Modelling Motility: The Mathematics of Spermatozoa

Construction of intelligent moving micro/nanomotors and their applications in biosensing and disease treatment

Micro/nanomotors are containers that pass through liquid media and carry cargo. Because they are tiny, micro/nanomotors exhibit excellent potential for biosensing and disease treatment applications. However, their size also makes overcoming random Brownian forces very challenging for micro/nanomotors moving on targets. Additionally, to achieve desired practical applications, the expensive materials, short lifetimes, poor biocompatibility, complex preparation methods, and side effects of micro/nanomotors must be addressed, and potential adverse effects must be evaluated both in vivo and in practical applications. This has led to the continuous development of key materials for driving micro/nanomotors. In this work, we review the working principles of micro/nanomotors. Metallic and nonmetallic nanocomplexes, enzymes, and living cells are explored as key materials for driving micro/nanomotors. We also consider the effects of exogenous stimulations and endogenous substance conditions on micro/nanomotor motions. The discussion focuses on micro/nanomotor applications in biosensing, treating cancer and gynecological diseases, and assisted fertilization. By addressing micro/nanomotor shortcomings, we propose directions for further developing and applying micro/nanomotors.

A novel Human Conception Optimizer for solving optimization problems

Computational techniques are widely used to solve complex optimization problems in different fields such as engineering, finance, biology, and so on. In this paper, the Human Conception Optimizer (HCO) is proposed as a novel metaheuristic algorithm to solve any optimization problems. The idea of this algorithm is based on some biological principles of the human conception process, such as the selective nature of cervical gel in the female reproductive system to allow only healthy sperm cells into the cervix, the guidance nature of mucus gel to help sperm track a genital tracking path towards the egg in the Fallopian tube, the asymmetric nature of flagellar movement which allows sperm cells to move in the reproductive system, the sperm hyperactivation process to make them able to fertilize an egg. Thus, the strategies pursued by the sperm in searching for the egg in the Fallopian tube are modeled mathematically. The best sperm which will meet the position of the egg will be the solution of the algorithm. The performance of the proposed HCO algorithm is examined with a set of basic benchmark test functions called IEEE CEC-2005 and IEEE CEC-2020. A comparative study is also performed between the HCO algorithm and other available algorithms. The significance of the results is verified with statistical test methods. To validate the proposed HCO algorithm, two real-world engineering optimization problems are examined. For this purpose, a complex 14 over-current relay based IEEE 8 bus distribution system is considered. With the proposed algorithm, an improvement of 50% to 60% in total relay operating times is observed comparing with some existing results for the same system. Another engineering problem of designing an optimal proportional integral derivative (PID) controller for a blower driven patient hose mechanical ventilator (MV) is examined. A significant improvement in terms of response time, settling time is observed in the MV system by comparing with existing results.

Most probable path of an active Brownian particle

In this study, we investigate the transition path of a free active Brownian particle (ABP) on a two-dimensional plane between two given states. The extremum conditions for the most probable path connecting the two states are derived using the Onsager-Machlup integral and its variational principle. We provide explicit solutions to these extremum conditions and demonstrate their nonuniqueness through an analogy with the pendulum equation indicating possible multiple paths. The pendulum analogy is also employed to characterize the shape of the globally most probable path obtained by explicitly calculating the path probability for multiple solutions. We comprehensively examine a translation process of an ABP to the front as a prototypical example. Interestingly, the numerical and theoretical analyses reveal that the shape of the most probable path changes from an I to a U shape and to the ℓ shape with an increase in the transition process time. The Langevin simulation also confirms this shape transition. We also discuss further method applications for evaluating a transition path in rare events in active matter.

Convergent evolution in the supercoiling of prokaryotic flagellar filaments

The supercoiling of bacterial and archaeal flagellar filaments is required for motility. Archaeal flagellar filaments have no homology to their bacterial counterparts and are instead homologs of bacterial type IV pili. How these prokaryotic flagellar filaments, each composed of thousands of copies of identical subunits, can form stable supercoils under torsional stress is a fascinating puzzle for which structural insights have been elusive. Advances in cryoelectron microscopy (cryo-EM) make it now possible to directly visualize the basis for supercoiling, and here, we show the atomic structures of supercoiled bacterial and archaeal flagellar filaments. For the bacterial flagellar filament, we identify 11 distinct protofilament conformations with three broad classes of inter-protomer interface. For the archaeal flagellar filament, 10 protofilaments form a supercoil geometry supported by 10 distinct conformations, with one inter-protomer discontinuity creating a seam inside of the curve. Our results suggest that convergent evolution has yielded stable superhelical geometries that enable microbial locomotion.

Fluid-structure interaction of bio-inspired flexible slender structures: a review of selected topics

Flexible slender structures are ubiquitous in biological systems and engineering applications. Fluid-structure interaction (FSI) plays a key role in the dynamics of such structures immersed in fluids. Here, we survey recent studies on highly simplified bio-inspired models (either mathematical or mechanical) that aim to revealthe flow physics associated with FSI. Various models from different sources of biological inspiration are included, namely flexible flapping foil inspired by fish and insects, deformable membrane inspired by jellyfish and cephalopods, beating filaments inspired by flagella and cilia of microorganisms, and flexible wall-mounted filaments inspired by terrestrial and aquatic plants. Suggestions on directions for future research are also provided.

Self-organized swimming with odd elasticity

We theoretically investigate self-oscillating waves of an active material, which were recently introduced as a nonsymmetric part of the elastic moduli, termed odd elasticity. Using Purcell's three-link swimmer model, we reveal that an odd-elastic filament at low Reynolds number can swim in a self-organized manner and that the time-periodic dynamics are characterized by a stable limit cycle generated by elastohydrodynamic interactions. Also, we consider a noisy shape gait and derive a swimming formula for a general elastic material in the Stokes regime with its elasticity modulus being represented by a nonsymmetric matrix, demonstrating that the odd elasticity produces biased net locomotion from random noise.