Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Exploring the parameter space of a rabbit ventricular action potential model to investigate the effect of variation on action potential and calcium transients

Computational models for cardiomyocyte action potentials (AP) often make use of a large parameter set. This parameter set can contain some elements that are fitted to experimental data independently of any other element, some elements that are derived concurrently with other elements to match experimental data, and some elements that are derived purely from phenomenological fitting to produce the desired AP output. Furthermore, models can make use of several different data sets, not always derived for the same conditions or even the same species. It is consequently uncertain whether the parameter set for a given model is physiologically accurate. Furthermore, it is only recently that the possibility of degeneracy in parameter values in producing a given simulation output has started to be addressed. In this study, we examine the effects of varying two parameters (the L-type calcium current (I(CaL)) and the delayed rectifier potassium current (I(Ks))) in a computational model of a rabbit ventricular cardiomyocyte AP on both the membrane potential (V(m)) and calcium (Ca(2+)) transient. It will subsequently be determined if there is degeneracy in this model to these parameter values, which will have important implications on the stability of these models to cell-to-cell parameter variation, and also whether the current methodology for generating parameter values is flawed. The accuracy of AP duration (APD) as an indicator of AP shape will also be assessed.

Preparation and characterisation of tri-calcium phosphate scaffolds with tunnel-like macro-pores for bone tissue engineering

Calcium Phosphate ceramics have been widely used in tissue engineering due to their excellent biocompatibility and biodegradability. In the physiological environment, they are able to gradually degrade, absorbed and promote bone growth. Ultimately, they are capable of replacing damaged bone with new tissue. However, their low mechanical properties limit calcium phosphate ceramics in load-bearing applications. To obtain sufficient mechanical properties as well as high biocompatibility is one of the main focuses in biomaterials research. Therefore, the current project focuses on the preparation and characterization of porous tri-calcium phosphate (TCP) ceramic scaffolds. Hydroxapatite (HA) was used as the raw material, and normal calcium phosphate bioglass was added to adjust the ratio between calcium and phosphate. It was found that when 20% bioglass was added to HA and sintered at 1400oC for 3 hours, the TCP scaffold was obtained and this was confirmed by X-ray diffraction (XRD) analysis. Test results have shown that by applying this method, TCP scaffolds have significantly higher compressive strength (9.98MPa) than those made via TCP powder (<3MPa). Moreover, in order to further increase the compressive strength of TCP scaffolds, the samples were then coated with bioglass. For normal bioglass coated TCP scaffold, compressive strength was 16.69±0.5MPa; the compressive strength for single layer mesoporous bioglass coated scaffolds was 15.03±0.63MPa. In addition, this project has also concentrated on sizes and shapes effects; it was found that the cylinder scaffolds have more mechanical property than the club ones. In addition, this project performed cell culture within scaffold to assess biocompatibility. The cells were well distributed in the scaffold, and the cytotoxicity test was performed by 3-(4,5)-dimethylthiahiazo(-z-y1)-3,5-di- phenytetrazoliumromide (MTT) assay. The Alkaline Phosphatase (Alp) activity of human bone marrow mesenchymal stem cell system (hBMSCs) seeded on scaffold expressed higher in vitro than that in the positive control groups in osteogenic medium, which indicated that the scaffolds were both osteoconductive and osteoinductive, showing potential value in bone tissue engineering.

Effects of varied ionic calcium and phosphate on the proliferation, osteogenic differentiation and mineralization of human periodontal ligament cells in vitro

Background and Objective: A number of bone filling materials containing calcium (Ca++) and phosphate (P) ions have been used in the repair of periodontal bone defects; however, the effect that local release of Ca++ and P ions have on biological reactions is not fully understood. In this study, we investigated the effects of various levels of Ca++ and P ions on the proliferation, osteogenic differentiation, and mineralization of human periodontal ligament cells (hPDLCs). Materials and Methods: hPDLCs were obtained using an explant culture method. Defined concentrations and ratios of ionic Ca++ to inorganic P were added to standard culture and osteogenic induction media. The ability of hPDLCs to proliferate in these growth media was assayed using the Cell Counting Kit-8 (CCK-8). Cell apoptosis was evaluated by FITC-Annexin V/PI double staining method. Osteogenic differentiation and mineralization were investigated by morphological observations, alkaline phosphatase (ALP) activity, and Alizarin red S/von Kossa staining. The mRNA expression of osteogenic related markers was analyzed using a reverse transcriptase polymerase chain reaction (RT-PCR). Results: Within the ranges of Ca++ and P ions concentrations tested, we observed that increased concentrations of Ca++ and P ions enhanced cell proliferation and formation of mineralized matrix nodules; whereas ALP activity was reduced. The RT-PCR results showed that elevated concentrations of Ca++ and P ions led to a general increase of Runx2 mRNA expression and decreased ALP mRNA expression, but gave no clear trend on OCN mRNA levels. Conclusion: The concentrations and ratios of Ca++ and P ions could significantly influence proliferation, differentiation, and mineralization of hPDLCs. Within the range of concentrations tested, we found that the combination of 9.0 mM Ca++ ions and 4.5 mM P ions were the optimum concentrations for proliferation, differentiation, and mineralization in hPDLCs.

