A mechanochemical model for rho GTPase mediated cell polarization.

Directed motility of eukaryotic cells requires the polarization of the actomyosin cytoskeleton. In many cell types the polar alignment of the actomyosin cytoskeleton occurs in response to a front-rear symmetry break of active Rho GTPase. Experimental evidence in neutrophils indicates that membrane tension plays an important role in the confinement of active Rac to the front domain. We suggest a mechanochemical model for polarization, including Rho GTPase mediated actomyosin cytoskeleton dynamics and changes in membrane tension as an upstream controller of Rho GTP that reflects this observation. The model comprises the Rho GTPases Rac and RhoA which can become activated in response to external signals. The active states regulate the actomyosin mechanics. The model cell is considered as a thin, effectively two dimensional, sheet adhering to a flat substrate. Morphological changes of the actomyosin cytoskeleton induce changes in membrane tension. We numerically show that the model exhibits key features of neutrophil polarization. The model accounts for a simple mechanochemical circuit with the ability to generate robust polarity patterns, wherein cell mechanics serve as a long range signal transmitter.

Modeling of the early stage of atherosclerosis with emphasis on the regulation of the endothelial permeability.

In this paper, we develop a mathematical model for the early stage of atherosclerosis, as a chronic inflammatory disease. It includes also processes that are relevant for the "thickening" of the vessel walls, and prepares a more complete model including also the later stages of atherosclerosis. The model consists of partial differential equations: Navier-Stokes equations modeling blood flow, Biot equations modeling the fluid flow inside the poroelastic vessel wall, and convection/chemotaxis-reaction-diffusion equations modeling transport, signaling and interaction processes initiating inflammation and atherosclerosis. The main innovations of this model are: a) quantifying the endothelial permeability to low-density-lipoproteins (LDL) and to the monocytes as a function of WSS, cytokines and LDL on the endothelial surface; b) transport of monocytes on the endothelial surface, mimicking the monocytes adhesion and rolling; c) the monocytes influx in the lumen, as a function of factor increasing monocytopoiesis; d) coupling between Navier-Stokes system, Biot system and convection/chemotaxis-reaction-diffusion equations. Numerical simulations of a simplified model were performed in an idealized two-dimensional geometry in order to investigate the dynamics of endothelial permeability, and the growth and spread of immune cells populations and their dependence in particular on low-density-lipoprotein and wall-shear stress.

Mathematical modeling and simulation of the evolution of plaques in blood vessels.

In this paper, a model is developed for the evolution of plaques in arteries, which is one of the main causes for the blockage of blood flow. Plaque rupture and spread of torn-off material may cause closures in the down-stream vessel system and lead to ischemic brain or myocardial infarctions. The model covers the flow of blood and its interaction with the vessel wall. It is based on the assumption that the penetration of monocytes from the blood flow into the vessel wall, and the accumulation of foam cells increasing the volume, are main factors for the growth of plaques. The dynamics of the vessel wall is governed by a deformation gradient, which is given as composition of a purely elastic tensor, and a tensor modeling the biologically caused volume growth. An equation for the evolution of the metric is derived quantifying the changing geometry of the vessel wall. To calculate numerically the solutions of the arising free boundary problem, the model system of partial differential equations is transformed to an ALE (Arbitrary Lagrangian-Eulerian) formulation, where all equations are given in fixed domains. The numerical calculations are using newly developed algorithms for ALE systems. The results of the simulations, obtained for realistic system parameters, are in good qualitative agreement with observations. They demonstrate that the basic modeling assumption can be justified. The increase of stresses in the vessel wall can be computed. Medical treatment tries to prevent critical stress values, which may cause plaque rupture and its consequences.

A quantitative model of population dynamics in malaria with drug treatment.

In this paper we build a population dynamics of malaria including drug treatment. By taking into account both sensitive and resistant parasites, we want to see the effect of treatments on resistance phenomenon and prevent it from overspreading. Our main results include a new dynamics model, its mathematical properties which are found through analysis, the determination of unknown parameters with help of a data set for malaria from Burkina Faso and the numerical simulations of the fitted model. Based on these results, treatment strategies to reduce drug resistance can be elaborated.

An integrated genome research network for studying the genetics of alcohol addiction.

Alcohol drinking is highly prevalent in many cultures and contributes to the global burden of disease. In fact, it was shown that alcohol constitutes 3.2% of all worldwide deaths in the year 2006 and is linked to more than 60 diseases, including cancers, cardiovascular diseases, liver cirrhosis, neuropsychiatric disorders, injuries and foetal alcohol syndrome. Alcoholism, which has been proven to have a high genetic load, is one potentially fatal consequence of chronic heavy alcohol consumption, and may be regarded as one of the most prevalent neuropsychiatric diseases afflicting our society today. The aim of the integrated genome research network 'Genetics of Alcohol Addiction'--which is a German inter-/trans-disciplinary life science consortium consisting of molecular biologists, behavioural pharmacologists, system biologists with mathematicians, human geneticists and clinicians--is to better understand the genetics of alcohol addiction by identifying and validating candidate genes and molecular networks involved in the aetiology of this pathology. For comparison, addictive behaviour to other drugs of abuse (e.g. cocaine) is studied as well. Here, we present an overview of our research consortium, the current state of the art on genetic research in the alcohol field, and list finally several of our recently published research highlights. As a result of our scientific efforts, better insights into the molecular and physiological processes underlying addictive behaviour will be obtained, new targets and target networks in the addicted brain will be defined, and subsequently, novel and individualized treatment strategies for our patients will be delivered.

