Swimming of Spermatozoa in a Maxwell Fluid

Spermatozoon-propelled microcellular submarines combining innate magnetic hyperthermia with derived nanotherapies for thrombolysis and ischemia mitigation

Thrombotic cardiovascular diseases are a prevalent factor contributing to both physical impairment and mortality. Thrombolysis and ischemic mitigation have emerged as leading contemporary therapeutic approaches for addressing the consequences of ischemic injury and reperfusion damage. Herein, an innovative cellular-cloaked spermatozoon-driven microcellular submarine (SPCS), comprised of multimodal motifs, was designed to integrate nano-assembly thrombolytics with an immunomodulatory ability derived from innate magnetic hyperthermia. Rheotaxis-based navigation was utilized to home to and cross the clot barrier, and finally accumulate in ischemic vascular organs, where the thrombolytic motif was "switched-on" by the action of thrombus magnetic red blood cell-driven magnetic hyperthermia. In a murine model, the SPCS system combining innate magnetic hyperthermia demonstrated the capacity to augment delivery efficacy, produce nanotherapeutic outcomes, exhibit potent thrombolytic activity, and ameliorate ischemic tissue damage. These findings underscore the multifaceted potential of our designed approach, offering both thrombolytic and ischemia-mitigating effects. Given its extended therapeutic effects and thrombus-targeting capability, this biocompatible SPCS system holds promise as an innovative therapeutic agent for enhancing efficacy and preventing risks after managing thrombosis.

Reviewing mathematical models of sperm signaling networks

Dave Garbers' work significantly contributed to our understanding of sperm's regulated motility, capacitation, and the acrosome reaction. These key sperm functions involve complex multistep signaling pathways engaging numerous finely orchestrated elements. Despite significant progress, many parameters and interactions among these elements remain elusive. Mathematical modeling emerges as a potent tool to study sperm physiology, providing a framework to integrate experimental results and capture functional dynamics considering biochemical, biophysical, and cellular elements. Depending on research objectives, different modeling strategies, broadly categorized into continuous and discrete approaches, reveal valuable insights into cell function. These models allow the exploration of hypotheses regarding molecules, conditions, and pathways, whenever they become challenging to evaluate experimentally. This review presents an overview of current theoretical and experimental efforts to understand sperm motility regulation, capacitation, and the acrosome reaction. We discuss the strengths and weaknesses of different modeling strategies and highlight key findings and unresolved questions. Notable discoveries include the importance of specific ion channels, the role of intracellular molecular heterogeneity in capacitation and the acrosome reaction, and the impact of pH changes on acrosomal exocytosis. Ultimately, this review underscores the crucial importance of mathematical frameworks in advancing our understanding of sperm physiology and guiding future experimental investigations.

The Effects of Viscoelasticity on Droplet Migration on Surfaces with Wettability Gradients

A finite-volume method based on the OpenFOAM is used to numerically study the factors affecting the migration of viscoelastic droplets on rigid surfaces with wettability gradients. Parameters investigated include droplet size, relaxation time, solvent viscosity, and polymer viscosity of the liquid comprising droplets. The wettability gradient is imposed numerically by assuming a linear change in the contact angle along the substrate. As reported previously for Newtonian droplets, the wettability gradient induces spontaneous migration from hydrophobic to hydrophilic region on the substrate. The migration of viscoelastic droplets reveals the increase in the migration speed and distance with the increase in the Weissenberg number. The increase in droplet size also shows the increase in both the migration speed and distance. The increase in polymer viscosity exhibits the increase in migration speed but the decrease in migration distance.

