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Computing numerical solutions to fractional differential equations can be computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In general, numerical approaches that depend on truncating part of the system history while efficient, can suffer from high degrees of error and inaccuracy. Here we present an adaptive time step memory method for smooth functions applied to the Grunwald-Letnikov fractional diffusion derivative. This method is computationally efficient and results in smaller errors during numerical simulations. Sampled points along the system history at progressively longer intervals are assumed to reflect the values of neighboring time points. By including progressively fewer points backward in time, a temporally weighted history is computed that includes contributions from the entire past of the system, maintaining accuracy, but with fewer points actually calculated, greatly improving computational efficiency., 25 pages; in press in The Journal of Computational Physics

The attachment of bioactive protein to surfaces underpins the development of biosensors and diagnostic microarrays. We present a surface treatment using plasma immersion ion implantation (PIII) to create stable covalent binding sites for the attachment of functional soya-bean peroxidase (SBP). Fourier transform infrared spectra of the surfaces show that protein is retained on the surface after boiling in sodium dodecyl sulphate and sodium hydroxide, which is indicative of covalent attachment. The activity of SBP on the treated surfaces remains high in comparison with SBP attached to control surfaces over the course of 11 days. Surface plasmon resonance was used to show that the surface coverage of the attached protein is close to a monolayer. We describe the potential of the PIII treatment method to be used as a one-step dry process to create surfaces for large-scale protein micro- or nanopatterning.

Calcium-dependent release of vasoactive gliotransmitters is widely assumed to trigger vasodilation associated with rapid increases in neuronal activity. Inconsistent with this hypothesis, intact stimulus-induced vasodilation was observed in inositol 1,4,5-triphosphate (IP3) type-2 receptor (R2) knock-out (KO) mice, in which the primary mechanism of astrocytic calcium increase—the release of calcium from intracellular stores following activation of an IP3-dependent pathway—is lacking. Further, our results in wild-type (WT) mice indicate thatin vivoonset of astrocytic calcium increase in response to sensory stimulus could be considerably delayed relative to the simultaneously measured onset of arteriolar dilation. Delayed calcium increases in WT mice were observed in both astrocytic cell bodies and perivascular endfeet. Thus, astrocytes may not play a role in the initiation of blood flow response, at least not via calcium-dependent mechanisms. Moreover, an increase in astrocytic intracellular calcium was not required for normal vasodilation in the IP3R2-KO animals.

We constructed a model of calcium signaling in astrocyte neural glial cells that incorporates a positive feedback nucleation mechanism, whereby small microdomain increases in local calcium can stochastically produce global cellular and intercellular network scale dynamics. The model is able to simultaneously capture dynamic spatial and temporal heterogeneities associated with intracellular calcium transients in individual cells and intercellular calcium waves (ICW) in spatially realistic networks of astrocytes, i.e., networks where the positions of cells were taken from real in vitro experimental data of spontaneously forming sparse networks, as opposed to artificially constructed grid networks or other non-realistic geometries. This is the first work we are aware of where an intracellular model of calcium signaling that reproduces intracellular dynamics inherently accounts for intercellular network dynamics. These results suggest that a nucleation type mechanism should be further investigated experimentally in order to test its contribution to calcium signaling in astrocytes and in other cells more broadly. It may also be of interest in engineered neuromimetic network systems that attempt to emulate biological signaling and information processing properties in synthetic hardwired neuromorphometric circuits or coded algorithms.

The contribution of astrocytes to the pathophysiology of AD (Alzheimer's disease) and the molecular and signalling mechanisms that potentially underlie them are still very poorly understood. However, there is mounting evidence that calcium dysregulation in astrocytes may be playing a key role. Intercellular calcium waves in astrocyte networks in vitro can be mechanically induced after Aβ (amyloid β-peptide) treatment, and spontaneously forming intercellular calcium waves have recently been shown in vivo in an APP (amyloid precursor protein)/PS1 (presenilin 1) Alzheimer's transgenic mouse model. However, spontaneous intercellular calcium transients and waves have not been observed in vitro in isolated astrocyte cultures in response to direct Aβ stimulation in the absence of potentially confounding signalling from other cell types. Here, we show that Aβ alone at relatively low concentrations is directly able to induce intracellular calcium transients and spontaneous intercellular calcium waves in isolated astrocytes in purified cultures, raising the possibility of a potential direct effect of Aβ exposure on astrocytes in vivo in the Alzheimer's brain. Waves did not occur immediately after Aβ treatment, but were delayed by many minutes before spontaneously forming, suggesting that intracellular signalling mechanisms required sufficient time to activate before intercellular effects at the network level become evident. Furthermore, the dynamics of intercellular calcium waves were heterogeneous, with distinct radial or longitudinal propagation orientations. Lastly, we also show that changes in the expression levels of the intermediate filament proteins GFAP (glial fibrillary acidic protein) and S100B are affected by Aβ-induced calcium changes differently, with GFAP being more dependent on calcium levels than S100B.

Network signaling through astrocyte syncytiums putatively contribute to the regulation of a number of both physiological and pathophysiological processes in the mammalian central nervous system. As such, an understanding of the underlying mechanisms is critical to determining any roles played by signaling through astrocyte networks. Astrocyte signaling is primarily mediated by the propagation of intercellular calcium waves in the sense that paracrine signaling results in measurable intracellular calcium transients. Although the molecular mechanisms are relatively well known, there is conflicting data regarding the mechanism by which the signal propagates through the network. Experimentally there is evidence for both a point source signaling model in which adenosine triphosphate (ATP) is released by an initially activated astrocyte only, and a regenerative signaling model in which downstream astrocytes release ATP. We modeled both conditions as a simple lumped parameter phenomenological diffusion model and show that the only possible mechanism that can accurately reproduce experimentally measured results is a dual signaling mechanism that incorporates elements of both proposed signaling models. Specifically, we were able to accurately simulate experimentally measured in vitro intercellular calcium wave dynamics by assuming a point source signaling model with a downstream regenerative component. These results suggest that seemingly conflicting data in the literature are actually complimentary, and represents a highly efficient and robustly engineered signaling mechanism.