Effects of a differentiating therapy on cancer-stem-cell-driven tumors.

The growth of many solid tumors has been found to be driven by chemo- and radiotherapy-resistant cancer stem cells (CSCs). A suitable therapeutic avenue in these cases may involve the use of a differentiating agent (DA) to force the differentiation of the CSCs and of conventional therapies to eliminate the remaining differentiated cancer cells (DCCs). To describe the effects of a DA that reprograms CSCs into DCCs, we adapt a differential equation model developed to investigate tumorspheres, which are assumed to consist of jointly evolving CSC and DCC populations. We analyze the mathematical properties of the model, finding the equilibria and their stability. We also present numerical solutions and phase diagrams to describe the system evolution and the therapy effects, denoting the DA strength by a parameter adif. To obtain realistic predictions, we choose the other model parameters to be those determined previously from fits to various experimental datasets. These datasets characterize the progression of the tumor under various culture conditions. Typically, for small values of adif the tumor evolves towards a final state that contains a CSC fraction, but a strong therapy leads to the suppression of this phenotype. Nonetheless, different external conditions lead to very diverse behaviors. For microchamber-grown tumorspheres, there is a threshold in therapy strength below which both subpopulations survive, while high values of adif lead to the complete elimination of the CSC phenotype. For tumorspheres grown on hard and soft agar and in the presence of growth factors, the model predicts a threshold not only in the therapy strength, but also in its starting time, an early beginning being potentially crucial. In summary, our model shows how the effects of a DA depend critically not only on the dosage and timing of the drug application, but also on the tumor nature and its environment.

Translational thresholds in a core circadian clock model.

Organisms have evolved in a daily cyclic environment, developing circadian cell-autonomous clocks that temporally organize a wide range of biological processes. Translation is a highly regulated process mainly associated with the activity of microRNAs (miRNAs) at the translation initiation step that impacts on the molecular circadian clock dynamics. Recently, a molecular titration mechanism was proposed to explain the interactions between some miRNAs and their target mRNAs; new evidence also indicates that regulation by miRNA is a nonlinear process such that there is a threshold level of target mRNA below which protein production is drastically repressed. These observations led us to use a theoretical model of the circadian molecular clock to study the effect of miRNA-mediated translational thresholds on the molecular clock dynamics. We model the translational threshold by introducing a phenomenological Hill equation for the kinetics of PER translation and show how the parameters associated with translation kinetics affect the period, amplitude, and time delays between clock mRNA and clock protein expression. We show that our results are useful for analyzing experiments related to the translational regulation of negative elements of transcriptional-translational feedback loops. We also provide new elements for thinking about the translational threshold as a mechanism that favors the emergence of circadian rhythmicity, the tuning of the period-delay relationship and the cell capacity to control the protein oscillation amplitude with almost negligible changes in the mRNA amplitudes.

Effects of rainfall on Culex mosquito population dynamics.

The dynamics of a mosquito population depends heavily on climatic variables such as temperature and precipitation. Since climate change models predict that global warming will impact on the frequency and intensity of rainfall, it is important to understand how these variables affect the mosquito populations. We present a model of the dynamics of a Culex quinquefasciatus mosquito population that incorporates the effect of rainfall and use it to study the influence of the number of rainy days and the mean monthly precipitation on the maximum yearly abundance of mosquitoes Mmax. Additionally, using a fracturing process, we investigate the influence of the variability in daily rainfall on Mmax. We find that, given a constant value of monthly precipitation, there is an optimum number of rainy days for which Mmax is a maximum. On the other hand, we show that increasing daily rainfall variability reduces the dependence of Mmax on the number of rainy days, leading also to a higher abundance of mosquitoes for the case of low mean monthly precipitation. Finally, we explore the effect of the rainfall in the months preceding the wettest season, and we obtain that a regimen with high precipitations throughout the year and a higher variability tends to advance slightly the time at which the peak mosquito abundance occurs, but could significantly change the total mosquito abundance in a year.

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.

Joint fitting reveals hidden interactions in tumor growth.

Tumor growth is often the result of the simultaneous development of two or more cancer cell populations. Crucial to the system evolution are the interactions between these populations. To obtain information about these interactions we apply the recently developed vector universality (VUN) formalism to various instances of competition between tumor populations. The formalism allows us (a) to quantify the growth mechanisms of a HeLa cell colony, describing the phenotype switching responsible for its fast expansion, (b) to reliably reconstruct the evolution of the necrotic and viable fractions in both in vitro and in vivo tumors using data for the time dependences of the total masses alone, and (c) to show how the shedding of cells leading to subspheroid formation is beneficial to both the spheroid and subspheroid populations, suggesting that shedding is a strong positive influence on cancer dissemination.

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.

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.

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.

Observed frequency-independent torque in flagellar bacterial motors optimizes space exploration.

