Biomedical subjects

Zhilin Qu

Publications and source records attributed to Zhilin Qu.

At least 19 recordsLinked to original sources

PubMed2006

Inferring the cellular origin of voltage and calcium alternans from the spatial scales of phase reversal during discordant alternans.

Beat-to-beat alternation of the action potential duration (APD) in paced cardiac cells has been linked to the onset of lethal arrhythmias. Both experimental and theoretical studies have shown that alternans at the single cell level can be caused by unstable membrane voltage (V(m)) dynamics linked to steep APD-restitution, or unstable intracellular calcium (Ca) cycling linked to high sensitivity of Ca release from the sarcoplasmic reticulum on sarcoplasmic reticulum Ca load. Identifying which of these two mechanisms is the primary cause of cellular alternans, however, has remained difficult since Ca and V(m) are bidirectionally coupled. Here, we use numerical simulations of a physiologically detailed ionic model to show that the origin of alternans can be inferred by measuring the length scales over which APD and Ca(i) alternans reverse phase during spatially discordant alternans. The main conclusion is that these scales are comparable to a few millimeters and equal when alternans is driven by APD restitution, but differ markedly when alternans is driven predominantly by unstable Ca cycling. In the latter case, APD alternans still reverses phase on a millimeter tissue scale due to electrotonic coupling, while Ca alternans reverses phase on a submillimeter cellular scale. These results show that experimentally accessible measurements of Ca(i) and V(m) in cardiac tissue can be used to shed light on the cellular origin of alternans.

Action Potentials↗

PubMed2006

Dynamic origin of spatially discordant alternans in cardiac tissue.

Alternans, a condition in which there is a beat-to-beat alternation in the electromechanical response of a periodically stimulated cardiac cell, has been linked to the genesis of life-threatening ventricular arrhythmias. Optical mapping of membrane voltage (V(m)) and intracellular calcium (Ca(i)) on the surface of animal hearts reveals complex spatial patterns of alternans. In particular, spatially discordant alternans has been observed in which regions with a large-small-large action potential duration (APD) alternate out-of-phase adjacent to regions of small-large-small APD. However, the underlying mechanisms that lead to the initiation of discordant alternans and govern its spatiotemporal properties are not well understood. Using mathematical modeling, we show that dynamic changes in the spatial distribution of discordant alternans can be used to pinpoint the underlying mechanisms. Optical mapping of V(m) and Ca(i) in paced rabbit hearts revealed that spatially discordant alternans induced by rapid pacing exhibits properties consistent with a purely dynamical mechanism as shown in theoretical studies. Our results support the viewpoint that spatially discordant alternans in the heart can be formed via a dynamical pattern formation process which does not require tissue heterogeneity.

Action Potentials↗

PubMed2006

Systems biology approaches to metabolic and cardiovascular disorders: network perspectives of cardiovascular metabolism.

In this review, we examine cardiovascular metabolism from three different, but highly complementary, perspectives. First, from the abstract perspective of a metabolite network, composed of nodes and links. We present fundamental concepts in network theory, including emergence, to illustrate how nature has designed metabolism with a hierarchal modular scale-free topology to provide a robust system of energy delivery. Second, from the physical perspective of a modular spatially compartmentalized network. We review evidence that cardiovascular metabolism is functionally compartmentalized, such that oxidative phosphorylation, glycolysis, and glycogenolysis preferentially channel ATP to ATPases in different cellular compartments, using creatine kinase and adenylate kinase to maximize efficient energy delivery. Third, from the dynamics perspective, as a network of dynamically interactive metabolic modules capable of self-oscillation. Whereas normally, cardiac metabolism exists in a regime in which excitation-metabolism coupling closely matches energy supply and demand, we describe how under stressful conditions, the network can be pushed into a qualitatively new dynamic regime, manifested as cell-wide oscillations in ATP levels, in which the coordination between energy supply and demand is lost. We speculate how this state of "metabolic fibrillation" leads to cell death if not corrected and discuss the implications for cardioprotection.

Animals↗

PubMed2006

Spatially discordant alternans in cardiac tissue: role of calcium cycling.

