, the radius of the central singularity on the first-order diffracted beam increases, and it convolves the other singularities. If their signs are opposite, the total TC value equals zero, and at the far-field, the light beam distribution becomes a Gaussian beam. For determining the TCs of the resulting far-field beams, we interfere experimentally and by simulation the resulting far-field beams with a plane wave and count the forked interference fringes. All the results are consistent.

Bio-hybrid micro-swimmers propelled by flagella isolated from C. reinhardtii.

Bio-hybrid micro-swimmers, composed of biological entities integrated with synthetic constructs, actively transport cargo by converting chemical energy into mechanical work. Here, using isolated and demembranated flagella from green algae Chlamydomonas reinhardtii (C. reinhardtii), we build efficient axonemally-driven micro-swimmers that consume ATP to propel micron-sized beads. Depending on the calcium concentration, we observed two main classes of motion: whereas beads move along curved trajectories at calcium concentrations below 0.03 mM, they are propelled along straight paths when the calcium concentration increases. In this regime, they reached velocities of approximately 20 µm s-1, comparable to human sperm velocity in vivo. We relate this transition to the properties of beating axonemes, in particular the reduced static curvature with increasing calcium concentration. Our designed system has potential applications in the fabrication of synthetic micro-swimmers, and in particular, bio-actuated medical micro-robots for targeted drug delivery.

Rapid multi-plane phase-contrast microscopy reveals torsional dynamics in flagellar motion.

High speed volumetric optical microscopy is an important tool for observing rapid processes in living cells or for real-time tracking of sub-cellular components. However, the 3D imaging capability often comes at the price of a high technical complexity of the imaging system and/or the requirement of demanding image analysis. Here, we propose a combination of conventional phase-contrast imaging with a customized multi-plane beam-splitter for enabling simultaneous acquisition of images in eight different focal planes. Our method is technically straightforward and does not require complex post-processing image analysis. We apply our multi-plane phase-contrast microscope to the real-time observation of the fast motion of reactivated Chlamydomonas axonemes with sub-µm spatial and 4 ms temporal resolution. Our system allows us to observe not only bending but also the three-dimensional torsional dynamics of these micro-swimmers.

Light-Powered Reactivation of Flagella and Contraction of Microtubule Networks: Toward Building an Artificial Cell.

Artificial systems capable of self-sustained movement with self-sufficient energy are of high interest with respect to the development of many challenging applications, including medical treatments, but also technical applications. The bottom-up assembly of such systems in the context of synthetic biology is still a challenging task. In this work, we demonstrate the biocompatibility and efficiency of an artificial light-driven energy module and a motility functional unit by integrating light-switchable photosynthetic vesicles with demembranated flagella. The flagellar propulsion is coupled to the beating frequency, and dynamic ATP synthesis in response to illumination allows us to control beating frequency of flagella in a light-dependent manner. In addition, we verified the functionality of light-powered synthetic vesicles in in vitro motility assays by encapsulating microtubules assembled with force-generating kinesin-1 motors and the energy module to investigate the dynamics of a contractile filamentous network in cell-like compartments by optical stimulation. Integration of this photosynthetic system with various biological building blocks such as cytoskeletal filaments and molecular motors may contribute to the bottom-up synthesis of artificial cells that are able to undergo motor-driven morphological deformations and exhibit directional motion in a light-controllable fashion.

Resistive force theory and wave dynamics in swimming flagellar apparatus isolated from C. reinhardtii.

Cilia-driven motility and fluid transport are ubiquitous in nature and essential for many biological processes, including swimming of eukaryotic unicellular organisms, mucus transport in airway apparatus or fluid flow in the brain. The-biflagellated micro-swimmer Chlamydomonas reinhardtii is a model organism to study the dynamics of flagellar synchronization. Hydrodynamic interactions, intracellular mechanical coupling or cell body rocking is believed to play a crucial role in the synchronization of flagellar beating in green algae. Here, we use freely swimming intact flagellar apparatus isolated from a wall-less strain of Chlamydomonas to investigate wave dynamics. Our analysis on phase coordinates shows that when the frequency difference between the flagella is high (10-41% of the mean), neither mechanical coupling via basal body nor hydrodynamics interactions are strong enough to synchronize two flagella, indicating that the beating frequency is perhaps controlled internally by the cell. We also examined the validity of resistive force theory for a flagellar apparatus swimming freely in the vicinity of a substrate and found quantitative agreement between the experimental data and simulations with a drag anisotropy of ratio 2. Finally, using a simplified wave form, we investigated the influence of phase and frequency differences, intrinsic curvature and wave amplitude on the swimming trajectory of flagellar apparatus. Our analysis shows that by controlling the phase or frequency differences between two flagella, steering can occur.

