A mathematical framework to study the effects of growth factor influences on fracture healing

During fracture healing, multipotential stem cells differentiate into specialized cells responsible for producing the different tissues involved in the bone regeneration process. This cell differentiation has been shown to be regulated by locally expressed growth factors. The details of their regulatory mechanisms need to be understood. In this work, we present a two-dimensional mathematical model of the bone healing process for moderate fracture gap sizes and fracture stability. The inflammatory and tissue regeneration stages of healing are simulated by modeling mesenchymal cell migration; mesenchymal cell, chondrocyte and osteoblast proliferation and differentiation, and extracellular matrix synthesis and degradation over time. The effects of two generic growth factors on cell differentiation are based on the experimentally studied chondrogenic and osteogenic effects of bone morphogenetic proteins-2 and 4 and transforming growth factor-beta-1, respectively. The model successfully simulates the progression of healing and predicts that the rate of osteogenic growth factor production by osteoblasts and the duration of the initial release of growth factors upon injury are particularly important parameters for complete ossification and successful healing. This temporo-spatial model of fracture healing is the first model to consider the effects of growth factors. It will help us understand the regulatory mechanisms involved in bone regeneration and provides a mathematical framework with which to design experiments and understand pathological conditions.     

Signaling networks in Leishmania macrophages deciphered through integrated systems biology: a mathematical modeling approach

Network of signaling proteins and functional interaction between the infected cell and the leishmanial parasite, though are not well understood, may be deciphered computationally by reconstructing the immune signaling network. As we all know signaling pathways are well-known abstractions that explain the mechanisms whereby cells respond to signals, collections of pathways form networks, and interactions between pathways in a network, known as cross-talk, enables further complex signaling behaviours. In silico perturbations can help identify sensitive crosstalk points in the network which can be pharmacologically tested. In this study, we have developed a model for immune signaling cascade in leishmaniasis and based upon the interaction analysis obtained through simulation, we have developed a model network, between four signaling pathways i.e., CD14, epidermal growth factor (EGF), tumor necrotic factor (TNF) and PI3 K mediated signaling. Principal component analysis of the signaling network showed that EGF and TNF pathways can be potent pharmacological targets to curb leishmaniasis. The approach is illustrated with a proposed workable model of epidermal growth factor receptor (EGFR) that modulates the immune response. EGFR signaling represents a critical junction between inflammation related signal and potent cell regulation machinery that modulates the expression of cytokines.     

Plasmodium development in the mosquito: biology bottlenecks and opportunities for mathematical modeling

Quantitative analyses of malaria parasite development are necessary to assess the efficacy of control measures. Such analyses in the mammalian host have been difficult to implement, lagging behind the use of antiparasitic drugs, vaccine development and transmission-blocking strategies. Even less is known about the genetic, environmental and other factors that impact sporogony in the mosquito host. Here, we summarize current knowledge and review a first attempt to model sporogonic development quantitatively.     

Quantitative measures for fracture healing: an in-vitro biomechanical study

A method is presented to assess the functional capabilities of plated osteotomized canine femora as load bearing structures and to quantify their healing status. In this method the osteotomized bones and their intact contralateral controls are tested in nondestructive bending, in twenty-four planes of loading at 15 degree angular increments. Flexural rigidity (EI), in each of the planes, is determined by using classical beam theory. It has been found that the EI values have the expected elliptical distribution. The 24 EI values, obtained for each bone, are curve fitted by regression analysis and the characteristics of each bone are described by the three parameters defining its ellipse. The parameters of the ellipses of the osteotomized bone and of its contralateral control are used to define four new parameters that may serve as measures for the healing efficiency. One of these serves as an indicator for the fragility of the healed bone and the other three add quantitative information on its mechanical state.     

