Smooth muscle stiffness variation due to external longitudinal oscillations

This research focuses on an in vitro investigation of the stiffness changes of contracted airway smooth muscles (ASM) subjected to external longitudinal oscillations. ASM tissues were dissected from excised pig tracheas and stimulated by a chemical stimulus (acetylcholine, 10(-3) M) to produce maximum contractions. The tissues were then systematically excited with external oscillations. Various frequencies, amplitudes and durations were used in the experiments to determine stiffness changes in response to these variations. Force changes were recorded to reflect the muscle stiffness changes. Two stiffness definitions were used to quantify the results, dynamic stiffness to reflect variations during oscillation and static stiffness to reflect the net effect of oscillation. Under isometric contractions, these two stiffnesses were determined before, during and after oscillations. Incorporating an empirical stiffness equation, a two-dimensional finite element model (FEM) was developed to generalize the tissue responses to oscillation. The main outcomes from this work are: the dynamic stiffness has the tendency to decrease as the frequency and/or amplitude of external oscillation increases; the static stiffness has the tendency of decreasing with an increase in the frequency and/or amplitude of excitation until it reaches almost a constant value for frequencies at and above 25 Hz. The difference in the behavior of the dynamic and static stiffness changes may be attributed to the effect of elasticity and mass inertia that are involved in the dynamic motion. The findings of this research are in agreement with the hypothesis that oscillations exert a direct action on the contractile processes by causing an increased rate of actin-myosin detachments.     

Correlated oscillations in glucose consumption, oxygen consumption, and intracellular free Ca(2+) in single islets of Langerhans

Micron-sized sensors were used to monitor glucose and oxygen levels in the extracellular space of single islets of Langerhans in real-time. At 10 mM glucose, oscillations in intraislet glucose concentration were readily detected. Changes in glucose level correspond to changes in glucose consumption by glycolysis balanced by mass transport into the islet. Oscillations had a period of 3.1 +/- 0.2 min and amplitude of 0.8 +/- 0.1 mM glucose (n = 21). Superimposed on these oscillations were faster fluctuations in glucose level during the periods of low glucose consumption. Oxygen level oscillations that were out of phase with the glucose oscillations were also detected. Oscillations in both oxygen and glucose consumption were strongly dependent upon extracellular Ca(2+) and sensitive to nifedipine. Simultaneous measurements of glucose with intracellular Ca(2+) ([Ca(2+)](i)) revealed that decreases in [Ca(2+)](i) preceded increases in glucose consumption by 7.4 +/- 2.1 s during an oscillation (n = 9). Conversely, increases in [Ca(2+)](i) preceded increases in oxygen consumption by 1.5 +/- 0.2 s (n = 4). These results suggest that during oscillations, bursts of glycolysis begin after Ca(2+) has stopped entering the cell. Glycolysis stimulates further Ca(2+) entry, which in turn stimulates increases in respiration. The data during oscillation are in contrast to the time course of events during initial exposure to glucose. Under these conditions, a burst of oxygen consumption precedes the initial rise in [Ca(2+)](i). A model to explain these results is described.     

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.     

Roles of protein ubiquitination and degradation kinetics in biological oscillations

Protein ubiquitination and degradation play important roles in many biological functions and are associated with many human diseases. It is well known that for biochemical oscillations to occur, proper degradation rates of the participating proteins are needed. In most mathematical models of biochemical reactions, linear degradation kinetics has been used. However, the degradation kinetics in real systems may be nonlinear, and how nonlinear degradation kinetics affects biological oscillations are not well understood. In this study, we first develop a biochemical reaction model of protein ubiquitination and degradation and calculate the degradation rate against the concentration of the free substrate. We show that the protein degradation kinetics mainly follows the Michaelis-Menten formulation with a time delay caused by ubiquitination and deubiquitination. We then study analytically how the Michaelis-Menten degradation kinetics affects the instabilities that lead to oscillations using three generic oscillation models: 1) a positive feedback mediated oscillator; 2) a positive-plus-negative feedback mediated oscillator; and 3) a negative feedback mediated oscillator. In all three cases, nonlinear degradation kinetics promotes oscillations, especially for the negative feedback mediated oscillator, resulting in much larger oscillation amplitudes and slower frequencies than those observed with linear kinetics. However, the time delay due to protein ubiquitination and deubiquitination generally suppresses oscillations, reducing the amplitude and increasing the frequency of the oscillations. These theoretical analyses provide mechanistic insights into the effects of specific proteins in the ubiquitination-proteasome system on biological oscillations.     

