Marius Buibas

Amyloid β-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 (Alzheimers 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) Alzheimers 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 Alzheimers 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.

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 vitro ICW 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.

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.

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.

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.

Latency and rate coding in a spiking model of retina

We describe a family of spiking retina computational models for large-scale simulations of the visual pathways. The models reproduce the overall spatial, temporal, and chromatic structure of the receptive fields of midget and parasol retinal ganglion cells (RGCs) of the primate retina, as well as their contrast response, while using fairly simple models of bipolar, horizontal, amacrine, and RGCs. These retina models provide input to a realistic model of visual cortex, presented in a separate submission. The retina model simulates cone and bipolar cell dynamics using a damped wave equation. Parameters are so chosen that an impulse retinal input gives rise to a damped biphasic output current, and that a coherent stimulus elicits a substantially stronger response than an incoherent stimulus of the same power (Figure ​(Figure1).1). Static or low-frequency visual inputs are smoothly rejected. In contrast to biology, this stage of the model is linear; rectification and adaptation mechanisms are all realized in the spiking ganglion cell layer. In the ganglion cell layer parasol, midget, and SBC cells are simulated. The spatio-temporal receptive fields of different RGCs are not prewired; they emerge via the lateral interactions between the horizontal, bipolar, and amacrine cells. Spike generation in the RGCs is modeled using spiking neurons with two dynamic variables and an intrinsic adaptation mechanism. Midget RGCs have an additional leaky temporal integration of the input current, to account for the relatively tonic character of their responses. Parasol RGCs have an additional partial divisive normalization of the input current, to reproduce the saturating parasol response to relative contrast of the stimulus. Simplified amacrine-cell dynamics is introduced to provide for the spatiotemporal structure of the parasol receptive field surrounds. Figure 1 A-E: model response to coherent vs. randomized stimulus. Moving edge stimulus is presented (A) and elicits strong response (B). Same stimulus with fixed random permutation of pixels (C) elicits much weaker response (D). (E) compares the total responses ... Desired latency encoding of input features is achieved by calibrating the parameters of the spiking RGC conductance dynamics. A near logarithmic latency to the first spike, for a step up in the input signal, provides for a good contrast invariance of the relative spike timing in the response. A combination of spike-latency and spike-count encoding of the input stimulus, together with the enhanced response of the simulated retina to coherent stimuli, results in an informative yet not too noisy spiking input to the LGN and V1; the information content analysis of the RGC spike-train vocabulary will be presented. This retina model was used to produce a fully-emergent orientation tuning in a spiking model [1] of V1 cortex.

Assessing predictive capability of neuronal network models by computing Lyapunov exponents

Mathematical models of biology are largely based on systems of nonlinear differential equations that are discretized to facilitate solving. In particular, models of neuronal networks need to incorporate delays between the transmission of information of one state variable to another in the system of equations. In reality delays exists in all physical entities, however; their magnitude relative to the time step needed to simulate the entity may be negligibly small. We quantitatively assessed the effect that delays in a system of nonlinear difference equations have on the accuracy of modeling neural networks by computing the Lyapunov exponents for systems of equations describing networks that are part of a previously published test set [1]. This is significant because it represents an objective metric of the ability of a model to represent the physical system being modeled. The maximal Lyapunov exponent is a measure of the exponential divergence over time of a pair of initially infinitesimally close points. Even if instruments existed to assess all the variables of a system with 100% fidelity the limited precision of computers in representing numbers would create small errors between the actual conditions of the system being modeled, and the starting conditions in a computational model. Therefore, all models of the real world that contain positive Lyapunov exponents have a limited predictive capability. Necessary computer code to accomplish this has been written for parallel processing on general purpose graphics processing units to accelerate computational time.