The p53 tumour-suppressor gene integrates numerous signals that control cell life and death. As when a highly connected node in the Internet breaks down, the disruption of p53 has severe consequences.

Surfing the p53 network

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

This book is the second of two volumes in a series on terrestrial and marine comparisons, focusing on the temporal complement of the earlier spatial analysis of patchiness and pattern (Levin et al. 1993). The issue of the relationships among pattern, scale, and patchiness has been framed forcefully in John Steele’s writings of two decades (e.g., Steele 1978). There is no pattern without an observational frame. In the words of Nietzsche, “There are no facts… only interpretations.”

https://esajournals.onlinelibrary.wiley.com/doi/pdf/10.2307/1941447

The Problem of Pattern and Scale in Ecology: The Robert H. MacArthur Award Lecture

▪ Abstract Synaptic transmission is a dynamic process. Postsynaptic responses wax and wane as presynaptic activity evolves. This prominent characteristic of chemical synaptic transmission is a crucial determinant of the response properties of synapses and, in turn, of the stimulus properties selected by neural networks and of the patterns of activity generated by those networks. This review focuses on synaptic changes that result from prior activity in the synapse under study, and is restricted to short-term effects that last for at most a few minutes. Forms of synaptic enhancement, such as facilitation, augmentation, and post-tetanic potentiation, are usually attributed to effects of a residual elevation in presynaptic [Ca2+]i, acting on one or more molecular targets that appear to be distinct from the secretory trigger responsible for fast exocytosis and phasic release of transmitter to single action potentials. We discuss the evidence for this hypothesis, and the origins of the different kinetic phases...

/pdf/short-term-synaptic-plasticity-5d4dx79319.pdf

Short-Term Synaptic Plasticity

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)

https://jxshix.people.wm.edu/2013-taiwan/Keller-Segel-1970-JTB.pdf

Initiation of slime mold aggregation viewed as an instability.

https://jxshix.people.wm.edu/2013-taiwan/Keller-Segel-1971-JTB.pdf

Model for Chemotaxis

https://jxshix.people.wm.edu/2013-taiwan/Keller-Segel-1971-JTB-2.pdf

Traveling bands of chemotactic bacteria: a theoretical analysis.

Dissipative structure: an explanation and an ecological example.

The intracellular activity of the p53 tumor suppressor protein is regulated through a feedback loop involving its transcriptional target, mdm2. We present a simple mathematical model suggesting that, under certain circumstances, oscillations in p53 and Mdm2 protein levels can emerge in response to a stress signal. A delay in p53-dependent induction of Mdm2 is predicted to be required, albeit not sufficient, for this oscillatory behavior. In line with the predictions of the model, oscillations of both p53 and Mdm2 indeed occur on exposure of various cell types to ionizing radiation. Such oscillations may allow cells to repair their DNA without risking the irreversible consequences of continuous excessive p53 activation.

https://www.pnas.org/content/pnas/97/21/11250.full.pdf

Lee A. Segel

Papers

Initiation of slime mold aggregation viewed as an instability.

Model for Chemotaxis

Traveling bands of chemotactic bacteria: a theoretical analysis.

Dissipative structure: an explanation and an ecological example.

Generation of oscillations by the p53-Mdm2 feedback loop: A theoretical and experimental study