Many biological processes happen on a nano- to millimeter scale and within milliseconds. Established methods such as confocal microscopy are suitable for precise 3D recordings but lack the temporal or spatial resolution to resolve fast 3D processes and require labeled samples. Multifocal imaging (MFI) allows high-speed 3D imaging but is limited by the compromise between high spatial resolution and large field-of-view (FOV), and the requirement for bright fluorescent labels. Here, we provide an open-source 3D reconstruction algorithm for multi-focal images that allows using MFI for fast, precise, label-free tracking spherical and filamentous structures in a large FOV and across a high depth. We characterize fluid flow and flagellar beating of human and sea urchin sperm with a z -precision of 0.15 µm, in a volume of 240 × 260 × 21 µm, and at high speed (500 Hz). The sampling volume allowed to follow sperm trajectories while simultaneously recording their flagellar beat. Our MFI concept is cost-effective, can be easily implemented, and does not rely on object labeling, which renders it broadly applicable.

Cilia serve as cellular antennae that translate sensory information into physiological responses. In the sperm flagellum, a single chemoattractant molecule can trigger a Ca2+ rise that controls motility. The mechanisms underlying such ultra-sensitivity are ill-defined. Here, we determine by mass spectrometry the copy number of nineteen chemosensory signaling proteins in sperm flagella from the sea urchin Arbacia punctulata. Proteins are up to 1,000-fold more abundant than the free cellular messengers cAMP, cGMP, H+ , and Ca2+ . Opto-chemical techniques show that high protein concentrations kinetically compartmentalize the flagellum: Within milliseconds, cGMP is relayed from the receptor guanylate cyclase to a cGMP-gated channel that serves as a perfect chemo-electrical transducer. cGMP is rapidly hydrolyzed, possibly via "substrate channeling" from the channel to the phosphodiesterase PDE5. The channel/PDE5 tandem encodes cGMP turnover rates rather than concentrations. The rate-detection mechanism allows continuous stimulus sampling over a wide dynamic range. The textbook notion of signal amplification-few enzyme molecules process many messenger molecules-does not hold for sperm flagella. Instead, high protein concentrations ascertain messenger detection. Similar mechanisms may occur in other small compartments like primary cilia or dendritic spines.

Sperm require a sense of direction to locate the egg for fertilization. They follow gradients of chemical and physical cues provided by the egg or the oviduct. However, the principles underlying three-dimensional (3D) navigation in chemical landscapes are unknown. Here using holographic microscopy and optochemical techniques, we track sea urchin sperm navigating in 3D chemoattractant gradients. Sperm sense gradients on two timescales, which produces two different steering responses. A periodic component, resulting from the helical swimming, gradually aligns the helix towards the gradient. When incremental path corrections fail and sperm get off course, a sharp turning manoeuvre puts sperm back on track. Turning results from an 'off' Ca(2+) response signifying a chemoattractant stimulation decrease and, thereby, a drop in cyclic GMP concentration and membrane voltage. These findings highlight the computational sophistication by which sperm sample gradients for deterministic klinotaxis. We provide a conceptual and technical framework for studying microswimmers in 3D chemical landscapes.

Calcium in the flagellum controls sperm navigation. In sperm of marine invertebrates and mammals, Ca(2+) signalling has been intensely studied, whereas for fish little is known. In sea urchin sperm, a cyclic nucleotide-gated K(+) channel (CNGK) mediates a cGMP-induced hyperpolarization that evokes Ca(2+) influx. Here, we identify in sperm of the freshwater fish Danio rerio a novel CNGK family member featuring non-canonical properties. It is located in the sperm head rather than the flagellum and is controlled by intracellular pH, but not cyclic nucleotides. Alkalization hyperpolarizes sperm and produces Ca(2+) entry. Ca(2+) induces spinning-like swimming, different from swimming of sperm from other species. The "spinning" mode probably guides sperm into the micropyle, a narrow entrance on the surface of fish eggs. A picture is emerging of sperm channel orthologues that employ different activation mechanisms and serve different functions. The channel inventories probably reflect adaptations to species-specific challenges during fertilization.

During chemotaxis and phototaxis, sperm, algae, marine zooplankton, and other microswimmers move on helical paths or drifting circles by rhythmically bending cell protrusions called motile cilia or flagella. Sperm of marine invertebrates navigate in a chemoattractant gradient by adjusting the flagellar waveform and, thereby, the swimming path. The waveform is periodically modulated by Ca(2+) oscillations. How Ca(2+) signals elicit steering responses and shape the path is unknown. We unveil the signal transfer between the changes in intracellular Ca(2+) concentration ([Ca(2+)](i)) and path curvature (κ). We show that κ is modulated by the time derivative d[Ca(2+)](i)/dt rather than the absolute [Ca(2+)](i). Furthermore, simulation of swimming paths using various Ca(2+) waveforms reproduces the wealth of swimming paths observed for sperm of marine invertebrates. We propose a cellular mechanism for a chemical differentiator that computes a time derivative. The cytoskeleton of cilia, the axoneme, is highly conserved. Thus, motile ciliated cells in general might use a similar cellular computation to translate changes of [Ca(2+)](i) into motion.