A surprising feature of many bacterial motors is the apparently conserved form of their torque-frequency relation. Experiments indicate that the torque provided by the bacterial rotary motor is approximately constant over a large range of angular speeds. This is observed in both monotrichous and peritrichous bacteria, independently of whether they are propelled by a proton flux or by a Na(+) ion flux. If the relation between angular speed ω and swimming speed is linear, a ω-independent torque implies that the power spent in active motion is proportional to the instantaneous bacterial speed. Using realistic values of the relevant parameters, we show that a constant torque maximizes the volume of the region explored by a bacterium in a resource-depleted medium. Given that nutrients in the ocean are often concentrated in separate, ephemeral patches, we propose that the observed constancy of the torque may be a trait evolved to maximize bacterial survival in the ocean.

Interplay between energetics and dynamics in bacterial motility.

We study how self-propelled organisms administer their energetic resources in order to optimize space exploration. Noting the existence of two very different time scales, we use a quasistatic approximation to analyze the relation between bacterial dynamics and changes in the energy stored by a bacterium. We then find both steady-state and time-dependent solutions for the bacterial speed and stored energy. The model also predicts the volume of the region that a bacterium may visit in a resource-depleted medium.

Concurrent growth of phenotypic features: a phenomenological universalities approach.

Different physical features of an organism are often measured concurrently, because their correlations can be used as predictors of longevity, future health, or adaptability to an ecological niche. Since, in general, we do not know a priori if the temporal variations in the measured quantities are causally related, it may be useful to have a method that could help us to identify possible correlations and to obtain parameters that may vary from population to population. In this paper we develop a procedure that may detect underlying relationships. We do this by generalizing the recently introduced concept of phenomenological universalities to the complex field. In this generalization, allometric growth is described by a complex function, whose real and imaginary parts represent two phenotypic traits of the same organism. As particular solutions of the resulting problem, we obtain generalizations of the Gompertz and the von Bertalanffy-West growth equations. We then apply the procedure to two biological systems in order to show how to determine the existence of mutual interference between trait variations.

Why does GM1 induce a potent beneficial response to experimental Chagas disease?

Being one of the world's neglected diseases, Chagas has neither a vaccine nor a satisfactory therapy. Inoculation of murine models with the ganglioside GM1 has shown a strikingly nonlinear effect, leading to a strong decrease in parasite load at low doses but reverting to a load increase at high doses. Cardiocyte destruction concomitant with the disease is also significantly reduced by a moderate application of GM1. A mathematical model for the interaction between the parasite and the immune system is shown to explain these effects and is used to predict an optimal dosage that maximizes parasite removal with minimal cardiocyte destruction.

Modeling tumor cell shedding.

Cell shedding is an important step in the development of tumor invasion and metastasis. It influences growth saturation, latency, and tumor surface roughness. In spite of careful experiments carried out using multicellular tumor spheroids (MTS), the effects of the shedding process are not yet completely understood. Using a simulational model, we study how the nature and intensity of cell shedding may influence tumor morphology and examine the dependence of the total number of shed cells with the relevant parameters, finding the ranges that maximize cell detachment. These ranges correspond to intermediate values of the adhesion, for which we observe the emergence of a rough tumor surface. They are also likely to maximize the probability of generating invasion and metastases. Using numerical values taken from experiments, we find that the shedding-induced reduction in the growth rate is not intense enough to lead to latency, except when cell adhesion is assumed to be very weak. This suggests that the presence of inhibitors is a necessary condition for the observed MTS growth saturation.

Cancer growth: predictions of a realistic model.

Simulations of avascular cancer growth are performed using experimental values of the relevant parameters. This permits a realistic assessment of the influence of these parameters on cancer growth dynamics. In general, an early exponential growth phase is followed by a linear regime (as observed in recent experiments), while the thickness of the viable cell layer remains approximately constant. Contrary to some predictions, a transition to latency is not observed.

Regularization of the displacement moments for asymmetric Lévy flights.

Although the second displacement moments for Lévy flights are not defined in their usual sense, a few years ago it was shown that nonextensive statistical mechanics can be used to define them for symmetric flights. Here it is shown that the displacement moments for long-jump asymmetric Lévy flights can also be regularized by calculating the averages in the form prescribed by nonextensive statistical mechanics. The dependence of the generalized diffusion coefficient on the asymmetry strength is investigated. It is also shown that no extremum q -entropy principle can be associated with the asymmetric Lévy attractors.

A multilevel approach to cancer growth modeling.

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.

Randomly curved runs interrupted by tumbling: a model for bacterial motion.

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.

Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids.

Multicellular tumor spheroids are valuable experimental tools in cancer research. By introducing an intermediate model, we have been able to successfully relate mesoscopic and macroscopic descriptions of spheroid growth. Since these descriptions stem from completely different roots (cell dynamics, and energy conservation and scaling arguments, respectively), their consistency validates both approaches and allows us to establish a direct correspondence between parameters characterizing processes occurring at different scales. Our approach may find applications as an example of bridging the gap between models at different scale levels in other contexts.

Dynamics of the antibody-T. cruzi competition during Chagas infection: prognostic relevance of intracellular replication.

A recently proposed model for the competitive parasite-antibody interactions in Chagas disease is extended by separately describing the parasitic intracellular and extracellular phases. The model solutions faithfully reproduce available population data and yield predictions for parasite-induced cardiac cell damage.

Competition effects in the dynamics of tumor cords.

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 microm, reaching a quasi-steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor.