Breakthrough-induced loop formation in evolving transport networks.

Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However, the dynamics of their formation is usually not considered. Such structures often grow in response to the gradient of an external field. During evolution, extending branches compete for the available flux of the field, which leads to effective repulsion between them and screening of the shorter ones. Yet, in remarkably diverse processes, from unstable fluid flows to the canal system of jellyfish, loops suddenly form near the breakthrough when the longest branch reaches the boundary of the system. We provide a physical explanation for this universal behavior. Using a 1D model, we explain that the appearance of effective attractive forces results from the field drop inside the leading finger as it approaches the outlet. Furthermore, we numerically study the interactions between two fingers, including screening in the system and its disappearance near the breakthrough. Finally, we perform simulations of the temporal evolution of the fingers to show how revival and attraction to the longest finger leads to dynamic loop formation. We compare the simulations to the experiments and find that the dynamics of the shorter finger are well reproduced. Our results demonstrate that reconnection is a prevalent phenomenon in systems driven by diffusive fluxes, occurring both when the ratio of the mobility inside the growing structure to the mobility outside is low and near the breakthrough.

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.

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.

First coarse grain then scale: How to estimate diffusion coefficients of confined molecules.

An approach for approximating position and orientation dependent translational and rotational diffusion coefficients of rigid molecules of any shape suspended in a viscous fluid under geometric confinement is proposed. It is an extension of the previously developed scheme for evaluating near-wall diffusion of macromolecules, now applied to any geometry of boundaries. The method relies on shape based coarse-graining combined with scaling of mobility matrix components by factors derived based on energy dissipation arguments for Stokes flows. Tests performed for a capsule shaped molecule and its coarse-grained model, a dumbbell, for three different types of boundaries (a sphere, an open cylinder, and two parallel planes) are described. An almost perfect agreement between mobility functions of the detailed and coarse-grained models, even close to boundary surfaces, is obtained. The proposed method can be used to simplify hydrodynamic calculations and reduce errors introduced due to coarse-graining of molecular shapes.

Correction: Stokesian dynamics of sedimenting elastic rings.

Correction for 'Stokesian dynamics of sedimenting elastic rings' by Magdalena Gruziel-Slomka et al., Soft Matter, 2019, 15, 7262-7274, https://doi.org/10.1039/C9SM00598F.

Generalized Rotne-Prager-Yamakawa approximation for Brownian dynamics in shear flow in bounded, unbounded, and periodic domains.

Inclusion of hydrodynamic interactions is essential for a quantitatively accurate Brownian dynamics simulation of colloidal suspensions or polymer solutions. We use the generalized Rotne-Prager-Yamakawa (GRPY) approximation, which takes into account all long-ranged terms in the hydrodynamic interactions, to derive the complete set of hydrodynamic matrices in different geometries: unbounded space, periodic boundary conditions of Lees-Edwards type, and vicinity of a free surface. The construction is carried out both for non-overlapping as well as for overlapping particles. We include the dipolar degrees of freedom, which allows one to use this formalism to simulate the dynamics of suspensions in a shear flow and to study the evolution of their rheological properties. Finally, we provide an open-source numerical package, which implements the GRPY algorithm in Lees-Edwards periodic boundary conditions.

Ions in an AC Electric Field: Strong Long-Range Repulsion between Oppositely Charged Surfaces.

Two oppositely charged surfaces separated by a dielectric medium attract each other. In contrast we observe a strong repulsion between two plates of a capacitor that is filled with an aqueous electrolyte upon application of an alternating potential difference between the plates. This long-range force increases with the ratio of diffusion coefficients of the ions in the medium and reaches a steady state after a few minutes, which is much larger than the millisecond timescale of diffusion across the narrow gap. The repulsive force, an order of magnitude stronger than the electrostatic attraction observed in the same setup in air, results from the increase in osmotic pressure as a consequence of the field-induced excess of cations and anions due to lateral transport from adjacent reservoirs.

Stokesian dynamics of sedimenting elastic rings.

