Spontaneous electrical potential oscillation on a filter impregnated with soybean lecithin placed between identical solutions of alanine

Filters impregnated with soybean lecithin, placed between two identical aqueous alanine solutions, display spontaneous electric potential oscillations. Alanine solutions used in a large concentration range from 1 mM to 1 M produce damped oscillatory behaviour with an exponential decay in time. The dependence of decay time on concentration shows saturation behaviour which is well fitted with a sigmoidal curve. Power spectra obtained by Fourier transform show peaks specific for each concentration. When fitted with a Lorentzian curve in the peak domain, the centre of the peak height and width at half height could be extracted. All these parameters depend on alanine concentration in a saturating pattern.     

On the activities in a continuous neural network

In this work an attempt is made to study the activities in a continuous neural system. The neural model considered here is a two dimensional continuous version of an earlier discrete model investigated in a series of papers [5–8]. The variations of the normalized firing rates in the present model are described by a nonlinear integro-partial differential equation. The conditions for the existence and uniqueness of the solutions of the describing equation subject to an initial condition are established and the steady-state solutions are investigated for inputs which are constant with respect to time. Depending on the parameters which are related to the self-inhibition and adaptation properties of the neural network, some of the oscillatory and stability properties of the solutions of the describing equation are discussed.     

Damped oscillatory hysteretic behaviour of butyrylcholinesterase with benzoylcholine as substrate.

Steady-state kinetics for the hydrolysis of benzoylcholine (BzCh) and benzoylthiocholine (BzSCh) by wild-type human butyrylcholinesterase (BuChE) and by the peripheral anionic site mutant D70G were compared. kcat/Km for the hydrolysis of BzSCh was 17-fold and 32-fold lower than that for hydrolysis of BzCh by wild-type and D70G, respectively. The rate-limiting step for hydrolysis of BzCh was deacylation, whereas acylation was rate-limiting for hydrolysis of BzSCh. Wild-type enzyme and the D70G mutant were found to reach steady-state velocity slowly with BzCh as the substrate. At pH 6, the approach to steady-state for both enzymes consisted of a mono-exponential acceleration upon which a set of damped oscillations was superimposed. From pH 7 to 8.5, the approach to steady-state consisted of a simple exponential acceleration. The damped oscillations were analyzed by both a numerical approximation and simulation based on a theoretical model. BuChE-catalyzed hydrolysis of the thiocholine analogue of BzCh showed neither lags nor oscillations, under the same conditions. The frequency and amplitude of the damped oscillations decreased as the BzCh concentration increased. The apparent induction time for the exponential portion of the lag was calculated from the envelope of the damped oscillations or from the smooth lag. Wild-type BuChE showed a hyperbolic increase in induction time as the BzCh concentration increased (tau max = 210 s at pH 6.0). However, the induction time for D70G was constant over the whole range of BzCh concentrations (tau max = 60 s at pH 6.0). Thus, the induction time does not conform to a simple hysteretic model in which there is a slow conformational transition of the enzyme from an inactive form E to an active form E'. No pH-dependence of the induction time was found between pH 6.0 and 8.5 in sodium phosphate buffers of various concentrations (from 1 mm to 1 m). However, increasing the pH tended to abolish the oscillations (increase the damping factor). This effect was more pronounced for D70G than for wild-type. Although the lyotropic properties of phosphate change from chaotropic at pH 6.0 to kosmotropic at pH > 8.0, no effect of phosphate concentration on the oscillations was noticed at the different pH values, suggesting that the oscillations are not related to a pH-dependent Hofmeister effect of phosphate ions. Simulation and theoretical analysis of the oscillatory behaviour of the approach to the steady-state for BuChE led us to propose a model for the hysteresis of BuChE with BzCh. In this model, the substrate-free enzyme is present as an equilibrium mixture of two forms, E and E'. Substrate binds to E and E', but only Epsilon'S makes products. It is proposed that oscillations originate from a time-dependent change in the local concentration, solvation and/or conformation of substrate in the bulk solution. 1H-NMR measurements provided evidence for a slow equilibrium between two BzCh conformers. Binding of the conformationally preferred substrate conformer leads to products.     

A model for the origin and properties of flicker-induced geometric phosphenes

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals.     

