Role of the community effect of cardiomyocyte in the entrainment and reestablishment of stable beating rhythms

To investigate the roles that the community effect and entrainment function of cultured cardiomyocyte play in decreasing beating fluctuation and reestablishing synchronized beating, we developed a single-cell-based two-dimensional network culture assay to measure and compare the dynamics of beating rhythm synchronization of individual cells before and after they form networks. Studying the formation of two-cell networks, we found that their synchronized beating tended to be determined by the cardiomyocyte whose beat rate fluctuated less than that of the other cardiomyocyte. We further found that the strength of this tendency increased with the number of cells in the network. These results indicate that (1) beating fluctuation is one of the important factors influencing the reestablishment of a stable synchronous beating rhythm, (2) the larger networks reduce fluctuation, and (3) the formation of a spatial network can itself stabilize cardiomyocyte beat rates.     

Interbeat Interval Modulation in the Sinoatrial Node as a Result of Membrane Current Stochasticity—A Theoretical and Numerical Study

A single isolated sinoatrial pacemaker cell presents intrinsic interbeat interval (IBI) variability that is believed to result from the stochastic characteristics of the opening and closing processes of membrane ion channels. To our knowledge, a novel mathematical framework was developed in this work to address the effect of current fluctuations on the IBIs of sinoatrial pacemaker cells. Using statistical modeling and employing the Fokker-Planck formalism, our mathematical analysis suggests that increased stochastic current fluctuation variance linearly increases the slope of phase-4 depolarization, hence the rate of activations. Single-cell and two-dimensional computerized numerical modeling of the sinoatrial node was conducted to validate the theoretical predictions using established ionic kinetics of the rabbit pacemaker and atrial cells. Our models also provide, to our knowledge, a novel complementary or alternative explanation to recent experimental observations showing a strong reduction in the mean IBI of Cx30 deficient mice in comparison to wild-types, not fully explicable by the effects of intercellular decoupling.     

Rigidity matching between cells and the extracellular matrix leads to the stabilization of cardiac conduction

Biomechanical dynamic interactions between cells and the extracellular environment dynamically regulate physiological tissue behavior in living organisms, such as that seen in tissue maintenance and remodeling. In this study, the substrate-induced modulation of synchronized beating in cultured cardiomyocyte tissue was systematically characterized on elasticity-tunable substrates to elucidate the effect of biomechanical coupling. We found that myocardial conduction is significantly promoted when the rigidity of the cell culture environment matches that of the cardiac cells (4 kiloPascals). The stability of spontaneous target wave activity and calcium transient alternans in high frequency-paced tissue were both enhanced when the cell substrate and cell tissue showed the same rigidity. By adapting a simple theoretical model, we reproduced the experimental trend on the rigidity matching for the synchronized excitation. We conclude that rigidity matching in cell-to-substrate interactions critically improves cardiomyocyte-tissue synchronization, suggesting that mechanical coupling plays an essential role in the dynamic activity of the beating heart.     

A novel method of cultivating cardiac myocytes in agarose microchamber chips for studying cell synchronization

We have developed a new method that enables agar microstructures to be used to cultivate cardiac myocyte cells in a manner that allows their connection patterns to be controlled. Non-contact three-dimensional photo-thermal etching with a 1064-nm infrared focused laser beam was used to form the shapes of agar microstructures. This wavelength was selected as it is not absorbed by water or agar. Identical rat cardiac myocytes were cultured in adjacent microstructures connected by microchannels and the interactions of asynchronous beating cardiac myocyte cells observed. Two isolated and independently beating cardiac myocytes were shown to form contacts through the narrow microchannels and by 90 minutes had synchronized their oscillations. This occurred by one of the two cells stopping their oscillation and following the pattern of the other cell. In contrast, when two sets of synchronized beating cells came into contact, those two sets synchronized without any observable interruptions to their rhythms. The results indicate that the synchronization process of cardiac myocytes may be dependent on the community size and network pattern of these cells.     

Fluctuations in interbeat interval in rhythmic heart-cell clusters. Role of membrane voltage noise.

