Carlos A. Condat

Geometrical guidance and trapping transition of human sperm cells

The guidance of human sperm cells under confinement in quasi-2D microchambers is investigated using a purely physical method to control their distribution. Transport property measurements and simulations are performed with diluted sperm populations, for which effects of geometrical guidance and concentration are studied in detail. In particular, a trapping transition at convex angular wall features is identified and analyzed. We also show that highly efficient microratchets can be fabricated by using curved asymmetric obstacles to take advantage of the spermatozoa specific swimming strategy.

Influence of swimming strategy on microorganism separation by asymmetric obstacles

It has been shown that a nanoliter chamber separated by a wall of asymmetric obstacles can lead to an inhomogeneous distribution of self-propelled microorganisms. Although it is well established that this rectification effect arises from the interaction between the swimmers and the noncentrosymmetric pillars, here we demonstrate numerically that its efficiency is strongly dependent on the detailed dynamics of the individual microorganism. In particular, for the case of run-and-tumble dynamics, the distribution of run lengths, the rotational diffusion, and the partial preservation of run orientation memory through a tumble are important factors when computing the rectification efficiency. In addition, we optimize the geometrical dimensions of the asymmetric pillars in order to maximize the swimmer concentration and we illustrate how it can be used for sorting by swimming strategy in a long array of parallel obstacles.

Quantifying the sorting efficiency of self-propelled run-and-tumble swimmers by geometrical ratchets

Suitable asymmetric microstructures can be used to control the direction of motion in microorganism populations. This rectification process makes it possible to accumulate swimmers in a region of space or to sort different swimmers. Here we study numerically how the separation process depends on the specific motility strategies of the microorganisms involved. Crucial properties such as the separation efficiency and the separation time for two bacterial strains are precisely defined and evaluated. In particular, the sorting of two bacterial populations inoculated in a box consisting of a series of chambers separated by columns of asymmetric obstacles is investigated. We show how the sorting efficiency is enhanced by these obstacles and conclude that this kind of sorting can be efficiently used even when the involved populations differ only in one aspect of their swimming strategy.

Effects of different per translational kinetics on the dynamics of a core circadian clock model.

Living beings display self-sustained daily rhythms in multiple biological processes, which persist in the absence of external cues since they are generated by endogenous circadian clocks. The period (per) gene is a central player within the core molecular mechanism for keeping circadian time in most animals. Recently, the modulation PER translation has been reported, both in mammals and flies, suggesting that translational regulation of clock components is important for the proper clock gene expression and molecular clock performance. Because translational regulation ultimately implies changes in the kinetics of translation and, therefore, in the circadian clock dynamics, we sought to study how and to what extent the molecular clock dynamics is affected by the kinetics of PER translation. With this objective, we used a minimal mathematical model of the molecular circadian clock to qualitatively characterize the dynamical changes derived from kinetically different PER translational mechanisms. We found that the emergence of self-sustained oscillations with characteristic period, amplitude, and phase lag (time delays) between per mRNA and protein expression depends on the kinetic parameters related to PER translation. Interestingly, under certain conditions, a PER translation mechanism with saturable kinetics introduces longer time delays than a mechanism ruled by a first-order kinetics. In addition, the kinetic laws of PER translation significantly changed the sensitivity of our model to parameters related to the synthesis and degradation of per mRNA and PER degradation. Lastly, we found a set of parameters, with realistic values, for which our model reproduces some experimental results reported recently for Drosophila melanogaster and we present some predictions derived from our analysis.

Disrupting the wall accumulation of human sperm cells by artificial corrugation

Many self-propelled microorganisms are attracted to surfaces. This makes their dynamics in restricted geometries very different from that observed in the bulk. Swimming along walls is beneficial for directing and sorting cells, but may be detrimental if homogeneous populations are desired, such as in counting microchambers. In this work, we characterize the motion of human sperm cells ∼60 μm long, strongly confined to ∼25 μm shallow chambers. We investigate the nature of the cell trajectories between the confining surfaces and their accumulation near the borders. Observed cell trajectories are composed of a succession of quasi-circular and quasi-linear segments. This suggests that the cells follow a path of intermittent trappings near the top and bottom surfaces separated by stretches of quasi-free motion in between the two surfaces, as confirmed by depth resolved confocal microscopy studies. We show that the introduction of artificial petal-shaped corrugation in the lateral boundaries removes the tendency of cells to accumulate near the borders, an effect which we hypothesize may be valuable for microfluidic applications in biomedicine.

Enhancement of microbial motility due to speed-dependent nutrient absorption.

Marine microorganisms often reach high swimming speeds, either to take advantage of evanescent nutrient patches or to beat Brownian forces. Since this implies that a sizable part of their energetic budget must be allocated to motion, it is reasonable to assume that some fast-swimming microorganisms may increase their nutrient intake by increasing their speed v. We formulate a model to investigate this hypothesis and its consequences, finding the steady-state solutions and analyzing their stability. Surprisingly, we find that even modest increases in nutrient absorption may lead to a significant increase of the microbial speed. In fact, evaluations obtained using realistic parameter values for bacteria indicate that the speed increase due to the enhanced nutrient absorption may be quite large.

Applications of the transfer integral techniques to two-dimensional lattices

The transfer integral formalism is used to study the statistical mechanical properties of a two-component field defined on a two-dimensional lattice. This field, taken to have anisotropic elasticity, is subject to both a nonlinear local potential and an external field. The free energy and magnetization are calculated using an approximate solution of the transfer integral problem. This solution employs a strong-coupling approximation to the transfer integral equation and a variational principle with correlated Gaussian trial functions. As a special case, the o4 model for a structural phase transition, in the absence of an applied field, is analyzed; a phase diagram consistent with previous calculations is obtained. The phase diagram for a two-component field, with anisotropic elasticity, a o4 local potential, and an external field, is also considered.

Stochastic resonance effects in the scattering of neutrons by modulated two-state systems

Recent work indicates that the stochastic resonance phenomenon (SR) can have a strong signature in the neutron scattering cross section. Here we consider neutron scattering by a sample containing a random distribution of bistable scattering centres. The robustness of the stochastic resonance signal is tested by performing suitable configurational averages over the potential parameters. By showing that the resonant line is not significantly weakened by the randomness, our results suggest that SR should be observable in a real glass.