On the mechanical origins of waving, coiling and skewing in Arabidopsis thaliana roots.

By masterfully balancing directed growth and passive mechanics, plant roots are remarkably capable of navigating complex heterogeneous environments to find resources. Here, we present a theoretical and numerical framework which allows us to interrogate and simulate the mechanical impact of solid interfaces on the growth pattern of plant organs. We focus on the well-known waving, coiling, and skewing patterns exhibited by roots of Arabidopsis thaliana when grown on inclined surfaces, serving as a minimal model of the intricate interplay with solid substrates. By modeling growing slender organs as Cosserat rods that mechanically interact with the environment, our simulations verify hypotheses of waving and coiling arising from the combination of active gravitropism and passive root-plane responses. Skewing is instead related to intrinsic twist due to cell file rotation. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving, coiling, and skewing patterns with substrate tilt angle. Simulations are found to corroborate theory and recapitulate a host of reported experimental observations, thus providing a systematic approach for studying in silico plant organs behavior in relation to their environment.

A quantitative model for spatio-temporal dynamics of root gravitropism.

Plant organs adapt their morphology according to environmental signals through growth-driven processes called tropisms. While much effort has been directed towards the development of mathematical models describing the tropic dynamics of aerial organs, these cannot provide a good description of roots due to intrinsic physiological differences. Here we present a mathematical model informed by gravitropic experiments on Arabidopsis thaliana roots, assuming a subapical growth profile and apical sensing. The model quantitatively recovers the full spatio-temporal dynamics observed in experiments. An analytical solution of the model enables us to evaluate the gravitropic and proprioceptive sensitivities of roots, while also allowing us to corroborate the requirement for proprioception in describing root dynamics. Lastly, we find that the dynamics are analogous to a damped harmonic oscillator, providing intuition regarding the source of the observed oscillatory behavior and the importance of proprioception for efficient gravitropic control. In all, the model provides not only a quantitative description of root tropic dynamics, but also a mathematical framework for the future investigation of roots in complex media.

A General 3D Model for Growth Dynamics of Sensory-Growth Systems: From Plants to Robotics.

In recent years, there has been a rise in interest in the development of self-growing robotics inspired by the moving-by-growing paradigm of plants. In particular, climbing plants capitalize on their slender structures to successfully negotiate unstructured environments while employing a combination of two classes of growth-driven movements: tropic responses, growing toward or away from an external stimulus, and inherent nastic movements, such as periodic circumnutations, which promote exploration. In order to emulate these complex growth dynamics in a 3D environment, a general and rigorous mathematical framework is required. Here, we develop a general 3D model for rod-like organs adopting the Frenet-Serret frame, providing a useful framework from the standpoint of robotics control. Differential growth drives the dynamics of the organ, governed by both internal and external cues while neglecting elastic responses. We describe the numerical method required to implement this model and perform numerical simulations of a number of key scenarios, showcasing the applicability of our model. In the case of responses to external stimuli, we consider a distant stimulus (such as sunlight and gravity), a point stimulus (a point light source), and a line stimulus that emulates twining of a climbing plant around a support. We also simulate circumnutations, the response to an internal oscillatory cue, associated with search processes. Lastly, we also demonstrate the superposition of the response to an external stimulus and circumnutations. In addition, we consider a simple example illustrating the possible use of an optimal control approach in order to recover tropic dynamics in a way that may be relevant for robotics use. In all, the model presented here is general and robust, paving the way for a deeper understanding of plant response dynamics and also for novel control systems for newly developed self-growing robots.

Towards a framework for collective behavior in growth-driven systems, based on plant-inspired allotropic pairwise interactions.

A variety of biological systems are not motile, but sessile in nature, relying on growth as the main driver of their movement. Groups of such growing organisms can form complex structures, such as the functional architecture of growing axons, or the adaptive structure of plant root systems. These processes are not yet understood, however the decentralized growth dynamics bear similarities to the collective behavior observed in groups of motile organisms, such as flocks of birds or schools of fish. Equivalent growth mechanisms make these systems amenable to a theoretical framework inspired by tropic responses of plants, where growth is considered implicitly as the driver of the observed bending towards a stimulus. We introduce two new concepts related to plant tropisms: point tropism, the response of a plant to a nearby point signal source, and allotropism, the growth-driven response of plant organs to neighboring plants. We first analytically and numerically investigate the 2D dynamics of single organs responding to point signals fixed in space. Building on this we study pairs of organs interacting via allotropism, i.e. each organ senses signals emitted at the tip of their neighbor and responds accordingly. In the case of local sensing we find a rich state-space. We describe the different states, as well as the sharp transitions between them. We also find that the form of the state-space depends on initial conditions. This work sets the stage towards a theoretical framework for the investigation and understanding of systems of interacting growth-driven individuals.

