Are physiological oscillations physiological?

Despite widespread and striking examples of physiological oscillations, their functional role is often unclear. Even glycolysis, the paradigm example of oscillatory biochemistry, has seen questions about its oscillatory function. Here, we take a systems approach to argue that oscillations play critical physiological roles, such as enabling systems to avoid desensitization, to avoid chronically high and therefore toxic levels of chemicals, and to become more resistant to noise. Oscillation also enables complex physiological systems to reconcile incompatible conditions such as oxidation and reduction, by cycling between them, and to synchronize the oscillations of many small units into one large effect. In pancreatic ß-cells, glycolytic oscillations synchronize with calcium and mitochondrial oscillations to drive pulsatile insulin release, critical for liver regulation of glucose. In addition, oscillation can keep biological time, essential for embryonic development in promoting cell diversity and pattern formation. The functional importance of oscillatory processes requires a re-thinking of the traditional doctrine of homeostasis, holding that physiological quantities are maintained at constant equilibrium values, a view that has largely failed in the clinic. A more dynamic approach will initiate a paradigm shift in our view of health and disease. A deeper look into the mechanisms that create, sustain and abolish oscillatory processes requires the language of nonlinear dynamics, well beyond the linearization techniques of equilibrium control theory. Nonlinear dynamics enables us to identify oscillatory ('pacemaking') mechanisms at the cellular, tissue and system levels.

Shaping Waves of Bone Morphogenetic Protein Inhibition During Vascular Growth.

RATIONALE: The BMPs (bone morphogenetic proteins) are essential morphogens in angiogenesis and vascular development. Disruption of BMP signaling can trigger cardiovascular diseases, such as arteriovenous malformations. OBJECTIVE: A computational model predicted that BMP4 and BMP9 and their inhibitors MGP (matrix gamma-carboxyglutamic acid [Gla] protein) and CV2 (crossveinless-2) would form a regulatory system consisting of negative feedback loops with time delays and that BMP9 would trigger oscillatory expression of the 2 inhibitors. The goal was to investigate this regulatory system in endothelial differentiation and vascular growth. METHODS AND RESULTS: Oscillations in the expression of MGP and CV2 were detected in endothelial cells in vitro, using quantitative real-time polymerase chain reaction and immunoblotting. These organized temporally downstream BMP-related activities, including expression of stalk-cell markers and cell proliferation, consistent with an integral role of BMP9 in vessel maturation. In vivo, the inhibitors were located in distinct zones in relation to the front of the expanding retinal network, as determined by immunofluorescence. Time-dependent changes of the CV2 location in the retina and the existence of an endothelial population with signs of oscillatory MGP expression in developing vasculature supported the in vitro findings. Loss of MGP or its BMP4-binding capacity disrupted the retinal vasculature, resulting in poorly formed networks, especially in the venous drainage areas, and arteriovenous malformations as determined by increased cell coverage and functional testing. CONCLUSIONS: Our results suggest a previously unknown mechanism of temporal orchestration of BMP4 and BMP9 activities that utilize the tandem actions of the extracellular antagonists MGP and CV2. Disruption of this mechanism may contribute to vascular malformations and disease.

Teaching Dynamics to Biology Undergraduates: the UCLA Experience.

There is a growing realization that traditional "Calculus for Life Sciences" courses do not show their applicability to the Life Sciences and discourage student interest. There have been calls from the AAAS, the Howard Hughes Medical Institute, the NSF, and the American Association of Medical Colleges for a new kind of math course for biology students, that would focus on dynamics and modeling, to understand positive and negative feedback relations, in the context of important biological applications, not incidental "examples." We designed a new course, LS 30, based on the idea of modeling biological relations as dynamical systems, and then visualizing the dynamical system as a vector field, assigning "change vectors" to every point in a state space. The resulting course, now being given to approximately 1400 students/year at UCLA, has greatly improved student perceptions toward math in biology, reduced minority performance gaps, and increased students' subsequent grades in physics and chemistry courses. This new course can be customized easily for a broad range of institutions. All course materials, including lecture plans, labs, homeworks and exams, are available from the authors; supporting videos are posted online.

