Astrocytes are extensively coupled through gap junctions into a syncytium. However, the basic role of this major brain network remains largely unknown. Using electrophysiological and computational modeling methods, we demonstrate that the membrane potential (VM) of an individual astrocyte in a hippocampal syncytium, but not in a single, freshly isolated cell preparation, can be well-maintained at quasi-physiological levels when recorded with reduced or K+ free pipette solutions that alter the K+ equilibrium potential to non-physiological voltages. We show that an astrocyte’s associated syncytium provides powerful electrical coupling, together with ionic coupling at a lesser extent, that equalizes the astrocyte’s VM to levels comparable to its neighbors. Functionally, this minimizes VM depolarization attributable to elevated levels of local extracellular K+ and thereby maintains a sustained driving force for highly efficient K+ uptake. Thus, gap junction coupling functions to achieve isopotentiality in astrocytic networks, whereby a constant extracellular environment can be powerfully maintained for crucial functions of neural circuits.

Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call Responsive/Signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and emergent behaviour of solutions, particularly temporal clustering and stability of clustered solutions. We establish the existence of certain periodic clustered solutions as well as “uniform” solutions and add to the evidence that cell-cycle dependent feedback robustly leads to cell-cycle clustering. We highlight the fundamental differences in dynamics between systems with negative and positive feedback. For positive feedback systems the most important mechanism seems to be the stability of individual isolated clusters. On the other hand we find that in negative feedback systems, clusters must interact with each other to reinforce coherence. We conclude from various details of the mathematical analysis that negative feedback is most consistent with observations in yeast experiments.

A detailed biophysical model for a neuron/astrocyte network is developed to explore mechanisms responsible for the initiation and propagation of cortical spreading depolarizations and the role of astrocytes in maintaining ion homeostasis, thereby preventing these pathological waves. Simulations of the model illustrate how properties of spreading depolarizations, such as wave speed and duration of depolarization, depend on several factors, including the neuron and astrocyte Na(+)-K(+) ATPase pump strengths. In particular, we consider the neuroprotective role of astrocyte gap junction coupling. The model demonstrates that a syncytium of electrically coupled astrocytes can maintain a physiological membrane potential in the presence of an elevated extracellular K(+) concentration and efficiently distribute the excess K(+) across the syncytium. This provides an effective neuroprotective mechanism for delaying or preventing the initiation of spreading depolarizations.

In order to gain a deeper understanding of the onset and progression of pulmonary infections we present and analyze a low dimensional, phenomenological model of infection and the innate immune response in the lungs. Because pulmonary innate immunity has features unique to itself, general mathematical models of the immune system may not be appropriate. The differential equations model that we propose is based on current knowledge of the biology of pulmonary innate immunity and accurately reproduces known features of the initial phase of the dynamics of pulmonary innate system as exhibited in recent experiments. Further, we propose to use the model as a starting point for interrogation with clinical data from a new noninvasive technique for sampling alveolar lining fluid.

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Background: Syncytial nuclei in Drosophila embryos undergo their first 13 divisions nearly synchronously. In the last several cell cycles, these division events travel across the anterior-posterior axis of the syncytial blastoderm in a wave. The phenomenon is well documented but the underlying mechanisms are not yet understood. Results: We study timing and positional data obtained from in vivo imaging of Drosophila embryos. We determine the statistical properties of the distribution of division times within and across generations with the null hypothesis that timing of division events is an independent random variable for each nucleus. We also compare timing data with a model of Drosophila cell cycle regulation that does not include internuclear signaling, and to a universal model of phase-dependent signaling to determine the probable form of internuclear signaling in the syncytial embryo. Conclusions: The statistical variance of division times is lower than one would expect from uncoordinated activity. In fact, the variance decreases between the 10th and 11th divisions, which demonstrates a contribution of internuclear signaling to the observed synchrony and division waves. Our comparison with a coupled oscillator model leads us to conclude that internuclear signaling must be of Response/Signaling type with a positive impulse. Developmental

We consider a dynamical model of cell cycles of n cells in a culture in which cells in one specific phase (S for signalling) of the cell cycle produce chemical agents that influence the growth/cell cycle progression of cells in another phase (R for responsive). In the case that the feedback is negative, it is known that subpopulations of cells tend to become clustered in the cell cycle; while for a positive feedback, all the cells tend to become synchronized. In this paper, we suppose that there is a gap between the two phases. The gap can be thought of as modelling the physical reality of a time delay in the production and action of the signalling agents. We completely analyse the dynamics of this system when the cells are arranged into two cell cycle clusters. We also consider the stability of certain important periodic solutions in which clusters of cells have a cyclic arrangement and there are just enough clusters to allow interactions between them. We find that the inclusion of a small gap does not greatly alter the global dynamics of the system; there are still large open sets of parameters for which clustered solutions are stable. Thus, we add to the evidence that clustering can be a robust phenomenon in biological systems. However, the gap does effect the system by enhancing the stability of the stable clustered solutions. We explain this phenomenon in terms of contraction rates (Floquet exponents) in various invariant subspaces of the system. We conclude that in systems for which these models are reasonable, a delay in signalling is advantageous to the emergence of clustering.