Flagellar beating drives sperm through the female reproductive tract and is vital for reproduction. Flagellar waves are generated by thousands of asymmetric molecular components; yet, paradoxically, forward swimming arises via symmetric side-to-side flagellar movement. This led to the preponderance of symmetric flagellar control hypotheses. However, molecular asymmetries must still dictate the flagellum and be manifested in the beat. Here, we reconcile molecular and microscopic observations, reconnecting structure to function, by showing that human sperm uses asymmetric and anisotropic controls to swim. High-speed three-dimensional (3D) microscopy revealed two coactive transversal controls: An asymmetric traveling wave creates a one-sided stroke, and a pulsating standing wave rotates the sperm to move equally on all sides. Symmetry is thus achieved through asymmetry, creating the optical illusion of bilateral symmetry in 2D microscopy. This shows that the sperm flagellum is asymmetrically controlled and anisotropically regularized by fast-signal transduction. This enables the sperm to swim forward.

The challenges faced in analyzing optical imaging data from neurons include a low signal-to-noise ratio of the acquired images and the multiscale nature of the tubular structures that range in size from hundreds of microns to hundreds of nanometers. In this paper, we address these challenges and present a computational framework for an automatic, three-dimensional (3D) morphological reconstruction of live nerve cells. The key aspects of this approach are: (i) detection of neuronal dendrites through learning 3D tubular models, and (ii) skeletonization by a new algorithm using a morphology-guided deformable model for extracting the dendritic centerline. To represent the neuron morphology, we introduce a novel representation, the Minimum Shape-Cost (MSC) Tree that approximates the dendrite centerline with sub-voxel accuracy and demonstrate the uniqueness of such a shape representation as well as its computational efficiency. We present extensive quantitative and qualitative results that demonstrate the accuracy and robustness of our method.

The reiterative process of lateral root (LR) formation is widespread and underlies root system formation. However, early LR primordium (LRP) morphogenesis is not fully understood. In this study, we conducted both a clonal analysis and time-lapse experiments to decipher the pattern and sequence of pericycle founder cell (FC) participation in LR formation. Most commonly, LRP initiation starts with the specification of just one FC longitudinally. Clonal and anatomical analyses suggested that a single FC gradually recruits neighboring pericycle cells to become FCs. This conclusion was validated by long-term time-lapse live-imaging experiments. Once the first FC starts to divide, its immediate neighbors, both lengthwise and laterally, are recruited within the hour, after which they recruit their neighboring cells within a few hours. Therefore, LRP initiation is a gradual, multistep process. FC recruitment is auxin-dependent and is abolished by treatment with a polar auxin transport inhibitor. Furthermore, FC recruitment establishes a morphogenetic field where laterally peripheral cells have a lower auxin response, which is associated with a lower proliferation potential, compared to centrally located FCs. The lateral boundaries of the morphogenetic field are determined by phloem-adjacent pericycle cells, which are the last cells to be recruited as FCs. The proliferation potential of these cells is limited, but their recruitment is essential for root system formation, resulting in the formation of a new vascular connection between the nascent and parent root, which is crucial for establishing a continuous and efficient vascular system.

Tracing tubular structures from biomedical images is important for a wide range of applications. Particularly, the spermatozoon is an essential cell whose flagella have a tubular form. Its main function is to fertilize the egg, and the flagellum is fundamental to achieve this task which depends importantly on the dynamics of intracellular calcium ([Ca]). Measuring [Ca] along the flagellum in 3-D is not a simple matter since it requires: 1) sophisticated fluorescence imaging techniques dealing with low intensity and signal to noise ratio (SNR) and 2) tracing the flagellum's centerline. Most of the algorithms proposed to trace tubular structures have been developed for multi-branch structures not being adequate for single tubular structures with low SNR. Taking into account the prior knowledge that the flagellum is constituted by a single tubular structure, we propose an automatic method to trace and track multiple single tubular structures from 3-D images. First, an algorithm based on one-class classification allows enhancement of the flagellum. This enhanced 3-D image permits guiding an iterative centerline algorithm toward the flagellum's centerline. Each sperm is assigned an ID to keep track of it in 3-D . Our algorithm was quantitatively evaluated using a ground truth 564 semi-manual traces (six 3-D image stacks) comparing them to those obtained from state-of-the-art tubular structure centerline extraction algorithms. The qualitative and quantitative results show that our algorithm is extracting similar traces as compared with ground truth, and it is more robust and accurate to trace the flagellum's centerline than multi-branch algorithms.

The canonical beating of the human sperm flagellum is postulated to be symmetric. This is despite the reported asymmetries inherent to the flagellar axonemal structure, from distribution and activation of molecular motors to, even, the localisation of regulatory ion channels. This raises a fundamental question: how symmetric beating is possible within such intrinsically asymmetric flagellar complex? Here, we employ high-speed 3D imaging with mathematical analysis capable of resolving the flagellar movement in 4D (3D+time). This reveals that the human sperm beating is both anisotropic and asymmetric, and composed by a superposition of two transversal waves: an asymmetric travelling wave and a symmetric standing wave. This novel anisotropic travellingpulsation mechanism induces sperm rolling self-organisation and causes a flagellar kinematic illusion, so that the beat appears to be symmetric if observed with 2D microscopy. The 3D beating anisotropy thus regularises the intrinsic flagellar asymmetry to achieve symmetric side-to-side movement and straight-line swimming.