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 dilute 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.PACS numbers: 87.17. Jj, 87.18.Hf, 87.17.Aa, 87.17.Rt Understanding sperm dynamics under confining microgeometries is a general problem and a major challenge both from the basic biophysics and the complex fluids points of view. It is also crucial for microfluidics and biomedical control applications. Our knowledge of the swimming cell motilities in unbounded media cannot be directly extrapolated to their behavior in complex environments such as those found in the oviduct or in the labon-a-chip microfluidic devices used to control and analyze small samples or for in-vitro reproduction procedures. In these cases, the characteristic length scales are of the same order as the cell size, i.e. a few micrometers. Under these circumstances, confined self-propelled microorganisms undergo substantial changes in their locomotion habits, adapting their dynamics to intricate porous media or to solid surfaces vicinity [1], reducing their speed close to boundaries [2] or adjusting their morphology and motility in very narrow channels [3].It has been shown that microswimmers with very different propulsion systems are similarly attracted to the walls and to swim parallel to the surface [2,[4][5][6][7][8][9][10][11]. It is believed that this attractive force has hydrodynamic origin although other possible mechanisms have been proposed [12][13][14]. Several models have been introduced to describe the swimming along surfaces (see Ref.[15] and references therein). Interestingly, the direct observation of the cell-wall attraction (see Fig. 1) have led to the design of ratchet devices that guide and sort self-propelled cells using asymmetric obstacles [16,17]. In particular, different microfluidic devices have been created to either increase sperm cell quality or enhance their concentration [18][19][20]. The creation of inhomogeneous distributions of swimmer populations via asymmetric obstacles has been shown to be particularly efficient for run-and-tumble bacteria [16,[21][22][23]. Alternative ways of achieving nonuniform distributions have also been obtained combining symmetric funnels and flux [24]. Nowadays, numerous theoretical treatments are available to account for the effects of asymmetric obstacles on active particles distributions [25][26][27][28]. Tumbles, rotational diffusion and collisions are efficient mechanisms for separating the cells from the surface, thus permitting bacteria to be reinserted into the bulk of the confining micro...

The thermodynamic properties of the double sine-Gordon chain are studied both analytically and numerically. Particular attention is given to the regime in which there are two different kinks (small and large) on the chain. The shape and energy of kinks are found in the continuum approximation.Comparison is made with numerical determination of the kink energies. The free energy, entropy, etc. of the chain are found. They are dominated by the small kinks. To see evidence for the participation of the large kinks the fluctuation in chain position and its equation of state are examined. The current carried by the chain is calculated. An unusual polarization precursor to activated conductivity is found. The polarization precursor is determined by the small kinks; the conductivity is determined by the large kinks.

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.

Aedes aegypti is the main vector of multiple diseases, such as Dengue, Zika, and Chikungunya.Due to modifications in weather patterns, its geographical range is continuously evolving. Temperature is a key factor for its expansion into regions with cool winters, but rainfall can also have a strong impact on the colonization of these regions, since larvae emerging after a rainfall are likely to die at temperatures below 10 • C. As climate change is expected to affect rainfall regimes, with a higher frequency of heavy storms and an increase in drought-affected areas, it is important to understand how different rainfall scenarios may shape Ae. aegypti's range. We develop a model for the population dynamics of Ae. aegypti, coupled with a rainfall model to study the effect of the temporal distribution of rainfall on mosquito abundance. Using a fracturing process, we then investigate the effect of a higher variability in the daily rainfall. As an example, we show that rainfall distribution is necessary to explain the geographic range of Ae. aegypti in Taiwan, an island characterized by rainy winters in the north and dry winters in the south. We also predict that a higher variability in the rainfall time distribution will decrease the maximum abundance of Ae. aegypti during the summer. An increase in daily rainfall variability will likewise enhance its extinction probability. Finally, we obtain a nonlinear relationship between dry season duration and extinction probability. These findings can have a significant impact on our ability to predict disease outbreaks.

Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the interactions between stem and non-stem cancer cell populations we develop a two-population mathematical model, which is suitable to describe tumorsphere growth. Both interspecific and intraspecific interactions, mediated by the microenvironment, are included. We show that there is a tipping point, characterized by a transcritical bifurcation, where a purely non-stem cell attractor is replaced by a new attractor that contains both stem and differentiated cancer cells. The model is then applied to describe the outcome of a recent experiment. This description reveals that, while the intraspecific interactions are inhibitory, the interspecific interactions stimulate growth. This can be understood in terms of stem cells needing differentiated cells to reinforce their niches, and phenotypic plasticity favoring the de-differentiation of differentiated cells into cancer stem cells. We posit that this is a consequence of the deregulation of the quorum sensing that maintains homeostasis in healthy tissues.