Maintaining and restoring hydrologic habitat connectivity in mediterranean streams: an integrated modeling framework

Hydrologic alterations designed to provide a stable water supply and to prevent flooding are commonly used in mediterranean-climate river (med-rivers) basins, and these alterations have led to habitat loss and significant declines in aquatic biodiversity. Often the health of freshwater ecosystems depends on maintaining and recovering hydrologic habitat connectivity, which includes structural components related to the physical landscape, functionality of flow dynamics, and an understanding of species habitat requirements for movement, reproduction, and survival. To advance our understanding of hydrologic habitat connectivity and benefits of habitat restoration alternatives we provide: (1) a review of recent perspectives on hydrologic connectivity, including quantitative methods; and (2) a modeling framework to quantify the effects of restoration on hydrologic habitat connectivity. We then illustrate this approach through a case study on lateral hydrologic habitat connectivity that results from channel restoration scenarios using scenarios with different historic and climate-change flows to restore fish floodplain habitat in a med-river, the San Joaquin River, California. Case study results show that in addition to the channel alterations, higher flows are required to recover significant flooded habitat area, especially given reductions in flows expected under climate change. These types of studies will help the planning for restoration of hydrologic habitat connectivity in med-rivers, a critical step for mediterranean species recovery.     

VisANT: an integrative framework for networks in systems biology

The essence of a living cell is adaptation to a changing environment, and a central goal of modern cell biology is to understand adaptive change under normal and pathological conditions. Because the number of components is large, and processes and conditions are many, visual tools are useful in providing an overview of relations that would otherwise be far more difficult to assimilate. Historically, representations were static pictures, with genes and proteins represented as nodes, and known or inferred correlations between them (links) represented by various kinds of lines. The modern challenge is to capture functional hierarchies and adaptation to environmental change, and to discover pathways and processes embedded in known data, but not currently recognizable. Among the tools being developed to meet this challenge is VisANT (freely available at http://visant.bu.edu) which integrates, mines and displays hierarchical information. Challenges to integrating modeling (discrete or continuous) and simulation capabilities into such visual mining software are briefly discussed.     

Mechanoregulation modeling of bone healing in realistic fracture geometries

Biomechanics and Modeling in Mechanobiology - In bone fracture healing, new tissue gradually forms, ossifies, and eventually remodels itself to restore mechanical stiffness and strength across...     

Understanding bone cell biology requires an integrated approach: Reliable opportunities to study osteoclast biology in vivo

The relative simplicity of all in vitro methods to study bone cell biology will at best result in oversimplification of the development and functional capacity of the skeleton in vivo. We have shown this to be true for selected aspects of bone cell biology, but numerous other examples are available. One alternative is to undertake skeletal research in vivo. It is important that those in bone research be willing to move increasingly in this direction not only to understand the true complexitities of skeletal versatility, but also to avoid repetition and perpetuation of erroneous or irrelevant conclusions which waste resources. Toward this end we have described two situations, osteopetrosis and tooth eruption, in which reproducible abrogations or local activations of bone resorption can be examined in vivo. The application of emerging molecular and morphological techniques that permit the subcellular dissection of metabolic pathways and their precise cellular localization, such as a combination of the variety of in situ hybridzation technologies with PCR, antisense probes, and antibody blockase, will allow the investigator greater control of variables in vivo. We expect that these technologies, largely worked out in vitro, combined with highly selected, appropriate models, as we have oulined here for osteoclast biology worked out in vitro, combined with highly selected, appropriate models, as we have ourlined here for osteoclast biology, will make research in vivo less intimidating and increase the frequency with which the real biology is studied directly.     

A modeling framework for the study of protein glycosylation

The key step in the asparagine-linked glycosylation of secretory proteins is the transfer of oligosaccharide from a dolichol precursor to the polypeptide at an Asp-X-Ser/Thr (NXS/T) consensus sequence. It is often the case, both in cultured cells and in vivo, that this reaction does not occur for every molecule of a given protein. Thus, the cell may create two protein populations, one bearing and one lacking oligosaccharide, for each potential glycosylation site. We present a structured kinetic modeling framework of the initial glycosylation event based on a balance of available glycosylation sites through the region of endoplasmic reticulum lumen proximal to the membrane. Oligosaccharyltransferase, a multimeric protein complex, catalyzes the sugar transfer. This enzyme is integral to the endoplasmic reticulum membrane, and it is thought to act cotranslationally. The nascent polypeptide may also fold in such a way as to prevent glycosylation from occurring. The net result is a potentially complex spatial and temporal relationship among translation, glycosylation, and other cotranslational events. Model results predict how fractional glycosylation site occupancy may depend on protein synthesis rate, oligosaccharyldolichol availability, and mRNA elongation rate. Although we are currently unable to quantitatively compare predicted to experimentally obtained fractional site occupancy, we are able to determine qualitative trends which may be confirmed experimentally. (c) 1996 John Wiley & Sons, Inc.     