External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory System

The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.     

Dynamic aspects of insulin action: synchronization of oscillatory glycolysis in isolated perifused rat fat cells by insulin and hydrogen peroxide

Glucose oxidation to CO2 was investigated in isolated perifused rat epididymal fat cells. Insulin stimulated rates of oxidation up to 30-fold. Multiple pulses of insulin or prolonged perifusion with the hormone led to a time-dependent desensitization of the cells. The action of insulin could be mimicked by H2O2. Reversal of H2O2 effects was associated with a damped oscillation of large initial amplitude. Initiation of perifusion with insulin induced rates of glucose oxidation that oscillated around a mean elevated rate with an amplitude of about +/- 4% of the mean, significantly larger than the measurement error. Basal rates did not show clear oscillations. The oscillations after insulin had a statistically significant period of around 14 min. The results were the same with C1- or C6-labeled glucose and occurred in the presence of both 0.275 and 5.5 mM glucose in the perifusion medium. The oscillations were interpreted as the result of insulin- or H2O2-induced synchronization of oscillatory glycolysis by individual fat cells. The similarity of the observed oscillatory period with the period of oscillatory insulin secretion by pancreatic beta cells suggests that oscillatory glycolysis may constitute the internal pacemaker for the latter process.     

Ca2+-sparks constitute elementary building blocks for global Ca2+-signals in myocytes of retinal arterioles

Spontaneous Ca2+-events were imaged in myocytes within intact retinal arterioles (diameter <40 microm) freshly isolated from rat eyes. Ca2+-sparks were often observed to spread across the width of these small cells, and could summate to produce prolonged Ca2+-oscillations and contraction. Application of cyclopiazonic acid (20 microM) transiently increased spark frequency and oscillation amplitude, but inhibited both sparks and oscillations within 60s. Both ryanodine (100 microM) and tetracaine (100 microM) reduced the frequency of sparks and oscillations, while tetracaine also reduced oscillation amplitude. None of these interventions affected spark amplitude. Nifedipine, which blocks store filling independently of any action on L-type Ca2+-channels in these cells, reduced the frequency and amplitude of both sparks and oscillations. Removal of external [Ca2+] (1mM EGTA) also reduced the frequency of sparks and oscillations but these reductions were slower in onset than those in the presence of tetracaine or cyclopiazonic acid. Cyclopiazonic acid, nifedipine and low external [Ca2+] all reduced SR loading, as indicated by the amplitude of caffeine evoked Ca2+-transients. This study demonstrates for the first time that spontaneous Ca2+-events in small arterioles of the eye result from activation of ryanodine receptors in the SR and suggests that this activation is not tightly coupled to Ca2+-influx. The data also supports a model in which Ca2+-sparks act as building blocks for more prolonged, global Ca2+-signals.     

Frequency tuning in animal locomotion

In locomotion that involves repetitive motion of propulsive structures (arms, legs, fins, wings) there are resonant frequencies f(*) at which the energy consumption is a minimum. As animals need to change their speed, they can maintain this energy minimum by tuning their body resonances. We discuss the physical principles of frequency tuning, and how it relates to forces, damping, and oscillation amplitude. The resonant frequency of pendulum-type oscillators (e.g. swinging arms and legs) may be changed by varying the mass moment of inertia, or the vertical acceleration of the pendulum pivot. The frequency of elastic vibrations (e.g. the bell of a jellyfish) can be tuned with a non-linear modulus of elasticity: soft for low deflection amplitudes (low resonant frequency), and stiff for large displacements (high resonant frequency). Tuning of elastic oscillations can also be achieved by changing the effective length or cross-sectional area of the elastic members, or by allowing springs in parallel or in series to become active. We propose that swimming and flying animals generate oscillating propulsive forces from precisely placed shed vortices and that these tuned motions can only occur when vortex shedding and the simple harmonic motion of the elastic elements of the propulsive structures are in resonance.     

