The blood-brain barrier, which is formed by the endothelial cells that line cerebral microvessels, has an important role in maintaining a precisely regulated microenvironment for reliable neuronal signalling. At present, there is great interest in the association of brain microvessels, astrocytes and neurons to form functional 'neurovascular units', and recent studies have highlighted the importance of brain endothelial cells in this modular organization. Here, we explore specific interactions between the brain endothelium, astrocytes and neurons that may regulate blood-brain barrier function. An understanding of how these interactions are disturbed in pathological conditions could lead to the development of new protective and restorative therapies.

Astrocyte–endothelial interactions at the blood–brain barrier

This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems Each chapter proceeds from the simple to the complex, and provides sample problems at the end The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience

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Dynamical Systems in Neuroscience

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl strm and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. strm and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines

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Feedback Systems: An Introduction for Scientists and Engineers

http://mcb.berkeley.edu/courses/mcb137/exercises/Tyson%20(2003).pdf

Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell

The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We review deterministic and stochastic mathematical models of the IPR, from the earliest ones of the 1970s and 1980s, to the most recent. The effects of IPR stochasticity on Ca2+Ca2+ dynamics are briefly discussed.

Models of the inositol trisphosphate receptor

Targeted phosphorylation of inositol 1,4,5-trisphosphate receptors selectively inhibits localized Ca2+ release and shapes oscillatory Ca2+ signals.

Traveling waves of calcium are widely observed under conditions where the free calcium is heavily buffered. It is thus of considerable physiological interest to determine the precise effects that buffers have on the properties of traveling waves. Since calcium waves are widely believed to be the result of the reaction and diffusion of calcium, we study the properties of traveling waves in simple reaction-diffusion equations in which the diffusing species is buffered. For the buffered bistable equation we derive a constraint on the model parameters in order for a traveling wave of excitation to exist, and we show that stationary buffers cannot eliminate traveling waves. When the buffer is of low affinity, a constant effective diffusion coefficient may be defined, but no effective diffusion coefficient can be defined for high affinity buffers. We derive an approximate expression for the wave speed, show numerically that this approximation applies for both high and low affinity buffers, and hence derive an a...

Traveling waves in buffered systems: applications to calcium waves

A buffering SERCA pump in models of calcium dynamics.

The dynamics of Ca2+ release and Ca2+-activated Cl− currents in two related, but functionally distinct exocrine cells, were studied to gain insight into how the molecular specialization of Ca2+ signalling machinery are utilized to produce different physiological endpoints: in this case, fluid or exocytotic secretion. Digital imaging and patch-clamp methods were used to monitor the temporal and spatial properties of changes in cytosolic Ca2+ concentration ([Ca2+]c) and Cl− currents following the controlled photolytic release of caged-InsP3 or caged-Ca2+. In parotid and pancreatic acinar cells, changes in [Ca2+]c and activation of a Ca2+-activated Cl− current occurred with close temporal coincidence. In parotid, a rapid global Ca2+ signal was invariably induced, even with low-level photolytic release of threshold amounts of InsP3. In pancreas, threshold stimulation generated an apically delimited [Ca2+]c signal, while a stronger stimulus induced a global [Ca2+]c signal which exhibited characteristics of a propagating wave. InsP3 was more effective in parotid, where [Ca2+]c signals initiated with shorter latency and exhibited a faster time-to-peak than in pancreas. The increased potency of InsP3 in parotid probably results from a four-fold higher number of InsP3 receptors as measured by radiolabelled InsP3 binding and western blot analysis. The Ca2+ sensitivity of the Cl− channels in parotid and pancreas was determined from the [Ca2+]-current relationship measured during a dynamic ‘Ca2+ ramp’ produced by the continuous, low-level photolysis of caged-Ca2+. In addition to a greater number of InsP3 receptors, the Cl− current density of parotid acinar cells was more than four-fold greater than that of pancreatic cells. Whereas activation of the current was tightly coupled to increases in Ca2+ in both cell types, local Ca2+ clearance was found to contribute substantially to the deactivation of the current in parotid. These data reveal specializations of common modules of Ca2+-release machinery and subsequent effector activation that are specifically suited to the distinct functional roles of these two related cell types.

James Sneyd

Papers

Models of the inositol trisphosphate receptor

Targeted phosphorylation of inositol 1,4,5-trisphosphate receptors selectively inhibits localized Ca2+ release and shapes oscillatory Ca2+ signals.

Traveling waves in buffered systems: applications to calcium waves

A buffering SERCA pump in models of calcium dynamics.

Cytosolic Ca2+ and Ca2+-activated Cl− current dynamics: insights from two functionally distinct mouse exocrine cells