A Copper-Selective Sensor and Its Inhibition of Copper-Amyloid Beta Aggregation.

Copper is an essential trace metal for biological processes in humans and animals. A low level of copper detection at physiological pH using fluorescent probes is very important for in vitro applications, such as the detection of copper in water or urine, and in vivo applications, such as tracking the dynamic copper concentrations inside cells. Copper homeostasis is disrupted in neurological diseases like Alzheimer's disease, and copper forms aggregates with amyloid beta (Ab42) peptide, resulting in senile plaques in Alzheimer's brains. Therefore, a selective copper detector probe that can detect amyloid beta peptide-copper aggregates and decrease the aggregate size has potential uses in medicine. We have developed a series of Cu2+-selective low fluorescent to high fluorescent tri and tetradentate dentate ligands and conjugated them with a peptide ligand to amyloid-beta binding peptide to increase the solubility of the compounds and make the resultant compounds bind to Cu2+-amyloid aggregates. The copper selective compounds were developed using chemical scaffolds known to have high affinity and selectivity for Cu2+, and their conjugates with peptides were tested for affinity and selectivity towards Cu2+. The test results were used to inform further improvement of the next compound. The final Cu2+ chelator-peptide conjugate we developed showed high selectivity for Cu2+ and high fluorescence properties. The compound bound 1:1 to Cu2+ ion, as determined from its Job's plot. Fluorescence of the ligand could be detected at nanomolar concentrations. The effect of this ligand on controlling Cu2+-Ab42 aggregation was studied using fluorescence assays and microscopy. It was found that the Cu2+-chelator-peptide conjugate efficiently reduced aggregate size and, therefore, acted as an inhibitor of Ab42-Cu2+ aggregation. Since high micromolar concentrations of Cu2+ are present in senile plaques, and Cu2+ accelerates the formation of toxic soluble aggregates of Ab42, which are precursors of insoluble plaques, the developed hybrid molecule can potentially serve as a therapeutic for Alzheimer's disease.

Trapping and scattering of a multiflagellated bacterium by a hard surface.

Thiovulum majus, which is one of the fastest known bacteria, swims using hundreds of flagella. Unlike typical pusher cells, which swim in circular paths over hard surfaces, T. majus localize near hard boundaries by turning their flagella to exert a net force normal to the surface. To probe the torques that stabilize this hydrodynamically bound state, the trajectories of several thousand collisions between a T. majus cell and a wall of a quasi-two-dimensional microfluidic chamber are analyzed. Measuring the fraction of cells escaping the wall either to the left or to the right of the point of contact-and how this probability varies with incident angle and time spent in contact with the surface-maps the scattering dynamics onto a first passage problem. These measurements are compared to the prediction of a Fokker-Planck equation to fit the angular velocity of a cell in contact with a hard surface. This analysis reveals a bound state with a narrow basin of attraction in which cells orient their flagella normal to the surface. The escape angle predicted by matching these near field dynamics with the far-field hydrodynamics is consistent with observation. We discuss the significance of these results for the ecology of T. majus and their self-organization into active chiral crystals.

Closed ecosystems extract energy through self-organized nutrient cycles.

Our planet is a self-sustaining ecosystem powered by light energy from the sun, but roughly closed to matter. Many ecosystems on Earth are also approximately closed to matter and recycle nutrients by self-organizing stable nutrient cycles, e.g., microbial mats, lakes, open ocean gyres. However, existing ecological models do not exhibit the self-organization and dynamical stability widely observed in such planetary-scale ecosystems. Here, we advance a conceptual model that explains the self-organization, stability, and emergent features of closed microbial ecosystems. Our model incorporates the bioenergetics of metabolism into an ecological framework. By studying this model, we uncover a crucial thermodynamic feedback loop that enables metabolically diverse communities to almost always stabilize nutrient cycles. Surprisingly, highly diverse communities self-organize to extract [Formula: see text]10[Formula: see text] of the maximum extractable energy, or [Formula: see text]100 fold more than randomized communities. Further, with increasing diversity, distinct ecosystems show strongly correlated fluxes through nutrient cycles. However, as the driving force from light increases, the fluxes of nutrient cycles become more variable and species-dependent. Our results highlight that self-organization promotes the efficiency and stability of complex ecosystems at extracting energy from the environment, even in the absence of any centralized coordination.