A mathematical framework for the study of morphogenetic development in the slime mold

A mathematical continuum model of the slime mold Dictyostelium discoideum in the morphogenetic development stage is presented, which represents the amoebae as a fluid with surface tension, acted upon by a body force due to the presence of a chemical attractant. Assuming that the amoebae at a given time are in quasi-equilibrium, and that the shape of the organism is prescribed, it is possible to calculate from the model plausible concentration and source-sink distributions that are consistent with the given shape. Typical observed shapes are accounted for by the presence of very large concentrations and concentration gradients of the chemical attractant at the top of the structure.     

Accumulation of lead by Anabaena cylindrica : mathematical modeling and an energy dispersive X-ray study

The ability of microorganisms to selectively adsorb various heavy metal ions has been recognized for over a decade. We have investigated the biosorption of lead by an active culture of the cyanobacterium Anabaena cylindrica. Energy dispersive X-ray microanalysis was used to evaluate the different uptake mechanisms in the various subcellular regions. Three were identified: a very fast adsorption mechanism in the cell envelope; a time-dependent deposition reaction on the cell surface; and an adsorption mechanism, also time dependent, on the polyphosphate body inside the cell. Atomic absorption spectrometry was then used to quantify the changes with time of bulk fluid concentrations of lead solutions exposed to cyanobacteria. A mass transfer kinetic model was developed which quantitatively predicts the concentration of lead in cells of Anabaena cylindrica as a function of spatial dimensions and time. The model predictions are consistent with a pattern, documented in literature and confirmed by our own experimental evidence, of a very fast uptake in the cell envelope and then a longer uptake period inside the cell. Our experimental evidence also revealed a time-dependent uptake mechanism on the surface of the cells, which is included in the model. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 408-418, 1997.     

Control of snakebite envenoming: A mathematical modeling study

A mathematical model is designed to assess the impact of some interventional strategies for curtailing the burden of snakebite envenoming in a community. The model is fitted with real data set. Numerical simulations have shown that public health awareness of the susceptible individuals on snakebite preventive measures could reduce the number of envenoming and prevent deaths and disabilities in the population. The simulations further revealed that if at least fifty percent of snakebite envenoming patients receive early treatment with antivenom a substantial number of deaths will be averted. Furthermore, it is shown using optimal control that combining public health awareness and antivenom treatment averts the highest number of snakebite induced deaths and disability adjusted life years in the study area. To choose the best strategy amidst limited resources in the study area, cost effectiveness analysis in terms of incremental cost effectiveness ratio is performed. It has been established that the control efforts of combining public health awareness of the susceptible individuals and antivenom treatment for victims of snakebite envenoming is the most cost effective strategy. Approximately the sum of US$72,548 is needed to avert 117 deaths or 2,739 disability adjusted life years that are recorded within 21 months in the study area. Thus, the combination of these two control strategies is recommended.     

ModEco: an integrated software package for ecological niche modeling

ModEco is a software package for ecological niche modeling. It integrates a range of niche modeling methods within a geographical information system. ModEco provides a user friendly platform that enables users to explore, analyze, and model species distribution data with relative ease. ModEco has several unique features: 1) it deals with different types of ecological observation data, such as presence and absence data, presence‐only data, and abundance data; 2) it provides a range of models when dealing with presence‐only data, such as presence‐only models, pseudo‐absence models, background vs presence data models, and ensemble models; and 3) it includes relatively comprehensive tools for data visualization, feature selection, and accuracy assessment.