Spatially discordant alternans, where the action potential duration (APD) and intracellular calcium transient (Ca(i)) alternate with opposite phase in different regions of tissue, is known to promote wave break and reentry. However, this phenomenon is not completely understood. It is known that alternans at the cellular level can be caused by dynamical instabilities arising from either membrane voltage (V(m)) attributable to steep APD restitution or to calcium (Ca) cycling. Here, we used a mathematical model of intracellular Ca cycling, coupled with membrane ion currents, to investigate the dynamics of V(m) and Ca(i) transient alternans in an isolated cell, in two electrotonically coupled cells, and in 1D spatially homogeneous tissue. Our main finding is a novel instability mechanism in which the bidirectional coupling of V(m) and Ca(i) can drive the Ca(i) transient of two neighboring cells to be out of phase. This instability is manifested in cardiac tissue by the dynamical formation of spatially discordant alternans. In this case, Ca(i) transient alternans can reverse phase over a length scale of one cell, whereas APD alternans reverses phase over a much longer length scale set by the electrotonic coupling. We analyze this mechanism in detail and show that it is a robust consequence of experimentally established properties of the bidirectional coupling between Ca cycling and V(m) dynamics. Finally, we address the experimental relevance of these findings and suggest physiological conditions under which these patterns can be observed.

Arrhythmias, Cardiac↗

PubMed2006

Short-term cardiac memory and mother rotor fibrillation.

Short-term cardiac memory refers to the effects of pacing history on action potential duration (APD). Although the ionic mechanisms for short-term memory occurring over many heartbeats (also called APD accommodation) are poorly understood, they may have important effects on reentry and fibrillation. To explore this issue, we incorporated a generic memory current into the Phase I Luo and Rudy action potential model, which lacks short-term memory. The properties of this current were matched to simulate quantitatively human ventricular monophasic action potential accommodation. We show that, theoretically, short-term memory can resolve the paradox of how mother rotor fibrillation is initiated in heterogeneous tissue by physiological pacing. In simulated heterogeneous two-dimensional tissue and three-dimensional ventricles containing an inward rectifier K(+) current gradient, short-term memory could spontaneously convert multiple wavelet fibrillation to mother rotor fibrillation or to a mixture of both fibrillation types. This was due to progressive acceleration and stabilization of rotors as accumulation of memory shortened APD and flattened APD restitution slope nonuniformly throughout the tissue.

Action Potentials↗

PubMed2006

Dynamics and cardiac arrhythmias.

Cardiac arrhythmias, characterized by single or multiple reentrant circuits, represent a dynamic phenomenon in an excitable medium. In this review, we provide a brief overview of how cardiac action potential duration restitution, conduction velocity restitution, and intracellular calcium cycling regulate the dynamics of action potential excitation and wave propagation in relation to the genesis and maintenance of cardiac arrhythmias.

Action Potentials↗

PubMed2006

From pulsus to pulseless: the saga of cardiac alternans.

Computer simulations and nonlinear dynamics have provided invaluable tools for illuminating the underlying mechanisms of cardiac arrhythmias. Here, we review how this approach has led to major insights into the mechanisms of spatially discordant alternans, a key arrhythmogenic factor predisposing the heart to re-entry and lethal arrhythmias. During spatially discordant alternans, the action potential duration (APD) alternates out of phase in different regions of the heart, markedly enhancing dispersion of refractoriness so that ectopic beats have a high probability of inducing reentry. We show how, at the cellular level, instabilities in membrane voltage (ie, steep APD restitution slope) and intracellular Ca (Cai) cycling dynamics cause APD and the Cai transient to alternate and how the characteristics of alternans are affected by different "modes" of the bidirectional coupling between voltage and Cai. We illustrate how, at the tissue level, additional factors, such as conduction velocity restitution and ectopic beats, promote spatially discordant alternans. These insights have illuminated the mechanistic basis underlying the clinical association of cardiac alternans (eg, T wave alternans) with arrhythmia risk, which may lead to novel therapeutic approaches to avert sudden cardiac death.

Animals↗

PubMed2006

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 1: single extrasystoles.

Spatial dispersion of refractoriness, which is amplified by genetic diseases, drugs, and electrical and structural remodeling during heart disease, is recognized as a major factor increasing the risk of lethal arrhythmias and sudden cardiac death. Dispersion forms the substrate for unidirectional conduction block, which is required for the initiation of reentry by extrasystoles or rapid pacing. In this study, we examine theoretically and numerically how preexisting gradients in refractoriness control the vulnerable window for unidirectional conduction block by a single premature extrasystole. Using a kinematic model to represent wavefront-waveback interactions, we first analytically derived the relationship (under simplified conditions) between the vulnerable window and various electrophysiological parameters such as action potential duration gradients, refractoriness barriers, conduction velocity restitution, etc. We then compared these findings to numerical simulations using the kinematic model or the Luo-Rudy action potential model in a one-dimensional cable of cardiac cells. The results from all three methods agreed well. We show that a critical gradient in action potential duration for conduction block can be analytically derived, and once this critical gradient is exceeded, the vulnerable window increases proportionately with the refractory barrier and is modulated by conduction velocity restitution and gap junctional conductance. Moreover, the critical gradient for conduction block is higher for an extrasystole traveling in the opposite direction from the sinus beat than for one traveling in the same direction (e.g., an epicardial extrasystole versus an endocardial extrasystole).