Elastowetting of Soft Hydrogel Spheres.

When a soft hydrogel sphere is placed on a rigid hydrophilic substrate, it undergoes arrested spreading by forming an axisymmetric foot near the contact line, while conserving its global spherical shape. In contrast, liquid water (that constitutes greater than 90% of the hydrogel's volume) spreads into a thin film on the same surface. We study systematically this elastowetting of gel spheres on substrates of different surface energies and find that their contact angle increases as the work of adhesion between the gel and the substrate decreases, as one would observe for drops of pure water-albeit being larger than in the latter case. This difference in the contact angles of gel and water appears to be due to the elastic shear stresses that develop in the gel and oppose its spreading. Indeed, by increasing the elastic modulus of the gel spheres, we find that their contact angle also increases. In addition, the length of the contact foot increases with the work of adhesion and sphere size, while it decreases when the elastic modulus of the gel is increased. We discuss those experimental results in light of a minimal analysis based on energy minimization, volume conservation, and scaling arguments.

Elastocapillary bending of microfibers around liquid droplets.

We report on the elastocapillary deformation of flexible microfibers in contact with liquid droplets. A fiber is observed to bend more as the size of the contacting droplet is increased. At a critical droplet size, proportional to the bending elastocapillary length, the fiber is seen to spontaneously wind around the droplet. To rationalize these observations, we invoke a minimal model based on elastic beam theory, and find agreement with experimental data. Further energetic considerations provide a consistent prediction for the winding criterion.

Widefield lensless imaging through a fiber bundle via speckle correlations.

Flexible fiber-optic endoscopes provide a solution for imaging at depths beyond the reach of conventional microscopes. Current endoscopes require focusing and/or scanning mechanisms at the distal end, which limit miniaturization, frame-rate, and field of view. Alternative wavefront-shaping based lensless solutions are extremely sensitive to fiber-bending. We present a lensless, bend-insensitive, single-shot imaging approach based on speckle-correlations in fiber bundles that does not require wavefront shaping. Our approach computationally retrieves the target image by analyzing a single camera frame, exploiting phase information that is inherently preserved in propagation through convnetional fiber bundles. Unlike conventional fiber-based imaging, planar objects can be imaged at variable working distances, the resulting image is unpixelated and diffraction-limited, and miniaturization is limited only by the fiber diameter.

A novel anion-exchange resin suitable for both discovery research and clinical manufacturing purposes.

Strong ion-exchange protein chromatography is one of the most powerful and most common steps for protein purification in both discovery research and manufacturing. However, the demands on protein purification of early drug discovery and later stage manufacturing are quite different. In order to shorten the time of developing a purification process for new protein drug candidates, there is a need for a strong ion-exchange resin that will be optimum for both stages. This article details a novel anion-exchange resin suitable for research, as well as for clinical manufacturing. In this study, a novel Q resin anion-exchange prototype was evaluated and compared to the GE Healthcare Q Sepharose® Fast Flow (QFF) and Q Sepharose® High Performance (QHP) resins. This study specifically focused on the following: resolution, dynamic binding capacity, flow rate, back pressure, and scale up. The evaluation was performed in both small- and large-scale experiments. From all the comparable data, the prototype resin is adaptable for both discovery research and manufacturing. Its wide-range operation suitability could potentially shorten the time required to develop conventional purification protocols for clinical manufacturing.

Redox-active cysteines of a membrane electron transporter DsbD show dual compartment accessibility.

The membrane-embedded domain of the unusual electron transporter DsbD (DsbDbeta) uses two redox-active cysteines to catalyze electron transfer between thioredoxin-fold polypeptides on opposite sides of the bacterial cytoplasmic membrane. How the electrons are transferred across the membrane is unknown. Here, we show that DsbDbeta displays an inherent functional and structural symmetry: first, the two cysteines of DsbDbeta can be alkylated from both the cytoplasm and the periplasm. Second, when the two cysteines are disulfide-bonded, cysteine scanning shows that the C-terminal halves of the cysteine-containing transmembrane segments 1 and 4 are exposed to the aqueous environment while the N-terminal halves are not. Third, proline residues located pseudo-symmetrically around the two cysteines are required for redox activity and accessibility of the cysteines. Fourth, mixed disulfide complexes, apparent intermediates in the electron transfer process, are detected between DsbDbeta and thioredoxin molecules on each side of the membrane. We propose a model where the two redox-active cysteines are located at the center of the membrane, accessible on both sides of the membrane to the thioredoxin proteins.

