Mathematical modelling of biofilm structures

The morphology of biofilms received much attention in the last years. Several concepts to explain the development of biofilm structures have been proposed. We believe that biofilm structure formation depends on physical as well as general and specific biological factors. The physical factors (e.g. governing substrate transport) as well as general biological factors such as growth yield and substrate conversion rates are the basic factors governing structure formation. Specific strain dependent factors will modify these, giving a further variation between different biofilm systems. Biofilm formation seems to be primarily dependent on the interaction between mass transport and conversion processes. When a biofilm is strongly diffusion limited it will tend to become a heterogeneous and porous structure. When the conversion is the rate-limiting step, the biofilm will tend to become homogenous and compact. On top of these two processes, detachment processes play a significant role. In systems with a high detachment (or shear) force, detachment will be in the form of erosion, giving smoother biofilms. Systems with a low detachment force tend to give a more porous biofilm and detachment occurs mainly by sloughing. Biofilm structure results from the interplay between these interactions (mass transfer, conversion rates, detachment forces) making it difficult to study systems taking only one of these factors into account. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mathematical modelling of nitric oxide regulation of rete peg formation in psoriasis.

Recent experiments have shown that in patients with psoriasis, highly elevated levels of nitric oxide (NO) are released at the surface of psoriatic plaques. Nitric oxide is a central biological regulator of many aspects of physiology, and it is a natural possibility that the high nitric oxide levels in psoriasis play a causal role in the onset of the disease. Here, we use mathematical modelling to investigate this possibility. We begin by discussing a simple model consisting of a single equation for nitric oxide concentration, which enables nitric oxide secretion rates in the basal epidermis to be calculated from the observed NO release rates at the skin surface. Using this key parameter value, we then develop an extended model that tests the hypothesis that nitric oxide regulates the formation of the extended rete pegs seen in psoriatic plaques. This occurs via the peroxynitrite-dependent activation of the collagenase MMP-8, which is produced by neutrophils present at high levels in psoriatic plaques. The plausibility of the hypothesis is demonstrated and specific testable quantitative predictions about the roles of the various cell types and signalling molecules are made.     

Dynamic modelling of bacterial cellulose formation

The interest in cellulose produced by bacteria from surface cultures has increased steadily in recent years because of its potential for use in medicine and cosmetics. Unfortunately, the low yield of this production process has limited the commercial usefulness of bacterial cellulose. The aim of this paper is to show the effect of substrate mass transfer on the growth of the bacteria and on their physiological potential for product formation by means of a dynamic mathematical model.     

A model for the formation of ring-shaped structures in colonies of mycelial fungi

Mathematical model of the development of the pattern of colonies is considered. The model represents the systems of differential equations of the first order. It includes non-dimensional parameters characterizing the following features: concentration of substrate, concentration of metabolic products--growth inhibitor, mycelium and spores, radial and specific rate of mycelium growth, rate of substrate consumption and production of metabolic products, coefficients of diffusion of substrate and metabolic products, initial concentration of mycelium and substrate, time of delay of mycelium reaction on metabolic products and spore formation, threshold concentration of metabolic products. The model is adequate to the experiments with cultivation of Penicillium chrysogenum. It was shown that necessary condition for the formation of the circle periodical structures (zoning) in the colonies is an ability for the production of growth inhibitors (antibiotics, etc.). It was proved that formation of colonies of "continuous lawn" type is caused by restrictions on growth because of mycelium satiation or exhaustion of substrate. Such growth scenario is realized in experiments either on reach substrate or on hungry agar. For the appearance of regulating of "zone structure" type limitation on critical level of metabolic product concentration is very important. The number of periodical zone structures and their widths are determined by the above parameters.     

Electron microscopic study of bacterial development in colonies. The morphology of bacterial colonies

The morphology of colonies of some pathogenic Gram-negative and Gram-positive bacteria has been studied by scanning and transmitted electron microscopy. The presence of covers on the surface of cells in colonies has been revealed. The examination of colony fragments in ultrathin section has revealed that cells exist in associations and the elements of cell covers are differentiated in the form of fibrillar structures in the intracellular space. This investigation has shown that covers in the colonies of the bacteria under study should be regarded as their morphological feature playing an important role in the development of the infectious process.     