Small bacteria are strongly buffeted by Brownian forces that make completely straight runs impossible. A model for bacterial motion is formulated in which the effects of fluctuational forces and torques on the run phase are taken into account by using coupled Langevin equations. An integrated description of the motion, including runs and tumbles, is then obtained by the use of convolution and Laplace transforms. The properties of the velocity-velocity correlation function, of the mean displacement, and of the two relevant diffusion coefficients are examined in terms of the bacterial sizes and of the magnitude of the propelling forces. For bacteria smaller than E. coli, the integrated diffusion coefficient crosses over from a jump-dominated to a rotational-diffusion-dominated form.

Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m. Although this relation is generally recognized to be of the form B͑m͒ = m p , the specific value of the exponent p is the object of an ongoing debate, with many mechanisms being postulated to support different predictions. We propose that multicellular tumor spheroids provide an ideal experimental model system for testing these allometric growth theories, especially under controlled conditions of malnourishment and applied mechanical It was recently proposed 1 that tumors may follow the general model of ontogenetic growth for all living organisms (from mammals to mollusks to plants) developed by West, Brown and Enquist (WBE). 2 The beauty of the WBE model is that it is entirely based on energy conservation and other general physical arguments, i.e., scaling. The authors start with the assumption that the energy intake, supplied by ingested nutrients, is spent partly to support the metabolic functions of the organism's existing cells and partly for cell replication, i.e., to reproduce new cells. Based on this key assumption, a universal growth curve is derived, which the authors conjectured to be applicable to all living organisms. Their conjecture, based on a fractal-like distribution model, is supported by data encompassing many different species. 2 Although they assumed B ϰ m p with p =3/4, their value of p is not universally accepted. Indeed there is strong evidence that growth may be consistent with a 2 / 3 law in the case of birds and small mammals. 3 Due to its implications for tumor metastasis, cell turnover rates, angiogenesis, and invasion, the proposal of Ref. 1 has immediately contributed to an ongoing debate. 4,5 Many different explanations have been put forward for the scaling laws, ranging from four-dimensional biology. 6 and quantum statistics 7 to long-bone allometry combined with muscular development, 8 but, as yet, the debate is far from being settled. In this letter we suggest that multicellular tumor spheroids (MTS) are excellent experimental model systems to test the validity of the proposed mechanisms. MTS are spherical aggregations of malignant cells, 9,10 which can be grown in vitro under strictly controlled nutritional and mechanical conditions. Although cells appear to preserve the evolutionary self-organization rules governing the growth of the original tumor line, they also evolve according to the environmental conditions of the particular experimental setting. Here we show that MTS indeed grow following a scaling law and obtain their expected properties under conditions of malnourishment and rising mechanical stress-conditions that often apply to tumors in vivo.Following WBE, we assume, for simplicity, that metabolism and growth are the same for all MTS cells. Let B be the resting metabolic energy expenditure. Then, at any time t and for any discrete sho...

Cancer growth models may be divided into macroscopic models, which describe the tumor as a single entity, and microscopic ones, which consider the tumor as a complex system whose behavior emerges from the local dynamics of its basic components, the neoplastic cells. Mesoscopic models (e.g. as based on the Local Interaction Simulation Approach [Delsanto, P.P., Mignogna, R., Scalerandi, M., Schechter, R., 1998. In: Delsanto, P.P. Saenz, A.W. (Eds.), New Perspectives on Problems in Classical and Quantum Physics, vol. 2. Gordon & Breach, New Delhi, p. 5174]), which explicitly consider the behavior of cell clusters and their interactions, may be used instead of the microscopic ones, in order to study the properties of cancer biology that strongly depend on the interactions of small groups of cells at intermediate spatial and temporal scales. All these approaches have been developed independently, which limits their usefulness, since they all include relevant features and information that should be cross-correlated for a deeper understanding of the mechanisms involved. In this contribution we consider multicellular tumor spheroids as biological reference systems and propose an intermediate model to bridge the gap between a macroscopic formulation of tumor growth and a mesoscopic one. Thus we are able to establish, as an important result of our formalism, a direct correspondence between parameters characterizing processes occurring at different scales. In particular, we analyze their dependence on an important limiting factor to tumor growth, i.e. the extra-cellular matrix pressure. Since the macro and meso-models stem from totally different roots (energy conservation and clinical observations vs. cell groups dynamics), their consistency may be used to validate both approaches. It may also be interesting to note that the proposed formalism fits well into a recently proposed conjecture of growth laws universality.