Biomechanical Phenomena↗

PubMed2006

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles.

Unidirectional conduction block of premature extrasystoles can lead to initiation of cardiac reentry, causing lethal arrhythmias including ventricular fibrillation. Multiple extrasystoles are often more effective at inducing unidirectional conduction block and reentry than a single extrasystole. Since the substrate for conduction block is spatial dispersion of refractoriness, in this study we investigate how the first extrasystole modulates this dispersion to influence the "vulnerable window" for conduction block by subsequent extrasystoles, particularly in relation to action potential duration restitution and conduction velocity restitution properties. Using a kinematic model to represent wavefront-waveback interactions and simulations with the Luo-Rudy model in a one-dimensional cable of cardiac cells, we show that in homogeneous tissue, a premature extrasystole can create a large dispersion of refractoriness leading to conduction block of a subsequent extrasystole. In heterogeneous tissue, however, a premature extrasystole can either reduce or enhance the dispersion of refractoriness depending on its propagation direction with respect to the previous beat. With multiple extrasystoles at random coupling intervals, vulnerability to conduction block is proportional to their number. In general, steep action potential duration restitution and broad conduction velocity restitution promote dispersion of refractoriness in response to multiple extrasystoles, and thus enhance vulnerability to conduction block. These restitution properties also promote spatially discordant alternans, a setting which is particularly prone to conduction block. The equivalent dispersion of refractoriness created dynamically in homogeneous tissue by spatially discordant alternans is more likely to cause conduction block than a comparable degree of preexisting dispersion in heterogeneous tissue.

Action Potentials↗

PubMed2006

Linking cell division to cell growth in a spatiotemporal model of the cell cycle.

Cell division must be tightly coupled to cell growth in order to maintain cell size, yet the mechanisms linking these two processes are unclear. It is known that almost all proteins involved in cell division shuttle between cytoplasm and nucleus during the cell cycle; however, the implications of this process for cell cycle dynamics and its coupling to cell growth remains to be elucidated. We developed mathematical models of the cell cycle which incorporate protein translocation between cytoplasm and nucleus. We show that protein translocation between cytoplasm and nucleus not only modulates temporal cell cycle dynamics, but also provides a natural mechanism coupling cell division to cell growth. This coupling is mediated by the effect of cytoplasmic-to-nuclear size ratio on the activation threshold of critical cell cycle proteins, leading to the size-sensing checkpoint (sizer) and the size-independent clock (timer) observed in many cell cycle experiments.

Animals↗

PubMed2006

Nonlinear dynamics of paced cardiac cells.

When a cardiac cell is rapidly paced it can exhibit a beat-to-beat alternation in the action potential duration (APD) and the intracellular calcium transient. This dynamical instability at the cellular level has been shown to correlate with the genesis of cardiac arrhythmias and has motivated the application of nonlinear dynamics in cardiology. In this article, we review mathematical approaches to describe the underlying mechanisms for alternans using beat-to-beat iterated maps. We explain the development and properties of these maps, and show that they provide a fruitful framework to understand dynamical instabilities of voltage and calcium in paced cardiac cells.

Action Potentials↗

PubMed2005

The dynamics of cardiac fibrillation.

Reentry occurs when the electrical wave propagating through the atria or ventricles breaks locally and forms a rotor (also called a scroll wave or functional reentry). If the waves propagating outward from a rotor develop additional wavebreaks (which may form new rotors), fibrillation results. Tissue heterogeneity, exacerbated by electrical and structural remodeling from cardiac disease, has traditionally been considered the major factor promoting wavebreak and its degeneration to fibrillation. Recently, however, dynamic factors have also been recognized to play a key role. Dynamic factors refer to cellular properties of the cardiac action potential and Ca(i) cycling, which dynamically generate wave instability and wavebreak, even in tissue that is initially completely homogeneous. Although the latter situation can only be created in computer simulations, its relevance to real (heterogeneous) cardiac tissue has been unequivocally demonstrated. Dynamic factors are related to membrane voltage (Vm) and Ca(i). Vm factors include electrical restitution of action potential duration and conduction velocity, short-term cardiac memory, and electrotonic currents. Ca(i) factors are related to dynamic Ca(i) cycling properties. They act synergistically, as well as with tissue heterogeneity, to promote wavebreak and fibrillation. As global properties, rather than local electrophysiological characteristics, dynamic factors represent an attractive target for novel therapies to prevent ventricular fibrillation.

