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A system of two generalized Hutchinson’s equations coupled by linear diffusion terms is considered. It is established that for an appropriate choice of parameters, the system has a stable relaxation cycle whose components turn into each other under a certain phase shift. A number of additional properties of this cycle are presented that allow one to interpret it as a self-organization mode.

Targeted temperature management is part of the standardized treatment for patients in cardiac arrest. Hypothermia decreases cerebral oxygen consumption and induces bradycardia; thus, increasing the heart rate may be considered to maintain cardiac output. We hypothesized that increasing heart rate during hypothermia would impair diastolic function. Human left ventricular trabeculae obtained from explanted hearts of patients with terminal heart failure were stimulated at 0.5 Hz, and contraction-relaxation cycles were recorded. Maximal developed force (Fmax), maximal rate of development of force [(dF/d t)max], time to peak force (TPF), time to 80% relaxation (TR80), and relaxation time (RT = TR80 − TPF) were measured at 37, 33, 31, and 29°C. At these temperatures, stimulation frequency was increased from 0.5 to 1.0 and to 1.5 Hz. At 1.5 Hz, concentration-response curves for the β-adrenergic receptor (β-AR) agonist isoproterenol were performed. Fmax, TPF, and RT increased when temperature was lowered, whereas (dF/d t)max decreased. At all temperatures, increasing stimulation frequency increased Fmax and (dF/d t)max, whereas TPF and RT decreased. At 31 and 29°C, resting tension increased at 1.5 Hz, which was ameliorated by β-AR stimulation. At all temperatures, maximal β-AR stimulation increased Fmax, (dF/d t)max, and maximal systolic force, whereas resting tension decreased progressively with lowering temperature. β-AR stimulation reduced TPF and RT to the same extent at all temperatures, despite the more elongated contraction-relaxation cycle at lower temperatures. Diastolic dysfunction during hypothermia results from an elongation of the contraction-relaxation cycle, which decreases the time for ventricular filling. Hypothermic bradycardia protects the heart from diastolic dysfunction and increasing the heart rate during hypothermia should be avoided. NEW & NOTEWORTHY Decreasing temperature increases the duration of the contraction-relaxation cycle in the human ventricular myocardium, significantly reducing the time for ventricular filling during diastole. During hypothermia, increasing heart rate further reduces the time for ventricular filling and in some situations increases resting tension further impairing diastolic function. Modest β-adrenergic receptor stimulation can ameliorate these potentially detrimental changes during diastole while improving contractile force generation during targeted temperature management.

We consider the so-called bilocal neuron model, which is a special system of two nonlinear delay differential equations coupled by linear diffusion terms. The system is invariant under the interchange of phase variables. We prove that, under an appropriate choice of parameters, the system under study has a stable relaxation cycle whose components turn into each other under a certain phase shift.

The three-dimensional nonlinear system of ordinary differential equations modeling the functioning of the simplest oscillatory genetic network, the so-called repressilator, is considered. The existence, asymptotics, and stability of the relaxation periodicmotion in this system are studied.

We study the logistic equation with two delays. When studying its nonlocal dynamics, we obtain a condition for the existence and the asymptotics of a relaxation cycle. When studying the local dynamics, we show that the behavior of solutions of the original equation is determined by the structure of solutions of special families of nonlinear boundary value problems of parabolic and degenerate-parabolic type.

A singularly perturbed system of ordinary differential equations with a fast and a slow variable is proposed, which is a modification of the well-known FitzHugh-Nagumo model from neuroscience. The existence and stability of a nonclassical relaxation cycle in this system are studied. The slow component of the cycle is asymptotically close to a discontinuous function, while the fast component is a δ-like function.

In this essay the authors argue that chamber pressure dominates the biomechanics of the contraction cycle of the heart, while tissue stiffness dominates the relaxation cycle. This appears to be an under-recognized challenge in cardiac tissue engineering. Optimal approaches will involve constructing chambers or modulating the stiffness of the scaffold/substrate in synchrony with the beating cycle.