Formulas for intrinsic noise evaluation in oscillatory genetic networks

The linear noise approximation is a useful method for stochastic noise evaluations in genetic regulatory networks, where the covariance equation described as a Lyapunov equation plays a central role. We discuss the linear noise approximation method for evaluations of an intrinsic noise in autonomously oscillatory genetic networks; in such oscillatory networks, the covariance equation becomes a periodic differential equation that provides generally an unbounded covariance matrix, so that the standard method of noise evaluation based on the covariance matrix cannot be adopted directly. In this paper, we develop a new method of noise evaluation in oscillatory genetic networks; first, we investigate structural properties, e.g., orbital stability and periodicity, of the solutions to the covariance equation given as a periodic Lyapunov differential equation by using the Floquet-Lyapunov theory, and propose a global measure for evaluating stochastic amplitude fluctuations on the periodic trajectory; we also derive an evaluation formula for the period fluctuation. Finally, we apply our method to a model of circadian oscillations based on negative auto-regulation of gene expression, and show validity of our method by comparing the evaluation results with stochastic simulations.     

An (1)H-MRS evaluation of the phosphocreatine/creatine pool (tCr) in human muscle

The human gastrocnemius was examined with and without creatine supplementation under the conditions of rest, ischemic fatigue (IF), and recovery to perturb the pool sizes and equilibrium between phosphocreatine (PCr) and creatine (Cr). (1)H- and (31)P-magnetic resonance spectroscopy (MRS) were used to examine the total creatine (tCr) pool in each of the metabolic states. (31)P-MRS monitored the depletion of the PCr peak during IF to <5% of that at rest. (1)H-MRS focused on the tCr methyl peak at 3.02 ppm (dipolar coupled triplet), at which point it was expected that the triplet peak intensity would be similar both in IF and rest. Initial (1)H-MRS data showed the peak intensity during IF decreased, suggesting a change in tCr pool size. Subsequent studies of transverse relaxation time (T(2)) revealed that this decline was primarily due to a more rapid T(2) decay of the tCr peak in IF (T(2) approximately 40 ms) compared with at rest (T(2) approximately 162 ms). Because Cr is the major contributor to tCr in IF, it is possible that there is a pool of Cr displaying reduced mobility in vivo. Moreover, the residual dipolar coupled triplet observed at rest collapsed into a broad singlet during IF, suggestive of significant changes in the ordered environment experienced at rest for PCr compared with when it is converted to Cr during IF. In addition, these data suggest that in (1)H-MRS studies whose goals include quantitative estimates of tCr pool sizes, standardized metabolic conditions or careful T(2) evaluations will be required.     

Improved neuronal models for studying neural networks

Previous neuronal models used for the study of neural networks are considered. Equations are developed for a model which includes: 1) a normalized range of firing rates with decreased sensitivity at large excitatory or large inhibitory input levels, 2) a single rate constant for the increase in firing rate following step changes in the input, 3) one or more rate constants, as required to fit experimental data for the adaptation of firing rates to maintained inputs. Computed responses compare well with the types of neuronal responses observed experimentally. Depending on the parameters, overdamped increases and decreases, damped oscillatory or maintained oscillatory changes in firing rate are observed to step changes in the input. The integrodifferential equations describing the neuronal models can be represented by a set of first-order differential equations. Steady-state solutions for these equations can be obtained for constant inputs, as well as the stability of the solutions to small perturbations. The linear frequency response function is derived for sufficiently small time-varying inputs. The linear responses are also compared with the computed solutions for larger non-linear responses.     

Two models for competition between age classes

We consider two lumped age-structured models of juvenile against adult competition, one of which is a compartmental ordinary differential equation (ODE) model and one of which is a system of ODEs with delay derived from the McKendrick partial differential equation (PDE) model. Existence and stability of positive equilibria and existence of oscillatory solutions of both models are studied. Using a competition parameter, which measures the intra-specific competition, we investigate the effects of the competitive interactions between juveniles and adults on the dynamics of the population for both models. We find that these effects are different for the two models and discuss the differences from the modeling perspective. The discussion reveals an interesting relation between the length of the maturation period and the vital rates' dependence on the competition parameter.     

Phase Transitions in a Logistic Metapopulation Model with Nonlocal Interactions

The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms causing such a phenomenon. We propose a single-species, continuous time metapopulation model taking nonlocal interactions into account. Discrete probability kernels are used to model these interactions in a patchy environment. A linear stability analysis of the model shows that solutions to this equation exhibit pattern formation if the dispersal rate of the species is sufficiently small and the discrete interaction kernel satisfies certain conditions. We numerically observe that traveling and stationary wave-type patterns arise near critical dispersal rate. We use weakly nonlinear analysis to better understand the behavior of formed patterns. We show that observed patterns arise through both supercritical and subcritical bifurcations from spatially homogeneous steady state. Moreover, we observe that as the dispersal rate decreases, amplitude of the patterns increases. For discontinuous transitions to instability, we also show that there exists a threshold for the amplitude of the initial condition, above which pattern formation is observed.     

