Andrej Vilfan

Self-assembled artificial cilia

Due to their small dimensions, microfluidic devices operate in the low Reynolds number regime. In this case, the hydrodynamics is governed by the viscosity rather than inertia and special elements have to be introduced into the system for mixing and pumping of fluids. Here we report on the realization of an effective pumping device that mimics a ciliated surface and imitates its motion to generate fluid flow. The artificial biomimetic cilia are constructed as long chains of spherical superparamagnetic particles, which self-assemble in an external magnetic field. Magnetic field is also used to actuate the cilia in a simple nonreciprocal manner, resulting in a fluid flow. We prove the concept by measuring the velocity of a cilia-pumped fluid as a function of height above the ciliated surface and investigate the influence of the beating asymmetry on the pumping performance. A numerical simulation was carried out that successfully reproduced the experimentally obtained data.

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 the 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.

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 four-state cycle (detached; attached with ADP.Pi; attached with ADP; and attached without nucleotide) and alternatively with a five-state cycle (where the powerstroke 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 powerstroke in the trail head and that it only undergoes its powerstroke after the trail head unbinds from actin. Both models (four- and five-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 five-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.

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. However, 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.

The mechanism of amyloid-fibril formation by stefin B: Temperature and protein concentration dependence of the rates

Cystatins, a family of structurally related cysteine proteinase inhibitors, have proved to be useful model system to study amyloidogenesis. We have extended previous studies of the kinetics of amyloid‐fibril formation by human stefin B (cystatin B) and some of its mutants, and proposed an improved model for the reaction. Overall, the observed kinetics follow the nucleation and growth behavior observed for many other amyloidogenic proteins. The minimal kinetic scheme that best fits measurements of changes in CD and thioflavin T fluorescence as a function of protein concentration and temperature includes nucleation (modeled as NI irreversible transitions with equivalent rates (kI), which fitted with NI = 64), fibril growth and nonproductive oligomerization, best explained by an off‐pathway state with a rate‐limiting escape rate. Three energies of activation were derived from global fitting to the minimal kinetic scheme, and independently through the fitting of the individual component rates. Nucleation was found to be a first‐order process within an oligomeric species with an enthalpy of activation of 55 ± 4 kcal mol−1. Fibril growth was a second‐order process with an enthalpy of activation (27 ± 5 kcal mol−1), which is indistinguishable from that of tetramer formation by cystatins, which involves limited conformational changes including proline trans to cis isomerization. The highest enthalpy of activation (95 ± 5 kcal mol−1 at 35°C), characteristic of a substantial degree of unfolding as observed prior to domain‐swapping reactions, equated with the escape rate of the off‐pathway oligomeric state. Proteins 2009.

Frequency Clustering in Spontaneous Otoacoustic Emissions from a Lizard's Ear

Spontaneous otoacoustic emissions (SOAEs) are indicators of an active process in the inner ear that enhances the sensitivity and frequency selectivity of hearing. They are particularly regular and robust in certain lizards, so these animals are good model organisms for studying how SOAEs are generated. We show that the published properties of SOAEs in the bobtail lizard are wholly consistent with a mathematical model in which active oscillators, with exponentially varying characteristic frequencies, are coupled together in a chain by visco-elastic elements. Physically, each oscillator corresponds to a small group of hair cells, covered by a tectorial sallet, so our theoretical analysis directly links SOAEs to the micromechanics of active hair bundles.

Instabilities in the Transient Response of Muscle

We investigate the isometric transient response of muscle using a quantitative stochastic model of the actomyosin cycle based on the swinging lever-arm hypothesis. We first consider a single pair of filaments, and show that when values of parameters such as the lever-arm displacement and the cross-bridge elasticity are chosen to provide effective energy transduction, the T(2) curve (the tension recovered immediately after a step displacement) displays a region of negative slope. If filament compliance and the discrete nature of the binding sites are taken into account, the negative slope is diminished, but not eliminated. This implies that there is an instability in the dynamics of individual half sarcomeres. However, when the symmetric nature of whole sarcomeres is taken into account, filament rearrangement becomes important during the transient: as tension is recovered, some half sarcomeres lengthen whereas others shorten. This leads to a flat T(2) curve, as observed experimentally. In addition, we investigate the isotonic transient response and show that for a range of parameter values the model displays damped oscillations, as recently observed in experiments on single muscle fibers. We conclude that it is essential to consider the collective dynamics of many sarcomeres, rather than the dynamics of a single pair of filaments, when interpreting the transient response of muscle.

Elastically coupled molecular motors

Abstract:We study the influence of filament elasticity on the motion of collective molecular motors. It is found that for a backbone flexibility exceeding a characteristic value (motor stiffness divided through the mean displacement between attached motors), the ability of motors to produce force reduces as compared to rigidly coupled motors, while the maximum velocity remains unchanged. The force-velocity-relation in two different analytic approximations is calculated and compared with Monte-Carlo simulations. Finally, we extend our model by introducing motors with a strain-dependent detachment rate. A remarkable crossover from the nearly hyperbolic shape of the Hill curve for stiff backbones to a linear force-velocity relation for very elastic backbones is found. With realistic model parameters we show that the backbone flexibility plays no role under physiological conditions in muscles, but it should be observable in certain in vitro assays.

Twirling Motion of Actin Filaments in Gliding Assays with Nonprocessive Myosin Motors

We present a model study of gliding assays in which actin filaments are moved by nonprocessive 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 toward 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 approximately 400 nm for low speeds and increases with higher speeds.

The Binding Dynamics of Tropomyosin on Actin

We discuss a theoretical model for the cooperative binding dynamics of tropomyosin to actin filaments. Tropomyosin binds to actin by occupying seven consecutive monomers. The model includes a strong attraction between attached tropomyosin molecules. We start with an empty lattice and show that the binding goes through several stages. The first stage represents fast initial binding and leaves many small vacancies between blocks of bound molecules. In the second stage the vacancies annihilate slowly as tropomyosin molecules detach and reattach. Finally, the system approaches equilibrium. Using a grain-growth model and a diffusion-coagulation model we give analytical approximations for the vacancy density in all regimes.