A singularly perturbed scalar nonlinear differential-difference equation with two delays is considered that is a mathematical model of an isolated neuron. It is shown that a one-dimensional chain of diffusively coupled oscillators of this type exhibits the well-known buffer phenomenon. Specifically, as the number of chain links increases consistently with decreasing diffusivity, the number of coexisting stable periodic motions in the chain grows indefinitely.

During hunting, bats of suborder Microchiropetra emit intense ultrasonic pulses and analyze the weak returning echoes with their highly developed auditory system to extract the information about insects or obstacles. These bats progressively shorten the duration, lower the frequency, decrease the intensity and increase the repetition rate of emitted pulses as they search, approach, and finally intercept insects or negotiate obstacles. This dynamic variation in multiple parameters of emitted pulses predicts that analysis of an echo parameter by the bat would be inevitably affected by other co-varying echo parameters. The progressive increase in the pulse repetition rate throughout the entire course of hunting would presumably enable the bat to extract maximal information from the increasing number of echoes about the rapid changes in the target or obstacle position for successful hunting. However, the increase in pulse repetition rate may make it difficult to produce intense short pulse at high repetition rate at the end of long-held breath. The increase in pulse repetition rate may also make it difficult to produce high frequency pulse due to the inability of the bat laryngeal muscles to reach its full extent of each contraction and relaxation cycle at a high repetition rate. In addition, the increase in pulse repetition rate increases the minimum threshold (i.e. decrease auditory sensitivity) and the response latency of auditory neurons. In spite of these seemingly physiological disadvantages in pulse emission and auditory sensitivity, these bats do progressively increase pulse repetition rate throughout a target approaching sequence. Then, what is the adaptive value of increasing pulse repetition rate during echolocation? What are the underlying mechanisms for obtaining maximal information about the target features during increasing pulse repetition rate? This article reviews the electrophysiological studies of the effect of pulse repetition rate on multiple-parametric selectivity of neurons in the central nucleus of the inferior colliculus of the big brown bat, Eptesicus fuscus using single repetitive sound pulses and temporally patterned trains of sound pulses. These studies show that increasing pulse repetition rate improves multiple-parametric selectivity of inferior collicular neurons. Conceivably, this improvement of multiple-parametric selectivity of collicular neurons with increasing pulse repetition rate may serve as the underlying mechanisms for obtaining maximal information about the prey features for successful hunting by bats.

We consider a scalar singularly perturbed nonlinear delay differential-difference equation modeling an individual neuron. We study the existence, asymptotics, and stability of its relaxation cycle.

Hutchinson's equation is a scalar equation with time delay which is well known in ecology. In this paper a complete asymptotic representation is constructed for a stable relaxation cycle of this equation, in the form of series in integer powers of a certain small parameter. The techniques of asymptotic integration developed on the way are then applied to analyse the question of attractors for a system of circularly interrelated Hutchinson equations. Bibliography: 8 titles.

Contractions of the guinea pigs vas deferens were induced by field stimulation and the effects of derivatives of cGMP were tested on the contraction-relaxation cycle. Relaxation was induced by 8-Br-cGMP and O2'-mb-cGMP. On the contrary, db-cGMP and N2-mb-cGMP potentiated the contraction. The relaxant effect of 8-Br-cGMP was not mimicked by 8-Br-5'GMP, instead the latter caused the opposite effect. Since neither 8-Br-cGMP nor db-cGMP affected the release of norepinephrine on field stimulation the cGMP derivatives induced their effects at a postsynaptic site. 8-Br-cGMP was found to be 100-fold more potent than cGMP to simulate protein kinase activity in crude extracts from guinea pig was deferens. N2-mb-cGMP and O2'-mb-cGMP were approximately equipotent to cGMP while db-cGMP was less active. 8-Br-5'-GMP did not stimulate the protein kinase. It is suggested that the results support the hypothesis that cGMP acts as a relaxant in the smooth muscle of the vas deferens. The potentiation caused by db-cGMP and N2-mb-cGMP on contractions could be dependent on the substitution in the guanine moiety of the molecules with the butyryl group. Their effect was thus probably unrelated to a specific cGMP effect.

