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.

A new perspective of molecular diffusion by nuclear magnetic resonance.

The diffusion-weighted NMR signal acquired using Pulse Field Gradient (PFG) techniques, allows for extrapolating microstructural information from porous materials and biological tissues. In recent years there has been a multiplication of diffusion models expressed by parametric functions to fit the experimental data. However, clear-cut criteria for the model selection are lacking. In this paper, we develop a theoretical framework for the interpretation of NMR attenuation signals in the case of Gaussian systems with stationary increments. The full expression of the Stejskal-Tanner formula for normal diffusing systems is devised, together with its extension to the domain of anomalous diffusion. The range of applicability of the relevant parametric functions to fit the PFG data can be fully determined by means of appropriate checks to ascertain the correctness of the fit. Furthermore, the exact expression for diffusion weighted NMR signals pertaining to Brownian yet non-Gaussian processes is also derived, accompanied by the proper check to establish its contextual relevance. The analysis provided is particularly useful in the context of medical MRI and clinical practise where the hardware limitations do not allow the use of narrow pulse gradients.

Evaluation of Disability Progression in Multiple Sclerosis via Magnetic-Resonance-Based Deep Learning Techniques.

Short-term disability progression was predicted from a baseline evaluation in patients with multiple sclerosis (MS) using their three-dimensional T1-weighted (3DT1) magnetic resonance images (MRI). One-hundred-and-eighty-one subjects diagnosed with MS underwent 3T-MRI and were followed up for two to six years at two sites, with disability progression defined according to the expanded-disability-status-scale (EDSS) increment at the follow-up. The patients' 3DT1 images were bias-corrected, brain-extracted, registered onto MNI space, and divided into slices along coronal, sagittal, and axial projections. Deep learning image classification models were applied on slices and devised as ResNet50 fine-tuned adaptations at first on a large independent dataset and secondly on the study sample. The final classifiers' performance was evaluated via the area under the curve (AUC) of the false versus true positive diagram. Each model was also tested against its null model, obtained by reshuffling patients' labels in the training set. Informative areas were found by intersecting slices corresponding to models fulfilling the disability progression prediction criteria. At follow-up, 34% of patients had disability progression. Five coronal and five sagittal slices had one classifier surviving the AUC evaluation and null test and predicted disability progression (AUC > 0.72 and AUC > 0.81, respectively). Likewise, fifteen combinations of classifiers and axial slices predicted disability progression in patients (AUC > 0.69). Informative areas were the frontal areas, mainly within the grey matter. Briefly, 3DT1 images may give hints on disability progression in MS patients, exploiting the information hidden in the MRI of specific areas of the brain.

Universal and Non-Universal Features in the Random Shear Model.

The stochastic transport of particles in a disordered two-dimensional layered medium, driven by correlated y-dependent random velocity fields is usually referred to as random shear model. This model exhibits a superdiffusive behavior in the x direction ascribable to the statistical properties of the disorder advection field. By introducing layered random amplitude with a power-law discrete spectrum, the analytical expressions for the space and time velocity correlation functions, together with those of the position moments, are derived by means of two distinct averaging procedures. In the case of quenched disorder, the average is performed over an ensemble of uniformly spaced initial conditions: albeit the strong sample-to-sample fluctuations, and universality appears in the time scaling of the even moments. Such universality is exhibited in the scaling of the moments averaged over the disorder configurations. The non-universal scaling form of the no-disorder symmetric or asymmetric advection fields is also derived.

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.

Machine learning classifier to identify clinical and radiological features relevant to disability progression in multiple sclerosis.

