Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation.

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al. Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove to be valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins.

Goldilocks Fluctuations: Dynamic Constraints on Loop Formation in Scale-Free Transport Networks.

Adaptive transport networks are known to contain loops when subject to hydrodynamic fluctuations. However, fluctuations are no guarantee that a loop will form, as shown by loop-free networks driven by oscillating flows. We provide a complete stability analysis of the dynamical behavior of any loop formed by fluctuating flows. We find a threshold for loop stability that involves an interplay of geometric constraints and hydrodynamic forcing mapped to constant and fluctuating components. Loops require fluctuation in the relative size of the flux between nodes, not just a temporal variation in the flux at a given node. Hence, there is both a minimum and a maximum amount of fluctuation relative to the constant-flux component where loops are supported.

Long-term day-by-day tracking of microvascular networks sprouting in fibrin gels: From detailed morphological analyses to general growth rules.

Understanding and controlling of the evolution of sprouting vascular networks remains one of the basic challenges in tissue engineering. Previous studies on the vascularization dynamics have typically focused only on the phase of intense growth and often lacked spatial control over the initial cell arrangement. Here, we perform long-term day-by-day analysis of tens of isolated microvasculatures sprouting from endothelial cell-coated spherical beads embedded in an external fibrin gel. We systematically study the topological evolution of the sprouting networks over their whole lifespan, i.e., for at least 14 days. We develop a custom image analysis toolkit and quantify (i) the overall length and area of the sprouts, (ii) the distributions of segment lengths and branching angles, and (iii) the average number of branch generations-a measure of network complexity. We show that higher concentrations of vascular endothelial growth factor (VEGF) lead to earlier sprouting and more branched networks, yet without significantly affecting the speed of growth of individual sprouts. We find that the mean branching angle is weakly dependent on VEGF and typically in the range of 60°-75°, suggesting that, by comparison with the available diffusion-limited growth models, the bifurcating tips tend to follow local VEGF gradients. At high VEGF concentrations, we observe exponential distributions of segment lengths, which signify purely stochastic branching. Our results-due to their high statistical relevance-may serve as a benchmark for predictive models, while our new image analysis toolkit, offering unique features and high speed of operation, could be exploited in future angiogenic drug tests.

DNA supercoiling-induced shapes alter minicircle hydrodynamic properties.

DNA in cells is organized in negatively supercoiled loops. The resulting torsional and bending strain allows DNA to adopt a surprisingly wide variety of 3-D shapes. This interplay between negative supercoiling, looping, and shape influences how DNA is stored, replicated, transcribed, repaired, and likely every other aspect of DNA activity. To understand the consequences of negative supercoiling and curvature on the hydrodynamic properties of DNA, we submitted 336 bp and 672 bp DNA minicircles to analytical ultracentrifugation (AUC). We found that the diffusion coefficient, sedimentation coefficient, and the DNA hydrodynamic radius strongly depended on circularity, loop length, and degree of negative supercoiling. Because AUC cannot ascertain shape beyond degree of non-globularity, we applied linear elasticity theory to predict DNA shapes, and combined these with hydrodynamic calculations to interpret the AUC data, with reasonable agreement between theory and experiment. These complementary approaches, together with earlier electron cryotomography data, provide a framework for understanding and predicting the effects of supercoiling on the shape and hydrodynamic properties of DNA.

DNA supercoiling-induced shapes alter minicircle hydrodynamic properties.

DNA in cells is organized in negatively supercoiled loops. The resulting torsional and bending strain allows DNA to adopt a surprisingly wide variety of 3-D shapes. This interplay between negative supercoiling, looping, and shape influences how DNA is stored, replicated, transcribed, repaired, and likely every other aspect of DNA activity. To understand the consequences of negative supercoiling and curvature on the hydrodynamic properties of DNA, we submitted 336 bp and 672 bp DNA minicircles to analytical ultracentrifugation (AUC). We found that the diffusion coefficient, sedimentation coefficient, and the DNA hydrodynamic radius strongly depended on circularity, loop length, and degree of negative supercoiling. Because AUC cannot ascertain shape beyond degree of non-globularity, we applied linear elasticity theory to predict DNA shapes, and combined these with hydrodynamic calculations to interpret the AUC data, with reasonable agreement between theory and experiment. These complementary approaches, together with earlier electron cryotomography data, provide a framework for understanding and predicting the effects of supercoiling on the shape and hydrodynamic properties of DNA.

The effect of morphology and particle-wall interaction on colloidal near-wall dynamics.

We investigated the near-wall Brownian dynamics of different types of colloidal particles with a typical size in the 100 nm range using evanescent wave dynamic light scattering (EWDLS). In detail we studied dilute suspensions of silica spheres and shells with a smooth surface and silica particles with controlled surface roughness. While the near wall dynamics of the particle with a smooth surface differ only slightly from the theoretical prediction for hard sphere colloids, the rough particles diffuse significantly slower. We analysed the experimental data by comparison with model calculations and suggest that the deviating dynamics of the rough particles are not due to increased hydrodynamic interaction with the wall. Rather, the particle roughness significantly changes their DLVO interaction with the wall, which in turn affects their diffusion.

The bank of swimming organisms at the micron scale (BOSO-Micro).

Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

Hydrodynamic effects in the capture of rod-like molecules by a nanopore.

In the approach of biomolecules to a nanopore, it is essential to capture the effects of hydrodynamic anisotropy of the molecules and the near-wall hydrodynamic interactions which hinder their diffusion. We present a detailed theoretical analysis of the behaviour of a rod-like molecule attracted electrostatically by a charged nanopore. We first estimate the time scales corresponding to Brownian and electrostatic translations and reorientation. We find that Brownian motion becomes negligible at distances within the pore capture radius, and numerically determine the trajectories of the nano-rod in this region to explore the effects of anisotropic mobility. This allows us to determine the range of directions from the pore in which hydrodynamic interactions with the boundary shape the approach dynamics and need to be accounted for in detailed modelling.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops.

