A Mathematical Model of the Disruption of Glucose Homeostasis in Cancer Patients.

In this paper, we investigate the disruption of the glucose homeostasis at the whole-body level by the presence of cancer disease. Of particular interest are the potentially different responses of patients with or without hyperglycemia (including diabetes mellitus) to the cancer challenge, and how tumor growth, in turn, responds to hyperglycemia and its medical management. We propose a mathematical model that describes the competition between cancer cells and glucose-dependent healthy cells for a shared glucose resource. We also include the metabolic reprogramming of healthy cells by cancer-cell-initiated mechanism to reflect the interplay between the two cell populations. We parametrize this model and carry out numerical simulations of various scenarios, with growth of tumor mass and loss of healthy body mass as endpoints. We report sets of cancer characteristics that show plausible disease histories. We investigate parameters that change cancer cells' aggressiveness, and we exhibit differing responses in diabetic and non-diabetic, in the absence or presence of glycemic control. Our model predictions are in line with observations of weight loss in cancer patients and the increased growth (or earlier onset) of tumor in diabetic individuals. The model will also aid future studies on countermeasures such as the reduction of circulating glucose in cancer patients.

A mathematical model of the disruption of glucose homeostasis in cancer patients.

In this paper we investigate the disruption of the glucose homeostasis at the whole-body level by the presence of cancer disease. Of particular interest are the potentially different responses of patients with or without hyperglycemia (including Diabetes Mellitus) to the cancer challenge, and how tumor growth, in turn, responds to hyperglycemia and its medical management. We propose a mathematical model that describes the competition between cancer cells and glucosedependent healthy cells for a shared glucose resource. We also include the metabolic reprogramming of healthy cells by cancer-cell-initiated mechanism to reflect the interplay between the two cell populations. We parametrize this model and carry out numerical simulations of various scenarios, with growth of tumor mass and loss of healthy body mass as endpoints. We report sets of cancer characteristics that show plausible disease histories. We investigate parameters that change cancer cells’ aggressiveness, and we exhibit differing responses in diabetic and non-diabetic, in the absence or presence of glycemic control. Our model predictions are in line with observations of weight loss in cancer patients and the increased growth (or earlier onset) of tumor in diabetic individuals. The model will also aid future studies on countermeasures such as the reduction of circulating glucose in cancer patients.

Homeostatic swimming of zooplankton upon crowding: the case of the copepod Centropages typicus.

Crowding has a major impact on the dynamics of many material and biological systems, inducing effects as diverse as glassy dynamics and swarming. While this issue has been deeply investigated for a variety of living organisms, more research remains to be done on the effect of crowding on the behaviour of copepods, the most abundant metazoans on Earth. To this aim, we experimentally investigate the swimming behaviour, used as a dynamic proxy of animal adaptations, of males and females of the calanoid copepod Centropages typicus at different densities of individuals (10, 50 and 100 ind. l-1) by performing three-dimensional single-organism tracking. We find that the C. typicus motion is surprisingly unaffected by crowding over the investigated density range. Indeed, the mean square displacements as a function of time always show a crossover from ballistic to Fickian regime, with poor variations of the diffusion constant on increasing the density. Close to the crossover, the displacement distributions display exponential tails with a nearly density-independent decay length. The trajectory fractal dimension, D3D ≅ 1.5, and the recently proposed 'ecological temperature' also remain stable on increasing the individual density. This suggests that, at least over the range of animal densities used, crowding does not impact on the characteristics of C. typicus swimming motion, and that a homeostatic mechanism preserves the stability of its swimming performance.

Modeling the bidirectional glutamine/ammonium conversion between cancer cells and cancer-associated fibroblasts.

Like in an ecosystem, cancer and other cells residing in the tumor microenvironment engage in various modes of interactions to buffer the negative effects of environmental changes. One such change is the consumption of common nutrients (such as glutamine/Gln) and the consequent accumulation of toxic metabolic byproducts (such as ammonium/NH4). Ammonium is a waste product of cellular metabolism whose accumulation causes cell stress. In tumors, it is known that it can be recycled into nutrients by cancer associated fibroblasts (CAFs). Here we present monoculture and coculture growth of cancer cells and CAFs on different substrates: glutamine and ammonium. We propose a mathematical model to aid our understanding. We find that cancer cells are able to survive on ammonium and recycle it to glutamine for limited periods of time. CAFs are able to even grow on ammonium. In coculture, the presence of CAFs results in an improved survival of cancer cells compared to their monoculture when exposed to ammonium. Interestingly, the ratio between the two cell populations is maintained under various concentrations of NH4, suggesting the ability of the mixed cell system to survive temporary metabolic stress and sustain the size and cell composition as a stable entity.

Automated feature extraction from large cardiac electrophysiological data sets.

