arXiv subjects

Andrej Vilfan

Publications and source records attributed to Andrej Vilfan.

At least 37 records · Page 2Linked to original sources

arXiv2021

Optimal swimmer can be puller, pusher, or neutral depending on the shape

The ability of microswimmers to deploy optimal propulsion strategies is of paramount importance for their locomotory performance and survival at low Reynolds numbers. Although for perfectly spherical swimmers minimum dissipation requires a neutral type swimming, any departure from the spherical shape may lead the swimmer to adopt a new propulsion strategy, namely those of puller- or pusher-type swimming. In this study, by using the minimum dissipation theorem for microswimmers, we determine the flow field of an optimal nearly spherical swimmer, and show that indeed depending on the shape profile, the optimal swimmer can be a puller, pusher, or neutral. Using an asymptotic approach, we find that amongst all the modes of the shape function, only the third mode determines to leading order the swimming type of the optimal swimmer.

physics.flu-dyn↗

arXiv2021

Active beating of a reconstituted synthetic minimal axoneme

Propelling microorganisms through fluids and moving fluids along cellular surfaces are essential biological functions accomplished by long, thin structures called motile cilia and flagella, whose regular, oscillatory beating breaks the time-reversal symmetry required for transport. Although top-down experimental approaches and theoretical models have allowed us to broadly characterize such organelles and propose mechanisms underlying their complex dynamics, constructing minimal systems capable of mimicking ciliary beating and identifying the role of each component remains a challenge. Here we report the bottom-up assembly of a minimal synthetic axoneme, which we call a synthoneme, using biological building blocks from natural organisms, namely pairs of microtubules and cooperatively associated axonemal dynein motors. We show that upon provision of energy by ATP, microtubules undergo rhythmic bending by cyclic association-dissociation of dyneins. Our simple and unique beating minimal synthoneme represents a self-organized nanoscale biomolecular machine that can also help understand the mechanisms underlying ciliary beating.

cond-mat.soft↗

arXiv2021

Minimum Dissipation Theorem for Microswimmers

We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at low Reynolds number. We show that, for any swimmer, the minimum dissipation at a given velocity can be expressed in terms of the resistance tensors of two passive bodies of the same shape with a no-slip and perfect-slip boundary. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body. Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly-used Lighthill efficiency, can never exceed unity. We validate the theory by calculating the efficiency limits of spheroidal swimmers.

physics.flu-dyn↗

arXiv2020

Wrinkling instability in 3D active nematics

In nature interactions between biopolymers and motor proteins give rise to biologically essential emergent behaviours. Besides cytoskeleton mechanics, active nematics arise from such interactions. Here we present a study on 3D active nematics made of microtubules, kinesin motors and depleting agent. It shows a rich behaviour evolving from a nematically ordered space-filling distribution of microtubule bundles toward a flattened and contracted 2D ribbon that undergoes a wrinkling instability and subsequently transitions into a 3D active turbulent state. The wrinkle wavelength is independent of the ATP concentration and our theoretical model describes its relation with the appearance time. We compare the experimental results with a numerical simulation that confirms the key role of kinesin motors in cross-linking and sliding the microtubules. Our results on the active contraction of the network and the independence of wrinkle wavelength on ATP concentration are important steps forward for the understanding of these 3D systems.

cond-mat.soft↗

arXiv2019

Emergent colloidal edge currents generated via exchange dynamics in a broken dimer state

Controlling the flow of matter down to micrometer-scale confinement is of central importance in materials and environmental sciences, with direct applications in nano-microfluidics, drug delivery and biothechnology. Currents of microparticles are usually generated with external field gradients of different nature [e.g., electric, magnetic, optical, thermal or chemical ones] which are difficult to control over spatially extended regions and samples. Here we demonstrate a general strategy to assemble and transport polarizable microparticles in fluid media through combination of confinement and magnetic dipolar interactions. We use a homogeneous magnetic modulation to assemble dispersed particles into rotating dimeric state and frustrated binary lattices, and generate collective edge currents which arise from a novel, field-synchronized particle exchange process. These dynamic states are similar to cyclotron and skipping orbits in electronic and molecular systems, thus paving the way toward understanding and engineering similar processes at different length scales across condensed matter.

