Emergence of Complex Dynamics in a Simple Model of Signaling Networks

A variety of physical, social and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by $1/f$-scaling of their power spectra, can emerge in networks of simple signaling units. We find that under general conditions, complex dynamics can be generated by systems fulfilling two requirements: i) a ``small-world'' topology and ii) the presence of noise. Our findings support two notable conclusions: first, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions (i) and (ii) are robust to some degree of degradation, i.e., they will still be able to generate $1/f$-dynamics

Multifractality in Human Heartbeat Dynamics

Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system --- the healthy human heartbeat. Further, we show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.Comment: 19 pages, latex2e using rotate and epsf, with 5 ps figures; to appear in Nature, 3 June, 199

Network Physiology reveals relations between network topology and physiological function

The human organism is an integrated network where complex physiologic systems, each with its own regulatory mechanisms, continuously interact, and where failure of one system can trigger a breakdown of the entire network. Identifying and quantifying dynamical networks of diverse systems with different types of interactions is a challenge. Here, we develop a framework to probe interactions among diverse systems, and we identify a physiologic network. We find that each physiologic state is characterized by a specific network structure, demonstrating a robust interplay between network topology and function. Across physiologic states the network undergoes topological transitions associated with fast reorganization of physiologic interactions on time scales of a few minutes, indicating high network flexibility in response to perturbations. The proposed system-wide integrative approach may facilitate the development of a new field, Network Physiology.Comment: 12 pages, 9 figure

Methods of electroencephalographic signal analysis for detection of small hidden changes

The aim of this study was to select and evaluate methods sensitive to reveal small hidden changes in the electroencephalographic (EEG) signal. Two original methods were considered

Fractal dynamics in physiology: Alterations with disease and aging

According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era

Endogenous circadian rhythm in human motor activity uncoupled from circadian influences on cardiac dynamics

The endogenous circadian pacemaker influences key physiologic functions, such as body temperature and heart rate, and is normally synchronized with the sleep/wake cycle. Epidemiological studies demonstrate a 24-h pattern in adverse cardiovascular events with a peak at ≈10 a.m. It is unknown whether this pattern in cardiac risk is caused by a day/night pattern of behaviors, including activity level and/or influences from the internal circadian pacemaker. We recently found that a scaling index of cardiac vulnerability has an endogenous circadian peak at the circadian phase corresponding to ≈10 a.m., which conceivably could contribute to the morning peak in cardiac risk. Here, we test whether this endogenous circadian influence on cardiac dynamics is caused by circadian-mediated changes in motor activity or whether activity and heart rate dynamics are decoupled across the circadian cycle. We analyze high-frequency recordings of motion from young healthy subjects during two complementary protocols that decouple the sleep/wake cycle from the circadian cycle while controlling scheduled behaviors. We find that static activity properties (mean and standard deviation) exhibit significant circadian rhythms with a peak at the circadian phase corresponding to 5–9 p.m. (≈9 h later than the peak in the scale-invariant index of heartbeat fluctuations). In contrast, dynamic characteristics of the temporal scale-invariant organization of activity fluctuations (long-range correlations) do not exhibit a circadian rhythm. These findings suggest that endogenous circadian-mediated activity variations are not responsible for the endogenous circadian rhythm in the scale-invariant structure of heartbeat fluctuations and likely do not contribute to the increase in cardiac risk at ≈10 a.m

Endogenous circadian rhythm in an index of cardiac vulnerability independent of changes in behavior

There exists a robust day/night pattern in the incidence of adverse cardiac events with a peak at ≈10 a.m. This peak traditionally has been attributed to day/night patterns in behaviors affecting cardiac function in vulnerable individuals. However, influences from the endogenous circadian pacemaker independent from behaviors may also affect cardiac control. Heartbeat dynamics under healthy conditions exhibit robust complex fluctuations characterized by self-similar temporal structures, which break down under pathologic conditions. We hypothesize that these dynamical features of the healthy human heartbeat have an endogenous circadian rhythm that brings the features closer to those observed under pathologic conditions at the endogenous circadian phase corresponding to ≈10 a.m. We investigate heartbeat dynamics in healthy subjects recorded throughout a 10-day protocol wherein the sleep/wake and behavior cycles are desynchronized from the endogenous circadian cycle, enabling assessment of circadian factors while controlling for behavior-related factors. We demonstrate that the scaling exponent characterizing temporal correlations in heartbeat dynamics does exhibit a significant circadian rhythm (with a sharp peak at the circadian phase corresponding to ≈10 a.m.), which is independent from scheduled behaviors and mean heart rate. Cardiac dynamics under pathologic conditions such as congestive heart failure also are associated with a larger value of the scaling exponent of the interbeat interval. Thus, the sharp peak in the scaling exponent at the circadian phase coinciding with the period of highest cardiac vulnerability observed in epidemiological studies suggests that endogenous circadian-mediated influences on cardiac control may be involved in the day/night pattern of adverse cardiac events in vulnerable individuals