Mathematical model for the effects of adhesion and mechanics on cell migration speed.

Migration of mammalian blood and tissue cells over adhesive surfaces is apparently mediated by specific reversible reactions between cell membrane adhesion receptors and complementary ligands attached to the substratum. Although in a number of systems these receptors and ligand molecules have been isolated and identified, a theory capable of predicting the effects of their properties on cell migration behavior currently does not exist. We present a simple mathematical model for elucidating the dependence of cell speed on adhesion-receptor/ligand binding and cell mechanical properties. Our model can be applied to propose answers to questions such as: does an optimal adhesiveness exist for cell movement? How might changes in receptor and ligand density and/or affinity affect the rate of migration? Can cell rheological properties influence movement speed? This model incorporates cytoskeletal force generation, cell polarization, and dynamic adhesion as requirements for persistent cell movement. A critical feature is the proposed existence of an asymmetry in some cell adhesion-receptor property, correlated with cell polarity. We consider two major alternative mechanisms underlying this asymmetry: (a) a spatial distribution of adhesion-receptor number due to polarized endocytic trafficking and (b) a spatial variation in adhesion-receptor/ligand bond strength. Applying a viscoelastic-solid model for cell mechanics allows us to represent one-dimensional locomotion with a system of differential equations describing cell deformation and displacement along with adhesion-receptor dynamics. In this paper, we solve these equations under the simplifying assumption that receptor dynamics are at a quasi-steady state relative to cell locomotion. Thus, our results are strictly valid for sufficiently slow cell movement, as typically observed for tissue cells such as fibroblasts. Numerical examples relevant to experimental systems are provided. Our results predict how cell speed might vary with intracellular contractile force, cell rheology, receptor/ligand kinetics, and receptor/ligand number densities. A biphasic dependence is shown to be possible with respect to some of the system parameters, with position of the maxima essentially governed by a balance between transmitted contractile force and adhesiveness. We demonstrate that predictions for the two alternative asymmetry mechanisms can be distinguished and could be experimentally tested using cell populations possessing different adhesion-receptor numbers.     

Mathematical model of flow through the patent ductus arteriosus

The ductus arteriosus is one of several shunts in the cardiovascular system. It is a small vessel connecting the aortic arch and pulmonary artery that allows blood to bypass the pulmonary circulation. It is open during foetal development because the foetal lungs cannot function and oxygenation of the blood occurs by exchange with the maternal blood in the placenta. Normally it closes a few days after birth; however, in a small number of people closure does not occur, leading to a condition known as patent ductus arteriosus. In this paper our aim is to investigate the resulting cardiovascular effects. We develop a mathematical model of the haemodynamics in three different idealised geometries by assuming that the entry flow is irrotational and remains so in the core until at least the shunt position. We argue that separation or diffusion of vorticity into the core flow is delayed due to the high frequency associated with the pulsatile component of the flow profile. The analysis uses complex potential theory, Schwarz–Christoffel transformations, conformal mappings and Fourier series. The main results are based on the assumption that the flow in patients with patent ductus arteriosus is similar to the flow in healthy adults, and we apply this assumption using boundary conditions that are representative of physiological values in healthy adults. The model suggests that the pressures in the aorta and pulmonary artery are likely to equalise, that the shear stress increases near the edges of the shunt and that backflow of large volumes may occur from the pulmonary artery into the aorta or towards the ventricles due to the presence of the patent shunt. Our results strongly suggest that an abnormal compensatory physiology develops in patients with patent ductus arteriosus.     

Development of radiographic and microscopic techniques for the characterization of bacterial transport in intact sediment cores from Oyster, Virginia.