cond-mat.soft↗

arXiv2019

Efficiency limits of the three-sphere swimmer

We consider a swimmer consisting of a collinear assembly of three spheres connected by two slender rods. This swimmer can propel itself forward by varying the lengths of the rods in a way that is not invariant under time reversal. Although any non-reciprocal strokes of the arms can lead to a net displacement, the energetic efficiency of the swimmer is strongly dependent on the details and sequences of these strokes, and also the sizes of the spheres. We define the efficiency of the swimmer using Lighthill's criterion, i.e., the power that is needed to pull the swimmer by an external force at a certain speed, divided by the power needed for active swimming with the same average speed. Here, we determine numerically the optimal stroke sequences and the optimal size ratio of the spheres, while limiting the maximum extension of the rods. Our calculation takes into account both far-field and near-field hydrodynamic interactions. We show that, surprisingly, the three-sphere swimmer with unequal spheres can be more efficient than the equally-sized case. We also show that the variations of efficiency with size ratio is not monotonic and there exists a specific size ratio at which the swimmer has the highest efficiency. We find that the swimming efficiency initially rises by increasing the maximum allowable extension of the rods, and then converges to a maximum value. We calculate this upper limit analytically and report the highest value of efficiency that the three-sphere swimmer can reach.

physics.flu-dyn↗

arXiv2019

Flagella-like beating of a single microtubule

Kinesin motors can induce a buckling instability in a microtubule with a fixed minus end. Here we show that by modifying the surface with a protein-repellent functionalization and using clusters of kinesin motors, the microtubule can exhibit persistent oscillatory motion, resembling the beating of sperm flagella. The observed period is of the order of 1 min. From the experimental images we theoretically determine a distribution of motor forces that explains the observed shapes using a maximum likelihood approach. A good agreement is achieved with a small number of motor clusters acting simultaneously on a microtubule. The tangential forces exerted by a cluster are mostly in the range 0 - 8 pN towards the microtubule minus end, indicating the action of 1 or 2 kinesin motors. The lateral forces are distributed symmetrically and mainly below 10 pN, while the lateral velocity has a strong peak around zero. Unlike well-known models for flapping filaments, kinesins are found to have a strong "pinning" effect on the beating filaments. Our results suggest new strategies to utilize molecular motors in dynamic roles that depend sensitively on the stress built-up in the system.

physics.bio-ph↗

arXiv2015

Hydrodynamic synchronization of autonomously oscillating optically trapped particles

Ellipsoidal micron-sized colloidal particles can oscillate spontaneously when trapped in a focused laser beam. If two oscillating particles are held in proximity their oscillations synchronize through hydrodynamic interactions. The degree of synchronization depends on the distance between the oscillators and on their orientation. Due to the anisotropic nature of hydrodynamic coupling the synchronization is strongest when particles are arranged along the direction of oscillations. Similar behavior is observed for many oscillating particles arranged in a row. Experimental observations are well reproduced with a model that uses a phenomenological description of the optical force and hydrodynamic interactions. Our results show that oscillating ellipsoidal particles can serve as a model system for studying hydrodynamic synchronization between biological cilia.

physics.flu-dyn↗

arXiv2014

Ensemble velocity of non-processive molecular motors with multiple chemical states

We study the ensemble velocity of non-processive motor proteins, described with multiple chemical states. In particular, we discuss the velocity as a function of ATP concentration. Even a simple model which neglects the strain-dependence of transition rates, reverse transition rates and nonlinearities in the elasticity can show interesting functional dependencies, which deviate significantly from the frequently assumed Michaelis-Menten form. We discuss how the oder of events in the duty cycle can be inferred from the measured dependence. The model also predicts the possibility of velocity reversal at a certain ATP concentration if the duty cycle contains several conformational changes of opposite directionalities.

physics.bio-ph↗

arXiv2012

Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low Reynolds number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.

physics.flu-dyn↗

arXiv2011

Finding the ciliary beating pattern with optimal efficiency

We introduce a measure for energetic efficiency of biological cilia acting individually or collectively and numerically determine the optimal beating patterns according to this criterion. Maximizing the efficiency of a single cilium leads to curly, often symmetric and somewhat counterintuitive patterns. But when looking at a densely ciliated surface, the optimal patterns become remarkably similar to what is observed in microorganisms like Paramecium. The optimal beating pattern then consists of a fast effective stroke and a slow sweeping recovery stroke. Metachronal coordination is essential for efficient pumping and the highest efficiency is achieved with antiplectic waves. Efficiency also increases with an increasing density of cilia up to the point where crowding becomes a problem. We finally relate the pumping efficiency of cilia to the swimming efficiency of a spherical microorganism and show that the experimentally estimated efficiency of Paramecium is surprisingly close to the theoretically possible optimum.

