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Biomedical subjects

Leon Glass

Publications and source records attributed to Leon Glass.

At least 19 recordsLinked to original sources
PubMed2006

The rule of bigeminy revisited: analysis in sudden cardiac death syndrome.

BACKGROUND: The rule of bigeminy is commonly explained by a reentrant mechanism. We hypothesize that in patients with prolonged ventricular repolarization, the rule of bigeminy may be caused by premature ventricular complexes (PVCs) due to early afterdepolarizations. We evaluated these ventricular arrhythmias over extended periods in patients with sudden cardiac death syndrome. METHODS: The electrocardiographic (ECG) characteristics of 15 recordings from the PhysioNet Sudden Cardiac Death Holter Database were analyzed for the persistence of bigeminy, interaction between the underlying cardiac rhythm and the coupling interval, and influence of a prolonged initiating RR cycle on the self-perpetuation of the arrhythmias. RESULTS: Eight (53%) patients had classic torsade de pointes (TdP), 5 (33%) had other polymorphic ventricular tachycardia (VT), and 2 (13%) had monomorphic VT. Group A, which comprised 6 of the patients with TdP, had the following ECG tetrad: (1) frequent ventricular bigeminy (>5% of total ventricular arrhythmias), (2) long corrected QT interval (>0.5 second), (3) relatively fixed coupling interval, and (4) onset of bigeminy (n = 4) and TdP (n = 6) after a short-long RR sequence. Patients in group A had slower heart rates (mean RR = 1.12 +/- 0.26 vs 0.77 +/- 0.13 seconds, P < .01), longer QT intervals (corrected QT = 0.57 +/- 0.06 vs 0.45 +/- 0.06 second; P < .01) and more cases with prominent U waves (83% vs 33%, P < .05) than patients in group B (n = 9), composed of patients who had other types of VT, or TdP without frequent bigeminy. CONCLUSIONS: We identified a set of ECG characteristics that supports the notion that premature ventricular complexes during self-perpetuating ventricular bigeminy ("rule of bigeminy") in long QT syndromes may be due to early afterdepolarizations.

Adult↗
PubMed2006

Reverse engineering the gap gene network of Drosophila melanogaster.

A fundamental problem in functional genomics is to determine the structure and dynamics of genetic networks based on expression data. We describe a new strategy for solving this problem and apply it to recently published data on early Drosophila melanogaster development. Our method is orders of magnitude faster than current fitting methods and allows us to fit different types of rules for expressing regulatory relationships. Specifically, we use our approach to fit models using a smooth nonlinear formalism for modeling gene regulation (gene circuits) as well as models using logical rules based on activation and repression thresholds for transcription factors. Our technique also allows us to infer regulatory relationships de novo or to test network structures suggested by the literature. We fit a series of models to test several outstanding questions about gap gene regulation, including regulation of and by hunchback and the role of autoactivation. Based on our modeling results and validation against the experimental literature, we propose a revised network structure for the gap gene system. Interestingly, some relationships in standard textbook models of gap gene regulation appear to be unnecessary for or even inconsistent with the details of gap gene expression during wild-type development.

Animals↗
PubMed2006

Sequential recruitment and combinatorial assembling of multiprotein complexes in transcriptional activation.

In human cells, estrogenic signals induce cyclical association and dissociation of specific proteins with the DNA in order to activate transcription of estrogen-responsive genes. These oscillations can be modeled by assuming a large number of sequential reactions represented by linear kinetics with random kinetic rates. Application of the model to experimental data predicts robust binding sequences in which proteins associate with the DNA at several different phases of the oscillation. Our methods circumvent the need to derive detailed kinetic graphs, and are applicable to other oscillatory biological processes involving a large number of sequential steps.

Animals↗
PubMed2006

The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue.

Electrical heterogeneities play a role in the initiation of cardiac arrhythmias. In certain pathological conditions such as ischaemia, current sinks can develop in the diseased cardiac tissue. In this study, we investigate the effects of changing the amount of heterogeneity and intercellular coupling on wavefront stability in a cardiac cell culture system and a mathematical model of excitable media. In both systems, we observe three types of behaviour: plane wave propagation without breakup, plane wave breakup into spiral waves and plane wave block. In the theoretical model, we observe a linear decrease in propagation velocity as the number of heterogeneities is increased, followed by a rapid, nonlinear decrease to zero. The linear decrease results from the heterogeneities acting independently on the wavefront. A general scaling argument that considers the degree of system heterogeneity and the properties of the excitable medium is used to derive a dimensionless parameter that describes the interaction of the wavefront with the heterogeneities.