OBJECTIVES: To evaluate the accuracy of a data-driven approach, such as machine learning classification, in predicting disability progression in MS. METHODS: We analyzed structural brain images of 163 subjects diagnosed with MS acquired at two different sites. Participants were followed up for 2-6 years, with disability progression defined according to the expanded disability status scale (EDSS) increment at follow-up. T2-weighted lesion load (T2LL), thalamic and cerebellar gray matter (GM) volumes, fractional anisotropy of the normal appearing white matter were calculated at baseline and included in supervised machine learning classifiers. Age, sex, phenotype, EDSS at baseline, therapy and time to follow-up period were also included. Classes were labeled as stable or progressed disability. Participants were randomly chosen from both sites to build a sample including 50% patients showing disability progression and 50% patients being stable. One-thousand machine learning classifiers were applied to the resulting sample, and after testing for overfitting, classifier confusion matrix, relative metrics and feature importance were evaluated. RESULTS: At follow-up, 36% of participants showed disability progression. The classifier with the highest resulting metrics had accuracy of 0.79, area under the true positive versus false positive rates curve of 0.81, sensitivity of 0.90 and specificity of 0.71. T2LL, thalamic volume, disability at baseline and administered therapy were identified as important features in predicting disability progression. Classifiers built on radiological features had higher accuracy than those built on clinical features. CONCLUSIONS: Disability progression in MS may be predicted via machine learning classifiers, mostly evaluating neuroradiological features.

Protein-driven lipid domain nucleation in biological membranes.

Lipid rafts are heterogeneous dynamic lipid domains of the cell membranes that are involved in several biological processes, such as protein and lipid specific transport and signaling. Our understanding of lipid raft formation is still limited due to the transient and elusive nature of these domains in vivo, in contrast with the stable phase-separated domains observed in artificial membranes. Inspired by experimental findings highlighting the relevance of transmembrane proteins for lipid rafts, we investigate lipid domain nucleation by coarse-grained molecular dynamics and Ising-model simulations. We find that the presence of a transmembrane protein can trigger lipid domain nucleation in a flat membrane from an otherwise mixed lipid phase. Furthermore, we study the role of the lipid domain in the diffusion of the protein showing that its mobility is hindered by the presence of the raft. The results of our coarse-grained molecular-dynamics and Ising-model simulations thus coherently support the important role played by transmembrane proteins in lipid domain formation and stability.

Cell Migration in Microfluidic Devices: Invadosomes Formation in Confined Environments.

The last 20 years have seen the blooming of microfluidics technologies applied to biological sciences. Microfluidics provides effective tools for biological analysis, allowing the experimentalists to extend their playground to single cells and single molecules, with high throughput and resolution which were inconceivable few decades ago. In particular, microfluidic devices are profoundly changing the conventional way of studying the cell motility and cell migratory dynamics. In this chapter we will furnish a comprehensive view of the advancements made in the research domain of confinement-induced cell migration, thanks to the use of microfluidic devices. The chapter is subdivided in three parts. Each section will be addressing one of the fundamental questions that the microfluidic technology is contributing to unravel: (i) where cell migration takes place, (ii) why cells migrate and, (iii) how the cells migrate. The first introductory part is devoted to a thumbnail, and partially historical, description of microfluidics and its impact in biological sciences. Stress will be put on two aspects of the devices fabrication process, which are crucial for biological applications: materials used and coating methods. The second paragraph concerns the cell migration induced by environmental cues: chemical, leading to chemotaxis, mechanical, at the basis of mechanotaxis, and electrical, which induces electrotaxis. Each of them will be addressed separately, highlighting the fundamental role of microfluidics in providing the well-controlled experimental conditions where cell migration can be induced, investigated and ultimately understood. The third part of the chapter is entirely dedicated to how the cells move in confined environments. Invadosomes (the joint name for podosomes and invadopodia) are cell protrusion that contribute actively to cell migration or invasion. The formation of invadosomes under confinement is a research topic that only recently has caught the attention of the scientific community: microfluidic design is helping shaping the future direction of this emerging field of research.

Author Correction: Probing spermiogenesis: a digital strategy for mouse acrosome classification.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

Atomic-Scale Front Propagation at the Onset of Frictional Sliding.

