Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth

In this paper we examine spatio-temporal pattern formation in reaction-diffusion systems on the surface of the unit sphere in 3D. We first generalise the usual linear stability analysis for a two-chemical system to this geometrical context. Noting the limitations of this approach (in terms of rigorous prediction of spatially heterogeneous steady-states) leads us to develop, as an alternative, a novel numerical method which can be applied to systems of any dimension with any reaction kinetics. This numerical method is based on the method of lines with spherical harmonics and uses fast Fourier transforms to expedite the computation of the reaction kinetics. Numerical experiments show that this method efficiently computes the evolution of spatial patterns and yields numerical results which coincide with those predicted by linear stability analysis when the latter is known. Using these tools, we then investigate the r?le that pre-pattern (Turing) theory may play in the growth and development of solid tumours. The theoretical steady-state distributions of two chemicals (one a growth activating factor, the other a growth inhibitory factor) are compared with the experimentally and clinically observed spatial heterogeneity of cancer cells in small, solid spherical tumours such as multicell spheroids and carcinomas. Moreover, we suggest a number of chemicals which are known to be produced by tumour cells (autocrine growth factors), and are also known to interact with one another, as possible growth promoting and growth inhibiting factors respectively. In order to connect more concretely the numerical method to this application, we compute spatially heterogeneous patterns on the surface of a growing spherical tumour, modelled as a moving-boundary problem. The numerical results strongly support the theoretical expectations in this case. Finally in an appendix we give a brief analysis of the numerical method. Received: 27 July 2000 / Revised version: 15 August 2000 / Published online: 16 February 2001     

Possible mechanisms of the formation of structures in bacterial populations consisting of motile cells

The formation of fixed and moving structures was studied in Escherichia coli populations. The moving and fixed structures were shown to be formed only by bacteria with a taxis system. The moving structures caused an uneven distribution of the substrate concentration. Bacterial growth on agar with the unevenly distributed substrate led to the appearance of fixed structures. Mechanisms responsible for the formation of bacterial structures remain obscure.     

Product formation in the continuous culture of microbial populations grown on carbohydrates

Experimental studies of the growth of a natural microbial population on a synthetic liquid effluent containing sugar, sodium alginate, and nutrients showed that: (I) the concentration of substrates in the feed to an activated sludge process exerts a significant effect upon its effluent chemical oxygen demand (COD) and (ii) there is an optimum sludge age for achieving minimum effluent COD, given by the relationship: optimum growth rate ∝ (feed COD)^0.5. These were explained by incorporating the concept of product formation into existing activated-sludge theory, which showed that at sludge ages longer than optimum, effluent COD increased due to product formation; at shorter sludge ages, the effluent COD increased owing to an increased concentration of degradable substrates.     

Deriving mechanisms responsible for the lack of correlation between hypoxia and acidity in solid tumors

Hypoxia and acidity are two main microenvironmental factors intimately associated with solid tumors and play critical roles in tumor growth and metastasis. The experimental results of Helmlinger and colleagues (Nature Medicine 3, 177, 1997) provide evidence of a lack of correlation between these factors on the micrometer scale in vivo and further show that the distribution of pH and pO(2) are heterogeneous. Here, using computational simulations, grounded in these experimental results, we show that the lack of correlation between pH and pO(2) and the heterogeneity in their shapes are related to the heterogeneous concentration of buffers and oxygen in the blood vessels, further amplified by the network of blood vessels and the cell metabolism. We also demonstrate that, although the judicious administration of anti-angiogenesis agents (normalization process) in tumors may lead to recovery of the correlation between hypoxia and acidity, it may not normalize the pH throughout the whole tumor. However, an increase in the buffering capacity inside the blood vessels does appear to increase the extracellular pH throughout the whole tumor. Based on these results, we propose that the application of anti-angiogenic agents and at the same time increasing the buffering capacity of the tumor extracellular environment may be the most efficient way of normalizing the tumor microenvironment. As a by-product of our simulation we show that the recently observed lack of correlation between glucose consumption and hypoxia in cells which rely on respiration is related to the inhomogeneous consumption of glucose to oxygen concentration. We also demonstrate that this lack of correlation in cells which rely on glycolysis could be related to the heterogeneous concentration of oxygen inside the blood vessels.     