The objective of this study was to ascertain the physical and mineralogical properties responsible for the retention of bacteria in subsurface sediments. The sediment core chosen for this study was a fine-grained, quartz-rich sand with minor amounts of Fe and Al hydroxides. A bacterial transport experiment was performed using an intact core collected from a recent excavation of the Butler's Bluff member of the Nassawadox formation in the borrow pit at Oyster, VA. and a 14C-labeled bacterial strain OYS2-A was selected for its relatively low adhesion. After the bacterial breakthrough was observed in the effluent, the intact core was dissected to determine the internal distribution of the injected bacteria retained in the sediment. The sediment was dried, epoxy fixed, and thin sectioned. The distribution of 14C activity in the thin sections was mapped using a phosphor screen and X-ray film. The remainder of the core was subsampled and the 14C activity of the subsamples was determined by liquid scintillation counting. The phosphor imaging technique was capable of directly imaging the distribution of radiolabeled bacteria in thin sections, because of its high sensitivity and linear response over a large activity range. The phosphor imaging signal intensity was utilized as a measure of bacterial concentration. The distribution of bacteria at the millimeter scale in the thin sections was compared to the grain size, porosity, and mineralogy as measured by scanning electron microscopy (SEM) and energy dispersive spectrum (EDS) analyses. No apparent correlation was observed between the retention or collision efficiency of bacteria in the sediment and the amount of Fe and Al hydroxides. This apparent lack of correlation can be qualitatively explained by combination of several factors including a nearly neutral surface charge of the bacterial strain, and texture of the Fe and Al hydroxides in the sediment. The combination of phosphor imaging with SEM-EDS proved to be a robust method for relating the physical and mineralogical microscopic properties of poorly indurated sediment to the distribution of adsorbed bacteria, allowing bacterial retention mechanisms to be unambiguously unraveled.     

Magnetic characterization of superparamagnetic nanoparticles pulled through model membranes

Background

To quantitatively compare in-vitro and in vivo membrane transport studies of targeted delivery, one needs characterization of the magnetically-induced mobility of superparamagnetic iron oxide nanoparticles (SPION). Flux densities, gradients, and nanoparticle properties were measured in order to quantify the magnetic force on the SPION in both an artificial cochlear round window membrane (RWM) model and the guinea pig RWM.

Methods

Three-dimensional maps were created for flux density and magnetic gradient produced by a 24-well casing of 4.1 kilo-Gauss neodymium-iron-boron (NdFeB) disc magnets. The casing was used to pull SPION through a three-layer cell culture RWM model. Similar maps were created for a 4 inch (10.16 cm) cube 48 MGOe NdFeB magnet used to pull polymeric-nanoparticles through the RWM of anesthetized guinea pigs. Other parameters needed to compute magnetic force were nanoparticle and polymer properties, including average radius, density, magnetic susceptibility, and volume fraction of magnetite.

Results

A minimum force of 5.04 × 10^-16 N was determined to adequately pull nanoparticles through the in-vitro model. For the guinea pig RWM, the magnetic force on the polymeric nanoparticles was 9.69 × 10^-20 N. Electron microscopy confirmed the movement of the particles through both RWM models.

Conclusion

As prospective carriers of therapeutic substances, polymers containing superparamagnetic iron oxide nanoparticles were succesfully pulled through the live RWM. The force required to achieve in vivo transport was significantly lower than that required to pull nanoparticles through the in-vitro RWM model. Indeed very little force was required to accomplish measurable delivery of polymeric-SPION composite nanoparticles across the RWM, suggesting that therapeutic delivery to the inner ear by SPION is feasible.

     

Mathematical analysis of haemopoietic grafted cell renewal and migration through the allogeneic or syngeneic mouse host

A mathematical analysis of results from kinetic studies of 125-iododeoxyuridine uptake and loss in almost all the lymphoid and non-lymphoid organs of mice is described. Applied to data gathered from a graft-versus-host reaction experiment, this analysis affords quantitative precision on the differential effects of organ alloantigens on the proliferating grafted cells. It is shown that, depending on the organ and the post-graft period, cell growth can be ascribed to alloantigen-driven cell renewal or to alloantigen-driven trapping or sequestration. Possible applications of the present approach in graft rejection monitoring are discussed.     

Lattice-Boltzmann model for bacterial chemotaxis

We present a new numerical approach for modeling bacterial chemotaxis and the fate and transport of a chemoattractant in bulk liquids. This Lattice-Boltzmann method represents the microorganisms and the chemoattractant by quasi-particles that move, collide, and react with each other on a two-dimensional numerical lattice. We use the model to simulate traveling bands of bacteria along self-generated gradients in substrate concentration in bulk liquids. Particularly, we simulate Pseudomonas putida that respond chemotactically to naphthalene dissolved in water. We find that only a fraction of a bacterial slug injected into a domain containing the chemoattractant at constant concentration forms a traveling band as the slug length exceeds a critical value. An expanding bacterial ring forms as one injects a droplet of bacteria into a two-dimensional domain.     

Mathematical model of electrogenic transport through biomembranes via oligomeric channels capable of conformational transitions

A mathematical model of electrogenic ion transport across biomembranes by oligomeric channels liable to conformational transformations has been derived. The model describes changes with time of the membrane potential and near--membrane ion concentrations. Different types of the channel conductance regulation such as activation or inhibition by the permeating ions and membrane potential have been considered. It appears that in the presence of such regulations 1) the channel voltage-current curves have negative resistance regions; 2) the dependence of the quasisteady state (or resting) potential on the ion concentrations in the solution is of hysteresis nature; 3) the model may have multiple steady-state and oscillating solutions.     