Redundancy and multifunctionality among spinal locomotor networks.

c-Fos is used to identify system-wide neural activation with cellular resolution in vivo. However, c-Fos can only capture neural activation of one event. Targeted recombination in active populations (TRAP) allows the capture of two different c-Fos activation patterns in the same animal. So far, TRAP has only been used to examine brain circuits. This study uses TRAP to investigate spinal circuit activation during resting and stepping, giving novel insights of network activation during these events. The level of colabeled (c-Fos+ and TRAP+) neurons observed after performing two bouts of stepping suggests that there is a probabilistic-like phenomenon that can recruit many combinations of neural populations (synapses) when repetitively generating many step cycles. Between two 30-min bouts of stepping, each consisting of thousands of steps, only ∼20% of the neurons activated from the first bout of stepping were also activated by the second bout. We also show colabeling of interneurons that have been active during stepping and resting. The use of the FosTRAP methodology in the spinal cord provides a new tool to compare the engagement of different populations of spinal interneurons in vivo under different motor tasks or under different conditions.NEW & NOTEWORTHY The results are consistent with there being an extensive amount of redundancy among spinal locomotor circuits. Using the newly developed FosTRAP mouse model, only ∼20% of neurons that were active (labeled by Fos-linked tdTomato expression) during a first bout of 30-min stepping were also labeled for c-Fos during a second bout of stepping. This finding suggests variability of neural networks that enables selection of many combinations of neurons (synapses) when generating each step cycle.

Memory-Induced Chaos in Cardiac Excitation.

Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos.

Electrophysiology of Heart Failure Using a Rabbit Model: From the Failing Myocyte to Ventricular Fibrillation.

Heart failure is a leading cause of death, yet its underlying electrophysiological (EP) mechanisms are not well understood. In this study, we use a multiscale approach to analyze a model of heart failure and connect its results to features of the electrocardiogram (ECG). The heart failure model is derived by modifying a previously validated electrophysiology model for a healthy rabbit heart. Specifically, in accordance with the heart failure literature, we modified the cell EP by changing both membrane currents and calcium handling. At the tissue level, we modeled the increased gap junction lateralization and lower conduction velocity due to downregulation of Connexin 43. At the biventricular level, we reduced the apex-to-base and transmural gradients of action potential duration (APD). The failing cell model was first validated by reproducing the longer action potential, slower and lower calcium transient, and earlier alternans characteristic of heart failure EP. Subsequently, we compared the electrical wave propagation in one dimensional cables of healthy and failing cells. The validated cell model was then used to simulate the EP of heart failure in an anatomically accurate biventricular rabbit model. As pacing cycle length decreases, both the normal and failing heart develop T-wave alternans, but only the failing heart shows QRS alternans (although moderate) at rapid pacing. Moreover, T-wave alternans is significantly more pronounced in the failing heart. At rapid pacing, APD maps show areas of conduction block in the failing heart. Finally, accelerated pacing initiated wave reentry and breakup in the failing heart. Further, the onset of VF was not observed with an upregulation of SERCA, a potential drug therapy, using the same protocol. The changes introduced at the cell and tissue level have increased the failing heart's susceptibility to dynamic instabilities and arrhythmias under rapid pacing. However, the observed increase in arrhythmogenic potential is not due to a steepening of the restitution curve (not present in our model), but rather to a novel blocking mechanism.

A Dynamical Threshold for Cardiac Delayed Afterdepolarization-Mediated Triggered Activity.

Ventricular myocytes are excitable cells whose voltage threshold for action potential (AP) excitation is ∼-60 mV at which INa is activated to give rise to a fast upstroke. Therefore, for a short stimulus pulse to elicit an AP, a stronger stimulus is needed if the resting potential lies further away from the INa threshold, such as in hypokalemia. However, for an AP elicited by a long duration stimulus or a diastolic spontaneous calcium release, we observed that the stimulus needed was lower in hypokalemia than in normokalemia in both computer simulations and experiments of rabbit ventricular myocytes. This observation provides insight into why hypokalemia promotes calcium-mediated triggered activity, despite the resting potential lying further away from the INa threshold. To understand the underlying mechanisms, we performed bifurcation analyses and demonstrated that there is a dynamical threshold, resulting from a saddle-node bifurcation mainly determined by IK1 and INCX. This threshold is close to the voltage at which IK1 is maximum, and lower than the INa threshold. After exceeding this dynamical threshold, the membrane voltage will automatically depolarize above the INa threshold due to the large negative slope of the IK1-V curve. This dynamical threshold becomes much lower in hypokalemia, especially with respect to calcium, as predicted by our theory. Because of the saddle-node bifurcation, the system can automatically depolarize even in the absence of INa to voltages higher than the ICa,L threshold, allowing for triggered APs in single myocytes with complete INa block. However, because INa is important for AP propagation in tissue, blocking INa can still suppress premature ventricular excitations in cardiac tissue caused by calcium-mediated triggered activity. This suppression is more effective in normokalemia than in hypokalemia due to the difference in dynamical thresholds.