We consider elastic microfilaments which form closed loops. We investigate how the loops change shape and orientation while settling under gravity in a viscous fluid. Loops are circular at the equilibrium. Their dynamics are investigated numerically based on the Stokes equations for the fluid motion and the bead-spring model of the microfilament. The Rotne-Prager approximation for the bead mobility is used. We demonstrate that the relevant dimensionless parameter is the ratio of the bending resistance of the filament to the gravitation force corrected for buoyancy. The inverse of this ratio, called the elasto-gravitation number B, is widely used in the literature for sedimenting elastic linear filaments. We assume that B is of the order of 104-106, which corresponds to easily deformable loops. We find out that initially tilted circles evolve towards different sedimentation modes, depending on B. Very stiff or stiff rings attain almost planar, oval shapes, which are vertical or tilted, respectively. More flexible loops deform significantly and converge towards one of several characteristic periodic motions. These sedimentation modes are also detected when starting from various shapes, and for different loop lengths. In general, multi-stability is observed: an elastic ring converges to one of several sedimentation modes, depending on the initial conditions. This effect is pronounced for very elastic loops. The surprising diversity of long-lasting periodic motions and shapes of elastic rings found in this work gives a new perspective for the dynamics of more complex deformable objects at micrometer and nanometer scales, sedimenting under gravity or rotating in a centrifuge, such as red blood cells, ring polymers or circular DNA.

GRPY: An Accurate Bead Method for Calculation of Hydrodynamic Properties of Rigid Biomacromolecules.

Two main problems that arise in the context of hydrodynamic bead modeling are an inaccurate treatment of bead overlaps and the necessity of using volume corrections when calculating intrinsic viscosity. We present a formalism based on the generalized Rotne-Prager-Yamakawa approximation that successfully addresses both of these issues. The generalized Rotne-Prager-Yamakawa method is shown to be highly effective for the calculation of transport properties of rigid biomolecules represented as assemblies of spherical beads of different sizes, both overlapping and nonoverlapping. We test the method on simple molecular shapes as well as real protein structures and compare its performance with other computational approaches.

Periodic Motion of Sedimenting Flexible Knots.

We study the dynamics of knotted deformable closed chains sedimenting in a viscous fluid. We show experimentally that trefoil and other torus knots often attain a remarkably regular horizontal toroidal structure while sedimenting, with a number of intertwined loops, oscillating periodically around each other. We then recover this motion numerically and find out that it is accompanied by a very slow rotation around the vertical symmetry axis. We analyze the dependence of the characteristic timescales on the chain flexibility and aspect ratio. It is observed in the experiments that this oscillating mode of the dynamics can spontaneously form even when starting from a qualitatively different initial configuration. In numerical simulations, the oscillating modes are usually present as transients or final stages of the evolution, depending on chain aspect ratio and flexibility, and the number of loops.

Path selection in the growth of rivers.

River networks exhibit a complex ramified structure that has inspired decades of studies. However, an understanding of the propagation of a single stream remains elusive. Here we invoke a criterion for path selection from fracture mechanics and apply it to the growth of streams in a diffusion field. We show that, as it cuts through the landscape, a stream maintains a symmetric groundwater flow around its tip. The local flow conditions therefore determine the growth of the drainage network. We use this principle to reconstruct the history of a network and to find a growth law associated with it. Our results show that the deterministic growth of a single channel based on its local environment can be used to characterize the structure of river networks.

Beware of Cocktails: Chain-Length Bidispersity Triggers Explosive Self-Assembly of Poly-L-Glutamic Acid ß2-Fibrils.

Chain-length polydispersity is among the least understood factors governing the fibrillation propensity of homopolypeptides. For monodisperse poly-L-glutamic acid (PLGA), the tendency to form fibrils depends of the main-chain length. Long-chained PLGA, so-called (Glu)200, fibrillates more readily than short (Glu)5 fragments. Here we show that conversion of α-helical (Glu)200 into amyloid-like ß-fibrils is dramatically accelerated in the presence of intrinsically disordered (Glu)5. While separately self-assembled fibrils of (Glu)200 and (Glu)5 reveal distinct morphological and infrared characteristics, accelerated fibrillation in mixed (Glu)200 and (Glu)5 leads to aggregates similar to neat (Glu)200 fibrils, even in excess of (Glu)5. According to molecular dynamics simulations and circular dichroism measurements, local events of "misfolding transfer" from (Glu)5 to (Glu)200 may play a key role in the initial stages of conformational dynamics underlying the observed phenomenon. Our results highlight chain-length polydispersity as a potent, although so-far unrecognized factor profoundly affecting the fibrillation propensity of homopolypeptides.

From ribbons to tubules: a computational study of the polymorphism in aggregation of helical filaments.

A simple, coarse-grained model of chiral, helical filaments is used to study the polymorphism of fibrous aggregates. Three generic morphologies of the aggregates are observed: ribbons, in which the filaments are joined side-by-side, twisted, helicoidal fibrils, in which filaments entwine along each other and tubular forms, with filaments wound together around a hollow core of the tube. A relative simplicity of the model allows us to supplement numerical simulations with an analytic description of the elastic properties of the aggregates. The model is capable of predicting geometric and structural characteristics of the composite structures, as well as their relative stabilities. We also investigate in detail the transitions between different morphologies of the aggregates.