Small clusters of ventricular cells prepared from 7-d chick heart maintain spontaneous, stationary, rhythmic beating in culture for many hours. For clusters containing I-125 cells, mean interbeat interval (IBI) is 0.45 +/- 0.08 s and is independent of cell number (N), whereas, the coefficient of variation of IBI (C) is proportional to N-1/2. Because membrane voltage noise in such clusters would also be expected to vary as N-1/2, we propose a model relating fluctuation in IBI (sigma IBI) to voltage noise (sigma v). A simplified model consisting of random voltage fluctuations superimposed upon a linear pacemaker depolarization of slope a is used to analyze the N-dependent shape of the IBI histogram. Values of sigma v derived from the relation sigma IBI = sigma v/a, or calculated from the skewness of the measured IBI histograms, both agree well with those extrapolated from steady-state noise recorded from resting heart-cell aggregates.     

Alternans Resonance and Propagation Block during Supernormal Conduction in Cardiac Tissue with Decreased [K]o

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K⁺]_o. In control [K⁺]_o simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.     

Improving biological indicators to better assess the condition of streams

Biological indicators of stream condition are in use by water resource managers worldwide. The State of Maryland and many other organizations that use Indices of Biotic Integrity (IBIs) must determine when and how to refine their IBIs so that better stream condition information is provided. With completion of the second statewide round in 2004, the Maryland Biological Stream Survey (MBSS) had collected data from 2500 stream sites, more than doubling the number of sites that were available for the original IBI development. This larger dataset provided an opportunity for the MBSS to address the following shortcomings in the original IBIs: (1) substantial disturbance apparent in some reference sites, (2) fish IBIs could not be applied to very small streams, (3) natural variability within IBIs (based on regions) resulted in some stream types (e.g., coldwater and blackwater streams) receiving lower IBI scores and (4) one IBI was not able to discriminate degradation as desired (i.e., Coastal Plain fish IBI). Therefore, development of new fish and benthic macroinvertebrate IBIs was undertaken to achieve the goals of: (1) increased confidence that the reference conditions are minimally disturbed, (2) including more natural variation (such as stream size) across the geographic regions and stream types of Maryland and (3) increased sensitivity of IBIs by using more classes (strata) and different metric combinations. New fish IBIs were developed for four geographical and stream type strata: Coastal Plain, Eastern Piedmont, warmwater Highlands and coldwater Highlands streams; new benthic macroinvertebrate IBIs were developed for three geographical strata: Coastal Plain, Eastern Piedmont and Highlands streams. The addition of one new fish IBI and one new benthic macroinvertebrate IBI partitioned natural variability into more homogeneous strata. At the same time, smaller streams (i.e., those draining catchments <300 ac), which constituted a greater proportion of streams (25%) sampled in Round Two (2000–2004) than Round One (1995–1997), because of the finer map scale, were included in the reference conditions used to develop the new IBIs. The resulting new IBIs have high classification efficiencies of 83–96% and are well balanced between Type I and Type II errors. By scoring coldwater streams, smaller streams and to some extent blackwater streams higher, the new IBIs improve on the original IBIs. Overall, the new IBIs provide better assessments of stream condition to support sound management decisions, without requiring substantial changes by cooperating stream assessment programs.     

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

Rhythmic bursting is the most striking behavior of cultured cortical networks and may start in the second week after plating. In this study, we focus on the intervals between spontaneously occurring bursts, and compare experimentally recorded values with model simulations. In the models, we use standard neurons and synapses, with physiologically plausible parameters taken from literature. All networks had a random recurrent architecture with sparsely connected neurons. The number of neurons varied between 500 and 5,000. We find that network models with homogeneous synaptic strengths produce asynchronous spiking or stable regular bursts. The latter, however, are in a range not seen in recordings. By increasing the synaptic strength in a (randomly chosen) subset of neurons, our simulations show interburst intervals (IBIs) that agree better with in vitro experiments. In this regime, called weakly synchronized, the models produce irregular network bursts, which are initiated by neurons with relatively stronger synapses. In some noise-driven networks, a subthreshold, deterministic, input is applied to neurons with strong synapses, to mimic pacemaker network drive. We show that models with such "intrinsically active neurons" (pacemaker-driven models) tend to generate IBIs that are determined by the frequency of the fastest pacemaker and do not resemble experimental data. Alternatively, noise-driven models yield realistic IBIs. Generally, we found that large-scale noise-driven neuronal network models required synaptic strengths with a bimodal distribution to reproduce the experimentally observed IBI range. Our results imply that the results obtained from small network models cannot simply be extrapolated to models of more realistic size. Synaptic strengths in large-scale neuronal network simulations need readjustment to a bimodal distribution, whereas small networks do not require such changes.     

Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise

Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods.     

Bushman birth spacing: A test for optimal interbirth intervals

Long interbirth intervals (IBIs) are reported by Lee and by Howell for !kung women, averaging around 4 years between births. Is this low rate of births maladaptive? An earlier analysis of the ecological constraints upon !kung women suggested that it might not be. Given the observed features of !kung ecology, shorter IBIs require a mother to carry much greater loads (backload) of baby and food on her foraging trips. Calculating this load for each IBI shows a sharp upturn in backload when IBIs fall below 4 years. It was suggested that sharply increased backload might lead to such a severe increase in mortality of offspring that the observed 4-year IBI actually maximized the number of offspring that the woman raised.This proposition is tested in this article using reproductive histories of individual !kung women collected by Howell. Backload calculated in the previous study is the best predictor of the observed losses of children at each IBI. Furthermore, mortality of the children is indeed so sharply related to IBI that the 4-year IBI appears to be the interval that maximizes reproductive success for most women.     

Changes in the fluctuation of interbeat intervals in spontaneously beating cultured cardiac myocytes: experimental and modeling studies

 Isolated and cultured neonatal cardiac myocytes contract spontaneously and cyclically, and have the properties of a non-linear oscillator. In this study, we have analyzed the relationship between the fluctuation of contraction rhythm of spontaneously beating cultured cardiac myocytes, and the coupling strength among them. The coefficient of variation of contraction intervals increased transiently in the early stages of incubation, and then decreased almost monotonically with time. The contraction rhythm of the myocytes became synchronized in the late stage of the culture. The day on which synchronization occurred almost coincided with the day when the coefficient of variation reached its lowest value. In addition, we have performed a mathematical analysis using interacting Bonhoeffer–van der Pol oscillators to clarify the mechanisms underlying the changes in the fluctuation of contraction rhythm with time. As the coupling strength among oscillators increased, the coefficient of variation of oscillation periods increased temporarily, but then decreased rapidly when the oscillators showed synchronization. These results suggest that the changes in the fluctuation of beating rhythm result from the increase in strength of electrical coupling among spontaneously beating cardiac myocytes. Received: 10 August 2000 / Accepted in revised form: 19 August 2001     

Bushman birth spacing: Direct tests of some simple predictions

Blurton Jones and Sibly (1978) developed a model of costs (weight of food and baby carried while foraging) of !Kung women's reproduction under ecological-economic constraints that were described by Lee (1972). Predictions are drawn from this model and tested on Howell's (1979) data from reproductive histories of 172 individual women.Women were rated on a scale of dependence on bush or cattlepost foods. The ratings were compared with what is known about the places at which the women gave birth to their children. Agreement was good and the population was divided into two groups for study: 65 women most dependent on bush foods and 70 women substantially dependent on agricultural produce. Thirty-seven women of uncertain or intermediate status were omitted.As predicted by the model, among the women who were dependent on bush foods: (1) first interbirth intervals (IBI) were shorter than were later IBI; (2) the survivorship of children in first IBIs was not strongly related to length of IBI, with shorter IBI giving as good survivorship as longer IBI; (3) IBIs lengthen as the number of surviving children increases, until the fourth child; (4) after the fourth child IBIs do not differ significantly although they tend to be shorter (contrary to the prediction, a null hypothesis whose statistical support is consequently poor); (5) for IBIs after the first IBI, mortality increased markedly as IBI decreased; (6) mortality was even more closely related to backloads entailed by each IBI, as calculated by Blurton Jones and Sibly (1978); (7) mortality was less closely related to backloads calculated from an alternative version of the model from which weight of food was excluded; (8) as reported by Howell (1979), a new pregnancy followed rapidly after the death of the preceeding child but (9) as predicted, a new pregnancy did not follow so fast after the death of older children; (10) for the cattlepost women IBIs were shorter than for women dependent mainly on bush foods; and (11) there was no significant relationship between IBI and mortality for the cattlepost women, and mortality at short IBI was lower than in bush women.The assumption that the benefit accruing from more births will be balanced against the costs (costs to survivorship assumed to result from the work entailed by caring for each child) was successful in giving many predictions confirmed by the data. The significance and limitations of this “optimization” study are discussed.     