Contacts between the cells in bacterial colonies

The interaction of cells in microbial colonies has been studied by electron-microscopic techniques. Two types of contacts between cells have been found to exist in the colonies of Gram-negative bacteria of the genera Escherichia, Shigella and Salmonella: close cell adhesion due to the fusion of cell-wall outer membranes and the formation of intersections consisting of membranous tubules. At the sites of close adhesion the fusion of cytoplasmic and outer membranes have been found to occur in Bayer's zones. In the colonies of Gram-positive bacteria of the genera Staphylococcus and Brevibacterium only one type of contacts has been revealed: the fusion of the peptidoglycan layers of the cell walls. The results of this study indicate that in colonies bacteria are not completely isolated; their interaction leads to the formation of a three-dimensional structure denoted as a cooperative cell system.     

Mathematical model of the role of intercellular signalling in intercellular cooperation during tumorigenesis

Objectives: Intercellular cooperation has been hypothesized to enhance cell proliferation during cancer metastasis through autocrine signalling cascades and mathematical models can provide valuable insights into underlying mechanisms of metastatic tumorigenesis. Here, we present a model that incorporates signal‐stimulated cell proliferation, and investigate influences of diffusion‐driven heterogeneity in signal concentration on proliferation dynamics. Materials and methods: Our model incorporates signal production through both autocrine and paracrine pathways, and signal diffusion and loss for a metastasizing cell population at a host site. We use the signalling pathway of IL‐6 for illustration where this signalling species forms an intermediate complex with its receptor IL‐6R. This in turn forms a heterodimeric complex with transmembrane protein gp130, ultimately resulting in production of downstream signals. Cell population dynamics are taken to follow a modified logistic equation for which the rate term is dependent on local IL‐6 concentration. Results and conclusions: Our spatiotemporal model agrees closely with experimental results. The model is also able to predict two phenomena typical of metastatic tumorigenesis – host tissue preference and long periods of proliferation dormancy. It confirms that diffusivity of the signalling species in a host tissue plays a significant role during the process. Our results show that the proliferation–apoptosis balance is tipped in favour of the former for host sites that have relatively smaller signal diffusivities.     

细菌生物膜的形成与调控机制

细菌通过自身合成的水合多聚物粘附在固体表面,以固着的方式生长从而形成生物膜,细菌生物膜的形成涉及到几个明显的阶段,包括起始的附着、细胞与细胞之间的吸附与增殖、生物膜的成熟、及最后细菌的脱离等四个阶段,生物膜的形成增加了细菌对抗生素的抗性以及帮助细菌逃逸寄主的免疫攻击等,从而引起临床上持续性的慢性感染等各种问题;生物膜结构非常复杂,除了细菌分泌的各种胞外多糖,胞外蛋白质外,最新的研究表明,DNA也是生物膜的一个重要成分.针对近年来的最新文献报道分别对生物膜的形成、结构以及调控机制等进行综述.     

Buckling instability in ordered bacterial colonies

Bacterial colonies often exhibit complex spatio-temporal organization. This collective behavior is affected by a multitude of factors ranging from the properties of individual cells (shape, motility, membrane structure) to chemotaxis and other means of cell-cell communication. One of the important but often overlooked mechanisms of spatio-temporal organization is direct mechanical contact among cells in dense colonies such as biofilms. While in natural habitats all these different mechanisms and factors act in concert, one can use laboratory cell cultures to study certain mechanisms in isolation. Recent work demonstrated that growth and ensuing expansion flow of rod-like bacteria Escherichia coli in confined environments leads to orientation of cells along the flow direction and thus to ordering of cells. However, the cell orientational ordering remained imperfect. In this paper we study one mechanism responsible for the persistence of disorder in growing cell populations. We demonstrate experimentally that a growing colony of nematically ordered cells is prone to the buckling instability. Our theoretical analysis and discrete-element simulations suggest that the nature of this instability is related to the anisotropy of the stress tensor in the ordered cell colony.     

