Allan Variance Analysis as Useful Tool to Determine Noise in Various Single-Molecule Setups

One limitation on the performance of optical traps is the noise inherently present in every setup. Therefore, it is the desire of most experimentalists to minimize and possibly eliminate noise from their optical trapping experiments. A step in this direction is to quantify the actual noise in the system and to evaluate how much each particular component contributes to the overall noise. For this purpose we present Allan variance analysis as a straightforward method. In particular, it allows for judging the impact of drift which gives rise to low-frequency noise, which is extremely difficult to pinpoint by other methods. We show how to determine the optimal sampling time for calibration, the optimal number of data points for a desired experiment, and we provide measurements of how much accuracy is gained by acquiring additional data points. Allan variances of both micrometer-sized spheres and asymmetric nanometer-sized rods are considered.Comment: 14 pages, 6 figures, presented at SPIE Optics+Photonics 2009 in San Diego, CA, US

Spectral content of a single non-Brownian trajectory

Time-dependent processes are often analysed using the power spectral density (PSD), calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble-average. Frequently, the available experimental data sets are too small for such ensemble averages, and hence it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from $S(f,T)$, the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable, parametrized by frequency $f$ and observation-time $T$, for a broad family of anomalous diffusions---fractional Brownian motion (fBm) with Hurst-index $H$---and derive exactly its probability density function. We show that $S(f,T)$ is proportional---up to a random numerical factor whose universal distribution we determine---to the ensemble-averaged PSD. For subdiffusion ($H<1/2$) we find that $S(f,T)\sim A/f^{2H+1}$ with random-amplitude $A$. In sharp contrast, for superdiffusion $(H>1/2)$ $S(f,T)\sim BT^{2H-1}/f^2$ with random amplitude $B$. Remarkably, for $H>1/2$ the PSD exhibits the same frequency-dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for $H>1/2$ the PSD is ageing and is dependent on $T$. Our predictions for both sub- and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels, and by extensive simulations.Comment: 13 pages, 5 figures, Supplemental Material can be found at https://journals.aps.org/prx/supplemental/10.1103/PhysRevX.9.011019/prx_SM_final.pd

Biomimetic Carbon-Fiber Systems Engineering: A Modular Design Strategy to Generate Biofunctional Composites from Graphene and Carbon Nanofibers

electrical conductivity. It is additionally advantageous if such materials resembled the structural and biochemical features of the natural extracellular environment. Here we show a novel modular design strategy to engineer biomimetic carbon-fiber based scaffolds. Highly porous ceramic zinc oxide (ZnO) microstructures serve as 3D sacrificial templates and are infiltrated with carbon nanotube (CNT) or graphene dispersions. Once the CNTs and graphene uniformly coat the ZnO template, the ZnO is either removed by hydrolysis or converted into carbon by chemical vapor deposition (CVD). The resulting 3D carbon scaffolds are both hierarchically ordered and free-standing. The properties of the micro-fibrous scaffolds were tailored with a high porosity (up to 93 %), high Young’s modulus (~0.027 to ~22 MPa), and an electrical conductivity of (~0.1 to ~330 S/m), as well as different surface compositions. Cell viability and fibroblast proliferation rate and protein adsorption rate assays have shown that the generated scaffolds are biocompatible and have a high protein adsorption capacity (up to 77.32 ±6.95 mg/cm3), so that they not only are able to resemble the ECM structurally, but also biochemically. The scaffolds also allow for the successful growth and adhesion of fibroblast cells showing that we provide a novel, highly scalable modular design strategy to generate biocompatible carbon-fiber systems that mimic the extracellular matrix with the additional feature of conductivity.RA gratefully acknowledges partial project funding by the Deutsche Forschungsgemeinschaft under contract FOR1616. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. GrapheneCore2 785219. CS is supported by the European Research Council (ERC StG 336104 CELLINSPIRED, ERC PoC 768740 CHANNELMAT), by the German Research Foundation (RTG 2154, SFB 1261 project B7). MT acknowledges support from the German Academic Exchange Service (DAAD) through a research grant for doctoral candidates (91526555-57048249). We acknowledge funding from EPSRC grants EP/P02534X/1, ERC grant 319277 (Hetero2D) the Royal Academy of Engineering Enterprise Scheme, the Trinity College, Cambridge, and the Isaac Newton Trust

Biological measurement beyond the quantum limit

Quantum noise places a fundamental limit on the per photon sensitivity attainable in optical measurements. This limit is of particular importance in biological measurements, where the optical power must be constrained to avoid damage to the specimen. By using non-classically correlated light, we demonstrated that the quantum limit can be surpassed in biological measurements. Quantum enhanced microrheology was performed within yeast cells by tracking naturally occurring lipid granules with sensitivity 2.4 dB beyond the quantum noise limit. The viscoelastic properties of the cytoplasm could thereby be determined with a 64% improved measurement rate. This demonstration paves the way to apply quantum resources broadly in a biological context

Investigation of size–dependent cell adhesion on nanostructured interfaces

BACKGROUND: Cells explore the surfaces of materials through membrane-bound receptors, such as the integrins, and use them to interact with extracellular matrix molecules adsorbed on the substrate surfaces, resulting in the formation of focal adhesions. With recent advances in nanotechnology, biosensors and bioelectronics are being fabricated with ever decreasing feature sizes. The performances of these devices depend on how cells interact with nanostructures on the device surfaces. However, the behavior of cells on nanostructures is not yet fully understood. Here we present a systematic study of cell-nanostructure interaction using polymeric nanopillars with various diameters. RESULTS: We first checked the viability of cells grown on nanopillars with diameters ranging from 200 nm to 700 nm. It was observed that when cells were cultured on the nanopillars, the apoptosis rate slightly increased as the size of the nanopillar decreased. We then calculated the average size of the focal adhesions and the cell-spreading area for focal adhesions using confocal microscopy. The size of focal adhesions formed on the nanopillars was found to decrease as the size of the nanopillars decreased, resembling the formations of nascent focal complexes. However, when the size of nanopillars decreased to 200 nm, the size of the focal adhesions increased. Further study revealed that cells interacted very strongly with the nanopillars with a diameter of 200 nm and exerted sufficient forces to bend the nanopillars together, resulting in the formation of larger focal adhesions. CONCLUSIONS: We have developed a simple approach to systematically study cell-substrate interactions on physically well-defined substrates using size-tunable polymeric nanopillars. From this study, we conclude that cells can survive on nanostructures with a slight increase in apoptosis rate and that cells interact very strongly with smaller nanostructures. In contrast to previous observations on flat substrates that cells interacted weakly with softer substrates, we observed strong cell-substrate interactions on the softer nanopillars with smaller diameters. Our results indicate that in addition to substrate rigidity, nanostructure dimensions are additional important physical parameters that can be used to regulate behaviour of cells

Impact of local versus global ligand density on cellular adhesion

α(v)β(3) integrin-mediated cell adhesion is crucially influenced by how far ligands are spaced apart. To evaluate the impact of local ligand density versus global ligand density of a given surface we used synthetic micro-nanostructured cell environments with user-defined ligand spacing and patterns to investigate cellular adhesion. The development of stable focal adhesions, their number and size as well as the cellular adhesion strength proved to be influenced by local more than global ligand density