physics.bio-ph↗

arXiv2009

Twirling motion of actin filaments in gliding assays with non-processive myosin motors

We present a model study of gliding assays in which actin filaments are moved by non-processive myosin motors. We show that even if the power stroke of the motor protein has no lateral component, the filaments will rotate around their axis while moving over the surface. Notably, the handedness of this twirling motion is opposite from that of the actin filament structure. It stems from the fact that the gliding actin filament has "target zones" where its subunits point towards the surface and are therefore more accessible for myosin heads. Each myosin head has a higher binding probability before it reaches the center of the target zone than afterwards, which results in a left-handed twirling. We present a stochastic simulation and an approximative analytical solution. The calculated pitch of the twirling motion depends on the filament velocity (ATP concentration). It reaches about 400nm for low speeds and increases with higher speeds.

physics.bio-ph↗

arXiv2008

Five models for myosin V

Myosin V was the first discovered processive motor from the myosin family. It has therefore been subject of a number of mechanical, kinetic, optical and structural studies and now belongs to the best characterised motor proteins. This effort has been accompanied by a number of different theoretical models. In this article we give an overview of them and discuss what they have in common and where the open questions are. The latter include the existence of sub-steps, the process that limits the run length, the nature of backward steps, the flexibility of the lever arm and the state of the lead head.

physics.bio-ph↗

arXiv2007

Myosin V passing over Arp2/3 junctions: branching ratio calculated from the elastic lever arm model

Myosin V is a two-headed processive motor protein that walks in a hand-over-hand fashion along actin filaments. When it encounters a filament branch, formed by the Arp2/3 complex, it can either stay on the straight mother filament, or switch to the daughter filament. We study both probabilities using the elastic lever arm model for myosin V. We calculate the shapes and bending energies of all relevant configurations in which the trail head is bound to the actin filament before Arp2/3 and the lead head is bound either to the mother or to the daughter filament. Based on the assumption that the probability for a head to bind to a certain actin subunit is proportional to the Boltzmann factor obtained from the elastic energy, we calculate the mother/daughter filament branching ratio. Our model predicts a value of 27% for the daughter and 73% for the mother filament. This result is in good agreement with recent experimental data.

physics.bio-ph↗

arXiv2006

Hydrodynamic flow patterns and synchronization of beating cilia

We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.

physics.bio-ph↗

arXiv2005

Influence of fluctuations in actin structure on myosin V step size

We study the influence of disorder in the helical actin structure on the myosin V step size, predicted from the elastic lever arm model. We show that fluctuations of +-5 degrees per actin subunit, as proposed by Egelman et al., significantly alter the distribution of step sizes and improve the agreement with experimental data.

physics.bio-ph↗

arXiv2005

Oscillations in molecular motor assemblies

Autonomous oscillations in biological systems may have a biochemical origin or result from an interplay between force-generating and visco-elastic elements. In molecular motor assemblies the force-generating elements are molecular engines and the visco-elastic elements are stiff cytoskeletal polymers. The physical mechanism leading to oscillations depends on the particular architecture of the assembly. Existing models can be grouped into two distinct categories: systems with a delayed force activation and anomalous force-velocity relations. We discuss these systems within phase plane analysis known from the theory of dynamic systems and by adopting methods from control theory, the Nyquist stability criterion.

physics.bio-ph↗

arXiv2005

Elastic lever arm model for myosin V

We present a mechanochemical model for myosin V, a two-headed processive motor protein. We derive the properties of a dimer from those of an individual head, which we model both with a 4-state cycle (detached, attached with ADP.Pi, attached with ADP and attached without nucleotide) and alternatively with a 5-state cycle (where the power stroke is not tightly coupled to the phosphate release). In each state the lever arm leaves the head at a different, but fixed, angle. The lever arm itself is described as an elastic rod. The chemical cycles of both heads are coordinated exclusively by the mechanical connection between the two lever arms. The model explains head coordination by showing that the lead head only binds to actin after the power stroke in the trail head and that it only undergoes its power stroke after the trail head unbinds from actin. Both models (4- and 5-state) reproduce the observed hand-over-hand motion and fit the measured force-velocity relations. The main difference between the two models concerns the load dependence of the run length, which is much weaker in the 5-state model. We show how systematic processivity measurement under varying conditions could be used to distinguish between both models and to determine the kinetic parameters.

physics.bio-ph↗