Microbial predation in a periodically operated chemostat: a global study of the interaction between natural and externally imposed frequencies.

Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When the chemostat is operated periodically, the interaction of the natural oscillation frequency with the external forcing gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions (local and especially global) between them as the amplitude and frequency of the forcing vary. The transition from low-forcing-amplitude quasiperiodicity to entrainment of the chemostat behavior by strong forcing (involving the concerted closing of resonance horns) is analyzed. We concentrate on certain strong resonance phenomena between the two frequencies and provide an extensive atlas of computed phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of periodically forced chemical oscillators. In particular, the existence and relative succession of several distinct types of global bifurcations resulting in chaotic transients and multistability are studied in detail. The location in the operating diagram of several key codimension 2 local bifurcations of periodic solutions is computed, and their interaction with an interesting feature we name "real-eigenvalues horns" is examined.     

Mitochondrial metabolism reveals a functional architecture in intact islets of Langerhans from normal and diabetic Psammomys obesus

The cells within the intact islet of Langerhans function as a metabolic syncytium, secreting insulin in a coordinated and oscillatory manner in response to external fuel. With increased glucose, the oscillatory amplitude is enhanced, leading to the hypothesis that cells within the islet are secreting with greater synchronization. Consequently, non-insulin-dependent diabetes mellitus (NIDDM; type 2 diabetes)-induced irregularities in insulin secretion oscillations may be attributed to decreased intercellular coordination. The purpose of the present study was to determine whether the degree of metabolic coordination within the intact islet was enhanced by increased glucose and compromised by NIDDM. Experiments were performed with isolated islets from normal and diabetic Psammomys obesus. Using confocal microscopy and the mitochondrial potentiometric dye rhodamine 123, we measured mitochondrial membrane potential oscillations in individual cells within intact islets. When mitochondrial membrane potential was averaged from all the cells in a single islet, the resultant waveform demonstrated clear sinusoidal oscillations. Cells within islets were heterogeneous in terms of cellular synchronicity (similarity in phase and period), sinusoidal regularity, and frequency of oscillation. Cells within normal islets oscillated with greater synchronicity compared with cells within diabetic islets. The range of oscillatory frequencies was unchanged by glucose or diabetes. Cells within diabetic (but not normal) islets increased oscillatory regularity in response to glucose. These data support the hypothesis that glucose enhances metabolic coupling in normal islets and that the dampening of oscillatory insulin secretion in NIDDM may result from disrupted metabolic coupling.     

Oscillatory enzyme reactions and Michaelis–Menten kinetics

Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis–Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis–Menten phosphorylation–dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase.     

Noise-Induced Coherence and Network Oscillations in a Reduced Bursting Model

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons. PACS 05.45.-a, 05.40.Ca, 87.18.Sn, 87.19     

Spontaneous myocardial calcium oscillations: overview with emphasis on ryanodine and caffeine

All mammalian cardiac preparations exhibit the capacity for periodic spontaneous Ca2+ release from the sarcoplasmic reticulum (SR) (Ca2+ oscillations). The occurrence of such oscillations in unstimulated preparations and their periodicity depend on the species and the Ca2+ load on the cell. When the spontaneous frequency of these oscillations exceeds the rate of external simulation, they appear between stimulated contractions and impart a variable Ca2+-dependent component of diastolic tonus and a propensity for extrasystoles and arrhythmias to occur; these diastolic oscillations can also affect systolic function as well. Although enhancing the spontaneous frequency of Ca2+ release, caffeine depresses the oscillation amplitude, whereas ryanodine suppresses both frequency and amplitude. Detailed studies of oscillation characteristics and of the different effects of caffeine and ryanodine on them may provide an understanding of and may be useful for modeling SR Ca2+ uptake and release in intact preparations.     