RATIONALE: A new multi-electrode array-based application for the long-term recording of action potentials from electrogenic cells makes possible exciting cardiac electrophysiology studies in health and disease. With hundreds of simultaneous electrode recordings being acquired over a period of days, the main challenge becomes achieving reliable signal identification and quantification. OBJECTIVE: We set out to develop an algorithm capable of automatically extracting regions of high-quality action potentials from terabyte size experimental results and to map the trains of action potentials into a low-dimensional feature space for analysis. METHODS AND RESULTS: Our automatic segmentation algorithm finds regions of acceptable action potentials in large data sets of electrophysiological readings. We use spectral methods and support vector machines to classify our readings and to extract relevant features. We are able to show that action potentials from the same cell site can be recorded over days without detrimental effects to the cell membrane. The variability between measurements 24 h apart is comparable to the natural variability of the features at a single time point. CONCLUSIONS: Our work contributes towards a non-invasive approach for cardiomyocyte functional maturation, as well as developmental, pathological and pharmacological studies. As the human-derived cardiac model tissue has the genetic makeup of its donor, a powerful tool for individual drug toxicity screening emerges.

Oscillations in the near-field feeding current of a calanoid copepod are useful for particle sensing.

Calanoid copepods are small crustaceans that constitute a major element of aquatic ecosystems. Key to their success is their feeding apparatus consisting of sensor-studded mouth appendages that are in constant motion. These appendages generate a feeding current to enhance the encounter probability with food items. Additionally, sensing enables the organism to determine the position and quality of food particles, and to alter the near-field flow to capture and manipulate the particles for ingestion or rejection. Here we observe a freely swimming copepod Leptodiaptomus sicilis in multiple perspectives together with suspended particles that allow us to analyse the flow field created by the animal. We observe a highly periodic motion of the mouth appendages that is mirrored in oscillations of nearby tracer particles. We propose that the phase shift between the fluid and the particle velocities is sufficient for mechanical detection of the particles entrained in the feeding current. Moreover, we propose that an immersed algal cell may benefit from the excitation by increased uptake of dissolved inorganic compounds.

Copepod manipulation of oil droplet size distribution.

Oil spills are one of the most dangerous sources of pollution in aquatic ecosystems. Owing to their pivotal position in the food web, pelagic copepods can provide crucial intermediary transferring oil between trophic levels. In this study we show that the calanoid Paracartia grani can actively modify the size-spectrum of oil droplets. Direct manipulation through the movement of the feeding appendages and egestion work in concert, splitting larger droplets (Ø = 16 µm) into smaller ones (Ø = 4-8 µm). The copepod-driven change in droplet size distribution can increase the availability of oil droplets to organisms feeding on smaller particles, sustaining the transfer of petrochemical compounds among different compartments. These results raise the curtain on complex small-scale interactions which can promote the understanding of oil spills fate in aquatic ecosystems.

Scaling behavior of drug transport and absorption in in silico cerebral capillary networks.

Drug delivery to the brain is challenging due to the presence of the blood-brain barrier. Mathematical modeling and simulation are essential tools for the deeper understanding of transport processes in the blood, across the blood-brain barrier and within the tissue. Here we present a mathematical model for drug delivery through capillary networks with increasingly complex topologies with the goal to understand the scaling behavior of model predictions on a coarse-to-fine sequence of grids. We apply our model to the delivery of L-Dopa, the primary drug used in the therapy of Parkinson's Disease. Our model replicates observed blood flow rates and ratios between plasma and tissue concentrations. We propose an optimal network grain size for the simulation of tissue volumes of 1 cm3 that allows to make reliable predictions with reasonable computational costs.

Olfaction in a viscous environment: the "color" of sexual smells in Temora longicornis.

We investigate chemical aspects of mating in the marine copepod Temora longicornis (Copepoda, Calanoidea). Our emphasis is the female pheromone signaling in form of well-defined trails for males to follow, observed in Doall et al. (Phil Trans R Soc Lond B 353:681-689, 1998). The viscous environment and the properties of the odorants play important roles as the spread of the pheromone trail limits the time during which it is useful for tracing. A key observation from our earlier work is the ability of a searching male to detect the direction of the female and to correct its swimming direction if necessary. We propose a simple mathematical model for the spread of a pheromone from a moving source and carry out numerical simulations of two possible detection mechanisms. We find that a searching agent that is capable to detect a ratio outperforms a searcher that depends on the gradient of a single compound. This suggests that copepod sex pheromones consist of blends of chemical compounds, and that a ratio detection mechanism similar to that in airborne insects is at work.

Signaled drug delivery and transport across the blood-brain barrier.

We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound (US). Thereupon, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain barrier (BBB). We present a compartmental model of a capillary that is able to capture the complex binding and transport processes the drug undergoes in the blood plasma and at the BBB. We apply this model to the delivery of levodopa (L-dopa, used to treat Parkinson's disease) and doxorubicin (an anticancer agent). The goal is to optimize the delivery of drug while at the same time minimizing possible side effects of the US.

Statistical Mechanics of Zooplankton.