Macroscopic frictional sliding emerges from atomic-scale interactions and processes at the contact interface, but bridging the gap between micro and macro scales still remains an unsolved challenge. Direct imaging of the contact surface and simultaneous measurement of stress fields during macroscopic frictional slip revealed the formation of crack precursors, questioning the traditional picture of frictional contacts described in terms of a single degree of freedom. Here we study the onset of frictional slip on the atomic scale by simulating the motion of an aluminum block pushed by a slider on a copper substrate. We show the formation of dynamic slip front propagation and precursory activity that resemble macroscopic observations. The analysis of stress patterns during slip, however, reveals subtle effects due to the lattice structures that hinder a direct application of linear elastic fracture mechanics. Our results illustrate that dynamic front propagation arises already on the atomic scales and shed light on the connections between atomic-scale and macroscopic friction.

Probing spermiogenesis: a digital strategy for mouse acrosome classification.

Classification of morphological features in biological samples is usually performed by a trained eye but the increasing amount of available digital images calls for semi-automatic classification techniques. Here we explore this possibility in the context of acrosome morphological analysis during spermiogenesis. Our method combines feature extraction from three dimensional reconstruction of confocal images with principal component analysis and machine learning. The method could be particularly useful in cases where the amount of data does not allow for a direct inspection by trained eye.

Single file dynamics in soft materials.

The term single file (SF) dynamics refers to the motion of an assembly of particles through a channel with cross-sections comparable to the particles' diameter. Single file diffusion (SFD) is then the diffusion of a tagged particle in a single file, i.e., under the condition that particle passing is not allowed. SFD accounts for a large variety of processes in nature, including diffusion of colloids in synthetic and natural channels, biological motors along molecular chains, electrons in proteins and liquid helium, ions through membranes, just to mention a few examples. Albeit introduced in 1965s, over the last decade the classical notion of SF dynamics has been generalised to account for a more realistic modelling of the particle properties, file geometry, particle-particle and channel-particle interactions, which paves the way to remarkable applications of the SF model, for instance, in the technology of bio-integrated nanodevices. We provide here a comprehensive review of the recent advances in the theory of SF dynamics with the purpose of spurring further experimental work.

Collisional statistics and dynamics of two-dimensional hard-disk systems: From fluid to solid.

We perform extensive MD simulations of two-dimensional systems of hard disks, focusing on the collisional statistical properties. We analyze the distribution functions of velocity, free flight time, and free path length for packing fractions ranging from the fluid to the solid phase. The behaviors of the mean free flight time and path length between subsequent collisions are found to drastically change in the coexistence phase. We show that single-particle dynamical properties behave analogously in collisional and continuous-time representations, exhibiting apparent crossovers between the fluid and the solid phases. We find that, both in collisional and continuous-time representation, the mean-squared displacement, velocity autocorrelation functions, intermediate scattering functions, and self-part of the van Hove function (propagator) closely reproduce the same behavior exhibited by the corresponding quantities in granular media, colloids, and supercooled liquids close to the glass or jamming transition.

Volume Changes During Active Shape Fluctuations in Cells.

Cells modify their volume in response to changes in osmotic pressure but it is usually assumed that other active shape variations do not involve significant volume fluctuations. Here we report experiments demonstrating that water transport in and out of the cell is needed for the formation of blebs, commonly observed protrusions in the plasma membrane driven by cortex contraction. We develop and simulate a model of fluid-mediated membrane-cortex deformations and show that a permeable membrane is necessary for bleb formation which is otherwise impaired. Taken together, our experimental and theoretical results emphasize the subtle balance between hydrodynamics and elasticity in actively driven cell morphological changes.

Scalar model for frictional precursors dynamics.

Recent experiments indicate that frictional sliding occurs by nucleation of detachment fronts at the contact interface that may appear well before the onset of global sliding. This intriguing precursory activity is not accounted for by traditional friction theories but is extremely important for friction dominated geophysical phenomena as earthquakes, landslides or avalanches. Here we simulate the onset of slip of a three dimensional elastic body resting on a surface and show that experimentally observed frictional precursors depend in a complex non-universal way on the sample geometry and loading conditions. Our model satisfies Archard's law and Amontons' first and second laws, reproducing with remarkable precision the real contact area dynamics, the precursors' envelope dynamics prior to sliding, and the normal and shear internal stress distributions close to the interfacial surface. Moreover, it allows to assess which features can be attributed to the elastic equilibrium, and which are attributed to the out-of-equilibrium dynamics, suggesting that precursory activity is an intrinsically quasi-static physical process. A direct calculation of the evolution of the Coulomb stress before and during precursors nucleation shows large variations across the sample, explaining why earthquake forecasting methods based only on accumulated slip and Coulomb stress monitoring are often ineffective.