Action Potentials↗

PubMed2005

Critical mass hypothesis revisited: role of dynamical wave stability in spontaneous termination of cardiac fibrillation.

The tendency of atrial or ventricular fibrillation to terminate spontaneously in finite-sized tissue is known as the critical mass hypothesis. Previous studies have shown that dynamical instabilities play an important role in creating new wave breaks that maintain cardiac fibrillation, but its role in self-termination, in relation to tissue size and geometry, is not well understood. This study used computer simulations of two- and three-dimensional tissue models to investigate qualitatively how, in relation to tissue size and geometry, dynamical instability affects the spontaneous termination of cardiac fibrillation. The major findings are as follows: 1) Dynamical instability promotes wave breaks, maintaining fibrillation, but it also causes the waves to extinguish, facilitating spontaneous termination of fibrillation. The latter effect predominates as dynamical instability increases, so that fibrillation is more likely to self-terminate in a finite-sized tissue. 2) In two-dimensional tissue, the average duration of fibrillation increases exponentially as tissue area increases. In three-dimensional tissue, the average duration of fibrillation decreases initially as tissue thickness increases as a result of thickness-induced instability but then increases after a critical thickness is reached. Therefore, in addition to tissue mass and geometry, dynamical instability is an important factor influencing the maintenance of cardiac fibrillation.

Atrial Fibrillation↗

PubMed2005

Effects of Na(+) and K(+) channel blockade on vulnerability to and termination of fibrillation in simulated normal cardiac tissue.

Na(+) and K(+) channel-blocking drugs have anti- and proarrhythmic effects. Their effects during fibrillation, however, remain poorly understood. We used computer simulation of a two-dimensional (2-D) structurally normal tissue model with phase I of the Luo-Rudy action potential model to study the effects of Na(+) and K(+) channel blockade on vulnerability to and termination of reentry in simulated multiple-wavelet and mother rotor fibrillation. Our main findings are as follows: 1) Na(+) channel blockade decreased, whereas K(+) channel blockade increased, the vulnerable window of reentry in heterogeneous 2-D tissue because of opposing effects on dynamical wave instability. 2) Na(+) channel blockade increased the cycle length of reentry more than it increased refractoriness. In multiple-wavelet fibrillation, Na(+) channel blockade first increased and then decreased the average duration or transient time ( ) of fibrillation. In mother rotor fibrillation, Na(+) channel blockade caused peripheral fibrillatory conduction block to resolve and the mother rotor to drift, leading to self-termination or sustained tachycardia. 3) K(+) channel blockade increased dynamical instability by steepening action potential duration restitution. In multiple-wavelet fibrillation, this effect shortened because of enhanced wave instability. In mother rotor fibrillation, this effect converted mother rotor fibrillation to multiple-wavelet fibrillation, which then could self-terminate. Our findings help illuminate, from a theoretical perspective, the possible underlying mechanisms of termination of different types of fibrillation by antiarrhythmic drugs.

Anti-Arrhythmia Agents↗

PubMed2005

Chronic nicotine in hearts with healed ventricular myocardial infarction promotes atrial flutter that resembles typical human atrial flutter.

The potential of chronic nicotine exposure for atrial fibrillation (AF) and atrial flutter (AFL) in hearts with and without chronic myocardial infarction (MI) remains poorly explored. MI was created in dogs by permanent occlusion of the left anterior descending coronary artery, and dogs were administered nicotine (5 mg.kg(-1).day(-1) sc) for 1 mo using osmotic minipumps. High-resolution epicardial (1,792 bipolar electrodes) and endocardial Halo catheters were used to map activation during induced atrial rhythms. Nicotine promoted inducible sustained AFL at a mean cycle length of 134 +/- 10 ms in all MI dogs (n = 6) requiring pacing and electrical shocks for termination. No AFL could be induced in MI dogs (n = 6), control (non-MI) dogs (n = 3) not exposed to nicotine, and dogs with no MI and exposed to nicotine (n = 3). Activation maps during AFL showed a single reentrant wavefront in the right atrium that rotated either clockwise (60%) or counterclockwise (40%) around the crista terminalis and through the isthmus. Ablation of the isthmus prevented the induction of AFL. Nicotine caused a significant (P < 0.01) but highly heterogeneous increase in atrial interstitial fibrosis (2- to 10-fold increase in left and right atria, respectively) in the MI group but only a 2-fold increase in the right atrium in the non-MI group. Nicotine also flattened (P < 0.05) the slope of the epicardial monophasic action potential duration (electrical restitution) curve of both atria in the MI but not in non-MI dogs. Two-dimensional simulation in an excitable matrix containing an isthmus and nicotine's restitutional and reduced gap junctional coupling (fibrosis) parameters replicated the experiments. Chronic nicotine in hearts with MI promotes AFL that closely resembles typical human AFL. Increased atrial interstitial fibrosis and flattened electrical restitution are important substrates for the AFL.

