Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications

In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral pattern, or retract causing the wave to vanish at boundaries. An asymptotic analysis of spiral motion and retraction is carried out in this weakly excitable large core regime starting from the free-boundary limit of the reaction-diffusion models, valid when the excited region is delimited by a thin interface. The wave description is shown to naturally split between the tip region and a far region that are smoothly matched on an intermediate scale. This separation allows us to rigorously derive an equation of motion for the wave tip, with the large scale motion of the spiral wavefront slaved to the tip. This kinematic description provides both a physical picture and exact predictions for a wide range of wave behavior, including: (i) steady rotation (frequency and core radius), (ii) exact treatment of the meandering instability in the free-boundary limit with the prediction that the frequency of unstable motion is half the primary steady frequency (iii) drift under external actions (external field with application to axisymmetric scroll ring motion in three-dimensions, and spatial or/and time-dependent variation of excitability), and (iv) the dynamics of multi-armed spiral waves with the new prediction that steadily rotating waves with two or more arms are linearly unstable. Numerical simulations of FitzHug-Nagumo kinetics are used to test several aspects of our results. In addition, we discuss the semi-quantitative extension of this theory to finite cores and pinpoint mathematical subtleties related to the thin interface limit of singly diffusive reaction-diffusion models

The commodification of human reproductive materials.

This essay develops a framework for thinking about the moral basis for the commnodification of human reproductive nmaterials. It argues that selling and buyinlg gametes and genes is morally acceptable although there should not be a market for zygotes, embryos, or genomes. Also a market in gametes and genes shouild be regutlated in order to address concerns about the adverse social consequences of conmmodification. Originally published Journal of Medical Ethics, Vol. 24, No. 6, Dec 199

Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.Comment: 9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Competing Patterns of Signaling Activity in Dictyostelium discoideum

Quantitative experiments are described on spatio-temporal patterns of coherent chemical signaling activity in populations of {\it Dictyostelium discoideum} amoebae. We observe competition between spontaneously firing centers and rotating spiral waves that depends strongly on the overall cell density. At low densities, no complete spirals appear and chemotactic aggregation is driven by periodic concentric waves, whereas at high densities the firing centers seen at early times nucleate and are apparently entrained by spiral waves whose cores ultimately serve as aggregation centers. Possible mechanisms for these observations are discussed.Comment: 10 pages, RevTeX, 4 ps figures, accepted in PR

Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems

This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schl\"{o}gl and FitzHugh-Nagumo model are discussed using three different approaches. First, an analytical solution is proposed. Second, the standard optimal control procedure is applied. The third approach extends standard optimal control to so-called sparse optimal control that results in very localized control signals and allows the analysis of second order optimality conditions.Comment: 22 pages, 3 figures, 2 table

Engendering harm: a critique of sex selection for 'family balancing'

The most benign rationale for sex-selection is deemed to be “family balancing.” On this view, provided the sex-distribution of an existing offspring group is “unbalanced,” one may legitimately use reproductive technologies to select the sex of the next child. I present four novel concerns with granting “family balancing” as a justification for sex-selection: (a) families or family subsets should not be subject to medicalization; (b) sex selection for “family balancing” entrenches heteronormativity, inflicting harm in at least three specific ways; (c) the logic of affirmative action is appropriated; (d) the moral mandate of reproductive autonomy is misused. I conclude that the harms caused by “family balancing” are sufficiently substantive to over-ride any claim arising from a supposed right to sex selection as an instantiation of procreative autonomy

Electroosmotic flow reversal outside glass nanopores.

We report observations of a striking reversal in the direction of electroosmotic flow (EOF) outside a conical glass nanopore as a function of salt concentration. At high ionic strengths (>100 mM), we observe EOF in the expected direction as predicted by classical electrokinetic theory, while at low salt concentrations (<1 mM) the direction of the flow is reversed. The critical crossover salt concentration depends on the pore diameter. Finite-element simulations indicate a competition between the EOF generated from the inner and outer walls of the pore, which drives flows in opposite directions. We have developed a simple analytical model which reveals that, as the salt concentration is reduced, the flow rates inside the pore are geometrically constrained, whereas there is no such limit for flows outside the pore. This model captures all of the essential physics of the system and explains the observed data, highlighting the key role the external environment plays in determining the overall electroosmotic behavior

Transverse electric field dragging of DNA in a nanochannel

Nanopore analysis is an emerging single-molecule strategy for non-optical and high-throughput DNA sequencing, the principle of which is based on identification of each constituent nucleobase by measuring trans-membrane ionic current blockade or transverse tunnelling current as it moves through the pore. A crucial issue for nanopore sequencing is the fact that DNA translocates a nanopore too fast for addressing sequence with a single base resolution. Here we report that a transverse electric field can be used to slow down the translocation. We find 400-fold decrease in the DNA translocation speed by adding a transverse field of 10 mV/nm in a gold-electrode-embedded silicon dioxide channel. The retarded flow allowed us to map the local folding pattern in individual DNA from trans-pore ionic current profiles. This field dragging approach may provide a new way to control the polynucleotide translocation kinetics

Human cloning laws, human dignity and the poverty of the policy making dialogue

BACKGROUND: The regulation of human cloning continues to be a significant national and international policy issue. Despite years of intense academic and public debate, there is little clarity as to the philosophical foundations for many of the emerging policy choices. The notion of "human dignity" is commonly used to justify cloning laws. The basis for this justification is that reproductive human cloning necessarily infringes notions of human dignity. DISCUSSION: The author critiques one of the most commonly used ethical justifications for cloning laws – the idea that reproductive cloning necessarily infringes notions of human dignity. He points out that there is, in fact, little consensus on point and that the counter arguments are rarely reflected in formal policy. Rarely do domestic or international instruments provide an operational definition of human dignity and there is rarely an explanation of how, exactly, dignity is infringed in the context reproductive cloning. SUMMARY: It is the author's position that the lack of thoughtful analysis of the role of human dignity hurts the broader public debate about reproductive cloning, trivializes the value of human dignity as a normative principle and makes it nearly impossible to critique the actual justifications behind many of the proposed policies