Phosphocreatine recovery kinetics following low- and high-intensity exercise in human triceps surae and rat posterior hindlimb muscles

Previous studies have suggested the recovery of phosphocreatine (PCr) after exercise is at least second-order in some conditions. Possible explanations for higher-order PCr recovery kinetics include heterogeneity of oxidative capacity among skeletal muscle fibers and ATP production via glycolysis contributing to PCr resynthesis. Ten human subjects (28 +/- 3 yr; mean +/- SE) performed gated plantar flexion exercise bouts consisting of one contraction every 3 s for 90 s (low-intensity) and three contractions every 3 s for 30 s (high-intensity). In a parallel gated study, the sciatic nerve of 15 adult male Sprague-Dawley rats was electrically stimulated at 0.75 Hz for 5.7 min (low intensity) or 5 Hz for 2.1 min (high intensity) to produce isometric contractions of the posterior hindlimb muscles. [(31)P]-MRS was used to measure relative [PCr] changes, and nonnegative least-squares analysis was utilized to resolve the number and magnitude of exponential components of PCr recovery. Following low-intensity exercise, PCr recovered in a monoexponential pattern in humans, but a higher-order pattern was typically observed in rats. Following high-intensity exercise, higher-order PCr recovery kinetics were observed in both humans and rats with an initial fast component (tau < 15 s) resolved in the majority of humans (6/10) and rats (5/8). These findings suggest that heterogeneity of oxidative capacity among skeletal muscle fibers contributes to a higher-order pattern of PCr recovery in rat hindlimb muscles but not in human triceps surae muscles. In addition, the observation of a fast component following high-intensity exercise is consistent with the notion that glycolytic ATP production contributes to PCr resynthesis during the initial stage of recovery.     

Stability switches,oscillatory multistability,and spatio-temporal patterns of nonlinear oscillations in recurrently delay coupled neural networks

A model of time-delay recurrently coupled spatially segregated neural assemblies is here proposed. We show that it operates like some of the hierarchical architectures of the brain. Each assembly is a neural network with no delay in the local couplings between the units. The delay appears in the long range feedforward and feedback inter-assemblies communications. Bifurcation analysis of a simple four-units system in the autonomous case shows the richness of the dynamical behaviors in a biophysically plausible parameter region. We find oscillatory multistability, hysteresis, and stability switches of the rest state provoked by the time delay. Then we investigate the spatio-temporal patterns of bifurcating periodic solutions by using the symmetric local Hopf bifurcation theory of delay differential equations and derive the equation describing the flow on the center manifold that enables us determining the direction of Hopf bifurcations and stability of the bifurcating periodic orbits. We also discuss computational properties of the system due to the delay when an external drive of the network mimicks external sensory input.     

Non-invasive assessment of oxidative capacity in young Indian men and women: a 31P magnetic resonance spectroscopy study

It is generally assumed that men display greater strength and muscle capacity than women. However, previous biochemical and histological studies have shown that men have greater capacity for anaerobic metabolism and women have higher or similar oxidative metabolism. Therefore, in the present study, we estimated oxidative capacity of gastrocnemius muscle and compared in Indian men and women using non-invasive in vivo 31P magnetic resonance spectroscopy (MRS). Healthy subjects (8 young males and 9 females, age-matched) performed plantar flexion exercise within a magnet and MRS measurements of inorganic phosphate (Pi), phosphocreatine (PCr), ADP, and pH of the calf muscles were carried out using a 1.5 T whole-body MRI system. PCr values during recovery were fitted to an exponential curve, and oxidative capacity was calculated using rate constant (k(PCr)), as an index of oxidative phosphorylation. When men and women were compared for different metabolic ratios, ADP, pH, k(PCr) and oxidative capacity, all parameters turned out to be statistically insignificant. The results showed no gender effect on skeletal muscle oxidative metabolism. The study demonstrated the usefulness of such non-invasive method to indirectly measure the oxidative capacity of the muscle based on PCr recovery.     

Dynamics of a biological fixed film for phenol degradation in a fluidized-bed bioreactor

Experimental and modeling studies were conducted to analyze the dynamic response behavior of a phenol-oxidizing fixed film using a differential, fluidized-bed bioreactor in a recycle loop with a well-mixed reservoir. With the bioreactor at steady state, a pulse of phenol was added to perturb the system, and the phenol concentration was monitored continuously until steady state was again achieved.The experimental dynamics were compared with a dynamic mathematical model based on diffusion and reaction within the biofilm, liquid mixing, and biofilm growth. Constant-pH experiments could be adequately described using an unstructured, double-Monod kinetic expression with substrate inhibition by phenol.However, in dynamic experiments without pH control, the pH of the liquid phase dropped, and damped oscillations were observed in the phenol concentration and reaction rate trajectories. Oscillatory solutions could not be induced in the model, even when product inhibition was included, and a linear stability analysis did not reveal tendencies toward instability. The cause of the experimental oscillations remains unknown.     