Stochastic pacing reveals the propensity to cardiac action potential alternans and uncovers its underlying dynamics.

KEY POINTS: Beat-to-beat alternation (alternans) of the cardiac action potential duration is known to precipitate life-threatening arrhythmias and can be driven by the kinetics of voltage-gated membrane currents or by instabilities in intracellular calcium fluxes. To prevent alternans and associated arrhythmias, suitable markers must be developed to quantify the susceptibility to alternans; previous theoretical studies showed that the eigenvalue of the alternating eigenmode represents an ideal marker of alternans. Using rabbit ventricular myocytes, we show that this eigenvalue can be estimated in practice by pacing these cells at intervals varying stochastically. We also show that stochastic pacing permits the estimation of further markers distinguishing between voltage-driven and calcium-driven alternans. Our study opens the perspective to use stochastic pacing during clinical investigations and in patients with implanted pacing devices to determine the susceptibility to, and the type of alternans, which are both important to guide preventive or therapeutic measures. ABSTRACT: Alternans of the cardiac action potential (AP) duration (APD) is a well-known arrhythmogenic mechanism. APD depends on several preceding diastolic intervals (DIs) and APDs, which complicates the prediction of alternans. Previous theoretical studies pinpointed a marker called λalt that directly quantifies how an alternating perturbation persists over successive APs. When the propensity to alternans increases, λalt decreases from 0 to -1. Our aim was to quantify λalt experimentally using stochastic pacing and to examine whether stochastic pacing allows discriminating between voltage-driven and Ca(2+) -driven alternans. APs were recorded in rabbit ventricular myocytes paced at cycle lengths (CLs) decreasing progressively and incorporating stochastic variations. Fitting APD with a function of two previous APDs and CLs permitted us to estimate λalt along with additional markers characterizing whether the dependence of APD on previous DIs or CLs is strong (typical for voltage-driven alternans) or weak (Ca(2+) -driven alternans). During the recordings, λalt gradually decreased from around 0 towards -1. Intermittent alternans appeared when λalt reached -0.8 and was followed by sustained alternans. The additional markers detected that alternans was Ca(2+) driven in control experiments and voltage driven in the presence of ryanodine. This distinction could be made even before alternans was manifest (specificity/sensitivity >80% for -0.4 > λalt  > -0.5). These observations were confirmed in a mathematical model of a rabbit ventricular myocyte. In conclusion, stochastic pacing allows the practical estimation of λalt to reveal the onset of alternans and distinguishes between voltage-driven and Ca(2+) -driven mechanisms, which is important since these two mechanisms may precipitate arrhythmias in different manners.

Perspective: a dynamics-based classification of ventricular arrhythmias.

Despite key advances in the clinical management of life-threatening ventricular arrhythmias, culminating with the development of implantable cardioverter-defibrillators and catheter ablation techniques, pharmacologic/biologic therapeutics have lagged behind. The fundamental issue is that biological targets are molecular factors. Diseases, however, represent emergent properties at the scale of the organism that result from dynamic interactions between multiple constantly changing molecular factors. For a pharmacologic/biologic therapy to be effective, it must target the dynamic processes that underlie the disease. Here we propose a classification of ventricular arrhythmias that is based on our current understanding of the dynamics occurring at the subcellular, cellular, tissue and organism scales, which cause arrhythmias by simultaneously generating arrhythmia triggers and exacerbating tissue vulnerability. The goal is to create a framework that systematically links these key dynamic factors together with fixed factors (structural and electrophysiological heterogeneity) synergistically promoting electrical dispersion and increased arrhythmia risk to molecular factors that can serve as biological targets. We classify ventricular arrhythmias into three primary dynamic categories related generally to unstable Ca cycling, reduced repolarization, and excess repolarization, respectively. The clinical syndromes, arrhythmia mechanisms, dynamic factors and what is known about their molecular counterparts are discussed. Based on this framework, we propose a computational-experimental strategy for exploring the links between molecular factors, fixed factors and dynamic factors that underlie life-threatening ventricular arrhythmias. The ultimate objective is to facilitate drug development by creating an in silico platform to evaluate and predict comprehensively how molecular interventions affect not only a single targeted arrhythmia, but all primary arrhythmia dynamics categories as well as normal cardiac excitation-contraction coupling.

