A mathematical model of integrin-mediated haptotactic cell migration

Haptotactic cell migration, a directed response to gradients of cell—extracellular matrix adhesion, is an important process in a number of biological phenomena such as wound healing and tumour cell invasion. Previously, mathematical models of haptotaxis have been developed on the premise that cells migrate in response to gradients in the density of the extracellular matrix. In this paper, we develop a novel mathematical model of haptotaxis which includes the adhesion receptors known as integrins and a description of their functional activation, local recruitment and protrusion as part of lamellipodia. Through the inclusion of integrins, the modelled cell matter is able to respond to a true gradient of cell–matrix adhesion, represented by functionally active integrins. We also show that previous matrix-mediated models are in fact a subset of the novel integrin-mediated models, characterised by specific choices of diffusion and haptotaxis coefficients in their model equations. Numerical solutions suggest the existence of travelling waves of cell migration that are confirmed via a phase plane analysis of a simplified model.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

A dynamic mathematical model for sequential leach bed anaerobic digestion of organic fraction of municipal solid waste

A mathematical model that describes the operation of a sequential leach bed process for anaerobic digestion of organic fraction of municipal solid waste (MSW) is developed and validated. This model assumes that ultimate mineralisation of the organic component of the waste occurs in three steps, namely solubilisation of particulate matter, fermentation to volatile organic acids (modelled as acetic acid) along with liberation of carbon dioxide and hydrogen, and methanogenesis from acetate and hydrogen. The model incorporates the ionic equilibrium equations arising due to dissolution of carbon dioxide, generation of alkalinity from breakdown of solids and dissociation of acetic acid. Rather than a charge balance, a mass balance on the hydronium and hydroxide ions is used to calculate pH. The flow of liquid through the bed is modelled as occurring through two zones-a permeable zone with high flushing rates and the other more stagnant. Some of the kinetic parameters for the biological processes were obtained from batch MSW digestion experiments. The parameters for flow model were obtained from residence time distribution studies conducted using tritium as a tracer. The model was validated using data from leach bed digestion experiments in which a leachate volume equal to 10% of the fresh waste bed volume was sequenced. The model was then tested, without altering any kinetic or flow parameters, by varying volume of leachate that is sequenced between the beds. Simulations for sequencing/recirculating 5 and 30% of the bed volume are presented and compared with experimental results. (C) 2002 Elsevier Science B.V. All rights reserved.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Determination of domain sizes in blends of poly(ethylene) and poly(styrene) formed in the presence of supercritical carbon dioxide

Well-mixed blends of poly(ethylene) and poly(styrene) have been synthesized using supercritical carbon dioxide as a solvent. The morphology of the blends has been conclusively characterized using differential scanning calorimetry (DSC), small-angle X-ray scattering (SAXS), Raman microprobe microscopy, and C-13 solid-state cross-polarization magic angle spinning NMR (C-13 CPMAS NMR). DSC measurements demonstrate that poly(styrene) in the blends resides solely in the amorphous regions of the poly(ethylene) matrix; however, corroborative evidence from the SAXS experiments shows that poly(styrene) resides within the interlamellar spaces. The existence of nanometer-sized domains of poly(styrene) was shown within a blend of poly(styrene) and poly(ethylene) when formed in supercritical carbon dioxide using Raman microprobe microscopy and C-13 CPMAS NMR spectroscopy coupled with a spin diffusion model. This contrasts with blends formed at ambient pressure in the absence of solvent, in which domains of poly(styrene) in the micrometer size range are formed. This apparent improved miscibility of the two components was attributed to better penetration of the monomer prior to polymerization and increased swelling of the polymer substrate by the supercritical carbon dioxide solvent.

A conceptual model of personalized virtual learning environments

The Virtual Learning Environment (VLE) is one of the fastest growing areas in educational technology research and development. In order to achieve learning effectiveness, ideal VLEs should be able to identify learning needs and customize solutions, with or without an instructor to supplement instruction. They are called Personalized VLEs (PVLEs). In order to achieve PVLEs success, comprehensive conceptual models corresponding to PVLEs are essential. Such conceptual modeling development is important because it facilitates early detection and correction of system development errors. Therefore, in order to capture the PVLEs knowledge explicitly, this paper focuses on the development of conceptual models for PVLEs, including models of knowledge primitives in terms of learner, curriculum, and situational models, models of VLEs in general pedagogical bases, and particularly, the definition of the ontology of PVLEs on the constructivist pedagogical principle. Based on those comprehensive conceptual models, a prototyped multiagent-based PVLE has been implemented. A field experiment was conducted to investigate the learning achievements by comparing personalized and non-personalized systems. The result indicates that the PVLE we developed under our comprehensive ontology successfully provides significant learning achievements. These comprehensive models also provide a solid knowledge representation framework for PVLEs development practice, guiding the analysis, design, and development of PVLEs. (c) 2005 Elsevier Ltd. All rights reserved.

Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

A probabilistic switch model of information flow in social networks: Application for virtual circuits to organizational design

Network building and exchange of information by people within networks is crucial to the innovation process. Contrary to older models, in social networks the flow of information is noncontinuous and nonlinear. There are critical barriers to information flow that operate in a problematic manner. New models and new analytic tools are needed for these systems. This paper introduces the concept of virtual circuits and draws on recent concepts of network modelling and design to introduce a probabilistic switch theory that can be described using matrices. It can be used to model multistep information flow between people within organisational networks, to provide formal definitions of efficient and balanced networks and to describe distortion of information as it passes along human communication channels. The concept of multi-dimensional information space arises naturally from the use of matrices. The theory and the use of serial diagonal matrices have applications to organisational design and to the modelling of other systems. It is hypothesised that opinion leaders or creative individuals are more likely to emerge at information-rich nodes in networks. A mathematical definition of such nodes is developed and it does not invariably correspond with centrality as defined by early work on networks.