Density-mediated spin correlations drive edge-to-bulk flow transition in active chiral matter.

We demonstrate that edge currents develop in active chiral matter due to boundary shielding over a wide range of densities corresponding to a gas, fluid, and crystal. The system is composed of spinning disk-shaped grains with chirally arranged tilted legs confined in a circular vibrating chamber. The edge currents are shown to increasingly drive circulating bulk flows with area fraction as percolating clusters develop due to increasing spin-coupling between neighbors mediated by frictional contacts. Edge currents are observed even in the dilute limit. While, at low area fraction, the average flux vanishes except within a distance that is of the order of a particle diameter of the boundary, the penetration depth grows with increasing area fraction until a solid-body rotation is achieved corresponding to the highest packing, where the particles are fully caged with hexagonal order and spin in phase with the entire packing. A coarse-grained model, based on the increased collisional interlocking of the particles with area fraction and the emergence of order, captures the observed flow fields.

Unstable Invasion of Sedimenting Granular Suspensions.

We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the timescale over which the instability develops is given by the volume fraction dependent settling timescale of the grains in the cell. We then show that the mobility inversion and the nonequilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.

Biophysical basis for convergent evolution of two veil-forming microbes.

Microbes living in stagnant water typically rely on chemical diffusion to draw nutrients from their environment. The sulfur-oxidizing bacterium Thiovulum majus and the ciliate Uronemella have independently evolved the ability to form a 'veil', a centimetre-scale mucous sheet on which cells organize to produce a macroscopic flow. This flow pulls nutrients through the community an order of magnitude faster than diffusion. To understand how natural selection led these microbes to evolve this collective behaviour, we connect the physical limitations acting on individual cells to the cell traits. We show how diffusion limitation and viscous dissipation have led individual T. majus and Uronemella cells to display two similar characteristics. Both of these cells exert a force of approximately 40 pN on the water and attach to boundaries by means of a mucous stalk. We show how the diffusion coefficient of oxygen in water and the viscosity of water define the force the cells must exert. We then show how the hydrodynamics of filter-feeding orient a microbe normal to the surface to which it attaches. Finally, we combine these results with new observations of veil formation and a review of veil dynamics to compare the collective dynamics of these microbes. We conclude that this convergent evolution is a reflection of similar physical limitations imposed by diffusion and viscosity acting on individual cells.

Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells.

We investigate a new form of collective dynamics displayed by Thiovulum majus, one of the fastest-swimming bacteria known. Cells spontaneously organize on a surface into a visually striking two-dimensional hexagonal lattice of rotating cells. As each constituent cell rotates its flagella, it creates a tornadolike flow that pulls neighboring cells towards and around it. As cells rotate against their neighbors, they exert forces on one another, causing the crystal to rotate and cells to reorganize. We show how these dynamics arise from hydrodynamic and steric interactions between cells. We derive the equations of motion for a crystal, show that this model explains several aspects of the observed dynamics, and discuss the stability of these active crystals.

Hydrodynamics and collective behavior of the tethered bacterium Thiovulum majus.

The ecology and dynamics of many microbial systems, particularly in mats and soils, are shaped by how bacteria respond to evolving nutrient gradients and microenvironments. Here we show how the response of the sulfur-oxidizing bacterium Thiovulum majus to changing oxygen gradients causes cells to organize into large-scale fronts. To study this phenomenon, we develop a technique to isolate and enrich these bacteria from the environment. Using this enrichment culture, we observe the formation and dynamics of T. majus fronts in oxygen gradients. We show that these dynamics can be understood as occurring in two steps. First, chemotactic cells moving up the oxygen gradient form a front that propagates with constant velocity. We then show, through observation and mathematical analysis, that this front becomes unstable to changes in cell density. Random perturbations in cell density create oxygen gradients. The response of cells magnifies these gradients and leads to the formation of millimeter-scale fluid flows that actively pull oxygenated water through the front. We argue that this flow results from a nonlinear instability excited by stochastic fluctuations in the density of cells. Finally, we show that the dynamics by which these modes interact can be understood from the chemotactic response of cells. These results provide a mathematically tractable example of how collective phenomena in ecological systems can arise from the individual response of cells to a shared resource.