Branching patterns emerge in a mathematical model of the dynamics of lung development.

Recent experimental work has described an elegant pattern of branching in the development of the lung. Multiple forms of branching have been identified, including side branching and tip bifurcation. A particularly interesting feature is the phenomenon of 'orthogonal rotation of the branching plane'. The lung must fill 3D space with the essentially 2D phenomenon of branching. It accomplishes this by rotating the branching plane by 90° with each generation. The mechanisms underlying this rotation are not understood. In general, the programmes that underlie branching have been hypothetically attributed to genetic 'subroutines' under the control of a 'global master routine' to invoke particular subroutines at the proper time and location, but the mechanisms of these routines are not known. Here, we demonstrate that fundamental mechanisms, the reaction and diffusion of biochemical morphogens, can create these patterns. We used a partial differential equation model that postulates three morphogens, which we identify with specific molecules in lung development. We found that cascades of branching events, including side branching, tip splitting and orthogonal rotation of the branching plane, all emerge immediately from the model, without further assumptions. In addition, we found that one branching mode can be easily switched to another, by increasing or decreasing the values of key parameters. This shows how a 'global master routine' could work by the alteration of a single parameter. Being able to simulate cascades of branching events is necessary to understand the critical features of branching, such as orthogonal rotation of the branching plane between successive generations, and branching mode switch during lung development. Thus, our model provides a paradigm for how genes could possibly act to produce these spatial structures. Our low-dimensional model gives a qualitative understanding of how generic physiological mechanisms can produce branching phenomena, and how the system can switch from one branching pattern to another using low-dimensional 'control knobs'. The model provides a number of testable predictions, some of which have already been observed (though not explained) in experimental work.

Nonlinear and Stochastic Dynamics in the Heart.

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Left-right symmetry breaking in tissue morphogenesis via cytoskeletal mechanics.

RATIONALE: Left-right (LR) asymmetry is ubiquitous in animal development. Cytoskeletal chirality was recently reported to specify LR asymmetry in embryogenesis, suggesting that LR asymmetry in tissue morphogenesis is coordinated by single- or multi-cell organizers. Thus, to organize LR asymmetry at multiscale levels of morphogenesis, cells with chirality must also be present in adequate numbers. However, observation of LR asymmetry is rarely reported in cultured cells. OBJECTIVES: Using cultured vascular mesenchymal cells, we tested whether LR asymmetry occurs at the single cell level and in self-organized multicellular structures. METHODS AND RESULTS: Using micropatterning, immunofluorescence revealed that adult vascular cells polarized rightward and accumulated stress fibers at an unbiased mechanical interface between adhesive and nonadhesive substrates. Green fluorescent protein transfection revealed that the cells each turned rightward at the interface, aligning into a coherent orientation at 20° relative to the interface axis at confluence. During the subsequent aggregation stage, time-lapse videomicroscopy showed that cells migrated along the same 20° angle into neighboring aggregates, resulting in a macroscale structure with LR asymmetry as parallel, diagonal stripes evenly spaced throughout the culture. Removal of substrate interface by shadow mask-plating, or inhibition of Rho kinase or nonmuscle myosin attenuated stress fiber accumulation and abrogated LR asymmetry of both single-cell polarity and multicellular coherence, suggesting that the interface triggers asymmetry via cytoskeletal mechanics. Examination of other cell types suggests that LR asymmetry is cell-type specific. CONCLUSIONS: Our results show that adult stem cells retain inherent LR asymmetry that elicits de novo macroscale tissue morphogenesis, indicating that mechanical induction is required for cellular LR specification.

Concise review: applying stem cell biology to vascular structures.

The vasculature, an organ that penetrates every other organ, is ideally poised to be the site where pools of stem cells are placed, to be deployed and committed in response to feedback regulation, and to respond to demands for new vascular structures. These pools of multipotent cells are often under the regulation of various members of the transforming growth factor-ß superfamily, including the bone morphogenetic proteins and their antagonists. Regulation of stem cell populations affects their recruitment, differentiation, spatial organization, and their coordination with host tissue. Loss and dysregulation of feedback control cause a variety of diseases that involve ectopic tissue formation, including atherosclerotic lesion formation and calcification, diabetic vasculopathies, and arteriovenous malformations.

Alternans and arrhythmias: from cell to heart.