Mathematical model for G-CSF administration after chemotherapy

Granulocyte-colony stimulating factor (G-CSF) is used clinically for treating chemotherapy-induced neutropenia (low neutrophil levels). Here we present a delay differential equation model for the regulation of neutrophil production that accounts for the effects of G-CSF. Using a combination of analysis and numerical simulations, we use this model to study the effects of delaying G-CSF treatment following chemotherapy for two recombinant forms of G-CSF (filgrastim and pegfilgrastim). We also examine the consequences of varying the duration of filgrastim treatment. We found that varying the starting day or the duration of G-CSF treatment can lead to different qualitative responses in the neutrophil count. These changes can be explained by the coexistence of two stable solutions in the mathematical model.     

Mathematical model for the self-organization of neural networks

Mutual inhibition between neurons combined with a learning principle similar to that proposed by Hebb is shown to secure a powerful selforganizing property for neural networks. Numerical analysis reveals that the system investigated always organizes itself into the same final state from any arbitrarily chosen initial state.     

Transport of bacterial inoculants through intact cores of two different soils as affected by water percolation and the presence of wheat plants

Abstract Water flow-innduced transport of Burkholderia cepacia strain P2 and Pseudomonas fluorescens strain R2f cells through intact cores of loamy sand and silt loam field soils was measured for two percolation regimes, 0.9 and 4.4 mm h⁻¹, applied daily during 1 hour. For each strain, transport was generally similar between the two water regimes. Translocation of B. cepacia , with 4.4 mm h⁻¹, did occur initially in both soils. In the loamy sand soil, no change in the bacterial distribution occurred during the experiment (51 days). In the silt loam, B. cepacia cell numbers in the lower soil layers were significantly reduced, to levels at or below the limit of detection. Transport of P. fluorescens in both soils also occurred initially and was comparable to that of B. cepacia . Later in the experiment, P. fluorescens was not detectable in the lower soil layers of the loamy sand cores, due to a large decrease in surviving cell numbers. In the silt loam, the inoculant cell distribution did not change with time. Pre-incubation of the inoculated cores before starting percolation reduced B. cepacia inoculant transport in the loamy sand soil measured after 5 days, but not that determined after 54 days. Delayed percolation in the silt loam soil affected bacterial transport only after 54 days. The presence of growing wheat plants overall enhanced bacterial translocation as compared to that in unplanted soil cores, but only with percolating water. Percolation water from silt loam cores appeared the day after the onset of percolation and often contained inoculant bacteria. With loamy sand, percolation water appeared only 5 days after the start of percolation, and no inoculant bacteria were found. The results presented aid in predicting the fate of genetically manipulated bacteria in a field experiment.     

Isolation and characterization of wastewater sand filter actinomycetes

One hundred twenty-two different actinomycete strains were isolated from sample collected from several depths of the Marrakech wastewater infiltration-percolation system. To evaluate the antimicrobial effect of the different actinomycetes recovered, eleven wastewater-associated micro-organisms known as human potential pathogens were used. Results showed that 44 isolates had an in vitro inhibitory effect toward at least seven of the indicator microorganisms while only five active strains inhibited all these pathogens. All five selected active isolates belonged to the genus Streptomyces. Three were identified as Streptomyces violaceorubidus. These isolates showed the broad activity spectrum against a wastewater-associated pathogenic yeast (Candida albicans), Gram-negative (Salmonella sp. CCMM B₁₇) and Gram-positive (Staphylococcus aureus CCMM B₃). These findings indicate the potential involvement of antagonistic actinomycetes in the removal of wastewater-associated pathogens.     

Physiological characterization of juvenile Chinook salmon utilizing different habitats during migration through the Columbia River Estuary

Although off-channel habitats in the estuaries of large rivers impart many benefits to fish that rear within them, it is less clear how these habitats benefit migrating anadromous species that utilize these habitats for short periods of time. We evaluated the physiological correlates (nutritional condition, growth, and smoltification) of habitat utilization (main-channel vs. off-channel) by juvenile Chinook salmon Oncorhynchus tshawytscha during emigration. Fish from the off-channel had higher condition factor scores and relative weights than fish from the main-channel throughout the study period. Plasma triglyceride and protein concentrations were significantly different between habitat types and across the sampling period, suggesting that fish utilizing the off-channel habitats were compensating for energy losses associated with emigration as compared to main-channel fish. Growth potential (RNA to DNA ratio) did not vary by habitat or sampling period, presumably due to short residency time. There were no differences in osmoregulatory capacity (gill Na(+), K(+)-ATPase activity) based on habitat type. Our results indicate that short-term off-channel habitat use may mitigate for energy declines incurred during migration, but likely does not impart significant gains in energy stores or growth.     

