Nonlinear-dynamical arrhythmia control in humans

Nonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.

Directionality principles in thermodynamics and evolution

Directionality in populations of replicating organisms can be parametrized in terms of a statistical concept: evolutionary entropy. This parameter, a measure of the variability in the age of reproducing individuals in a population, is isometric with the macroscopic variable body size. Evolutionary trends in entropy due to mutation and natural selection fall into patterns modulated by ecological and demographic constraints, which are delineated as follows: (i) density-dependent conditions (a unidirectional increase in evolutionary entropy), and (ii) density-independent conditions, (a) slow exponential growth (an increase in entropy); (b) rapid exponential growth, low degree of iteroparity (a decrease in entropy); and (c) rapid exponential growth, high degree of iteroparity (random, nondirectional change in entropy). Directionality in aggregates of inanimate matter can be parametrized in terms of the statistical concept, thermodynamic entropy, a measure of disorder. Directional trends in entropy in aggregates of matter fall into patterns determined by the nature of the adiabatic constraints, which are characterized as follows: (i) irreversible processes (an increase in thermodynamic entropy) and (ii) reversible processes (a constant value for entropy). This article analyzes the relation between the concepts that underlie the directionality principles in evolutionary biology and physical systems. For models of cellular populations, an analytic relation is derived between generation time, the average length of the cell cycle, and temperature. This correspondence between generation time, an evolutionary parameter, and temperature, a thermodynamic variable, is exploited to show that the increase in evolutionary entropy that characterizes population processes under density-dependent conditions represents a nonequilibrium analogue of the second law of thermodynamics.

Protonation dynamics of the extracellular and cytoplasmic surface of bacteriorhodopsin in the purple membrane.

The dynamics of proton binding to the extracellular and the cytoplasmic surfaces of the purple membrane were measured by laser-induced proton pulses. Purple membranes, selectively labeled by fluorescein at Lys-129 of bacteriorhodopsin, were pulsed by protons released in the aqueous bulk from excited pyranine (8-hydroxy-1,3,6-pyrenetrisulfonate) and the reaction of protons with the indicators was measured. Kinetic analysis of the data imply that the two faces of the membrane differ in their buffer capacities and in their rates of interaction with bulk protons. The extracellular surface of the purple membrane contains one anionic proton binding site per protein molecule with pK = 5.1. This site is within a Coulomb cage radius (approximately 15 A) from Lys-129. The cytoplasmic surface of the purple membrane bears 4-5 protonable moieties (pK = 5.1) that, due to close proximity, function as a common proton binding site. The reaction of the proton with this cluster is at a very fast rate (3.10(10) M-1.s-1). The proximity between the elements is sufficiently high that even in 100 mM NaCl they still function as a cluster. Extraction of the chromophore retinal from the protein has a marked effect on the carboxylates of the cytoplasmic surface, and two to three of them assume positions that almost bar their reaction with bulk protons. The protonation dynamics determined at the surface of the purple membrane is of relevance both for the vectorial proton transport mechanism of bacteriorhodopsin and for energy coupling, not only in halobacteria, but also in complex chemiosmotic systems such as mitochondrial and thylakoid membranes.

Microfabricated structures for integrated DNA analysis.

Photolithographic micromachining of silicon is a candidate technology for the construction of high-throughput DNA analysis devices. However, the development of complex silicon microfabricated systems has been hindered in part by the lack of a simple, versatile pumping method for integrating individual components. Here we describe a surface-tension-based pump able to move discrete nanoliter drops through enclosed channels using only local heating. This thermocapillary pump can accurately mix, measure, and divide drops by simple electronic control. In addition, we have constructed thermal-cycling chambers, gel electrophoresis channels, and radiolabeled DNA detectors that are compatible with the fabrication of thermocapillary pump channels. Since all of the components are made by conventional photolithographic techniques, they can be assembled into more complex integrated systems. The combination of pump and components into self-contained miniaturized devices may provide significant improvements in DNA analysis speed, portability, and cost. The potential of microfabricated systems lies in the low unit cost of silicon-based construction and in the efficient sample handling afforded by component integration.

In vitro cloning of complex mixtures of DNA on microbeads: Physical separation of differentially expressed cDNAs

We describe a method for cloning nucleic acid molecules onto the surfaces of 5-μm microbeads rather than in biological hosts. A unique tag sequence is attached to each molecule, and the tagged library is amplified. Unique tagging of the molecules is achieved by sampling a small fraction (1%) of a very large repertoire of tag sequences. The resulting library is hybridized to microbeads that each carry ≈106 strands complementary to one of the tags. About 105 copies of each molecule are collected on each microbead. Because such clones are segregated on microbeads, they can be operated on simultaneously and then assayed separately. To demonstrate the utility of this approach, we show how to label and extract microbeads bearing clones differentially expressed between two libraries by using a fluorescence-activated cell sorter (FACS). Because no prior information about the cloned molecules is required, this process is obviously useful where sequence databases are incomplete or nonexistent. More importantly, the process also permits the isolation of clones that are expressed only in given tissues or that are differentially expressed between normal and diseased states. Such clones then may be spotted on much more cost-effective, tissue- or disease-directed, low-density planar microarrays.

Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

Ultrafast diffraction and structural dynamics: The nature of complex molecules far from equilibrium

Studies of molecular structures at or near their equilibrium configurations have long provided information on their geometry in terms of bond distances and angles. Far-from-equilibrium structures are relatively unknown—especially for complex systems—and generally, neither their dynamics nor their average geometries can be extrapolated from equilibrium values. For such nonequilibrium structures, vibrational amplitudes and bond distances play a central role in phenomena such as energy redistribution and chemical reactivity. Ultrafast electron diffraction, which was developed to study transient molecular structures, provides a direct method for probing the nature of complex molecules far from equilibrium. Here we present our ultrafast electron diffraction observations of transient structures for two cyclic hydrocarbons. At high internal energies of ≈4 eV, these molecules display markedly different behavior. For 1,3,5-cycloheptatriene, excitation results in the formation of hot ground-state structures with bond distances similar to those of the initial structure, but with nearly three times the average vibrational amplitude. Energy is redistributed within 5 ps, but with a negative temperature characterizing the nonequilibrium population. In contrast, the ring-opening reaction of 1,3-cyclohexadiene is shown to result in hot structures with a C—C bond distance of over 1.7 Å, which is 0.2 Å away from any expected equilibrium value. Even up to 400 ps, energy remains trapped in large-amplitude motions comprised of torsion and asymmetric stretching. These studies promise a new direction for studying structural dynamics in nonequilibrium complex systems.

Complex dynamics of multilocus systems subjected to cyclical selection.

Earlier we have shown that oscillations with a long period ("supercycles") may arise in two-locus systems experiencing cyclical selection with a short period. However, this mode of complex limiting behavior appeared to be possible for narrow ranges of parameters. Here we demonstrate that a multilocus system subjected to stabilizing selection with cyclically moving optimum can generate ubiquitous complex limiting behavior including supercycles, T-cycles, and chaotic-like phenomena. This mode of multilocus dynamics far exceeds the potential attainable under ordinary selection models resulting in simple behavior. It may represent a novel evolutionary mechanism increasing genetic diversity over long-term time periods.