Spatial heterogeneities shape the collective behavior of signaling amoeboid cells.

In its natural habitat in the forest soil, the cellular slime mold Dictyostelium discoideum is exposed to obstacles. Starving Dictyostelium cells secrete cAMP, which is the key extracellular signaling molecule that promotes the aggregation process required for their long-term survival. Here, we investigated the influence of environmental inhomogeneities on the signaling and pattern formation of Dictyostelium cells. We present experimental data and numerical simulations on the pattern formation of signaling Dictyostelium cells in the presence of periodic arrays of millimeter-sized pillars. We observed concentric cAMP waves that initiated almost synchronously at the pillars and propagated outward. In response to these circular waves, the Dictyostelium cells streamed toward the pillars, forming aggregates arranged in patterns that reflected the periodicity of the lattice of pillars. Our results suggest that, in nature, the excitability threshold and synchronization level of the cells are two key parameters that control the nature of the interaction between cells and spatial heterogeneities in their environment.

Experimental observation of boundary-driven oscillations in a reaction-diffusion-advection system.

Boundary-driven oscillations were numerically predicted to exist in a reaction-diffusion-advection system, namely in the signaling population of social amoeba D. discoideum. If deprived of nutrients, D. discoideum aggregates by producing cAMP waves at precisely timed intervals. In the presence of an advecting flow, holding the upstream boundary to a zero concentration of cAMP produces an instability that sends periodic wave trains downstream. This instability is expected to exist at lower degradation rates of cAMP and thus provides a mechanism for wave creation in phosphodiesterase deficient systems, such as PdsA- cells. Degradation of extracellular cAMP by the enzyme phosphodiesterase PdsA is fundamental to successfully producing waves, regulating the external cAMP gradient field and preventing the accumulation of cAMP. Using a flow-through microfluidic setup filled with PdsA- cells, we confirm experimentally that boundary-driven oscillations indeed exist. Above a minimum flow velocity, decaying waves are induced, with a decay length that increases with the imposed flow velocity. We performed extensive numerical simulations and showed that these waves have a boundary-driven origin, where the lack of cAMP in the upstream flow destabilizes the system. We explored the properties of these waves and the parameter region where they exist, finding good agreement with our experimental observations. These results provide experimental confirmation of the destabilizing effect of the upstream boundary in an otherwise stable reaction-diffusion system. We expect this mechanism to be relevant for wave creation in other oscillatory or excitable systems that are incapable of wave generation in the absence of flow.

Publisher Correction: Spontaneous center formation in Dictyostelium discoideum.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Spontaneous center formation in Dictyostelium discoideum.

Dictyostelium discoideum (D.d.) is a widely studied amoeba due to its capabilities of development, survival, and self-organization. During aggregation it produces and relays a chemical signal (cAMP) which shows spirals and target centers. Nevertheless, the natural emergence of these structures is still not well understood. We present a mechanism for creation of centers and target waves of cAMP in D.d. by adding cell inhomogeneity to a well known reaction-diffusion model of cAMP waves and we characterize its properties. We show how stable activity centers appear spontaneously in areas of higher cell density with the oscillation frequency of these centers depending on their density. The cAMP waves have the characteristic dispersion relation of trigger waves and a velocity which increases with cell density. Chemotactically competent cells react to these waves and create aggregation streams even with very simple movement rules. Finally we argue in favor of the existence of bounded phosphodiesterase to maintain the wave properties once small cell clusters appear.

Influence of cross-linking and retrograde flow on formation and dynamics of lamellipodium.

The forces that arise from the actin cortex play a crucial role in determining the membrane deformation. These include protrusive forces due to actin polymerization, pulling forces due to transient attachment of actin filaments to the membrane, retrograde flow powered by contraction of actomyosin network, and adhesion to the extracellular matrix. Here we present a theoretical model for membrane deformation resulting from the feedback between the membrane shape and the forces acting on the membrane. We model the membrane as a series of beads connected by springs and determine the final steady-state shape of the membrane arising from the interplay between pushing/pulling forces of the actin network and the resisting membrane tension. We specifically investigate the effect of the gel dynamics on the spatio-temporal deformation of the membrane until a stable lamellipodium is formed. We show that the retrograde flow and the cross-linking velocity play an essential role in the final elongation of the membrane. Interestingly, in the simulations where motor-induced contractility is switched off, reduced retrograde flow results in an increase in the rate and amplitude of membrane protrusion. These simulations are consistent with experimental observations that report an enhancement in protrusion efficiency as myosin II molecular motors are inhibited.

