A framework for simulating and estimating the state and functional topology of complex dynamic geometric networks.

We introduce a framework for simulating signal propagation in geometric networks (networks that can be mapped to geometric graphs in some space) and developing algorithms that estimate (i.e., map) the state and functional topology of complex dynamic geometric networks. Within the framework, we define the key features typically present in such networks and of particular relevance to biological cellular neural networks: dynamics, signaling, observation, and control. The framework is particularly well suited for estimating functional connectivity in cellular neural networks from experimentally observable data and has been implemented using graphics processing unit high-performance computing. Computationally, the framework can simulate cellular network signaling close to or faster than real time. We further propose a standard test set of networks to measure performance and compare different mapping algorithms.

Mapping the spatiotemporal dynamics of calcium signaling in cellular neural networks using optical flow.

An optical flow gradient algorithm was applied to spontaneously forming networks of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution. Optical flow estimates the direction and speed of motion of objects in an image between subsequent frames in a recorded digital sequence of images (i.e., a movie). Computed vector field outputs by the algorithm were able to track the spatiotemporal dynamics of calcium signaling patterns. We begin by briefly reviewing the mathematics of the optical flow algorithm, and then describe how to solve for the displacement vectors and how to measure their reliability. We then compare computed flow vectors with manually estimated vectors for the progression of a calcium signal recorded from representative astrocyte cultures. Finally, we applied the algorithm to preparations of primary astrocytes and hippocampal neurons and to the rMC-1 Muller glial cell line in order to illustrate the capability of the algorithm for capturing different types of spatiotemporal calcium activity. We discuss the imaging requirements, parameter selection and threshold selection for reliable measurements, and offer perspectives on uses of the vector data.

Amyloid ß-peptide directly induces spontaneous calcium transients, delayed intercellular calcium waves and gliosis in rat cortical astrocytes.

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 Aß (amyloid ß-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 Aß stimulation in the absence of potentially confounding signalling from other cell types. Here, we show that Aß 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 Aß exposure on astrocytes in vivo in the Alzheimer's brain. Waves did not occur immediately after Aß 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 Aß-induced calcium changes differently, with GFAP being more dependent on calcium levels than S100B.

Characterization of Calcium-Mediated Intracellular and Intercellular Signaling in the rMC-1 Glial Cell Line.

Retinal Müller glial cells, in addition to providing homeostatic support to retinal neurons, have been shown to engage in modulation of neuronal activity and regulate vasomotor responses in the retina, among other functions. Calcium-mediated signaling in Müller cells has been implicated to play a significant role in the intracellular and intercellular interactions necessary to carry out these functions. Although the basic molecular mechanisms of calcium signaling in Müller cells have been described, the dynamics of calcium responses in Müller cells have not been fully explored. Here, we provide a quantitative characterization of calcium signaling in an in vitro model of Müller cell signaling using the rMC-1 cell line, a well-established line developed from rat Müller cells. rMC-1 cells displayed robust intracellular calcium transients and the capacity to support calcium transient-mediated intercellular calcium waves with signaling dynamics similar to that reported for Müller cells in in situ retinal preparations. Furthermore, pharmacological perturbations of intracellular calcium transients with thapsigargin and intercellular calcium waves with purinergic receptor antagonists and gap junction blockers (PPADS and FFA, respectively) suggest that the molecular mechanisms that underlie calcium signaling in rMC-1 cells has been conserved with those of Müller cells. This model provides a robust in vitro system for investigating specific mechanistic hypotheses of intra- and intercellular calcium signaling in Müller cells.

Diffusion modeling of ATP signaling suggests a partially regenerative mechanism underlies astrocyte intercellular calcium waves.

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 (ICW) 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 vitroICW 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.

Automated detection of intercellular signaling in astrocyte networks using the converging squares algorithm.

Intercellular calcium waves in central nervous system astrocyte networks underline the principle mechanism of cell signaling in astrocyte syncsytiums, which putatively contribute to the modulation of neuronal signaling and metabolic regulation. In support of carrying out systems level analyses of astrocyte networks, we have optimized and validated the converging squares image segmentation algorithm to automatically detect the relative spatial locations of all cells in a visible network as a preliminary step towards analyzing the dynamics of astrocyte intracellular calcium transients, which are the signals that mediate intercellular calcium waves. We used the temporal derivatives of pixel intensities as the data source for the algorithm. The method works by converging progressively smaller squares until the signal peak is reached. It is robust to noise and performs comparably to manual cell signal identification, but is much faster and efficient. This is the first reported application of this algorithm to glial networks that we are aware of.