Transition from active motion to anomalous diffusion for Bacillus subtilis confined in hydrogel matrices

We investigate the motility of B. subtilis under different degrees of confinement induced by transparent porous hydrogels. The dynamical behavior of the bacteria at short times is linked to characteristic parameters describing the hydrogel porosity. Mean squared displacements (MSDs) reveal that the run-and-tumble dynamics of unconfined B. subtilis progressively turns into sub-diffusive motion with increasing confinement. Correspondingly, the median instantaneous velocity of bacteria decreases and becomes more narrowly distributed, while the reorientation rate increases and reaches a plateau value. Analyzing single-trajectories, we show that the average dynamical behavior is the result of complex displacements, in which active, diffusive and sub-diffusive segments coexist. For small and moderate confinements, the number of active segments reduces, while the diffusive and sub-diffusive segments increase. The alternation of sub-diffusion, diffusion and active motion along the same trajectory can be described as a hopping ad trapping motion, in which hopping events correspond to displacements with an instantaneous velocity exceeding the corresponding mean value along a trajectory. Different from previous observations, escape from local trapping occurs for B. subtilis through active runs but also diffusion. Interestingly, the contribution of diffusion is maximum at intermediate confinements. At sufficiently long times transport coefficients estimated from the experimental MSDs under different degrees of confinement can be reproduced using a recently proposed hopping and trapping model. Finally, we propose a quantitative relationship linking the median velocity of confined and unconfined bacteria through the characteristic confinement length of the hydrogel matrix. Our work provides new insights for the bacterial motility in complex media that mimic natural environments and are relevant to important problems like sterilization, water purification, biofilm formation, membrane permeation and bacteria separation.

A biocomputing platform with electrochemical and fluorescent signal outputs based on multi-sensitive copolymer film electrodes with entrapped Au nanoclusters and tetraphenylethene and electrocatalysis of NADH

In this work, poly(N,N'-dimethylaminoethylmethacrylate-co-N-isopropylacrylamide) copolymer films were polymerized on the surface of Au electrodes with a facile one-step method, and Au nanoclusters (AuNCs) and tetraphenylethene (TPE) were synchronously embedded in the films, designated as P(DMA-co-NIPA)/AuNCs/TPE. Ferrocene dicarboxylic acid (FDA), an electroactive probe in solution displayed inverse pH- and SO42--sensitive on-off cyclic voltammetric (CV) behaviors at the film electrodes. The electrocatalytic oxidation of nicotinamide adenine dinucleotide (NADH) mediated by FDA in solution could substantially amplify the CV response difference between the on and off states. Moreover, the two fluorescence emission (FL) signals from the TPE constituent at 450 nm and AuNCs component at 660 nm in the films also demonstrated SO42-- and pH-sensitive behaviors. Based on the aforementioned results, a 4-input/9-output biomolecular logic circuit was constructed with pH, Na2SO4, FDA and NADH as the inputs, and the CV signals and the FL responses at 450 and 660 nm at different levels as the outputs. Additionally, some functional non-Boolean devices were elaborately designed on an identical platform, including a 1-to-2 decoder, a 2-to-1 encoder, a 1-to-2 demultiplexer and different types of keypad locks. This work combines copolymer films, bioelectrocatalysis, and fluorescence together so that more complicated biocomputing systems could be established. This work may pave a new way to develop advanced and sophisticated biocomputing logic circuits and functional devices in the future.

Non-invasive study of the three-dimensional structure of nanoporous triblock terpolymer membranes

Nanoporous media are of great importance for drug delivery or filtration. Typically the pore structure of such media is characterized using high-resolution techniques such as electron microscopy or atomic force microscopy. However, these techniques are restricted to the surface of the material and/or are highly invasive. In a proof-of-concept experiment we have employed three-dimensional single-particle orbit tracking for testing the three-dimensional pore structure of a liquid filled nanoporous polystyrene-block-polyisoprene-block-poly(N-isopropylacrylamide) (PS-b-PI-b-PNiPAAm) triblock terpolymer membrane. Using fluorescent tracers with a diameter of about 10% of the relevant void structures, the tracking experiments yielded results that were comparable to those obtained from reference experiments using environmental scanning electron microscopy (eSEM). This testifies that single-particle orbit tracking can serve as a useful non-invasive alternative for characterising the structure of nanoporous materials.

Classification and Segmentation of Nanoparticle Diffusion Trajectories in Cellular Micro Environments

Darkfield and confocal laser scanning microscopy both allow for a simultaneous observation of live cells and single nanoparticles. Accordingly, a characterization of nanoparticle uptake and intracellular mobility appears possible within living cells. Single particle tracking allows to measure the size of a diffusing particle close to a cell. However, within the more complex system of a cell’s cytoplasm normal, confined or anomalous diffusion together with directed motion may occur. In this work we present a method to automatically classify and segment single trajectories into their respective motion types. Single trajectories were found to contain more than one motion type. We have trained a random forest with 9 different features. The average error over all motion types for synthetic trajectories was 7.2%. The software was successfully applied to trajectories of positive controls for normal- and constrained diffusion. Trajectories captured by nanoparticle tracking analysis served as positive control for normal diffusion. Nanoparticles inserted into a diblock copolymer membrane was used to generate constrained diffusion. Finally we segmented trajectories of diffusing (nano-)particles in V79 cells captured with both darkfield- and confocal laser scanning microscopy. The software called “TraJClassifier” is freely available as ImageJ/Fiji plugin via https://git.io/v6uz2.

Measuring a diffusion coefficient by single-particle tracking: statistical analysis of experimental mean squared displacement curves

We provide experimental results on the accuracy of diffusion coefficients obtained by a mean squared displacement (MSD) analysis of single-particle trajectories. We have recorded very long trajectories comprising more than 1.5 × 10(5) data points and decomposed these long trajectories into shorter segments providing us with ensembles of trajectories of variable lengths. This enabled a statistical analysis of the resulting MSD curves as a function of the lengths of the segments. We find that the relative error of the diffusion coefficient can be minimized by taking an optimum number of points into account for fitting the MSD curves, and that this optimum does not depend on the segment length. Yet, the magnitude of the relative error for the diffusion coefficient does, and achieving an accuracy in the order of 10% requires the recording of trajectories with about 1000 data points. Finally, we compare our results with theoretical predictions and find very good qualitative and quantitative agreement between experiment and theory.

Wanted: a positive control for anomalous subdiffusion

Anomalous subdiffusion in cells and model systems is an active area of research. The main questions are whether diffusion is anomalous or normal, and if it is anomalous, its mechanism. The subject is controversial, especially the hypothesis that crowding causes anomalous subdiffusion. Anomalous subdiffusion measurements would be strengthened by an experimental standard, particularly one able to cross-calibrate the different types of measurements. Criteria for a calibration standard are proposed. First, diffusion must be anomalous over the length and timescales of the different measurements. The length-scale is fundamental; the time scale can be adjusted through the viscosity of the medium. Second, the standard must be theoretically well understood, with a known anomalous subdiffusion exponent, ideally readily tunable. Third, the standard must be simple, reproducible, and independently characterizable (by, for example, electron microscopy for nanostructures). Candidate experimental standards are evaluated, including obstructed lipid bilayers; aqueous systems obstructed by nanopillars; a continuum percolation system in which a prescribed fraction of randomly chosen obstacles in a regular array is ablated; single-file diffusion in pores; transient anomalous subdiffusion due to binding of particles in arrays such as transcription factors in randomized DNA arrays; and computer-generated physical trajectories.

Setup for single-particle orbit tracking: artifacts and corrections

We report on an experimental setup for single-particle orbit tracking, which allows following fluorescent nanoparticles for more than 10 min with a temporal resolution of 4 ms and a dynamic position accuracy of better than 10 nm. On a model sample--20 nm sized fluorescent polymer beads in glycerol--we will illustrate how artifacts caused by unavoidable experimental shortcomings (might) obscure the experimental result and how misinterpretations can be prevented.