MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research

Motility of a model bristle-bot: A theoretical analysis

Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided

Modelling biological and bio-inspired swimming at microscopic scales: Recent results and perspectives

Some recent results on biological and bio-inspired swimming at microscopic scales are reviewed, and used to identify promising research directions for the future. We focus on broad conceptual principles such as looping in the space of shapes, loss of controllability of systems in which shape is only partially controlled, and steering by modulating the actuation rate. Moreover, we discuss propulsion mechanism that are most common for unicellular swimmers, such as flagellar and ciliary beating, and we examine amoeboid motion and flagellar propulsion in Euglena. The Helix Theorem, a universal law characterising orbits traced by ciliated and flagellated unicellular swimmers propelled by the periodic beating of cilia and flagella, is proved and discussed as a principle of self-assembly for helical structures

The biomechanical role of extra-axonemal structures in shaping the flagellar beat of euglena gracilis

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed ’spinning lasso’, arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum

Morphable structures from unicellular organisms with active, shape-shifting envelopes: Variations on a theme by Gauss

We discuss some recent results on biological and bio-inspired morphing, and use them to identify promising research directions for the future. In particular, we consider issues related to morphing at microscopic scales inspired by unicellular organisms. We focus on broad conceptual principles and, in particular, on morphing approaches based on the use of Gauss’ theorema egregium (Gaussian morphing). We highlight some connections with biological cell envelopes containing filaments and motors, and discuss ideas for the implementation of Gaussian morphing in surfaces actuated by active shearing or stretching

Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes

The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement

Which men with non-malignant pathology at magnetic resonance imaging-targeted prostate biopsy and persistent PI-RADS 3-5 lesions should repeat biopsy?

Purpose: To assess predictors of clinically significant (cs) prostate cancer (PCa) in men who had a non-malignant Multiparametric magnetic resonance imaging (mpMRI)-targeted biopsy and persistent Prostate Imaging-Reporting Data System (PI-RADS) 3 to 5 lesions in subsequent mpMRI. Materials and Methods: We retrospectively analyzed MRI-targeted biopsy database in three centers. Inclusion criteria: persistence of at least one PI-RADS ≥3 lesion found negative for cancer in a previous MRI-targeted plus systemic biopsy (baseline biopsy). Exclusion criteria: downgrading to PI-RADS 1-2. A logistic regression analysis was performed to estimate the predictors of csPCa. Results: Fifty-seven patients were included. Median interval between biopsies was 12.9(2.43) months. Median age was 68.0(12) years. Median PSA was 7.0(5.45) ng/ml. At follow-up, 24.6%, 54.4%, and 21% of patients had a PI-RADS score 3, 4, and 5 index lesion (IL), respectively. At re-biopsy, 28/57(49.1%) men were found to harbor PCa. Among these, 22(78.6%) had csPCa. csPCa was found outside the IL in only 2 patients. Eleven, 13, and 5 patients with PI-RADS 3, 4, and 5, respectively, had no cancer. Three patients with a PI-RADS 3 lesion had cancer (2 with Gleason score 3+3, 1 with Gleason score 3+4). 14/43 men with a PI-RADS 4/5 lesion harbored Gleason score ≥3+4 PCa. Logistic regression analysis found that PSA (HR 1.281, 95% CI: 1.013–1.619, P = 0.039) and IL size (HR 1.146, 95% CI: 1.018–1.268, P = 0.041) were the predictors of csPCa at re-biopsy. Conclusions: Patients with non-malignant pathology from PI-RADS ≥3 lesions targeted biopsy should be follow-up with mpMRI, and those with persistent PI-RADS 4 to 5 lesions should repeat MRI-targeted and systematic biopsy