Hypoxia-mimicking mesoporous bioactive glass scaffolds with controllable cobalt ion release for bone tissue engineering

Low oxygen pressure (hypoxia) plays an important role in stimulating angiogenesis; there are, however, few studies to prepare hypoxia-mimicking tissue engineering scaffolds. Mesoporous bioactive glass (MBG) has been developed as scaffolds with excellent osteogenic properties for bone regeneration. Ionic cobalt (Co) is established as a chemical inducer of hypoxia-inducible factor (HIF)-1α, which induces hypoxia-like response. The aim of this study was to develop hypoxia-mimicking MBG scaffolds by incorporating ionic Co2+ into MBG scaffolds and investigate if the addition of Co2+ ions would induce a cellular hypoxic response in such a tissue engineering scaffold system. The composition, microstructure and mesopore properties (specific surface area, nano-pore volume and nano-pore distribution) of Co-containing MBG (Co-MBG) scaffolds were characterized and the cellular effects of Co on the proliferation, differentiation, vascular endothelial growth factor (VEGF) secretion, HIF-1α expression and bone-related gene expression of human bone marrow stromal cells (BMSCs) in MBG scaffolds were systematically investigated. The results showed that low amounts of Co (< 5%) incorporated into MBG scaffolds had no significant cytotoxicity and that their incorporation significantly enhanced VEGF protein secretion, HIF-1α expression, and bone-related gene expression in BMSCs, and also that the Co-MBG scaffolds support BMSC attachment and proliferation. The scaffolds maintain a well-ordered mesopore channel structure and high specific surface area and have the capacity to efficiently deliver antibiotics drugs; in fact, the sustained released of ampicillin by Co-MBG scaffolds gives them excellent anti-bacterial properties. Our results indicate that incorporating cobalt ions into MBG scaffolds is a viable option for preparing hypoxia-mimicking tissue engineering scaffolds and significantly enhanced hypoxia function. The hypoxia-mimicking MBG scaffolds have great potential for bone tissue engineering applications by combining enhanced angiogenesis with already existing osteogenic properties.

Calcium ions promote osteogenic differentiation and mineralization of human dental pulp cells : implication for pulp capping materials

Calcium (Ca) is the main element of most pulp capping materials and plays an essential role in mineralization. Different pulp capping materials can release various concentrations of Ca ions leading to different clinical outcomes. The purpose of this study was to investigate the effects of various concentrations of Ca ions on the growth and osteogenic differentiation of human dental pulp cells (hDPCs). Different concentrations of Ca ions were added to growth culture medium and osteogenic inductive culture medium. A Cell Counting Kit-8 (CCK-8) was used to determine the proliferation of hDPCs in growth culture medium. Osteogenic differentiation and mineralization were measured by alkaline phosphatase (ALP) assay, Alizarin red S/von kossa staining, calcium content quantitative assay. The selected osteogenic differentiation markers were investigated by quantitative real-time polymerase chain reaction (qRT-PCR). Within the range of 1.8–16.2 mM, increased concentrations of Ca ions had no effect on cell proliferation, but led to changes in osteogenic differentiation. It was noted that enhanced mineralized matrix nodule formation was found in higher Ca ions concentrations; however, ALP activity and gene expression were reduced. qRT-PCR results showed a trend towards down-regulated mRNA expression of type I collagen (COL1A2) and Runx2 at elevated concentrations of Ca ions, whereas osteopontin (OPN) and osteocalcin (OCN) mRNA expression was significantly up-regulated. Ca ions content in the culture media can significantly influence the osteogenic properties of hDPCs, indicating the importance of optimizing Ca ions release from dental pulp capping materials in order to achieve desirable clinical outcomes.

The undesirable acetylation of cellulose by the acetate ion of 1-ethyl-3-methylimidazolium acetate

The ionic liquid (IL) 1-ethyl-3-methylimidazolium acetate ([C2mim]OAc) is considered to be an inert solvent of cellulose and lignocellulosic biomass. Acetylation (1.7 % mol, or DS 0.017) of cellulose after dissolution in [C2mim]OAc (150 °C for 20 min), is demonstrated by compositional analysis, FTIR analysis and 13C NMR spectroscopy (in [C2min]OAc with 13C enriched acetate). This acetylation, in the absence of added acylating agents, has not been reported before and may limit [C2mim]OAc utility in industrial scale biomass processing, even at this low extent. For example, cellulose acetylation may contribute to IL loss in processes where the IL is recovered and reused and inhibit enzyme saccharification of cellulose in lignocellulosic biofuel production processes based on saccharification and fermentation.