Bifurcation dynamics of natural drainage networks.

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle α=2π/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.

Bifurcation dynamics of natural drainage networks.

As water erodes a landscape, streams form and channellize the surficial flow. In time, streams become highly ramified networks that can extend over a continent. Here, we combine physical reasoning, mathematical analysis and field observations to understand a basic feature of network growth: the bifurcation of a growing stream. We suggest a deterministic bifurcation rule arising from a relationship between the position of the tip in the network and the local shape of the water table. Next, we show that, when a stream bifurcates, competition between the stream and branches selects a special bifurcation angle alpha = 2pi/5. We confirm this prediction by measuring several thousand bifurcation angles in a kilometre-scale network fed by groundwater. In addition to providing insight into the growth of river networks, this result presents river networks as a physical manifestation of a classical mathematical problem: interface growth in a harmonic field. In the final sections, we combine these results to develop and explore a one-parameter model of network growth. The model predicts the development of logarithmic spirals. We find similar features in the kilometre-scale network.

Ramification of stream networks.

The geometric complexity of stream networks has been a source of fascination for centuries. However, a comprehensive understanding of ramification--the mechanism of branching by which such networks grow--remains elusive. Here we show that streams incised by groundwater seepage branch at a characteristic angle of 2π/5 = 72°. Our theory represents streams as a collection of paths growing and bifurcating in a diffusing field. Our observations of nearly 5,000 bifurcated streams growing in a 100 km(2) groundwater field on the Florida Panhandle yield a mean bifurcation angle of 71.9° ± 0.8°. This good accord between theory and observation suggests that the network geometry is determined by the external flow field but not, as classical theories imply, by the flow within the streams themselves.

Shape and dynamics of seepage erosion in a horizontal granular bed.

We investigate erosion patterns observed in a horizontal granular bed resulting from seepage of water motivated by observation of beach rills and channel growth in larger scale land forms. Our experimental apparatus consists of a wide rectangular box filled with glass beads with a narrow opening in one of the side walls from which eroded grains can exit. Quantitative data on the shape of the pattern and erosion dynamics are obtained with a laser-aided topography technique. We show that the spatial distribution of the source of groundwater can significantly impact the shape of observed patterns. An elongated channel is observed to grow upstream when groundwater is injected at a boundary adjacent to a reservoir held at constant height. An amphitheater (semicircular) shape is observed when uniform rainfall infiltrates the granular bed to maintain a water table. Bifurcations are observed as the channels grow in response to the groundwater. We further find that the channels grow by discrete avalanches as the height of the granular bed is increased above the capillary rise, causing the deeper channels to have rougher fronts. The spatiotemporal distribution of avalanches increase with bed height when partial saturation of the bed leads to cohesion between grains. However, the overall shape of the channels is observed to remain unaffected indicating that seepage erosion is robust to perturbation of the erosion front.

Reaction-diffusion model of nutrient uptake in a biofilm: theory and experiment.