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Light-switchable propulsion of active particles with reversible interactions.

Active systems such as microorganisms and self-propelled particles show a plethora of collective phenomena, including swarming, clustering, and phase separation. Control over the propulsion direction and switchability of the interactions between the individual self-propelled units may open new avenues in designing of materials from within. Here, we present a self-propelled particle system, consisting of half-gold-coated titania (TiO2) particles, in which we can quickly and on-demand reverse the propulsion direction, by exploiting the different photocatalytic activities on both sides. We demonstrate that the reversal in propulsion direction changes the nature of the hydrodynamic interaction from attractive to repulsive and can drive the particle assemblies to undergo both fusion and fission transitions. Moreover, we show these active colloids can act as nucleation sites, and switch rapidly the interactions between active and passive particles, leading to reconfigurable assembly and disassembly. Our experiments are qualitatively described by a minimal hydrodynamic model.

Swimming eukaryotic microorganisms exhibit a universal speed distribution.

One approach to quantifying biological diversity consists of characterizing the statistical distribution of specific properties of a taxonomic group or habitat. Microorganisms living in fluid environments, and for whom motility is key, exploit propulsion resulting from a rich variety of shapes, forms, and swimming strategies. Here, we explore the variability of swimming speed for unicellular eukaryotes based on published data. The data naturally partitions into that from flagellates (with a small number of flagella) and from ciliates (with tens or more). Despite the morphological and size differences between these groups, each of the two probability distributions of swimming speed are accurately represented by log-normal distributions, with good agreement holding even to fourth moments. Scaling of the distributions by a characteristic speed for each data set leads to a collapse onto an apparently universal distribution. These results suggest a universal way for ecological niches to be populated by abundant microorganisms.

Hydrodynamic coupling and rotational mobilities near planar elastic membranes.

We study theoretically and numerically, the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance toward shear and bending. Using a combination of the multipole expansion and Faxén's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self mobilities and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where very good agreement is obtained over the whole range of applied frequencies.

State diagram of a three-sphere microswimmer in a channel.

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.

Swimming trajectories of a three-sphere microswimmer near a wall.

The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that the swimming trajectories near a no-slip wall reveal various scenarios of motion depending on the initial orientation and the distance separating the swimmer from the wall. We find that the swimmer can either be trapped by the wall, completely escape, or perform an oscillatory gliding motion at a constant mean height above the wall. Using a far-field approximation, we find that, at leading order, the wall-induced correction has a source-dipolar or quadrupolar flow structure where the translational and angular velocities of the swimmer decay as inverse third and fourth powers with distance from the wall, respectively. The resulting equations of motion for the trajectories and the relevant order parameters fully characterize the transition between the states and allow for an accurate description of the swimming behavior near a wall. We demonstrate that the transition between the trapping and oscillatory gliding states is first order discontinuous, whereas the transition between the trapping and escaping states is continuous, characterized by non-trivial scaling exponents of the order parameters. In order to model the circular motion of flagellated bacteria near solid interfaces, we further assume that the spheres can undergo rotational motion around the swimming axis. We show that the general three-dimensional motion can be mapped onto a quasi-two-dimensional representational model by an appropriate redefinition of the order parameters governing the transition between the swimming states.

Autophoretic motion in three dimensions.

Janus particles with the ability to move phoretically in self-generated chemical concentration gradients are model systems for active matter. Their motion typically consists of straight paths with rotational diffusion being the dominant reorientation mechanism. In this paper, we show theoretically that by a suitable surface coverage of both activity and mobility, translational and rotational motion can be induced arbitrarily in three dimensions. The resulting trajectories are in general helical, and their pitch and radius can be controlled by adjusting the angle between the translational and angular velocity. Building on the classical mathematical framework for axisymmetric self-phoretic motion under fixed-flux chemical boundary conditions, we first show how to calculate the most general three-dimensional motion for an arbitrary surface coverage of a spherical particle. After illustrating our results on surface distributions, we next introduce a simple intuitive patch model to serve as a guide for designing arbitrary phoretic spheres.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane. II. Asymmetric motion.

In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance toward shearing and bending. Together with the results obtained in the first part [Daddi-Moussa-Ider and Gekle, Phys. Rev. E 95, 013108 (2017)2470-004510.1103/PhysRevE.95.013108], where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero-frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a nonvanishing resistance toward shearing. We further compute the in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.

The non-Gaussian tops and tails of diffusing boomerangs.

Experiments involving the two-dimensional passive diffusion of colloidal boomerangs tracked off their centre of mobility have shown striking non-Gaussian tails in their probability distribution function [Chakrabarty et al., Soft Matter, 2016, 12, 4318]. This in turn can lead to anomalous diffusion characteristics, including mean drift. In this paper, we develop a general theoretical explanation for these measurements. The idea relies on calculating the two-dimensional probability densities at the centre of mobility of the particle, where all distributions are Gaussian, and then transforming them to a different reference point. Our model clearly captures the experimental results, without any fitting parameters, and demonstrates that the one-dimensional probability distributions may also exhibit strongly non-Gaussian tops. These results indicate that the choice of tracking point can cause a considerable departure from Gaussian statistics, potentially causing some common modelling techniques to fail.

Near-wall diffusion tensor of an axisymmetric colloidal particle.

Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple functions in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings.

Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations.

In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.