Influence of fast advective flows on pattern formation of Dictyostelium discoideum.

We report experimental and numerical results on pattern formation of self-organizing Dictyostelium discoideum cells in a microfluidic setup under a constant buffer flow. The external flow advects the signaling molecule cyclic adenosine monophosphate (cAMP) downstream, while the chemotactic cells attached to the solid substrate are not transported with the flow. At high flow velocities, elongated cAMP waves are formed that cover the whole length of the channel and propagate both parallel and perpendicular to the flow direction. While the wave period and transverse propagation velocity are constant, parallel wave velocity and the wave width increase linearly with the imposed flow. We also observe that the acquired wave shape is highly dependent on the wave generation site and the strength of the imposed flow. We compared the wave shape and velocity with numerical simulations performed using a reaction-diffusion model and found excellent agreement. These results are expected to play an important role in understanding the process of pattern formation and aggregation of D. discoideum that may experience fluid flows in its natural habitat.

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model.

In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant.

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

Variability and Order in Cytoskeletal Dynamics of Motile Amoeboid Cells.

The chemotactic motion of eukaryotic cells such as leukocytes or metastatic cancer cells relies on membrane protrusions driven by the polymerization and depolymerization of actin. Here we show that the response of the actin system to a receptor stimulus is subject to a threshold value that varies strongly from cell to cell. Above the threshold, we observe pronounced cell-to-cell variability in the response amplitude. The polymerization time, however, is almost constant over the entire range of response amplitudes, while the depolymerization time increases with increasing amplitude. We show that cell-to-cell variability in the response amplitude correlates with the amount of Arp2/3, a protein that enhances actin polymerization. A time-delayed feedback model for the cortical actin concentration is consistent with all our observations and confirms the role of Arp2/3 in the observed cell-to-cell variability. Taken together, our observations highlight robust regulation of the actin response that enables a reliable timing of cell movement.

Dynamic regimes and bifurcations in a model of actin-based motility.

Propulsion by actin polymerization is widely used in cell motility. Here, we investigate a model of the brush range of an actin gel close to a propelled object, describing the force generation and the dynamics of the propagation velocity. We find transitions between stable steady states and relaxation oscillations when the attachment rate of actin filaments to the obstacle is varied. The oscillations set in at small values of the attachment rate via a homoclinic bifurcation. A second transition from a stable steady state to relaxation oscillations, found for higher values of the attachment rate, occurs via a supercritical Hopf bifurcation. The behavior of the model near the second transition is similar that of a system undergoing a canard explosion. Consequently, we observe excitable dynamics also. The model further exhibits bistability between stationary states or stationary states and limit cycles. Therefore, the brush of actin filament ends appears to have a much richer dynamics than was assumed until now.

Entropic forces generated by grafted semiflexible polymers.

The entropic force exerted by the Brownian fluctuations of a grafted semiflexible polymer upon a rigid smooth wall are calculated both analytically and by Monte Carlo simulations. Such forces are thought to play an important role for several cellular phenomena, in particular, the physics of actin-polymerization-driven cell motility and movement of bacteria like Listeria. In the stiff limit, where the persistence length of the polymer is larger than its contour length, we find that the entropic force shows scaling behavior. We identify the characteristic length scales and the explicit form of the scaling functions. In certain asymptotic regimes, we give simple analytical expressions which describe the full results to a very high numerical accuracy. Depending on the constraints imposed on the transverse fluctuations of the filament, there are characteristic differences in the functional form of the entropic forces. In a two-dimensional geometry, the entropic force exhibits a marked peak.

Effects of ultra-low doses of nicotine on the expression of morphine-induced conditioned place preference in mice.