The Effect of Surface Wettability on Viscoelastic Droplet Dynamics under Electric Fields

The effects of surface wettability and viscoelasticity on the dynamics of liquid droplets under an electric field are studied experimentally. A needle-plate electrode system is used as the power source to polarize a dielectric plate by the corona discharge emitted at the needle electrode, creating a new type of steerable electric field realized. The dynamics of droplets between the dielectric plate and a conductive substrate include three different phenomena: equilibrium to a stationary shape on substrates with higher wettability, deformation to form a bridge between the top acrylic plate and take-off on the substrates with lower wettability. Viscoelastic droplets differ from water in the liquid bridge and takeoff phenomena in that thin liquid filaments appear in viscoelastic droplets, not observed for Newtonian droplets. The equilibrated droplet exhibits more pronounced heights for Newtonian droplets compared to viscoelastic droplets, with a decrease in height with the increase in the concentration of the elastic constituent in the aqueous solution. In the take-off phenomenon, the time required for the droplet to contact the upper plate decreases with the concentration of the elastic constituent increases. It is also found that the critical voltage required for the take-off phenomenon to occur decreases as the elasticity increases.

MODELING OF FLAGELLUM BEHAVIOR AND TWO-DIMENSIONAL SPERM CELL MOTILITY WITHIN THE CONTEXT OF FLUID–SOLID INTERACTIONS

In this study, the flagellar motility of a swimmer microorganism as a model of a human sperm cell, inside a two-dimensional channel as a model of the female reproductive tract containing a viscous fluid, is numerically investigated. The Navier–Stokes equations governing the fluid are coupled with the equations governing the models flagellum via applying a fluid–solid interaction approach and then solved using the finite element method. To stimulate the flagellum to move, a prescribed sinusoidal waveform is applied to it. The strain induced by this waveform along the flagellum initiates a continuous interaction between the flagellum and the fluid. The simulations are validated using data available in the literature. A very good agreement is seen between them. The results show that by decreasing the Young modulus of the flagellum as well as increasing the fluid viscosity, the swimming velocity of the model significantly decreases. It is found that for lower Young modulus of the flagellum, the effect of the fluid viscosity on the flagellar deformation is stronger. It is also found that for higher amplitude of the waveform applied to stimulate the flagellum, both the swimming velocity of the model and the average work rate are greater. Moreover, it is found that in a channel with a smaller height, the model swims at a higher speed and with a higher average work rate.

A Bayesian Framework to Estimate Fluid and Material Parameters in Micro-swimmer Models

To advance our understanding of the movement of elastic microstructures in a viscous fluid, techniques that utilize available data to estimate model parameters are necessary. Here, we describe a Bayesian uncertainty quantification framework that is highly parallelizable, making parameter estimation tractable for complex fluid-structure interaction models. Using noisy in silico data for swimmers, we demonstrate the methodology's robustness in estimating fluid and elastic swimmer parameters, along with their uncertainties. We identify correlations between model parameters and gain insight into emergent swimming trajectories of a single swimmer or a pair of swimmers. Our proposed framework can handle data with a spatiotemporal resolution representative of experiments, showing that this framework can be used to aid in the development of artificial micro-swimmers for biomedical applications, as well as gain a fundamental understanding of the range of parameters that allow for certain motility patterns.

The anatomy, movement, and functions of human sperm tail: an evolving mystery

Sperms have attracted attention of many researchers since it was discovered by Antonie van Leeuwenhoek in 1677. Though a small cell, its every part has complex structure and different function to play in carrying life. Sperm tail is most complicated structure with more than 1000 proteins involved in its functioning. With the advent of three-dimensional microscopes, many studies are undergoing to understand exact mechanism of sperm tail movement. Most recent studies have shown that sperms move by spinning rather than swimming. Each subunit of tail, including axonemal, peri-axonemal structures, plays essential roles in sperm motility, capacitation, hyperactivation, fertilization. Furthermore, over 2300 genes are involved in spermatogenesis. A number of genetic mutations have been linked with abnormal sperm flagellar development leading to motility defects and male infertility. It was found that 6% of male infertility cases are related to genetic causes, and 4% of couples undergoing intracytoplasmic sperm injection for male subfertility have chromosomal abnormalities. Hence, an understanding of sperm tail development and genes associated with its normal functioning can help in better diagnosis of male infertility and its management. There is still a lot that needs to be discovered about genes, proteins contributing to normal human sperm tail development, movement, and role in male fertility. Sperm tail has complex anatomy, with surrounding axoneme having 9 + 2 microtubules arrangement along its entire length and peri-axonemal structures that contribute in sperm motility and fertilization. In future sperm tail-associated genes, proteins and subunits can be used as markers of male fertility.