An experimental device with an inexpensive electronic-mechanical measurement system was designed to clarify the role of mechanical tensions in cell activation. This device provides for maintaining a specified kinetics of either the object’s length or applied load to measure its tension force or deformation. The experiments were performed with the plasmodium of Physarum polycephalum, a giant unicellular organism, which is a classical object for studying a nonmuscle motility. Several examples of the longitudinal dynamics of the plasmodial strand and its activation in response to periodic switching at certain phases of the contraction- relaxation cycle are described.

We establish conditions under which, in three-dimensional relaxation systems of the form {fx066-01}, where 0 < e << 1, |μ| << 1, and ƒ, g ∈ C ∞, the so-called “blue-sky catastrophe” is observed, i.e., there appears a stable relaxation cycle whose period and length tend to infinity as μ tends to a certain critical value μ*(e), μ*(0) 0 = 0.

Phasic contractions of collecting lymphatic vessels aid in the centripetal propulsion of lymph. The numerical model published in PNAS by Kunert et al. (1) describes how two “complementary feedback loops” involving Ca2+ and nitric oxide (NO) interact to drive the phasic contraction/relaxation cycle of lymphatic smooth muscle. The cycle is proposed to be initiated by a stretch-induced rise in lymphatic muscle Ca2+, triggering a contraction (systole) that propels lymph through unidirectional valves. Subsequent elevation of shear stress in the narrow valve opening produces a burst … [↵][1]1Email: davismj{at}health.missouri.edu. [1]: #xref-corresp-1-1

We demonstrate thermo-mechanical relaxation oscillations in a strongly driven quartz crystal. Dynamic bifurcation leads to two stable oscillation states with a distinct electrical impedance. Slow Joule-heating, which shifts the susceptibility of the crystal, provides a feedback that leads to thermally-induced oscillations, in which the amplitude of the crystal is modulated by a relaxation cycle. The frequency of the relaxation cycle is roughly a million times lower than the resonance frequency of the crystal, and it can be adjusted by the detuning from the critical point for dynamic bifurcation. The experimental observations are reproduced by a simple model that takes into account the slow dynamics of the system., Comment: Main text: 8 pages, 4 figures. Supplementary information: 4 pages, 3 figures

The temperature bias instability of high-voltage oxides is analyzed. For the investigation of negative bias temperature instability (NBTI) we present an enhanced reaction–diffusion model including trap-controlled transport, the amphoteric nature of the Pb centers at the Si/SiO2 interface, Fermi-level dependent interface charges, and fully self-consistent coupling to the semiconductor device equations. Comparison to measurement data for a stress/relaxation cycle and a wide range of temperatures shows excellent agreement. 2007 Elsevier Ltd. All rights reserved.

Cardiac mitochondria provide energy for the contraction/relaxation cycle. The aim of our study was to isolate and characterize mitochondria from Caprine hearts under control and in-vitro induced ischemia. A decrease in activities of all the enzymes was observed in the ischemic models. Further characterization of proteins was done by SDS-PAGE and BN-PAGE. Lipids have been characterized by analyzing the phospholipids by HPTLC and fatty acids by GLC in both groups. Our results indicated that injury occurs early in the course of ischemia and progresses during ischemia. TBARS and carbonyl content have also been measured. The in-vitro effects of fatty acids have been studied on the enzymes and complexes of mitochondria.

The existence of a relaxation cycle with unusual properties is proved for a certain system with delay encountered in mathematical ecology. The theoretical result is applied to the explanation of a concrete natural phenomenon.

A system whose state is described by a scalar parameter is considered. The parameter undergoes relaxation from the initial to a critical value. As soon as the latter is attained, the system is instantaneously brought back into the standard state an the relaxation process begins again. Because relaxation can be described by an equation with delay, each relaxation cycle that follows is different from the previous ones, in general. Some properties of the mathematical model under consideration are established. In particular, conditions are given, under which the long-term behaviour of the system becomes asymptotically periodic.