The Transfer Functions of Cardiac Tissue during Stochastic Pacing

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K⁺]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.     

Stability of beating frequency in cardiac myocytes by their community effect measured by agarose microchamber chip

To understand the contribution of community effect on the stability of beating frequency in cardiac myocyte cell groups, the stepwise network formation of cells as the reconstructive approach using the on-chip agarose microchamber cell microcultivation system with photo-thermal etching method was applied. In the system, the shapes of agarose microstructures were changed step by step with photo-thermal etching of agarose-layer of the chip using a 1064-nm infrared focused laser beam to increase the interaction of cardiac myocyte cells during cultivation. First, individual rat cardiac myocyte in each microstructure were cultivated under isolated condition, and then connected them one by one through newly-created microchannels by photo-thermal etching to compare the contribution of community size for the magnitude of beating stability of the cell groups. Though the isolated individual cells have 50% fluctuation of beating frequency, their stability increased as the number of connected cells increased. And finally when the number reached to eight cells, they stabilized around the 10% fluctuation, which was the same magnitude of the tissue model cultivated on the dish. The result indicates the importance of the community size of cells to stabilize their performance for making cell-network model for using cells for monitoring their functions like the tissue model.     

Analysis of fluctuation in protein abundance without promoter regulation based on Escherichia coli continuous culture

Fluctuation of protein abundance of isogenic Escherichia coli cells in uniform environment was studied. Based on a continuous culture system, which provides homogeneous culture environment, we investigated the fluctuation in GlnA protein abundance regardless of known glnALG promoter regulation. As results by flow cytometer, we found that the GlnA protein abundance in the cells exhibit a large fluctuation, even though GlnA protein is an essential factor for cell growth and the environment is homogeneous. Furthermore, among several steady states, transient processes of such heterogeneous cell population were investigated, by changing the environmental conditions. The results showed that the expression of GlnA protein can be controlled, depending on its necessity, even though there is no known regulatory machinery. These results may provide a clue to understand the nature of regulation of protein expression dynamics with the stochastic fluctuation.     

The Index of Biological Integrity and the bootstrap: Can random sampling error affect stream impairment decisions?

Multimetric indices, such as the Index of Biological Integrity (IBI), are increasingly used by management agencies to determine whether surface water quality is impaired. However, important questions about the variability of these indices have not been thoroughly addressed in the scientific literature. In this study, we used a bootstrap approach to quantify variability associated with fish IBIs developed for streams in two Minnesota river basins. We further placed this variability into a management context by comparing it to impairment thresholds currently used in water quality determinations for Minnesota streams. We found that 95% confidence intervals ranged as high as 40 points for IBIs scored on a 0–100 point scale. However, on average, 90% of IBI scores calculated from bootstrap replicate samples for a given stream site yielded the same impairment status as the original IBI score. We suggest that sampling variability in IBI scores is related to both the number of fish and the number of rare taxa in a field collection. A comparison of the effects of different scoring methods on IBI variability indicates that a continuous scoring method may reduce the amount of bias in IBI scores.     