Mathematical model for cyclic scheduling with work-in-process minimization

This paper is part of an original approach of mathematical modeling for solving cyclic scheduling problems. More precisely, we consider the cyclic job shop. This kind of manufacturing systems is well fitted to medium and large production demands. Many methods have been proposed to solve the cyclic scheduling problem. Among them, we chose the exact techniques, and we focus on the mathematical programming approach. We proposed, in an earlier study, a mathematical programming model for cyclic scheduling with Work-In-Process minimization. We propose here several cutting techniques to improve the practical performances of the model resolution. Some numerical experiments are used to assess the relevance of our propositions. We made a comparison between the original mathematical model and the one endowed by the proposed cuts. This comparison is based on a set of benchmarks generated for this reason. In addition, we make another comparison based on some examples from the literature.     

Mathematical model of immune processes

In the model the time lags of the antibody production and immune memory formation are taken into account explicitly. The antibody-antigen reaction is supposed to be very fast. The cases of a reproducing antigen as well as that of a non-reproducting antigen are considered. The conditions of the infinite increase of the antigen quantity and of the antigen elimination are obtained. For the rapidly reproducing antigen the latter condition includes the requirement for the time lag of the immune response to be not too short or not too long. In the case of the poorly catabolized non-reproducing antigen the cyclic appearance of the antibody producing cells due to the immune memory is described in the frame-work of the model.The mathematical structure of the model is similar to that of the Volterra-Lotka jequations. The only difference is the presence of the time lags in the non-linear terms. The time lags lead to the instability of the stationary state. In the prolonged reaction the antigen quantity may perform several oscillations before the elimination of the antigen.     

Mathematical model for the fluidized bed biofilm reactor

A mathematical model is proposed for the fluidized bed biofilm reactor (FBBR). For individual biofilm-covered particles (bioparticles) within the reactor, an analysis of intrabiofilm mass transfer and simultaneous intrinsic zero order reaction yields an effectiveness factor expression which is a function of the modified, zero order Thiele modulus, Φ_0,m. This expression is linked to a one-dimensional reactor flow model and a fluidization model to yield an overall reactor model describing convective transport and simultaneous biochemical conversion of substrate within a FBBR. For Φ_0,m<1.15, FBBR is mass transfer limited and 0.45 order kinetics are observed. For Φ_0,m<1.15, mass transfer limitations are insignificant and intrinsic zero order kinetics are observed. A sensitivity analysis using the proposed mathematical model indicates that biofilm thickness and media size are the two most important operating parameters. These two parameters can be optimized simultaneously for a specific application. The proposed model provides a rational approach for FBBR design.     

Mathematical model for the cancer stem cell hypothesis

Recent research on the origin of brain cancer has implicated a subpopulation of self-renewing brain cancer stem cells for malignant tumour growth. Various genes that regulate self-renewal in normal stem cells are also found in cancer stem cells. This implies that cancers can occur because of mutations in normal stem cells and early progenitor cells. A predictive mathematical model based on the cell compartment method is presented here to pose and validate non-intuitive scenarios proposed through the neural cancer stem cell hypothesis. The growths of abnormal (stem and early progenitor) cells from their normal counterparts are ascribed with separate mutation probabilities. Stem cell mutations are found to be more significant for the development of cancer than a similar mutation in the early progenitor cells. The model also predicts that, as previously hypothesized, repeated insult to mature cells increases the formation of abnormal progeny, and hence the risk of cancer.     

Mathematical model of visual perception

A mathematical model of visual perception is presented with the intention of throwing some light on the problem of perceptual invariance. Two types of differential manifolds (receptive and effector) are associated with the repertoire which is the fundamental concept in the model. The elements of the repertoire carry weights which control the input-output relation in the repertoire and which can be modified by a learning process. It is shown that, under reasonable conditions, these repertoires possess good stability properties and can adjust to the various environments to which they may be subjected. In particular cases, it is shown that the stochastic learning process can be considered as deterministic to a first approximation.