A model of the neural mechanisms responsible for pattern recognition and stimulus specific habituation in toads

A neural model of the mechanisms possibly responsible for stimulus-specific habituation in toads is proposed. The model follows the hypothesis that preypredator recognition is performed by command units as a result of retina-tectum-pretectum interaction. The model allow us to study the possible coding that the nervous system of toads uses for different prey stimuli, the neural mechanisms of habituation and dishabituation, and the dynamic changes that the command units may have during these processes. The model proposes specific hypothesis and experiments to clarify the nature of these processes and to test the validity of the command unit hypothesis.Research supported in part by CONACYT under grant PCCBBNA 021005Research supported in part by the NIH under grant NS 14971-05 from National Institute of Neurological and Communicative Disorders and Stroke     

A new apparatus for continuous cultivation of bacterial plaque on solid surfaces and human dental enamel

A new apparatus for the continuous cultivation of mono and mixed bacterial plaque on solid surfaces is described. The features are: (i) easy preparation and handling; (ii) freedom from technical problems and microbial contamination; (iii) self-sufficient for periods of up to 56 d; (iv) 12 samples are taken simultaneously; (v) programmable supply inlet. Experiments were performed with Streptococcus mutans C 67–1 for mono bacterial inoculation and in combination with Veillonella alcalescens V-1 for mixed bacterial inoculations. The results showed that the controlled conditions and versatility of the apparatus make possible the study of plaque-development and lesion production on a time-dependent basis. It is concluded that the apparatus is suitable for a wide range of dental and non-dental applications.     

The adenosine-triphosphatase system responsible for cation transport in electric organ: exclusion of phospholipids as intermediates

1. Subcellular fractions were prepared from the electric organs of Electrophorus and Torpedo and assayed for adenosine-triphosphatase activity. 2. Treatment of the `low-speed' fraction from Torpedo with m-urea gave an adenosine-triphosphatase preparation that was almost completely (98%) inhibited by ouabain (0·1mg./ml.) and dependent on the simultaneous presence of Na<sup>+</sup> and K<sup>+</sup>. 3. The adenosine-triphosphatase preparations were exposed to [γ-<sup>32</sup>P]ATP for 30sec. in the presence of (i) Na<sup>+</sup>, (ii) K<sup>+</sup>, (iii) Na<sup>+</sup>+K<sup>+</sup> and (iv) Na<sup>+</sup>+K<sup>+</sup>+ouabain. No significant labelling of phosphatidic acid, triphosphoinositide or any other phospholipid was observed. 4. The results suggest that phospholipids do not act as phosphorylated intermediates in the `transport adenosine-triphosphatase' system of electric organ.     

A new apparatus for continuous cultivation of bacterial plaque on solid surfaces and human dental enamel

A new apparatus for the continuous cultivation of mono and mixed bacterial plaque on solid surfaces is described. The features are: easy preparation and handling; freedom from technical problems and microbial contamination; self-sufficient for periods of up to 56 d; 12 samples are taken simultaneously; programmable supply inlet. Experiments were performed with Streptococcus mutans C 67-1 for mono bacterial inoculation and in combination with Veillonella alcalescens V-1 for mixed bacterial inoculations. The results showed that the controlled conditions and versatility of the apparatus make possible the study of plaque-development and lesion production on a time-dependent basis. It is concluded that the apparatus is suitable for a wide range of dental and non-dental applications.     

The organization of the corticonuclear and olivocerebellar climbing fiber projections to the rat cerebellar vermis: The congruence of projection zones and the zebrin pattern

The zonal organization of the corticonuclear and the olivocerebellar climbing fiber projections to the vermis of the cerebellum of the rat was compared to the pattern of zebrin-positive and zebrin-negative bands in material double-stained for zebrin II and for different anterograde tracers injected in subnuclei of the inferior olive, or retrograde tracers injected in the cerebellar and vestibular target nuclei of the Purkinje cells of the vermis. Projection zones A₁, A_X, X, B, C_X in the vermis and A₂ (accessory A zone) and C₂ in the hemisphere were defined by their efferent corticonuclear and their afferent climbing fiber connections, and were found to share the same topographical framework with the zebrin pattern.     