The presence of a paternal grandmother lengthens interbirth interval following the birth of a granddaughter in Krummhörn (18th and 19th centuries)

Because only daughters inherit the paternal X-chromosome, an asymmetry in adaptive investment decisions has been suggested for certain patrilineal kin. Namely, paternal grandmothers (PGMs) may favor a granddaughter over a grandson, because (within the limits of paternity uncertainty) the former definitely carries one of their X-chromosomes, while the latter definitely does not. Here, we test the hypothesis that the PGMs' sex-specific favoritism influences reproductive scheduling. Using family-reconstitution data, we analyzed interbirth intervals (IBIs) in the historical population from the Krummhörn (Ostfriesland, Germany). In order to account for potentially timevarying effects on IBIs we applied (and combined) both the additive hazards regression of Aalen and the Cox proportional hazards model. We found that the presence of the PGM but not that of the maternal grandmother (MGM), correlates with the IBI following the birth of a grandchild as a function of the grandchild's sex. Specifically, in the presence of a PGM, the IBIs following the birth of a granddaughter are longer than in her absence. However, contrary to predictions from theoretical life history framework, model estimates for a PGM's effect on a mother's IBI did not significantly vary over time This study supports the hypothesis that PGM behavior differs according to her grandchild's sex. Further research should now explore the biological mechanism underlying this phenomenon.     

Contribution of Nav1.1 to cellular synchronization and automaticity in spontaneous beating cultured neonatal rat ventricular cells

Two factors of cell coupling influence cellular synchronization and automaticity: gap junction coupling and ion channels activity. However, the role of Na(+) channel isoforms underlying cell-to-cell interaction and cellular automaticity is not well understood. To address these questions, we studied mRNA expression of Na(+) channel isoforms and the effects of TTX on spontaneously beating cultured ventricle cells. Using RT-PCR technique we demonstrated the presence of Na(v)1.1 and Na(v)1.5 channels. The reduction of Na(v)1.1 channel activity disturbed cell-to-cell interaction and changed beating rates. Thus, Na(v)1.1 channel is involved in cellular synchronization and automaticity.     

On-chip single-cell-based microcultivation method for analysis of genetic information and epigenetic correlation of cells

We have developed an on-chip single-cell based microcultivation method for analyzing the variability of genetic information stored in single cells and their epigenetic correlations. The method uses four systems: an on-chip cell sorter for purifying the cells in a non-destructive manner; an on-chip single-cell cultivation chip for isolating single cells; an on-chip agarose microchamber system for constructive cell-cell network formation during cultivation; and an on-chip single-cell-based expression analysis system. Using these systems, we could measure the variability of prokaryotic cells and eukaryotic cells having the same DNA and found that, although prokaryotic cells have a large variability in their interdivision times, sister eukaryotic cells having the same DNA synchronized well. We also measured the dynamics of synchronization of beating cardiac myocytes and found that two isolated cells synchronize by one cell following the other after a short pause in beating. These results showed the potential of the on-chip microcultivation method's constructive approach to analyzing cell systems.     

Fast Synchronization of Ultradian Oscillators Controlled by Delta-Notch Signaling with Cis-Inhibition

While it is known that a large fraction of vertebrate genes are under the control of a gene regulatory network (GRN) forming a clock with circadian periodicity, shorter period oscillatory genes like the Hairy-enhancer-of split (Hes) genes are discussed mostly in connection with the embryonic process of somitogenesis. They form the core of the somitogenesis-clock, which orchestrates the periodic separation of somites from the presomitic mesoderm (PSM). The formation of sharp boundaries between the blocks of many cells works only when the oscillators in the cells forming the boundary are synchronized. It has been shown experimentally that Delta-Notch (D/N) signaling is responsible for this synchronization. This process has to happen rather fast as a cell experiences at most five oscillations from its ‘birth’ to its incorporation into a somite. Computer simulations describing synchronized oscillators with classical modes of D/N-interaction have difficulties to achieve synchronization in an appropriate time. One approach to solving this problem of modeling fast synchronization in the PSM was the consideration of cell movements. Here we show that fast synchronization of Hes-type oscillators can be achieved without cell movements by including D/N cis-inhibition, wherein the mutual interaction of DELTA and NOTCH in the same cell leads to a titration of ligand against receptor so that only one sort of molecule prevails. Consequently, the symmetry between sender and receiver is partially broken and one cell becomes preferentially sender or receiver at a given moment, which leads to faster entrainment of oscillators. Although not yet confirmed by experiment, the proposed mechanism of enhanced synchronization of mesenchymal cells in the PSM would be a new distinct developmental mechanism employing D/N cis-inhibition. Consequently, the way in which Delta-Notch signaling was modeled so far should be carefully reconsidered.