Mechanical properties of growing melanocytic nevi and the progression to melanoma.

Melanocytic nevi are benign proliferations that sometimes turn into malignant melanoma in a way that is still unclear from the biochemical and genetic point of view. Diagnostic and prognostic tools are then mostly based on dermoscopic examination and morphological analysis of histological tissues. To investigate the role of mechanics and geometry in the morpholgical dynamics of melanocytic nevi, we study a computation model for cell proliferation in a layered non-linear elastic tissue. Numerical simulations suggest that the morphology of the nevus is correlated to the initial location of the proliferating cell starting the growth process and to the mechanical properties of the tissue. Our results also support that melanocytes are subject to compressive stresses that fluctuate widely in the nevus and depend on the growth stage. Numerical simulations of cells in the epidermis releasing matrix metalloproteinases display an accelerated invasion of the dermis by destroying the basal membrane. Moreover, we suggest experimentally that osmotic stress and collagen inhibit growth in primary melanoma cells while the effect is much weaker in metastatic cells. Knowing that morphological features of nevi might also reflect geometry and mechanics rather than malignancy could be relevant for diagnostic purposes.

Stationary growth and unique invariant harmonic measure of cylindrical diffusion limited aggregation.

We prove that the harmonic measure is stationary, unique, and invariant on the interface of diffusion limited aggregation (DLA) growing on a cylinder surface. We provide a detailed theoretical analysis puzzling together multiscaling, multifractality, and conformal invariance, supported by extensive numerical simulations of clusters built using conformal mappings and on a lattice. The growth properties of the active and frozen zones are clearly elucidated. We show that the unique scaling exponent characterizing the stationary growth is the DLA fractal dimension.

Entropy-driven single molecule tug-of-war of DNA at micro-nanofluidic interfaces.

Entropy-driven polymer dynamics at the nanoscale is fundamentally important in biological systems but the dependence of the entropic force on the nanoconfinement remains elusive. Here, we established an entropy-driven single molecule tug-of-war (TOW) at two micro-nanofluidic interfaces bridged by a nanoslit, performed the force analysis from a modified wormlike chain in the TOW scenario and the entropic recoiling process, and determined the associated scalings on the nanoconfinement. Our results provide a direct experimental evidence that the entropic forces in these two regimes, though unequal, are essentially constant at defined slit heights, irrespective of the slit lengths and the DNA segments within. Our findings have the implications to polymer transport at the nanoscale, device design for single molecule analysis, and biotechnological applications.

Unusual response to a localized perturbation in a generalized elastic model.

The generalized elastic model encompasses several physical systems such as polymers, membranes, single-file systems, fluctuating surfaces, and rough interfaces. We consider the case of an applied localized potential, namely, an external force acting only on a single (tagged) probe, leaving the rest of the system unaffected. We derive the fractional Langevin equation for the tagged probe, as well as for a generic (untagged) probe, where the force is not directly applied. Within the framework of the fluctuation-dissipation relations, we discuss the unexpected physical scenarios arising when the force is constant and time periodic, whether or not the hydrodynamic interactions are included in the model. For short times, in the case of the constant force, we show that the average drift is linear in time for long-range hydrodynamic interactions and behaves ballistically or exponentially for local hydrodynamic interactions. Moreover, it can be opposite to the direction of the external disturbance for some values of the model's parameters. When the force is time periodic, the effects are macroscopic: the system splits into two distinct spatial regions whose size is proportional to the value of the applied frequency. These two regions are characterized by different amplitudes and phase shifts in the response dynamics.

Foundation of fractional Langevin equation: harmonization of a many-body problem.

In this study we derive a single-particle equation of motion, from first principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models and a relation derived by Kollmann.