Action Potentials↗
PubMed2006

Spiral wave dynamics in excitable media with spherical geometries.

We describe the spatial and temporal organization of spiral and scroll waves in spherical shells of different sizes and solid spheres. We present simulation results for the evolution of the dynamics and clustering of spiral waves as a function of the excitability of the medium. The excitability, topology, and size of the domain places restrictions on how single and multiarmed spiral waves are organized in space. The results in spherical geometries are compared with those in planar two-dimensional media. These studies are relevant to the dynamics of spiral waves in a variety of media including the heart, and chemical reactions on spherical surfaces.

Biophysics↗
PubMed2005

Dynamical properties of model gene networks and implications for the inverse problem.

We study the inverse problem, or the "reverse-engineering" problem, for two abstract models of gene expression dynamics, discrete-time Boolean networks and continuous-time switching networks. Formally, the inverse problem is similar for both types of networks. For each gene, its regulators and its Boolean dynamics function must be identified. However, differences in the dynamical properties of these two types of networks affect the amount of data that is necessary for solving the inverse problem. We derive estimates for the average amounts of time series data required to solve the inverse problem for randomly generated Boolean and continuous-time switching networks. We also derive a lower bound on the amount of data needed that holds for both types of networks. We find that the amount of data required is logarithmic in the number of genes for Boolean networks, matching the general lower bound and previous theory, but are superlinear in the number of genes for continuous-time switching networks. We also find that the amount of data needed scales as 2(K), where K is the number of regulators per gene, rather than 2(2K), as previous theory suggests.

Models, Genetic↗
PubMed2005

Global organization of dynamics in oscillatory heterogeneous excitable media.

An oscillatory heterogeneous excitable medium undergoes a transition from periodic target patterns to a bursting rhythm driven by the spontaneous initiation and termination of spiral waves as coupling or density is reduced. We illustrate these phenomena in monolayers of chick embryonic heart cells using calcium-sensitive fluorescent dyes. These results are modeled in a heterogeneous cellular automaton in which the neighborhood of interaction and cell density is modified. Parameters that give rise to bursting rhythms are organized in distinct zones in parameter space, leading to a global organization that should be applicable to the dynamics in a large class of excitable media.

Animals↗
PubMed2005

Effects of antiarrhythmic drug therapy on atrioventricular nodal function during atrial fibrillation in humans.

AIMS: To assess the effects of metoprolol and amiodarone on atrial and ventricular activity during atrial fibrillation (AF) in post-surgical patients, and to develop and use a mathematical model of the atrioventricular (AV) node during AF that incorporates parameters describing the properties of the AV node to evaluate the physiological basis of the drug effects. METHODS AND RESULTS: Ten post-surgical patients were evaluated where three received no medical therapy, three received metoprolol, three received amiodarone, and one received both metoprolol and amiodarone. The medications led to increases of 37-310 ms in the mean VV interval in treated patients, but much smaller changes in the mean AA intervals in the right and left atria. The mathematical model incorporating a random influence of the concealed conduction parameter was capable of reproducing the histograms of the VV intervals based on the input from the right atrium by systematically searching parameter space. CONCLUSIONS: Changes in the ventricular rate are mainly due to the alteration in the AV nodal properties rather than changes in the atrial rhythm. The medications can display differential effects on the physiological properties of the AV node, and therefore the mathematical model may help to identify novel pharmacological targets.

Aged↗
PubMed2004

Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability.

We analyze the way topological constraints and inhomogeneity in the excitability influence the dynamics of spiral waves on spheres and punctured spheres of excitable media. We generalize the definition of an index such that it characterizes not only each spiral but also each hole in punctured, oriented, compact, two-dimensional differentiable manifolds and show that the sum of the indices is conserved and zero. We also show that heterogeneity and geometry are responsible for the formation of various spiral-wave attractors, in particular pairs of spirals in which one spiral acts as a source and a second as a sink--the latter similar to an antispiral. The results provide a basis for the analysis of the propagation of waves in heterogeneous excitable media in physical and biological systems.

Journal Article↗
PubMed2004

Inferring models of gene expression dynamics.