In the present study, the effects of acute administration of nicotine, as well as nicotinic and muscarinic acetylcholine receptor antagonists, on the expression of morphine-induced conditioned place preference, have been investigated in male Swiss-Webster mice. Animals received different doses of morphine 5 days after surgical cannulation in the lateral ventricle. Subcutaneous injections of morphine (2-5 mg/kg) in mouse produced place preference in a dose-dependent manner. Furthermore, both intraperitoneal (0.0006-0.1 mg/kg) and intracerebroventricular (0.007-25 ng) nicotine administration significantly reduced the expression of morphine-induced place preference, in a dose-dependent manner. Nicotine, however, was effective over narrow ultra-low dose ranges (0.0012, 0.0025, 0.005 and 0.01 mg/kg; intraperitoneal) and (0.03, 0.1, 0.3 and 0.6 ng/mouse; intracerebroventricular). In addition, locomotor activity was reduced when higher doses of nicotine [both intraperitoneal (0.02, 0.03 and 0.1 mg/kg) and intracerebroventricular (10 and 24 ng/mouse)] were used. Nicotine alone, however, did not cause motivational effects. Intracerebroventricular injection of hexamethonium (0.03, 0.1 and 0.3 mug/mouse; 10 min before nicotine) diminished the effects of nicotine on morphine-induced conditioned place preference. This effect could neither be obtained by intraperitoneal administration of hexamethonium (1, 5 and 10 mg/kg; 30 min before nicotine), nor be reproduced after either intracerebroventricular or intraperitoneal injection of atropine (a muscarinic receptor antagonist). The antagonists, themselves, did not show any motivational effects when used alone and were unable to affect the expression of morphine-induced conditioned place preference. It appears that ultra-low doses of nicotine can reduce the expression of morphine-induced place preference, and that central nicotinic acetylcholine receptors play a role in this regard.

Role of nitric oxide in the acquisition and expression of apomorphine- or morphine-induced locomotor sensitization.

In the present study, the effects of L-arginine, a nitric oxide (NO) precursor, and N(G)-nitro-L-arginine methyl ester (L-NAME), a nitric oxide synthase (NOS) inhibitor, on apomorphine- or morphine-induced locomotor sensitization in male albino mice were investigated. Our data showed that subcutaneous (s.c.) injection of apomorphine (2-10 mg/kg) or morphine sulphate (5-50 mg/kg) significantly increased locomotor behaviour in a dose-dependent manner. Intraperitoneal (i.p.) administration of L-arginine (100 mg/kg) increased locomotor activity, whereas L-NAME (20 mg/kg) decreased it. L-Arginine and L-NAME increased and decreased apomorphine- or morphine-induced locomotions, respectively. The locomotor behavioural response was enhanced in mice pretreated with apomorphine (2 mg/kg, daily x3 days) or morphine (10 mg/kg, daily x3 days) alone, indicating that sensitization had developed. Administration of L-arginine 30 min before each of three daily doses of apomorphine or morphine increased the development of sensitization, while administration of L-NAME 30 min before each of three daily doses of apomorphine or morphine decreased the acquisition of sensitization induced by apomorphine or morphine. Administration of L-arginine significantly increased and L-NAME significantly and dose-dependently decreased the expression of both apomorphine- and morphine-induced sensitization. The results indicate that NO may be involved in the acquisition and expression of apomorphine- or morphine-induced sensitization.

Nitric oxide within the ventral tegmental area is involved in mediating morphine reward.

In the present study, the effects of intra-ventral tegmental area injection of L-arginine, a nitric oxide (NO) precursor, and N(G)-nitro-L-arginine methyl ester (L-NAME), a nitric oxide synthase (NOS) inhibitor, on morphine-induced conditioned place preference in male Wistar rats were investigated. Our data showed that subcutaneous (s.c.) injection of morphine sulphate (0.5-10 mg/kg) significantly increased the time spent in the drug-paired compartment in a dose-dependent manner. Intra-ventral tegmental area administration of a low dose of L-arginine (0.05 microg/rat) with an ineffective dose of morphine (0.5 mg/kg) elicited significant conditioned place preference; however, a higher dose of L-arginine (0.1 microg/rat) reduced the morphine response. Intra-ventral tegmental area administration of L-NAME (0.03 and 0.1 microg/rat) decreased the acquisition of morphine (7.5 mg/kg)-induced place preference. The response to different doses of L-arginine was decreased by L-NAME (0.03 microg/rat). L-Arginine and L-NAME by themselves did not elicit any effect on place conditioning; however, intra-ventral tegmental area administration of L-arginine (0.01-0.1 microg/rat) and a higher dose of L-NAME (0.1 microg/rat) significantly decreased the expression of morphine (7.5 mg/kg)-induced place preference. The attenuation of already established morphine-induced place preference on the test day by L-arginine was inhibited by L-NAME (0.03 microg/rat). The results indicate that NO may be involved in the acquisition and expression of morphine-induced place preference.