Microbes in natural settings typically live attached to surfaces in complex communities called biofilms. Despite the many advantages of biofilm formation, communal living forces microbes to compete with one another for resources. Here we combine mathematical models with stable isotope techniques to test a reaction-diffusion model of competition in a photosynthetic biofilm. In this model, a nutrient is transported through the mat by diffusion and is consumed at a rate proportional to its local concentration. When the nutrient is supplied from the surface of the biofilm, the balance between diffusion and consumption gives rise to gradients of nutrient availability, resulting in gradients of nutrient uptake. To test this model, a biofilm was incubated for a fixed amount of time with an isotopically labeled nutrient that was incorporated into cellular biomass. Thus, the concentration of labeled nutrient in a cell is a measure of the mean rate of nutrient incorporation over the course of the experiment. Comparison of this measurement to the solution of the reaction-diffusion model in the biofilm confirms the presence of gradients in nutrient uptake with the predicted shape. The excellent agreement between theory and experiment lends strong support to this one-parameter model of reaction and diffusion of nutrients in a biofilm. Having validated this model empirically, we discuss how these dynamics may arise from diffusion through a reactive heterogeneous medium. More generally, this result identifies stable isotope techniques as a powerful tool to test quantitative models of chemical transport through biofilms.

Biophysical basis for the geometry of conical stromatolites.

Stromatolites may be Earth's oldest macroscopic fossils; however, it remains controversial what, if any, biological processes are recorded in their morphology. Although the biological interpretation of many stromatolite morphologies is confounded by the influence of sedimentation, conical stromatolites form in the absence of sedimentation and are, therefore, considered to be the most robust records of biophysical processes. A qualitative similarity between conical stromatolites and some modern microbial mats suggests a photosynthetic origin for ancient stromatolites. To better understand and interpret ancient fossils, we seek a quantitative relationship between the geometry of conical stromatolites and the biophysical processes that control their growth. We note that all modern conical stromatolites and many that formed in the last 2.8 billion years display a characteristic centimeter-scale spacing between neighboring structures. To understand this prominent-but hitherto uninterpreted-organization, we consider the role of diffusion in mediating competition between stromatolites. Having confirmed this model through laboratory experiments and field observation, we find that organization of a field of stromatolites is set by a diffusive time scale over which individual structures compete for nutrients, thus linking form to physiology. The centimeter-scale spacing between modern and ancient stromatolites corresponds to a rhythmically fluctuating metabolism with a period of approximately 20 hr. The correspondence between the observed spacing and the day length provides quantitative support for the photosynthetic origin of conical stromatolites throughout geologic time.

Morphological record of oxygenic photosynthesis in conical stromatolites.

Conical stromatolites are thought to be robust indicators of the presence of photosynthetic and phototactic microbes in aquatic environments as early as 3.5 billion years ago. However, phototaxis alone cannot explain the ubiquity of disrupted, curled, and contorted laminae in the crests of many Mesoproterozoic, Paleoproterozoic, and some Archean conical stromatolites. Here, we demonstrate that cyanobacterial production of oxygen in the tips of modern conical aggregates creates contorted laminae and submillimeter-to-millimeter-scale enmeshed bubbles. Similarly sized fossil bubbles and contorted laminae may be present only in the crestal zones of some conical stromatolites 2.7 billion years old or younger. This implies not only that cyanobacteria built Proterozoic conical stromatolites but also that fossil bubbles may constrain the timing of the evolution of oxygenic photosynthesis.

Scaling relations for a functionally two-dimensional plant: Chamaesyce setiloba (Euphorbiaceae).

Many characteristics of plants and animals scale with body size as described by allometric equations of the form Y = ßM(α), where Y is an attribute of the organism, ß is a coefficient that varies with attribute, M is a measure of organism size, and α is another constant, the scaling exponent. In current models, the frequently observed quarter-power scaling exponents are hypothesized to be due to fractal-like structures. However, not all plants or animals conform to the assumptions of these models. Therefore, they might be expected to have different scaling relations. We studied one such plant, Chamaesyce setiloba, a prostrate annual herb that grows to functionally fill a two-dimensional space. Number of leaves scaled slightly less than isometrically with total aboveground plant mass (α ≈ 0.9) and substantially less than isometrically with dry total stem mass (α = 0.82), showing reduced allocation to leaf as opposed to stem tissue with increasing plant size. Additionally, scalings of the lengths and radii of parent and daughter branches differed from those predicted for three-dimensional trees and shrubs. Unlike plants with typical three-dimensional architectures, C. setiloba has distinctive scaling relations associated with its particular prostrate herbaceous growth form.