We study the problem of identifying genetic networks in which expression dynamics are modeled by a differential equation that uses logical rules to specify time derivatives. We make three main contributions. First, we describe computationally efficient procedures for identifying the structure and dynamics of such networks from expression time series. Second, we derive predictions for the expected amount of data needed to identify randomly generated networks. Third, if expression values are available for only some of the genes, we show that the structure of the network for these "visible" genes can be identified and that the size and overall complexity of the network can be estimated. We validate these procedures and predictions using simulation experiments based on randomly generated networks with up to 30,000 genes and 17 distinct regulators per gene and on a network that models floral morphogenesis in Arabidopsis thaliana.

Arabidopsis↗
PubMed2004

Evolving complex dynamics in electronic models of genetic networks.

Ordinary differential equations are often used to model the dynamics and interactions in genetic networks. In one particularly simple class of models, the model genes control the production rates of products of other genes by a logical function, resulting in piecewise linear differential equations. In this article, we construct and analyze an electronic circuit that models this class of piecewise linear equations. This circuit combines CMOS logic and RC circuits to model the logical control of the increase and decay of protein concentrations in genetic networks. We use these electronic networks to study the evolution of limit cycle dynamics. By mutating the truth tables giving the logical functions for these networks, we evolve the networks to obtain limit cycle oscillations of desired period. We also investigate the fitness landscapes of our networks to determine the optimal mutation rate for evolution.

Biological Evolution↗
PubMed2003

Reentrant waves in a ring of embryonic chick ventricular cells imaged with a Ca2+ sensitive dye.

According to the classic model initially formulated by Mines, reentrant cardiac arrhythmias may be associated with waves circulating in a ring geometry. This study was designed to study the dynamics of reentry in a ring geometry of cardiac tissue culture. Reentrant calcium waves in rings of cultured embryonic chick cardiac myocytes were imaged using a macroscope to monitor the fluorescence of intracellular Calcium Green-1 dye. The rings displayed a variety of stable rhythms including pacemaker activity and spontaneous reentry. Waves originating from a localized pacemaker could lead to reentry as a consequence of unidirectional block. In addition, more complex patterns were observed due to the interactions between reentrant and pacemaker rhythms. These rhythms included instances in which pacemakers accelerated the reentrant rhythm, and instances in which the excitation was blocked in the vicinity of pacemakers. During reentrant activity an appropriately timed electrical stimulus could induce resetting of activity or cause complete annihilation of the propagating waves. This experimental preparation reveals many spontaneously occuring complex rhythms. These complex rhythms are hypothesized to reflect interactions between spontaneous pacemakers, wave propagation, refractory period, and overdrive suppression. This preparation may serve as a useful model system to further investigate complex dynamics arising during reentrant rhythms in cardiac tissue.

Animals↗
PubMed2003

Spontaneous initiation and termination of complex rhythms in cardiac cell culture.

INTRODUCTION: Complex cardiac arrhythmias often start and stop spontaneously. These poorly understood behaviors frequently are associated with pathologic modification of the structural heterogeneity and functional connectivity of the myocardium. To evaluate underlying mechanisms, we modify heterogeneity by varying the confluence of embryonic chick monolayer cultures that display complex bursting behaviors. A simple mathematical model was developed that reproduces the experimental behaviors and reveals possible generic mechanisms for bursting dynamics in heterogeneous excitable systems. METHODS AND RESULTS: Wave propagation was mapped in embryonic chick myocytes monolayers using calcium-sensitive dyes. Monolayer confluence was varied by plating cultures with different cell densities and by varying times in culture. At high plating densities, waves propagate without breaks, whereas monolayers plated at low densities display spirals with frequent breaks and irregular activation fronts. Monolayers at intermediate densities display bursting rhythms in which there is paroxysmal starting and stopping of spiral waves of activity. Similar spatiotemporal patterns of activity were also observed as a function of the time in culture; irregular activity dominates the first 30 hours, followed by repetitive bursting dynamics until 54 hours, after which periodic target patterns or stable spirals prevail. In some quiescent cultures derived from older embryos, it was possible to trigger pacemaker activity following a single activation. We are able to reproduce all of these behaviors by introducing spatial heterogeneity and varying neighborhood size, equivalent to cell connectivity, in a spontaneous cellular automaton model containing a rate-dependent fatigue term. CONCLUSION: We observe transitions from irregular propagating waves, to spiral waves that spontaneously start and stop, to target waves originating from localized pacemakers in cell culture and a simple theoretical model of heterogeneous excitable media. The results show how physiologic properties of spontaneous activity, heterogeneity, and fatigue can give rise to a wide range of different complex dynamic behaviors similar to clinically observed cardiac arrhythmias.

Algorithms↗