Mathematical modelling in physiology

The article illustrates the method of mathematical modelling in physiology as a unique tool to study physiological processes. A number of demonstrated examples appear as a result of long-term experience in mathematical modelling of electrical and mechanical phenomena in the heart muscle. These examples are presented here to show that the modelling provides insight into mechanisms underlying these phenomena and is capable to predict new ones that were previously unknown. While potentialities of the mathematical modelling are analyzed with regard to the myocardium, they are quite universal to deal with any physiological processes.     

Mathematical modelling the systemic regulation of blood glucose: 'a top-down' systems biology approach

The objective of this article is to review the mechanisms which the body uses to regulate its function. The author considers, in particular, the nature and structure of the physiological systems with a specific focus upon the systemic regulation of blood glucose and highlights an innovative technology, based upon the top-down cognitive approach, which incorporates a unique mathematical model of the physiological systems and autonomic nervous system. Most systems biology is a development of the prevailing reductionist biomedical paradigm. It adopts a bottom-up approach seeking systemic justification for biochemical and biophysical research findings. By contrast the 'top-down' approach considers the neural regulation of the physiological systems and the neurological, cognitive and biochemical consequences of systemic dysfunction i.e. the consequences of sensory input upon the neural regulation of the body's systems, organs, and its cellular and molecular biochemistry. In conclusion, the evidence suggests that the onset and progression of Diabetes Mellitus cannot be accurately assessed by individual biomedical indices but instead that the regulation of blood glucose is one of a number of inter-related physiological systems which act in a coordinated manner in order to maintain the body's physiological stability.     

敦煌莫高窟第98窟壁画表面菌斑的群落结构分析

【目的】确定第98窟壁画表面白色污染物内微生物微观特征, 分析其群落组成、结构特点及诱发壁画病害微生物产生的因素, 为石窟寺保护和旅游管理提供建议。【方法】利用无菌手术刀收集壁画表面白色污染物样品; 利用扫描电子显微镜(SEM)分析样品中微生物体微观形貌; 通过提取样品总DNA、扩增细菌16S rDNA、构建克隆文库、测序和系统发生关系分析等技术研究壁画微生物群落组成与结构特点。【结果】壁画白色污染物中存在大量具有微生物特征的结构体, 形态多呈短杆状和卵圆形, 大小在 (3.0?5.5)?μm×(1.5?2.5) μm之间。共得到克隆文库序列111条, 主要为变形菌门γ-变形菌亚门肠杆菌科(Enterobacteriaceae)与假单孢菌科(Pseudomonadaceae)成员。群落组成和结构分析表明所得序列主要隶属于肠杆菌属(Enterobacter)、埃希菌属(Escherichia)、固氮菌属(Azotobacter)、沙雷氏菌属(Serratia)和克雷伯菌属(Klebsiella); 埃希菌属和肠杆菌属为优势属, 分别占克隆文库中总序列的46.8%和35.1%, 二者在自然界分布广泛, 大多属于人类致病菌。【结论】莫高窟第98窟壁画表面白色污染物主要为病害细菌生长所形成的菌斑群落集成。变形菌门在壁画细菌克隆文库中占绝对优势, 壁画病害微生物的出现和蔓延可能与该洞窟之前长期旅游开放存在一定关联。     

Mathematical modelling of the formation of coated vesicles. A theoretical geometrical approach.

The mechanism by which flat hexagonal lattices of clathrin trimers transform into pentagonal/hexagonal spheres remains a mystery. In light of the geometrical nature of this process we have pursued a mathematical approach to the question. Through the geometrical analysis of flat hexagonal lattices we have discovered three possible forms of transformation to introduce curvature into the centre of the lattice: hub-centre transformation; hub-edge transformation; fringe transformation. Hub-edge and fringe transformations are used first to close the lattice while introducing localized curvature at the edges of the lattice. Hub-centre transformation is used after closure to relax the severely localized curvature generated during closure. This scheme not only maximizes the size of the coated vesicle generated, but also minimizes the number of transformations, thus minimizing the energy expended.