Flagellar flows around bacterial swarms

Flagellated bacteria on nutrient-rich substrates can differentiate into a swarming state and move in dense swarms across surfaces. A recent experiment measured the flow in the fluid around an Escherichia coli swarm (Wu, Hosu and Berg, 2011 Proc. Natl. Acad. Sci. USA 108 4147). A systematic chiral flow was observed in the clockwise direction (when viewed from above) ahead of the swarm with flow speeds of about 10 µm/s, about 3 times greater than the radial velocity at the edge of the swarm. The working hypothesis is that this flow is due to the action of cells stalled at the edge of a colony which extend their flagellar filaments outwards, moving fluid over the virgin agar. In this work we quantitatively test his hypothesis. We first build an analytical model of the flow induced by a single flagellum in a thin film and then use the model, and its extension to multiple flagella, to compare with experimental measurements. The results we obtain are in agreement with the flagellar hypothesis. The model provides further quantitative insight on the flagella orientations and their spatial distributions as well as the tangential speed profile. In particular, the model suggests that flagella are on average pointing radially out of the swarm and are not wrapped tangentially.This work was funded in part by the Engineering and Physical Sciences Research Council (JD) and the European Union through a Marie Curie CIG Grant (EL).This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by the American Physical Society

Ice shelves as floating channel flows of viscous power-law fluids

IB is supported by a Science and Technology Facilities Council studentship.We explain the force balance in flowing marine ice sheets and the ice shelves they often feed. Treating ice as a viscous shear-thinning power law fluid, we develop an asymptotic (late-time) theory in two cases: the presence or absence of contact with sidewalls. Most real-world situations fall somewhere between the two extreme cases considered. The solution when sidewalls are absent is a fairly simple generalization of that found by Robison (JFM, 648, 363). In this case, we obtain the equilibrium grounding line thickness using a simple computer model and have an analytic approximation. For shelves in contact with sidewalls, we obtain an asymptotic theory valid for long shelves. We determine when this is. Our theory is based on the velocity profile across the channel being a generalized version of Poiseuille flow, which works when lateral shear dominates the force balance. We conducted experiments using a laboratory model for ice. This was a suspension of xanthan in water, at a concentration of 0.5% by mass. The model has n ≈ 3.8, similar to that of ice. Our theories agreed extremely well with our experiments for all relevant parameters (front position, thickness profile, lateral velocity profile, longitudinal velocity gradient and grounding line thickness). We also saw detailed features similar to natural systems. Thus, we believe we have understood the dominant force balance in both types of ice shelf. Combining our understanding of the forces in the system with a basic model for basal melting and iceberg formation, we uncovered some instabilities of the natural system. Laterally confined ice shelves can rapidly disintegrate but ice tongues cannot. However, ice tongues can be shortened until they no longer exist, at which point the sheet becomes unstable and ultimately the grounding line should retreat above sea level. While the ice tongue still exists, the flow of ice into it should not be speeded up and the grounding line should also not retreat, assuming that only conditions in the ocean change. However, laterally confined ice shelves experience significant buttressing. If removed, this leads to a rapid speed-up of the sheet and a new equilibrium grounding line thickness. We believe that something like this occurred in the Larsen B ice shelf.Publisher PDFPeer reviewe

Leading-order Stokes flows near a corner

Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, and can be exploited to derive asymptotic flows in a wide range of physical problems. The most funda- mental singular solution is the flow’s Green function due to a point force, termed the Stokeslet. Its expression is classical both in free space and near a flat surface. Motivated by problems in biological physics occurring near corners, we derive in this paper the asymptotic behaviour for the Stokeslet both near and far from a corner geometry by using complex analysis on a known double integral solution for corner flows. We investigate all possible orientations of the point force relative to the corner and all corner geometries from acute to obtuse. The case of salient corners is also addressed for point forces aligned with both walls. We use experiments on beads sed- imenting in corn syrup to qualitatively test the applicability of our results. The final results and scaling laws will allow to address the role of hydrodynamic interactions in problems from colloidal science to microfluidics and biological physics

Helical micropumps near surfaces

Recent experiments proposed to use confined bacteria in order to generate flows near surfaces. We develop a mathematical and a computational model of this fluid transport using a linear superposition of fundamental flow singularities. The rotation of a helical bacterial flagellum induces both a force and a torque on the surrounding fluid, both of which lead to a net flow along the surface. The combined flow is in general directed at an angle to the axis of the flagellar filament. The optimal pumping is thus achieved when bacteria are tilted with respect to the direction in which one wants to move the fluid, in good agreement with experimental results. We further investigate the optimal helical shapes to be used as micropumps near surfaces and show that bacterial flagella are nearly optimal, a result which could be relevant to the expansion of bacterial swarms.This work was funded in part by an ERC Consolidator grant from the European Union (EL)