Animals↗

PubMed2004

Hysteresis and cell cycle transitions: how crucial is it?

Recently, experiments have shown that cyclin-dependent kinase (CDK) activity exhibits hysteresis in its response to total cyclin when cyclin is made nondegradable and controlled externally. This observation was taken to support mathematical modeling predictions regarding the underlying dynamics of the cell cycle. However, cell cycle dynamics can also be generated by other nonhysteretic mechanisms. To examine the robustness of the hysteretic response of CDK activity to total cyclin, we simulated various cell cycle signal transduction networks, and correlated the dynamics to the response function of CDK activity versus total cyclin. By randomly searching the parameter space, we assessed robustness by estimating the frequency of hysteretic versus nonhysteretic dynamical mechanisms. When the dynamical instabilities were caused by feedback loops in CDK phosphorylation and dephosphorylation or by feedback between cyclin and the CDK inhibitor, the response function of CDK activity versus total cyclin correlated well with the dynamical instabilities. However, when the dynamical instabilities originated from feedback between cyclin and APC-CDH1 or RB-E2F, the response function did not correlate with dynamical instabilities. Thus, although a hysteretic response is neither necessary nor sufficient, it is in general a much more robust mechanism for generating cell cycle dynamics than nonhysteretic mechanisms.

Biological Clocks↗

PubMed2004

Mother rotors and the mechanisms of D600-induced type 2 ventricular fibrillation.

BACKGROUND: Two types of ventricular fibrillation (VF) have been demonstrated in isolated rabbit hearts during D600 infusion. Type 1 VF is characterized by the presence of multiple, wandering wavelets, whereas type 2 VF shows local spatiotemporal periodicity. We hypothesized that a single mother rotor underlies type 2 VF. METHODS AND RESULTS: One (protocol I) or 2 (protocol II) cameras were used to map the epicardial ventricular activations in Langendorff-perfused rabbit hearts. Multiple episodes of type 2 VF were induced in 22 hearts by high-concentration (> or =2.5 mg/L) D600 (protocol I). During type 2 VF, a single spiral wave (n=19) and/or an epicardial breakthrough pattern (n=11) was present in 14 hearts. These spiral waves either slowly drifted or intermittently anchored on the papillary muscle (PM) of the left ventricle. Dominant-frequency (DF) analyses showed that the highest local DF was near the PM (12.5+/-1.1 Hz). There was an excellent correlation between the highest local DF of these spiral waves and breakthroughs (11.8+/-1.7 Hz) and the DF of simultaneously obtained global pseudo-ECG (11.2+/-1.8 Hz, r=0.97, P<0.0001) during type 2 VF. We also successfully reproduced the major features of type 2 VF by using the Luo-Rudy action-potential model in a simulated, 3-dimensional tissue slab, under conditions of reduced excitability and flat action-potential duration restitution. CONCLUSIONS: Either a stationary or a slowly drifting mother rotor can result in type 2 VF. Colocalization of the stationary mother rotors with the PM suggests the importance of underlying anatomic structures in mother rotor formation.

Action Potentials↗

PubMed2004

Coordination of cell growth and cell division: a mathematical modeling study.

Although there is general agreement that cell growth and division are functionally coordinated, the mechanisms that link the two processes are poorly understood. In this study, we have developed a mathematical model based on current biological concepts of the signaling transduction pathways involved in cell growth, which predicts that cell growth rate is proportional to cell surface area at birth. To investigate the relationship between growth control and cell division, we then applied our mathematical model to three classic experiments measuring cycle time versus cell birth size in fission yeast and Xenopus laevis, and the cell cycle delay in mammalian cells after serum withdrawal. When coupled to a cell cycle exhibiting 'sizer' and 'timer' phases, we show that a simple model in which growth rate is proportional to the cell surface area immediately after division reproduces the experimental observations including the relationship between cycle time and birth size in fission yeast and Xenopus laevis. The model also accounts for the cell cycle delay seen in restriction point experiments performed in HeLa cells.

Animals↗