Characterization of fecal bacterial populations in canines: effects of age,breed and dietary fiber

The effects of age, breed, and diet on fecal chemistry, enzyme activity, and bacterial populations of dogs were studied. Eighteen dogs from two age groups (young: 2.5 +/- 0.5 years, old: 10.9 +/-0.7 years) and three different breeds (German shepherds, miniature schnauzers, and English setters) were rotated through a Latin Square design such that every dog was fed each of the diets. The test diets included a low-fiber (control) diet and a 10% fiber diet which contained 5% soybean hulls and 5% beet pulp. Inclusion of 10% fiber in the diet decreased the fecal concentration of ammonia, sulfide, and indole. Fiber inclusion significantly increased acetic, propionic, and butyric acid concentrations, while fecal pH decreased by 0.4 units. Fresh fecal samples were plated on selected aerobic and anaerobic culture media and DNA extracted for denaturing gradient gel electrophoresis (DGGE) analysis of PCR-amplified 16S ribosomal DNA fragments. Plate counts showed significant effects of breed (p < or = 0.05) and age (p < or = 0.01) on selected aerobic and anaerobic bacterial counts, while no significant effect of diet was found. Analysis of PCR-DGGE banding patterns showed there was a tendency for individual dogs to cluster together according to age (young or old dogs) and also for size (large or small dogs). However, the outstanding conclusion obtained from the DGGE analysis of fecal bacterial profiles was that individual dogs had their own characteristic banding pattern which was unique and stable. The relative stability and individuality of the patterns indicates that each individual harbored a characteristic fecal bacterial community which was independent of diet.     

Discrimination between random and non-random processes in early bacterial colonization on biomaterial surfaces: application of point pattern analysis

The dynamics of adhesion and growth of bacterial cells on biomaterial surfaces play an important role in the formation of biofilms. The surface properties of biomaterials have a major impact on cell adhesion processes, eg the random/non-cooperative adhesion of bacteria. In the present study, the spatial arrangement of Escherichia coli on different biomaterials is investigated in a time series during the first hours after exposure. The micrographs are analyzed via an image processing routine and the resulting point patterns are evaluated using second order statistics. Two main adhesion mechanisms can be identified: random adhesion and non-random processes. Comparison with an appropriate null-model quantifies the transition between the two processes with statistical significance. The fastest transition to non-random processes was found to occur after adhesion on PTFE for 2–3 h. Additionally, determination of cell and cluster parameters via image processing gives insight into surface influenced differences in bacterial micro-colony formation.     

The effect of solid surface tension and exposure to elevated hydrodynamic shear on Pseudomonas fluorescens biofilms grown on modified titanium surfaces

The solid surface tension of titanium was varied by using organosilane monolayers of various terminations, minimising differences in other material properties. Both the quantity of Pseudomonas fluorescens biofilms grown on the modified surfaces, and the percentage of biofilm remaining after exposure to hydrodynamic shear stress, varied significantly as a function of solid surface tension. The quantity of biofilm was less on chloropropyl-terminated surfaces than on an alkyl-terminated surfaces. However, the percentage of biofilm remaining after exposure to hydrodynamic shear stress (which depends on the adhesion and cohesion strengths of the biofilm) was less for the alkyl-terminated surface than for the chloropropyl-terminated surface, for one of the two sample sets analysed. These results demonstrate the importance of differentiating between the quantity of biofilm on a surface and the adhesion and cohesion strength of the biofilm, and may help explain discrepancies in the existing literature regarding the effect of solid surface tension on the propensity of a surface for microfouling.     

The effect of solid surface tension and exposure to elevated hydrodynamic shear on Pseudomonas fluorescens biofilms grown on modified titanium surfaces

Abstract

The solid surface tension of titanium was varied by using organosilane monolayers of various terminations, minimising differences in other material properties. Both the quantity of Pseudomonas fluorescens biofilms grown on the modified surfaces, and the percentage of biofilm remaining after exposure to hydrodynamic shear stress, varied significantly as a function of solid surface tension. The quantity of biofilm was less on chloropropyl-terminated surfaces than on an alkyl-terminated surfaces. However, the percentage of biofilm remaining after exposure to hydrodynamic shear stress (which depends on the adhesion and cohesion strengths of the biofilm) was less for the alkyl-terminated surface than for the chloropropyl-terminated surface, for one of the two sample sets analysed. These results demonstrate the importance of differentiating between the quantity of biofilm on a surface and the adhesion and cohesion strength of the biofilm, and may help explain discrepancies in the existing literature regarding the effect of solid surface tension on the propensity of a surface for microfouling.     

The mechanisms of the formation and the role of the oscillatory activity of the neuronal populations in brain systemic activities

Experimental findings and theoretical concepts that have led to a new insight into the neurophysiological mechanisms underlying information processing and brain state are presented in this review. It is assumed that the brain information processing associated with elementary neuronal assembles is reflected by oscillations in the range of 30-70 Hz and their spatio-temporal organization in millisecond intervals. He functional brain state associated with the non-specific systems is reflected in synchronization or desynchronization of activity of large neuronal populations in the frequency range of 20 Hz.     