The goal of systems biology is to relate events at the molecular level to more integrated scales from organelle to cell, tissue, and living organism. Here, we review how normal and abnormal excitation-contraction coupling properties emerge from the protein scale, where behaviors are dominated by randomness, to the cell and tissue scales, where heart has to beat with reliable regularity for a lifetime. Beginning with the fundamental unit of excitation-contraction coupling, the couplon where L-type Ca channels in the sarcolemmal membrane adjoin ryanodine receptors in the sarcoplasmic reticulum membrane, we show how a network of couplons with 3 basic properties (random activation, refractoriness, and recruitment) produces the classic physiological properties of excitation-contraction coupling and, under pathophysiological conditions, leads to Ca alternans and Ca waves. Moving to the tissue scale, we discuss how cellular Ca alternans and Ca waves promote both reentrant and focal arrhythmias in the heart. Throughout, we emphasize the qualitatively novel properties that emerge at each new scale of integration.

Dynamics of early afterdepolarization-mediated triggered activity in cardiac monolayers.

Early afterdepolarizations (EADs) are voltage oscillations that occur during the repolarizing phase of the cardiac action potential and cause cardiac arrhythmias in a variety of clinical settings. EADs occur in the setting of reduced repolarization reserve and increased inward-over-outward currents, which intuitively explains the repolarization delay but does not mechanistically explain the time-dependent voltage oscillations that are characteristic of EADs. In a recent theoretical study, we identified a dual Hopf-homoclinic bifurcation as a dynamical mechanism that causes voltage oscillations during EADs, depending on the amplitude and kinetics of the L-type Ca(2+) channel (LTCC) current relative to the repolarizing K(+) currents. Here we demonstrate this mechanism experimentally. We show that cardiac monolayers exposed to the LTCC agonists BayK8644 and isoproterenol produce EAD bursts that are suppressed by the LTCC blocker nitrendipine but not by the Na(+) current blocker tetrodoxin, depletion of intracellular Ca(2+) stores with thapsigargin and caffeine, or buffering of intracellular Ca(2+) with BAPTA-AM. These EAD bursts exhibited a key dynamical signature of the dual Hopf-homoclinic bifurcation mechanism, namely, a gradual slowing in the frequency of oscillations before burst termination. A detailed cardiac action potential model reproduced the experimental observations, and identified intracellular Na(+) accumulation as the likely mechanism for terminating EAD bursts. Our findings in cardiac monolayers provide direct support for the Hopf-homoclinic bifurcation mechanism of EAD-mediated triggered activity, and raise the possibility that this mechanism may also contribute to EAD formation in clinical settings such as long QT syndromes, heart failure, and increased sympathetic output.

Somatosensory control of balance during locomotion in decerebrated cat.

Postmammillary decerebrated cats can generate stepping on a moving treadmill belt when the brain stem or spinal cord is stimulated tonically and the hindquarters are supported both vertically and laterally. While adequate propulsion seems to be generated by the hindlimbs under these conditions, the ability to sustain equilibrium during locomotion has not been examined extensively. We found that tonic epidural spinal cord stimulation (5 Hz at L5) of decerebrated cats initiated and sustained unrestrained weight-bearing hindlimb stepping for extended periods. Detailed analyses of the relationships among hindlimb muscle EMG activity and trunk and limb kinematics and kinetics indicated that the motor circuitries in decerebrated cats actively maintain equilibrium during walking, similar to that observed in intact animals. Because of the suppression of vestibular, visual, and head-neck-trunk sensory input, balance-related adjustments relied entirely on the integration of somatosensory information arising from the moving hindquarters. In addition to dynamic balance control during unperturbed locomotion, sustained stepping could be reestablished rapidly after a collapse or stumble when the hindquarters switched from a restrained to an unrestrained condition. Deflecting the body by pulling the tail laterally induced adaptive modulations in the EMG activity, step cycle features, and left-right ground reaction forces that were sufficient to maintain lateral stability. Thus the brain stem-spinal cord circuitry of decerebrated cats in response to tonic spinal cord stimulation can control dynamic balance during locomotion using only somatosensory input.

Focal high cell density generates a gradient of patterns in self-organizing vascular mesenchymal cells.