Protein unfolding by biological unfoldases: insights from modeling.

The molecular determinants of the high efficiency of biological machines like unfoldases (e.g., the proteasome) are not well understood. We propose a model to study protein translocation into the chamber of biological unfoldases represented as a funnel. It is argued that translocation is a much faster way of unfolding a protein than end-to-end stretching, especially in a low-force regime, because it allows for a conformational freedom while concentrating local tension on consecutive regions of a protein chain and preventing refolding. This results in a serial unfolding of the protein structures dominated by unzipping. Thus, pulling against the unfoldase pore is an efficient catalyst of the unfolding reaction. We also show that the presence of the funnel makes the tension along the backbone of the substrate protein nonuniform even when the protein gets unfolded. Hence, the stalling force measured by single-molecule force spectroscopy techniques may be smaller than the traction force of the unfoldase motor.

The Rotne-Prager-Yamakawa approximation for periodic systems in a shear flow.

Rotne-Prager-Yamakawa approximation is a commonly used approach to model hydrodynamic interactions between particles suspended in fluid. It takes into account all the long-range contributions to the hydrodynamic tensors, with the corrections decaying at least as fast as the inverse fourth power of the interparticle distances, and results in a positive definite mobility matrix, which is fundamental in Brownian dynamics simulations. In this communication, we show how to construct the Rotne-Prager-Yamakawa approximation for the bulk system under shear flow, which is modeled using the Lees-Edwards boundary conditions.

The Development of Sustainable Polyethylene Terephthalate Glycol-Based (PETG) Blends for Additive Manufacturing Processing-The Use of Multilayered Foil Waste as the Blend Component.

The polymer foil industry is one of the leading producers of plastic waste. The development of new recycling methods for packaging products is one of the biggest demands in today's engineering. The subject of this research was the melt processing of multilayered PET-based foil waste with PETG copolymer. The resulting blends were intended for additive manufacturing processing using the fused deposition modeling (FDM) method. In order to improve the properties of the developed materials, the blends compounding procedure was conducted with the addition of a reactive chain extender (CE) and elastomeric copolymer used as an impact modifier (IM). The samples were manufactured using the 3D printing technique and, for comparison, using the traditional injection molding method. The obtained samples were subjected to a detailed characterization procedure, including mechanical performance evaluation, thermal analysis, and rheological measurements. This research confirms that PET-based film waste can be successfully used for the production of filament, and for most samples, the FDM printing process can be conducted without any difficulties. Unfortunately, the unmodified blends are characterized by brittleness, which makes it necessary to use an elastomer additive (IM). The presence of a semicrystalline PET phase improves the thermal resistance of the prepared blends; however, an annealing procedure is required for this purpose.

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.

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.

Tight knots in proteins: can they block the mitochondrial pores?

Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process since the diameter of the pore is smaller than the size of maximally tightened knot. In the present article, I briefly review the experimental and numerical studies of tight knots in proteins, with a particular emphasis on the estimates of the size of these knots. Next, I discuss the process of protein translocation through the mitochondrial pores and report the results of molecular dynamics simulations of knotted protein translocation, which show how the knot can indeed block the pore.

A multi-scale molecular dynamics study of the assembly of micron-size supraparticles from 30 nm alkyl-coated nanoparticles.

Atomistic and meso scale computer simulations of nanoparticle aggregation are combined to describe the self-assembly of supraparticles in bulk and on surfaces under vacuum conditions. At the nano scale, atomic resolution molecular dynamics simulations provide the structures of 30 nm-diameter nanoparticles bound to each other and to coated hydrophobic surfaces, through the physical contacting of their alkyl coats. This "molecular velcro" has been recently exploited in experiments to direct the aggregation of coated nanoparticles into stable assemblies on electronics platforms. Interaction potentials are extracted from the nano scale simulations and transferred to coarse grained Brownian dynamics simulations that describe multi-nanoparticle aggregation and surface deposition. The simulation results show that the large interaction area between 30 nm nanoparticles provides a strong driving force for assembly of strongly-welded, porous supraparticles under vacuum conditions. Interaction forces are significantly larger than those found in earlier simulations of the aggregation of smaller nanoparticles, indicating that supraparticle assembly using large 30 nm nanoparticles may be kinetically controlled. The porosity programmed into kinetic assembly may potentially benefit emerging applications of nanoparticle assemblies in medicine, in particular the development of nanostructured drug-eluting stent coatings. Future work will involve potential of mean force calculations in a variety of solvents to estimate the porosity obtainable for specific applications.