Neurochemical oscillations in the basal ganglia.

This work represents an attempt to elucidate the neurochemical processes in the basal ganglia by mathematical modelling. The correlation between neurochemistry and electrophysiology has been used to construct a dynamical system based on the basal ganglia's network structure. Mathematical models were constructed for different physical scales to reformulate the neurochemical and electrophysiological behaviour from synapses up to multi-compartment systems. Transformation functions have been developed to transit between the different scales. We show through numerical simulations that this network produces oscillations in the electrical potentials as well as in neurotransmitter concentrations. In agreement with pharmacological experiments, a parameter sensitivity analysis reveals temporary changes in the neurochemical and electrophysiological systems after single exposure to antipsychotic drugs. This behaviour states the structural stability of the system. The correlation between the neurochemical dynamics and drug-induced behaviour provides the perspective for novel neurobiological hypotheses.

Modeling of asymmetric cell division in hematopoietic stem cells--regulation of self-renewal is essential for efficient repopulation.

Hematopoietic stem cells (HSCs) are characterized by their ability of self-renewal to replenish the stem cell pool and differentiation to more mature cells. The subsequent stages of progenitor cells also share some of this dual ability. It is yet unknown whether external signals modulate proliferation rate or rather the fraction of self-renewal. We propose three multicompartment models, which rely on a single external feedback mechanism. In Model 1 the signal enhances proliferation, whereas the self-renewal rates in all compartments are fixed. In Model 2 the signal regulates the rate of self-renewal, whereas the proliferation rate is unchanged. In Model 3, the signal regulates both proliferation and self-renewal rates. This study demonstrates that a unique strictly positive stable steady state can only be achieved by regulation of the rate of self-renewal. Furthermore, it requires a lower number of effective cell doublings. In order to maintain the stem cell pool, the self-renewal ratio of the HSC has to be > or =50% and it has to be higher than the self-renewal ratios of all downstream compartments. Interestingly, the equilibrium level of mature cells depends only on the parameters of self-renewal of HSC and it is independent of the parameters of dynamics of all upstream compartments. The model is compatible with the increase of leukocyte numbers following HSC transplantation. This study demonstrates that extrinsic regulation of the self-renewal rate of HSC is most essential in the process of hematopoiesis.

Modelling in vitro growth of dense root networks.

Hairy roots are plants genetically transformed by Agrobacterium rhizogenes, which do not produce shoots and are composed mainly by roots. Hairy roots of Ophiorrhiza mungos Linn. are currently gaining interest of pharmacologists, since a secondary product of their metabolism, camptothecin, is used in chemotherapy. To optimize the production of valuable secondary metabolites it is necessary to understand the metabolism and growth of these roots systems. In this work, a mathematical model for description of apical growth of a dense root network (e.g. hairy roots) is derived. A continuous approach is used to define densities of root tips and root volume. Equations are posed to describe the evolution of these and are coupled to the distribution of nutrient concentration in the medium and inside the network. Following the principles of irreversible thermodynamics, growth velocity is defined as the sum over three different driving forces: nutrient concentration gradients, space gradients and root tip diffusion. A finite volume scheme was used for the simulation and parameters were chosen to fit experimental data from O. mungos Linn. hairy roots. Internal nutrient concentration determines short-term growth. Long-term behavior is limited by the total nutrient amount in the medium. Therefore, mass yield could be increased by guaranteeing a constant supply of nutrients. Increasing the initial mass of inoculation did not result in higher mass yields, since nutrient consumption due to metabolism also rose. Four different growth strategies are compared and their properties discussed. This allowed to understand which strategy might be the best to increase mass production optimally. The model is able to describe very well the temporal evolution of mass increase and nutrient uptake. Our results provide further understanding of growth and density distribution of hairy root network and therefore it is a sound base for future applications to describe, e.g., secondary metabolite production.

Primary root growth: a biophysical model of auxin-related control.

Plant hormones control many aspects of plant development and play an important role in root growth. Many plant reactions, such as gravitropism and hydrotropism, rely on growth as a driving motor and hormones as signals. Thus, modelling the effects of hormones on expanding root tips is an essential step in understanding plant roots. Here we achieve a connection between root growth and hormone distribution by extending a model of root tip growth, which describes the tip as a string of dividing and expanding cells. In contrast to a former model, a biophysical growth equation relates the cell wall extensibility, the osmotic potential and the yield threshold to the relative growth rate. This equation is used in combination with a refined hormone model including active auxin transport. The model assumes that the wall extensibility is determined by the concentration of a wall enzyme, whose production and degradation are assumed to be controlled by auxin and cytokinin. Investigation of the effects of auxin on the relative growth rate distribution thus becomes possible. Solving the equations numerically allows us to test the reaction of the model to changes in auxin production. Results are validated with measurements found in literature.