Limits...
Search for a small egg by spermatozoa in restricted geometries.

Yang J, Kupka I, Schuss Z, Holcman D - J Math Biol (2015)

Bottom Line: In the proposed model the swimmers' trajectories are rectilinear and the speed is constant.Because hitting a small target by a trajectory is a rare event, asymptotic approximations and stochastic simulations are needed to estimate the mean search time in various geometries.We consider searches in a disk, in convex planar domains, and in domains with cusps.

View Article: PubMed Central - PubMed

Affiliation: Applied Mathematics and Computational Biology, Ecole Normale Supérieure, IBENS, 46 rue d'Ulm, 75005, Paris, France.

ABSTRACT
The search by swimmers for a small target in a bounded domain is ubiquitous in cellular biology, where a prominent case is that of the search by spermatozoa for an egg in the uterus. This is one of the severest selection processes in animal reproduction. We present here a mathematical model of the search, its analysis, and numerical simulations. In the proposed model the swimmers' trajectories are rectilinear and the speed is constant. When a trajectory hits an obstacle or the boundary, it is reflected at a random angle and continues the search with the same speed. Because hitting a small target by a trajectory is a rare event, asymptotic approximations and stochastic simulations are needed to estimate the mean search time in various geometries. We consider searches in a disk, in convex planar domains, and in domains with cusps. The exploration of the parameter space for spermatozoa motion in different uterus geometries leads to scaling laws for the search process.

No MeSH data available.


Related in: MedlinePlus

Particle moving from point  to
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4940446&req=5

Fig3: Particle moving from point to

Mentions: When a trajectory starts at it ends at another point (see Fig. 3), the probability that the angular deviation of the particle moving path (assuming the path is a straight line) will lie between angle and is , in which is the angle between the moving path and the tangent line at point .Fig. 3


Search for a small egg by spermatozoa in restricted geometries.

Yang J, Kupka I, Schuss Z, Holcman D - J Math Biol (2015)

Particle moving from point  to
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4940446&req=5

Fig3: Particle moving from point to
Mentions: When a trajectory starts at it ends at another point (see Fig. 3), the probability that the angular deviation of the particle moving path (assuming the path is a straight line) will lie between angle and is , in which is the angle between the moving path and the tangent line at point .Fig. 3

Bottom Line: In the proposed model the swimmers' trajectories are rectilinear and the speed is constant.Because hitting a small target by a trajectory is a rare event, asymptotic approximations and stochastic simulations are needed to estimate the mean search time in various geometries.We consider searches in a disk, in convex planar domains, and in domains with cusps.

View Article: PubMed Central - PubMed

Affiliation: Applied Mathematics and Computational Biology, Ecole Normale Supérieure, IBENS, 46 rue d'Ulm, 75005, Paris, France.

ABSTRACT
The search by swimmers for a small target in a bounded domain is ubiquitous in cellular biology, where a prominent case is that of the search by spermatozoa for an egg in the uterus. This is one of the severest selection processes in animal reproduction. We present here a mathematical model of the search, its analysis, and numerical simulations. In the proposed model the swimmers' trajectories are rectilinear and the speed is constant. When a trajectory hits an obstacle or the boundary, it is reflected at a random angle and continues the search with the same speed. Because hitting a small target by a trajectory is a rare event, asymptotic approximations and stochastic simulations are needed to estimate the mean search time in various geometries. We consider searches in a disk, in convex planar domains, and in domains with cusps. The exploration of the parameter space for spermatozoa motion in different uterus geometries leads to scaling laws for the search process.

No MeSH data available.


Related in: MedlinePlus