Leading-order Stokes flows near a corner

Singular solutions of the Stokes equations play important roles in a variety of fluid dynamics problems. They allow the calculation of exact flows, are the basis of the boundary integral methods used in numerical computations, and can be exploited to derive asymptotic flows in a wide range of physical problems. The most funda- mental singular solution is the flow’s Green function due to a point force, termed the Stokeslet. Its expression is classical both in free space and near a flat surface. Motivated by problems in biological physics occurring near corners, we derive in this paper the asymptotic behaviour for the Stokeslet both near and far from a corner geometry by using complex analysis on a known double integral solution for corner flows. We investigate all possible orientations of the point force relative to the corner and all corner geometries from acute to obtuse. The case of salient corners is also addressed for point forces aligned with both walls. We use experiments on beads sed- imenting in corn syrup to qualitatively test the applicability of our results. The final results and scaling laws will allow to address the role of hydrodynamic interactions in problems from colloidal science to microfluidics and biological physics

Rapid and automated design of two-component protein nanomaterials using ProteinMPNN

The design of protein-protein interfaces using physics-based design methods such as Rosetta requires substantial computational resources and manual refinement by expert structural biologists. Deep learning methods promise to simplify protein-protein interface design and enable its application to a wide variety of problems by researchers from various scientific disciplines. Here, we test the ability of a deep learning method for protein sequence design, ProteinMPNN, to design two-component tetrahedral protein nanomaterials and benchmark its performance against Rosetta. ProteinMPNN had a similar success rate to Rosetta, yielding 13 new experimentally confirmed assemblies, but required orders of magnitude less computation and no manual refinement. The interfaces designed by ProteinMPNN were substantially more polar than those designed by Rosetta, which facilitated in vitro assembly of the designed nanomaterials from independently purified components. Crystal structures of several of the assemblies confirmed the accuracy of the design method at high resolution. Our results showcase the potential of deep learning-based methods to unlock the widespread application of designed protein-protein interfaces and self-assembling protein nanomaterials in biotechnology

Robust deep learning-based protein sequence design using ProteinMPNN

Although deep learning has revolutionized protein structure prediction, almost all experimentally characterized de novo protein designs have been generated using physically based approaches such as Rosetta. Here, we describe a deep learning-based protein sequence design method, ProteinMPNN, that has outstanding performance in both in silico and experimental tests. On native protein backbones, ProteinMPNN has a sequence recovery of 52.4% compared with 32.9% for Rosetta. The amino acid sequence at different positions can be coupled between single or multiple chains, enabling application to a wide range of current protein design challenges. We demonstrate the broad utility and high accuracy of ProteinMPNN using x-ray crystallography, cryo-electron microscopy, and functional studies by rescuing previously failed designs, which were made using Rosetta or AlphaFold, of protein monomers, cyclic homo-oligomers, tetrahedral nanoparticles, and target-binding proteins

Improving Protein Expression, Stability, and Function with ProteinMPNN

Natural proteins are highly optimized for function but are often difficult to produce at a scale suitable for biotechnological applications due to poor expression in heterologous systems, limited solubility, and sensitivity to temperature. Thus, a general method that improves the physical properties of native proteins while maintaining function could have wide utility for protein-based technologies. Here, we show that the deep neural network ProteinMPNN, together with evolutionary and structural information, provides a route to increasing protein expression, stability, and function. For both myoglobin and tobacco etch virus (TEV) protease, we generated designs with improved expression, elevated melting temperatures, and improved function. For TEV protease, we identified multiple designs with improved catalytic activity as compared to the parent sequence and previously reported TEV variants. Our approach should be broadly useful for improving the expression, stability, and function of biotechnologically important proteins

De novo design of luciferases using deep learning.

De novo enzyme design has sought to introduce active sites and substrate-binding pockets that are predicted to catalyse a reaction of interest into geometrically compatible native scaffolds1,2, but has been limited by a lack of suitable protein structures and the complexity of native protein sequence-structure relationships. Here we describe a deep-learning-based 'family-wide hallucination' approach that generates large numbers of idealized protein structures containing diverse pocket shapes and designed sequences that encode them. We use these scaffolds to design artificial luciferases that selectively catalyse the oxidative chemiluminescence of the synthetic luciferin substrates diphenylterazine3 and 2-deoxycoelenterazine. The designed active sites position an arginine guanidinium group adjacent to an anion that develops during the reaction in a binding pocket with high shape complementarity. For both luciferin substrates, we obtain designed luciferases with high selectivity; the most active of these is a small (13.9 kDa) and thermostable (with a melting temperature higher than 95 °C) enzyme that has a catalytic efficiency on diphenylterazine (kcat/Km = 106 M-1 s-1) comparable to that of native luciferases, but a much higher substrate specificity. The creation of highly active and specific biocatalysts from scratch with broad applications in biomedicine is a key milestone for computational enzyme design, and our approach should enable generation of a wide range of luciferases and other enzymes

Improving Protein Expression, Stability, and Function with ProteinMPNN

Natural proteins are highly optimized for function but are often difficult to produce at a scale suitable for biotechnological applications due to poor expression in heterologous systems, limited solubility, and sensitivity to temperature. Thus, a general method that improves the physical properties of native proteins while maintaining function could have wide utility for protein-based technologies. Here, we show that the deep neural network ProteinMPNN, together with evolutionary and structural information, provides a route to increasing protein expression, stability, and function. For both myoglobin and tobacco etch virus (TEV) protease, we generated designs with improved expression, elevated melting temperatures, and improved function. For TEV protease, we identified multiple designs with improved catalytic activity as compared to the parent sequence and previously reported TEV variants. Our approach should be broadly useful for improving the expression, stability, and function of biotechnologically important proteins