The reducing activity of glutaredoxin 3 toward cytoplasmic substrate proteins is restricted by methionine 43.

The reducing proteins glutaredoxin 3 (Grx3) and glutaredoxin 1 (Grx1) are structurally similar but exhibit different specificities toward substrates. Grx1 efficiently reduces ribonucleotide reductase and PAPS reductase, while Grx3 reduces these enzymes inefficiently or not at all. We previously described a selection for Grx3 mutants with increased activity toward substrates of Grx1 in vivo. Remarkably, we repeatedly isolated mutants with changes in only one of the amino acids of Grx3, methionine 43, converting it to either valine, leucine, or isoleucine. In this paper we present additional genetic studies and a biochemical characterization of Grx3-Met43Val, the most efficient mutant. We show that Grx3-Met43Val is able to reduce ribonucleotide reductae and PAPS reductase much more efficiently than the wild-type protein in vitro. The altered protein has an increased Vmax over that of Grx3, nearly the same Vmax as Grx1 while the Km remains high. Molecular dynamics simulations suggest that the Met43Val substitution results in changes in properties of the N-terminal cysteine of the active site leading to a considerably lower pKa. Furthermore, Grx3-Met43Val shows an 11 mV lower redox potential than the wild-type Grx3. These findings provide biochemical and structural explanations for the increased reductive efficiency of the mutant Grx3.

The unusual transmembrane electron transporter DsbD and its homologues: a bacterial family of disulfide reductases.

The bacterial membrane protein DsbD transfers electrons across the cytoplasmic membrane to reduce protein disulfide bonds in extracytoplasmic proteins. Its substrates include protein disulfide isomerases and a protein involved in cytochrome c assembly. Two membrane-embedded cysteines in DsbD alternate between the disulfide-bonded (oxidized) and reduced states in this process.

Interactions of glutaredoxins, ribonucleotide reductase, and components of the DNA replication system of Escherichia coli.

A strain of Escherichia coli missing three members of the thioredoxin superfamily, thioredoxins 1 and 2 and glutaredoxin 1, is unable to grow, a phenotype presumed to be due to the inability of cells to reduce the essential enzyme ribonucleotide reductase. Two classes of mutations can restore growth to such a strain. First, we have isolated a collection of mutations in the gene for the protein glutaredoxin 3 that suppress the growth defect. Remarkably, all eight independent mutations alter the same amino acid, methionine-43, changing it to valine, isoleucine, or leucine. From the position of the amino acid changes and their effects, we propose that these alterations change the protein so that its properties are closer to those of glutaredoxin 1. The second means of suppressing the growth defects of the multiply mutant strain was by mutations in the DNA replication genes, dnaA and dnaN. These mutations substantially increase the expression of ribonucleotide reductase, most likely by altering the interaction of the regulatory protein DnaA with the ribonucleotide reductase promoter. Our results suggest that this increase in the concentration of ribonucleotide reductase in the cell allows more effective interaction with glutaredoxin 3, thus restoring an effective pool of deoxyribonucleotides. Our studies present direct evidence that ribonucleotide reductase is the only essential enzyme that requires the three reductive proteins missing in our strains. Our results also suggest an unexpected regulatory interaction between the DnaA and DnaN proteins.

Intra-Golgi protein transport depends on a cholesterol balance in the lipid membrane.

Transport of proteins between intracellular membrane compartments is mediated by a protein machinery that regulates the budding and fusion processes of individual transport steps. Although the core proteins of both processes are defined at great detail, much less is known about the involvement of lipids. Here we report that changing the cellular balance of cholesterol resulted in changes of the morphology of the Golgi apparatus, accompanied by an inhibition of protein transport. By using a well characterized cell-free intra-Golgi transport assay, these observations were further investigated, and it was found that the transport reaction is sensitive to small changes in the cholesterol content of Golgi membranes. Addition as well as removal of cholesterol (10 +/- 6%) to Golgi membranes by use of methyl-beta-cyclodextrin specifically inhibited the intra-Golgi transport assay. Transport inhibition occurred at the fusion step. Modulation of the cholesterol content changed the lipid raft partitioning of phosphatidylcholine and heterotrimeric G proteins, but not of other (non) lipid raft proteins and lipids. We suggest that the cholesterol balance in Golgi membranes plays an essential role in intra-Golgi protein transport and needs to be carefully regulated to maintain the structural and functional organization of the Golgi apparatus.