Statistical mechanics provides the link between microscopic properties of many-particle systems and macroscopic properties such as pressure and temperature. Observations of similar "microscopic" quantities exist for the motion of zooplankton, as well as many species of other social animals. Herein, we propose to take average squared velocities as the definition of the "ecological temperature" of a population under different conditions on nutrients, light, oxygen and others. We test the usefulness of this definition on observations of the crustacean zooplankton Daphnia pulicaria. In one set of experiments, D. pulicaria is infested with the pathogen Vibrio cholerae, the causative agent of cholera. We find that infested D. pulicaria under light exposure have a significantly greater ecological temperature, which puts them at a greater risk of detection by visual predators. In a second set of experiments, we observe D. pulicaria in cold and warm water, and in darkness and under light exposure. Overall, our ecological temperature is a good discriminator of the crustacean's swimming behavior.

Special issue dedicated to the 70th birthday of Glenn F. Webb. Preface.

This special issue is dedicated to the 70th birthday of Glenn F. Webb. The topics of the 12 articles appearing in this special issue include evolutionary dynamics of population growth, spatio-temporal dynamics in reaction-diffusion biological models, transmission dynamics of infectious diseases, modeling of antibiotic-resistant bacteria in hospitals, analysis of Prion models, age-structured models in ecology and epidemiology, modeling of immune response to infections, modeling of cancer growth, etc. These topics partially represent the broad areas of Glenn's research interest.

Algebraic and topological indices of molecular pathway networks in human cancers.

Protein-protein interaction networks associated with diseases have gained prominence as an area of research. We investigate algebraic and topological indices for protein-protein interaction networks of 11 human cancers derived from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database. We find a strong correlation between relative automorphism group sizes and topological network complexities on the one hand and five year survival probabilities on the other hand. Moreover, we identify several protein families (e.g. PIK, ITG, AKT families) that are repeated motifs in many of the cancer pathways. Interestingly, these sources of symmetry are often central rather than peripheral. Our results can aide in identification of promising targets for anti-cancer drugs. Beyond that, we provide a unifying framework to study protein-protein interaction networks of families of related diseases (e.g. neurodegenerative diseases, viral diseases, substance abuse disorders).

Pathogen evolution in switching environments: a hybrid dynamical system approach.

We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a version of the Fisher-Haldane-Wright equation while the switching between environments follows a Markov jump process. We investigate how the qualitative behavior of a simple single-host deterministic system changes when the stochastic switching process is added. In particular, we study the stability in probability of monomorphic equilibria. We prove that in a "constantly" fluctuating environment, the genotype with the highest mean fitness is asymptotically stable in probability while all others are unstable in probability. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.

Kinetics of bile salt binding to liposomes revealed by carboxyfluorescein release and mathematical modeling.

We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membrane permeability is modified by the binding of different bile salts to the leaflets of the lipid bilayer. We find that the permeability of the liposomal bilayer depends on the difference in the concentrations of bile salt in the inner and outer leaflets and is only minimally influenced by the total concentration of bile salt in the bilayer. Deoxycholate and cholate are found to behave similarly in enhancing permeability for limited times, whereas the novel bile salt, 12-monoketocholate, flips from the outer to inner leaflet slowly, thereby enhancing membrane permeability for a prolonged time.

Modeling the effects of drug binding on the dynamic instability of microtubules.

We propose a stochastic model that accounts for the growth, catastrophe and rescue processes of steady-state microtubules assembled from MAP-free tubulin in the possible presence of a microtubule-associated drug. As an example of the latter, we both experimentally and theoretically study the perturbation of microtubule dynamic instability by S-methyl-D-DM1, a synthetic derivative of the microtubule-targeted agent maytansine and a potential anticancer agent. Our model predicts that among the drugs that act locally at the microtubule tip, primary inhibition of the loss of GDP tubulin results in stronger damping of microtubule dynamics than inhibition of GTP tubulin addition. On the other hand, drugs whose action occurs in the interior of the microtubule need to be present in much higher concentrations to have visible effects.

Physiologically structured populations with diffusion and dynamic boundary conditions.

We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. We equip the model with generalized Wentzell-Robin (or dynamic) boundary conditions. This approach allows the modelling of populations in which individuals may have distinguished physiological states. We establish existence and positivity of solutions by showing that solutions are governed by a positive quasicontractive semigroup of linear operators on the biologically relevant state space. These results are obtained by establishing dissipativity of a suitably perturbed semigroup generator. We also show that solutions of the model exhibit balanced exponential growth, that is, our model admits a finite-dimensional global attractor. In case of strictly positive fertility we are able to establish that solutions in fact exhibit asynchronous exponential growth.

The ciliate Paramecium shows higher motility in non-uniform chemical landscapes.

We study the motility behavior of the unicellular protozoan Paramecium tetraurelia in a microfluidic device that can be prepared with a landscape of attracting or repelling chemicals. We investigate the spatial distribution of the positions of the individuals at different time points with methods from spatial statistics and Poisson random point fields. This makes quantitative the informal notion of "uniform distribution" (or lack thereof). Our device is characterized by the absence of large systematic biases due to gravitation and fluid flow. It has the potential to be applied to the study of other aquatic chemosensitive organisms as well. This may result in better diagnostic devices for environmental pollutants.

Structured and unstructured continuous models for Wolbachia infections.

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.