Heterogeneous anomalous transport in cellular and molecular biology.

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Ensemble heterogeneity mimics ageing for endosomal dynamics within eukaryotic cells.

Transport processes of many structures inside living cells display anomalous diffusion, such as endosomes in eukaryotic cells. They are also heterogeneous in space and time. Large ensembles of single particle trajectories allow the heterogeneities to be quantified in detail and provide insights for mathematical modelling. The development of accurate mathematical models for heterogeneous dynamics has the potential to enable the design and optimization of various technological applications, for example, the design of effective drug delivery systems. Central questions in the analysis of anomalous dynamics are ergodicity and statistical ageing which allow for selecting the proper model for the description. It is believed that non-ergodicity and ageing occur concurrently. However, we found that the anomalous dynamics of endosomes is paradoxical since it is ergodic but shows ageing. We show that this behaviour is caused by ensemble heterogeneity that, in addition to space-time heterogeneity within a single trajectory, is an inherent property of endosomal motion. Our work introduces novel approaches for the analysis and modelling of heterogeneous dynamics.

Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast Moving Endosomes.

Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display switching between persistent and anti-persistent motion, while others jiggle around in one position for the whole measurement time. By splitting the ensemble of endosome trajectories into slow moving subdiffusive and fast moving superdiffusive endosomes, we analyzed them separately. The mean squared displacements and velocity auto-correlation functions confirm the effectiveness of the splitting methods. Applying the local analysis, we show that both ensembles are characterized by a spectrum of local anomalous exponents and local generalized diffusion coefficients. Slow and fast endosomes have exponential distributions of local anomalous exponents and power law distributions of generalized diffusion coefficients. This suggests that heterogeneous fractional Brownian motion is an appropriate model for both fast and slow moving endosomes. This article is part of a Special Issue entitled: "Recent Advances In Single-Particle Tracking: Experiment and Analysis" edited by Janusz Szwabinski and Aleksander Weron.

Advances in the microrheology of complex fluids.

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.