In embryogenesis, structural patterns, such as vascular branching, may form via a reaction-diffusion mechanism in which activator and inhibitor morphogens guide cells into periodic aggregates. We previously found that vascular mesenchymal cells (VMCs) spontaneously aggregate into nodular structures and that morphogen pairs regulate the aggregation into patterns of spots and stripes. To test the effect of a focal change in activator morphogen on VMC pattern formation, we created a focal zone of high cell density by plating a second VMC layer within a cloning ring over a confluent monolayer. After 24 h, the ring was removed and pattern formation monitored by phase-contrast microscopy. At days 2-8, the patterns progressed from uniform distributions to swirl, labyrinthine and spot patterns. Within the focal high-density zone (HDZ) and a narrow halo zone, cells aggregated into spot patterns, whilst in the outermost zone of the plate, cells formed a labyrinthine pattern. The area occupied by aggregates was significantly greater in the outermost zone than in the HDZ or halo. The rate of pattern progression within the HDZ increased as a function of its plating density. Thus, focal differences in cell density may drive pattern formation gradients in tissue architecture, such as vascular branching.

Spark-induced sparks as a mechanism of intracellular calcium alternans in cardiac myocytes.

RATIONALE: Intracellular calcium (Ca) alternans has been widely studied in cardiac myocytes and tissue, yet the underlying mechanism remains controversial. OBJECTIVE: In this study, we used computational modeling and simulation to study how randomly occurring Ca sparks interact collectively to result in whole-cell Ca alternans. METHODS AND RESULTS: We developed a spatially distributed intracellular Ca cycling model in which Ca release units (CRUs) are locally coupled by Ca diffusion throughout the myoplasm and sarcoplasmic reticulum (SR) network. Ca sparks occur randomly in the CRU network when periodically paced with a clamped voltage waveform, but Ca alternans develops as the pacing speeds up. Combining computational simulation with theoretical analysis, we show that Ca alternans emerges as a collective behavior of Ca sparks, determined by 3 critical properties of the CRU network from which Ca sparks arise: "randomness" (of Ca spark activation), "refractoriness" (of a CRU after a Ca spark), and "recruitment" (Ca sparks inducing Ca sparks in adjacent CRUs). We also show that the steep nonlinear relationship between fractional SR Ca release and SR Ca load arises naturally as a collective behavior of Ca sparks, and Ca alternans can occur even when SR Ca is held constant. CONCLUSIONS: We present a general theory for the mechanisms of intracellular Ca alternans, which mechanistically links Ca sparks to whole-cell Ca alternans, and is applicable to Ca alternans in both physiological and pathophysiological conditions.

Synchronization of chaotic early afterdepolarizations in the genesis of cardiac arrhythmias.

The synchronization of coupled oscillators plays an important role in many biological systems, including the heart. In heart diseases, cardiac myocytes can exhibit abnormal electrical oscillations, such as early afterdepolarizations (EADs), which are associated with lethal arrhythmias. A key unanswered question is how cellular EADs partially synchronize in tissue, as is required for them to propagate. Here, we present evidence, from computational simulations and experiments in isolated myocytes, that irregular EAD behavior is dynamical chaos. We then show in electrically homogeneous tissue models that chaotic EADs synchronize globally when the tissue is smaller than a critical size. However, when the tissue exceeds the critical size, electrotonic coupling can no longer globally synchronize EADs, resulting in regions of partial synchronization that shift in time and space. These regional partially synchronized EADs then form premature ventricular complexes that propagate into recovered tissue without EADs. This process creates multiple premature ventricular complexes that propagate as [corrected] "shifting" foci resembling polymorphic ventricular tachycardia. Shifting foci encountering shifting repolarization gradients can also develop localized wave breaks leading to reentry and fibrillation. As predicted by the theory, rabbit hearts exposed to oxidative stress (H(2)O(2)) exhibited multiple shifting foci causing polymorphic tachycardia and fibrillation. This mechanism explains how collective cellular behavior integrates at the tissue scale to generate lethal cardiac arrhythmias over a wide range of heart rates.

A common pathway to cancer: Oncogenic mutations abolish p53 oscillations.

The tumor suppressor p53 oscillates in response to DNA double-strand breaks, a behavior that has been suggested to be essential to its anti-cancer function. Nearly all human cancers have genetic alterations in the p53 pathway; a number of these alterations have been shown to be oncogenic by experiment. These alterations include somatic mutations and copy number variations as well as germline polymorphisms. Intriguingly, they exhibit a mixed pattern of interactions in tumors, such as co-occurrence, mutual exclusivity, and paradoxically, mutual antagonism. Using a differential equation model of p53-Mdm2 dynamics, we employ Hopf bifurcation analysis to show that these alterations have a common mode of action, to abolish the oscillatory competence of p53, thereby, we suggest, impairing its tumor suppressive function. In this analysis, diverse genetic alterations, widely associated with human cancers clinically, have a unified mechanistic explanation of their role in oncogenesis.