Magnetically Powered Biodegradable Microswimmers

The propulsive efficiency and biodegradability of wireless microrobots play a significant role in facilitating promising biomedical applications. Mimicking biological matters is a promising way to improve the performance of microrobots. Among diverse locomotion strategies, undulatory propulsion shows remarkable efficiency and agility. This work proposes a novel magnetically powered and hydrogel-based biodegradable microswimmer. The microswimmer is fabricated integrally by 3D laser lithography based on two-photon polymerization from a biodegradable material and has a total length of 200 μm and a diameter of 8 μm. The designed microswimmer incorporates a novel design utilizing four rigid segments, each of which is connected to the succeeding segment by spring to achieve undulation, improving structural integrity as well as simplifying the fabrication process. Under an external oscillating magnetic field, the microswimmer with multiple rigid segments connected by flexible spring can achieve undulatory locomotion and move forward along with the directions guided by the external magnetic field in the low Reynolds number (Re) regime. In addition, experiments demonstrated that the microswimmer can be degraded successfully, which allows it to be safely applied in real-time in vivo environments. This design has great potential in future in vivo applications such as precision medicine, drug delivery, and diagnosis.

Dynamics of Swimmers in Fluids with Resistance

Micro-swimmers such as spermatozoa are able to efficiently navigate through viscous fluids that contain a sparse network of fibers or other macromolecules. We utilize the Brinkman equation to capture the fluid dynamics of sparse and stationary obstacles that are represented via a single resistance parameter. The method of regularized Brinkmanlets is utilized to solve for the fluid flow and motion of the swimmer in 2-dimensions when assuming the flagellum (tail) propagates a curvature wave. Extending previous studies, we investigate the dynamics of swimming when varying the resistance parameter, head or cell body radius, and preferred beat form parameters. For a single swimmer, we determine that increased swimming speed occurs for a smaller cell body radius and smaller fluid resistance. Progression of swimmers exhibits complex dynamics when considering hydrodynamic interactions; attraction of two swimmers is a robust phenomenon for smaller beat amplitude of the tail and smaller fluid resistance. Wall attraction is also observed, with a longer time scale of wall attraction with a larger resistance parameter.

Effect of Viscous Dissipation in Heat Transfer of MHD Flow of Micropolar Fluid Partial Slip Conditions: Dual Solutions and Stability Analysis

In this study, first-order slip effect with viscous dissipation and thermal radiation in micropolar fluid on a linear shrinking sheet is considered. Mathematical formulations of the governing equations of the problem have been derived by employing the fundamental laws of conservations which then converted into highly non-linear coupled partial differential equations (PDEs) of boundary layers. Linear transformations are employed to change PDEs into non-dimensional ordinary differential equations (ODEs). The solutions of the resultant ODEs have been obtained by using of numerical method which is presented in the form of shootlib package in MAPLE 2018. The results reveal that there is more than one solution depending upon the values of suction and material parameters. The ranges of dual solutions are S ≥ S c i , i = 0 , 1 , 2 and no solution is S < S c i where S c i is the critical values of S . Critical values have been obtained in the presence of dual solutions and the stability analysis is carried out to identify more stable solutions. Variations of numerous parameters have been also examined by giving tables and graphs. The numerical values have been obtained for the skin friction and local Nusselt number and presented graphically. Further, it is observed that the temperature and thickness of the thermal boundary layer increase when thermal radiation parameter is increased in both solutions. In addition, it is also noticed that the fluid velocity increases in the case of strong magnetic field effect in the second solution.