Computational Models Describing Possible Mechanisms for Generation of Excessive Beta Oscillations in Parkinson’s Disease

In Parkinson’s disease, an increase in beta oscillations within the basal ganglia nuclei has been shown to be associated with difficulty in movement initiation. An important role in the generation of these oscillations is thought to be played by the motor cortex and by a network composed of the subthalamic nucleus (STN) and the external segment of globus pallidus (GPe). Several alternative models have been proposed to describe the mechanisms for generation of the Parkinsonian beta oscillations. However, a recent experimental study of Tachibana and colleagues yielded results which are challenging for all published computational models of beta generation. That study investigated how the presence of beta oscillations in a primate model of Parkinson’s disease is affected by blocking different connections of the STN-GPe circuit. Due to a large number of experimental conditions, the study provides strong constraints that any mechanistic model of beta generation should satisfy. In this paper we present two models consistent with the data of Tachibana et al. The first model assumes that Parkinsonian beta oscillation are generated in the cortex and the STN-GPe circuits resonates at this frequency. The second model additionally assumes that the feedback from STN-GPe circuit to cortex is important for maintaining the oscillations in the network. Predictions are made about experimental evidence that is required to differentiate between the two models, both of which are able to reproduce firing rates, oscillation frequency and effects of lesions carried out by Tachibana and colleagues. Furthermore, an analysis of the models reveals how the amplitude and frequency of the generated oscillations depend on parameters.     

Simulation of gait and gait initiation associated with body oscillating behavior in the gravity environment on the Moon, Mars and Phobos

 A double-inverted pendulum model of body oscillations in the frontal plane during stepping [Brenière and Ribreau (1998) Biol Cybern 79: 337–345] proposed an equivalent model for studying the body oscillating behavior induced by step frequency in the form of: (1) a kinetic body parameter, the natural body frequency (NBF), which contains gravity and which is invariable for humans, (2) a parametric function of frequency, whose parameter is the NBF, which explicates the amplitude ratio of center of mass to center of foot pressure oscillation, and (3) a function of frequency which simulates the equivalent torque necessary for the control of the head-arms-trunk segment oscillations. Here, this equivalent model is used to simulate the duration of gait initiation, i.e., the duration necessary to initiate and execute the first step of gait in subgravity, as well as to calculate the step frequencies that would impose the same minimum and maximum amplitudes of the oscillating responses of the body center of mass, whatever the gravity value. In particular, this simulation is tested under the subgravity conditions of the Moon, Mars, and Phobos, where gravity is 1/6, 3/8, and 1/1600 times that on the Earth, respectively. More generally, the simulation allows us to establish and discuss the conditions for gait adaptability that result from the biomechanical constraints particular to each gravity system. Received: 15 February 1999 / Accepted in revised form: 9 October 2000     

Synchronization in two interacting oscillatory systems.

Nonlinear phenomena arising from the interaction of two oscillating systems of chemical reactions are studied experimentally. The system of two connected flow-through continuous stirred tank reactors (cells) with controlled exchange of reaction mixture is used. The Belousov reaction (oxidation of malonic acid by bromate in sulphuric acid with ceric/cerous ions as catalyst) served as model system. The frequency of oscillations was controlled by change of the reaction temperature. Phenomena such as synchronization of oscillations at a common frequency, synchronization at multiples of a common frequency, rhythm splitting and amplitude amplification were observed, depending on the degree of interaction and the differences in the original oscillation frequencies. Mathematical modelling of the above phenomena failed, probably due to insufficient knowledge of a kinetic model.     

Temperature dependence and temperature compensation of kinetics of chemical oscillations; Belousov-Zhabotinskii reaction, glycolysis and circadian rhythms

Based on the distribution of activation energies around the experimental mean and averaging of rate constants we propose a theoretical scheme to examine the temperature dependence and temperature compensation of time periods of chemical oscillations. The critical finite width of the distribution is characteristic of endogeneous oscillations for compensating kinetics as observed in circadian oscillations, while the vanishing width corresponds to Arrhenius temperature dependent kinetics of non-endogeneous chemical oscillation in Belousov-Zhabotinskii reaction in a CSTR or glycolysis in cell-free yeast extracts. Our theoretical analysis is corroborated with experimental data.