Active regulation of the epidermal calcium profile

A distinct calcium profile is strongly implicated in regulating the multi-layered structure of the epidermis. However, the mechanisms that govern the regulation of this calcium profile are currently unclear. It clearly depends on the relatively impermeable barrier of the stratum corneum (passive regulation) but may also depend on calcium exchanges between keratinocytes and extracellular fluid (active regulation). Using a mathematical model that treats the viable sublayers of unwounded human and murine epidermis as porous media and assumes that their calcium profiles are passively regulated, we demonstrate that these profiles are also actively regulated. To obtain this result, we found that diffusion governs extracellular calcium motion in the viable epidermis and hence intracellular calcium is the main source of the epidermal calcium profile. Then, by comparison with experimental calcium profiles and combination with a hypothesised cell velocity distribution in the viable epidermis, we found that the net influx of calcium ions into keratinocytes from extracellular fluid may be constant and positive throughout the stratum basale and stratum spinosum, and that there is a net outflux of these ions in the stratum granulosum. Hence the calcium exchange between keratinocytes and extracellular fluid differs distinctly between the stratum granulosum and the underlying sublayers, and these differences actively regulate the epidermal calcium profile. Our results also indicate that plasma membrane dysfunction may be an early event during keratinocyte disintegration in the stratum granulosum.

Vibrational spectroscopy and solubility study of the mineral stringhamite CaCuSiO4•H2O

Stringhamite CaCuSiO4·H2O is a hydrated calcium copper silicate and is commonly known as a significant ‘healing’ mineral and is potentially a semi-precious jewel. Stringhamite is a neosilicate with Cu2+ in square planar coordination. Vibrational spectroscopy has been used to characterise the molecular structure of stringhamite. The intense sharp Raman band at 956 cm−1 is assigned to the ν1 (A1g) symmetric stretching vibration. Raman bands at 980, 997, 1061 cm−1 are assigned to the ν3 (A2u, B1g) antisymmetric stretching vibrations. Splitting of the ν3 vibrational mode supports the concept that the stringhamite SiO4 tetrahedron is strongly distorted. The intense bands at 505 and 519 cm−1 and at 570 cm−1 are assigned to the ν2 and ν4 vibrational modes. The question arises as to whether the mineral stringhamite can actually function as a healing mineral. An estimation of the solubility product at pH < 5 shows that the cupric ion can be released. The copper ion is a very powerful antibiological agent and thus the mineral stringhamite may well function as a healing mineral.

Improved sugar cane juice clarification by understanding calcium oxide-phosphate-sucrose systems

It is accepted that the efficiency of sugar cane clarification is closely linked with sugar juice composition (including suspended or insoluble impurities), the inorganic phosphate content, the liming condition and type, and the interactions between the juice components. These interactions are not well understood, particularly those between calcium, phosphate, and sucrose in sugar cane juice. Studies have been conducted on calcium oxide (CaO)/phosphate/sucrose systems in both synthetic and factory juices to provide further information on the defecation process (i.e., simple liming to effect impurity removal) and to identify an effective clarification process that would result in reduced scaling of sugar factory evaporators, pans, and centrifugals. Results have shown that a two-stage process involving the addition of lime saccharate to a set juice pH followed by the addition of sodium hydroxide to a final juice pH or a similar two-stage process where the order of addition of the alkalis is reversed prior to clarification reduces the impurity loading of the clarified juice compared to that of the clarified juice obtained by the conventional defecation process. The treatment process showed reductions in CaO (27% to 50%) and MgO (up to 20%) in clarified juices with no apparent loss in juice clarity or increase in residence time of the mud particles compared to those in the conventional process. There was also a reduction in the SiO2 content. However, the disadvantage of this process is the significant increase in the Na2O content.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Microcosm study of ion mobilization and greenhouse gas evolution in soils of a plantation-forested subtropical coastal catchment

This study examined the potential for Fe mobilization and greenhouse gas (GHG, e.g. CO2, and CH4) evolution in SEQ soils associated with a range of plantation forestry practices and water-logged conditions. Intact, 30-cm-deep soil cores collected from representative sites were saturated and incubated for 35 days in the laboratory, with leachate and headspace gas samples periodically collected. Minimal Fe dissolution was observed in well-drained sand soils associated with mature, first-rotation Pinus and organic Fe complexation, whereas progressive Fe dissolution occurred over 14 days in clear-felled and replanted Pinus soils with low organic matter and non-crystalline Fe fractions. Both CO2 and CH4 effluxes were relatively lower in clear-felled and replanted soils compared with mature, first-rotation Pinus soils, despite the lack of statistically significant variations in total GHG effluxes associated with different forestry practices. Fe dissolution and GHG evolution in low-lying, water-logged soils adjacent to riparian and estuarine, native-vegetation buffer zones were impacted by mineral and physical soil properties. Highest levels of dissolved Fe and GHG effluxes resulted from saturation of riparian loam soils with high Fe and clay content, as well as abundant organic material and Fe-metabolizing bacteria. Results indicate Pinus forestry practices such as clear-felling and replanting may elevate Fe mobilization while decreasing CO2 and CH4 emissions from well-drained, SEQ plantation soils upon heavy flooding. Prolonged water-logging accelerates bacterially mediated Fe cycling in low-lying, clay-rich soils, leading to substantial Fe dissolution, organic matter mineralization, and CH4 production in riparian native-vegetation buffer zones.