Both cardiac and skeletal calsequestrin (CASQ2 and CASQ1) serve as a major Ca(2+) storage/buffer protein in the sarcoplasmic reticulum (SR) by sequestering and releasing large numbers of Ca(2+) ions during each muscular contraction and relaxation cycle. CASQ isolated from various species often exists in a phosphorylated form, but phosphorylation's role is not yet understood. Here, the authors identified two phosphorylation sites, Ser(385) and Ser(393), for the first time, in human CASQ2 (hCASQ2) by mass-spectroscopy and evaluated the consequences of such phosphorylation. Substitution of these two serines with phosphoserine-mimicking aspartic-acid residues results in a significant increase in helical content, solubility and Ca(2+)-binding capacity above 6 mM [Ca(2+)]. However, neither substitution of Ser(385) nor Ser(393) alone produce any significant changes. Based on the crystal structures of hCASQ2, Ca(2+) binding capacity data, turbidity, and light scattering profiles, it was propose that phosphorylation at these two positions produces a disorder-to-order or coil-to-helix transition of the C-terminus, which in turn provides a more stable network of polyanions. Therefore, considering all the previous reports and the new data, the observed dynamic in vivo phosphorylation of CASQ could provide the basis not only for effective regulation of Ca(2+) buffering capacity, but also for the junctional SR trafficking mechanism.

The method of rapid superfusion of the single isolated ventricular myocytes of guinea-pig heart was used in order to inhibit the Na-Ca exchange throughout the physiological contraction-relaxation cycle. Superfusion of the cell at selected intervals during the contraction with the Na,Ca-free solution resulted in increase in its amplitude, increase in time to peak shortening and in delay of relaxation, albeit the cells relaxed before reperfusion of normal Tyrode solution. The largest increase in amplitude of contraction (to 134 +/- 16%) was observed when the effective exchange of the cell's environment was attained approximately 50 ms after the pulse stimulating contraction. The effects declined promptly when the delay was increased beyond 100 ms. In the cells treated with 10 mM caffeine superfusion with the Na,Ca-free solution after the delay of 50-100 ms resulted in decrease in extent of shortening. Increase in delay resulted in slight increase in extent of shortening with respect to control and strong inhibition of relaxation. The strongest effects were observed when the delay was approximately 200 ms. Superfusion of the normal cells and of the cells treated with caffeine between contractions resulted in slight potentiation of the next beat. It is concluded that Na-Ca exchange provides an important mechanism of relaxation and outward Ca2+ transport in the physiological contraction of the ventricular cardiomyocyte.

Spin-coupling and spin memory effects of F H (OH − ) and F H (CN - ) centers have been studied in various hosts at 2 K. The spin-memory loss ϵ, i.e. the probability of spin-flip during a complete electronic excitation and relaxation cycle, has been determined. The main result is a strong increase of the spin-memory loss ϵ for F H (CN - ) in CsCl and CsBr compared to F centers, while ϵ remains nearly unchanged (only a slight decrease) for F H (OH - ) centers in KCl and KBr. First attempts will be made to explain these spin-memory loss results in correlation to the electron relaxation and electron-vibrational energy transfer processes occuring in the same optical cycle.

Dinoflagellates possess two flagella. One of them, the longitudinal flagellum, retracts from time to time in some species, such asCeratium andPeridinium. Additional structures which run along the axoneme seem to be responsible for this particular behaviour. The retraction which is rapid (less than 60 ms) may be subdivided into several steps: i) the undulating movement stops; ii) the flagellum appears then as a jagged line during 20 ms; iii) finally a rapid retraction (20 ms) takes place, the flagellum being folded 20 times inside the cylindrical flagellar pocket. The measurements on video-records suggest that the R-fibre shortens to 30% of its original length. The contraction and relaxation mechanism of nanofilaments is proposed to be through coiling and uncoiling dependent on Ca2+ concentration.