耕作与栽培方式对瓜类土壤细菌数量及枯萎病拮抗细菌分布的影响

以新疆、福建和浙江等地采集的132份土壤样品为对象,利用平板计数和Biolog等方法研究了不同耕作与栽培制度下瓜类土壤细菌数量及瓜类枯萎病拮抗细菌的分布与主要类群.结果表明,瓜类耕作土壤中的可培养细菌种群数量平均为非耕作土壤的16.2倍,根际为根围的2.0倍,轮作为连作的3.5倍,未嫁接平均为嫁接的1.5倍;水旱轮作和嫁接处理的瓜类土壤易获得拮抗细菌,其中荧光假单胞菌是主要类群,占总数的80%以上.     

Quantitative characterization of the influence of the nanoscale morphology of nanostructured surfaces on bacterial adhesion and biofilm formation

Bacterial infection of implants and prosthetic devices is one of the most common causes of implant failure. The nanostructured surface of biocompatible materials strongly influences the adhesion and proliferation of mammalian cells on solid substrates. The observation of this phenomenon has led to an increased effort to develop new strategies to prevent bacterial adhesion and biofilm formation, primarily through nanoengineering the topology of the materials used in implantable devices. While several studies have demonstrated the influence of nanoscale surface morphology on prokaryotic cell attachment, none have provided a quantitative understanding of this phenomenon. Using supersonic cluster beam deposition, we produced nanostructured titania thin films with controlled and reproducible nanoscale morphology respectively. We characterized the surface morphology; composition and wettability by means of atomic force microscopy, X-ray photoemission spectroscopy and contact angle measurements. We studied how protein adsorption is influenced by the physico-chemical surface parameters. Lastly, we characterized Escherichia coli and Staphylococcus aureus adhesion on nanostructured titania surfaces. Our results show that the increase in surface pore aspect ratio and volume, related to the increase of surface roughness, improves protein adsorption, which in turn downplays bacterial adhesion and biofilm formation. As roughness increases up to about 20 nm, bacterial adhesion and biofilm formation are enhanced; the further increase of roughness causes a significant decrease of bacterial adhesion and inhibits biofilm formation. We interpret the observed trend in bacterial adhesion as the combined effect of passivation and flattening effects induced by morphology-dependent protein adsorption. Our findings demonstrate that bacterial adhesion and biofilm formation on nanostructured titanium oxide surfaces are significantly influenced by nanoscale morphological features. The quantitative information, provided by this study about the relation between surface nanoscale morphology and bacterial adhesion points towards the rational design of implant surfaces that control or inhibit bacterial adhesion and biofilm formation.     

FA2H is responsible for the formation of 2-hydroxy galactolipids in peripheral nervous system myelin

Myelin in the mammalian nervous system has a high concentration of galactolipids [galactosylceramide (GalCer) and sulfatide] with 2-hydroxy fatty acids. We recently reported that fatty acid 2-hydroxylase (FA2H), encoded by the FA2H gene, is the major fatty acid 2-hydroxylase in the mouse brain. In this report, we show that FA2H also plays a major role in the formation of 2-hydroxy galactolipids in the peripheral nervous system. FA2H mRNA and FA2H activity in the neonatal rat sciatic nerve increased rapidly during developmental myelination. The contents of 2-hydroxy fatty acids were approximately 5% of total galactolipid fatty acids at 4 days of age and increased to 60% in GalCer and to 35% in sulfatides at 60 days of age. The chain length of galactolipid fatty acids also increased significantly during myelination. FA2H expression in cultured rat Schwann cells was highly increased in response to dibutyryl cyclic AMP, which stimulates Schwann cell differentiation and upregulates myelin genes, such as UDP-galactose:ceramide galactosyltransferase and protein zero. These observations indicate that FA2H is a myelination-associated gene. FA2H-directed RNA interference (RNAi) by short-hairpin RNA expression resulted in a reduction of cellular 2-hydroxy fatty acids and 2-hydroxy GalCer in D6P2T Schwannoma cells, providing direct evidence that FA2H-dependent fatty acid 2-hydroxylation is required for the formation of 2-hydroxy galactolipids in peripheral nerve myelin. Interestingly, FA2H-directed RNAi enhanced the migration of D6P2T cells, suggesting that, in addition to their structural role in myelin, 2-hydroxy lipids may greatly influence the migratory properties of Schwann cells.