Cluster associative memory formation in a three-layer network of phase oscillators

A three-layer network model of oscillatory associative memory is proposed. The network is capable of storing binary images, which can be retrieved upon presenting an appropriate stimulus. Binary images are encoded in the form of the spatial distribution of oscillatory phase clusters in-phase and anti-phase relative to a reference periodic signal. The information is loaded into the network using a set of interlayer connection weights. A condition for error-free pattern retrieval is formulated, delimiting the maximal number of patterns to be stored in the memory (storage capacity). It is shown that the capacity can be significantly increased by generating an optimal alphabet (basis pattern set). The number of stored patterns can reach values of the network size (the number of oscillators in each layer), which is significantly higher than the capacity of conventional oscillatory memory models. The dynamical and information characteristics of the retrieval process based on the optimal alphabet, including the size of “attraction basins“ and the input pattern distortion admissible for error-free retrieval, are investigated.     

The Relative Influences of Phosphometabolites and pH on Action Potential Morphology during Myocardial Reperfusion: A Simulation Study

Myocardial ischemia-reperfusion (IR) injury represents a constellation of pathological processes that occur when ischemic myocardium experiences a restoration of perfusion. Reentrant arrhythmias, which represent a particularly lethal manifestation of IR injury, can result when ischemic tissue exhibits decreased excitability and/or changes of action potential duration (APD), conditions that precipitate unidirectional conduction block. Many of the cellular components that are involved with IR injury are modulated by pH and/or phosphometabolites such as ATP and phosphocreatine (PCr), all of which can be manipulated in vivo and potentially in the clinical setting. Using a mathematical model of the cardiomyocyte that we previously developed to study ischemia and reperfusion, we performed a series of simulations with the aim of determining whether pH- or phosphometabolite-related processes play a more significant role in generating changes in excitability and action potential morphology that are associated with the development of reentry. In our simulations, persistent shortening of APD, action potential amplitude (APA), and depolarization of the resting membrane potential were more severe when ATP and PCr availability were suppressed during reperfusion than when extracellular pH recovery was inhibited. Reduced phosphometabolite availability and pH recovery affected multiple ion channels and exchangers. Some of these effects were the result of direct modulation by phosphometabolites and/or acidosis, while others resulted from elevated sodium and calcium loads during reperfusion. In addition, increasing ATP and PCr availability during reperfusion was more beneficial in terms of increasing APD and APA than was increasing the amount of pH recovery. Together, these results suggest that therapies directed at increasing ATP and/or PCr availability during reperfusion may be more beneficial than perturbing pH recovery with regard to mitigating action potential changes that increase the likelihood of reentrant arrhythmias.     

Linear model of brain electrical activity—EEG as a superposition of damped oscillatory modes

EEG time series were modeled as an output of the linear filter driven by white noise. Parameters describing the signal were determined in a way fulfilling the maximum entropy principle. Transfer function and the impulse response function were found. The solutions of the differential equations describing the system have the form of the damped oscillatory modes. The representation of the EEG time series as a superposition of the resonant modes with characteristic decay factors seems a valuable method of the analysis of the signal, since it offers high reduction of the data to the few parameters of a clear physiological meaning.     

Use of phosphocreatine kinetics to determine the influence of creatine on muscle mitochondrial respiration: an in vivo 31P-MRS study of oral creatine ingestion.

Recent human isolated muscle fiber studies suggest that phosphocreatine (PCr) and creatine (Cr) concentrations play a role in the regulation of mitochondrial respiration rate. To determine whether similar regulatory mechanisms are present in vivo, this study examined the relationship between skeletal muscle mitochondrial respiration rate and end-exercise PCr, Cr, PCr-to-Cr ratio (PCr/Cr), ADP, and pH by using (31)P-magnetic resonance spectroscopy in 16 men and women (36.9 +/- 4.6 yr). The initial PCr resynthesis rate and time constant (T(c)) were used as indicators of mitochondrial respiration after brief (10-12 s) and exhaustive (1-4 min) dynamic knee extension exercise performed in placebo and creatine-supplemented conditions. The results show that the initial PCr resynthesis rate has a strong relationship with end-exercise PCr, Cr, and PCr/Cr (r > 0.80, P < 0.001), a moderate relationship with end-exercise ADP (r = 0.77, P < 0.001), and no relationship with end-exercise pH (r = -0.14, P = 0.34). The PCr T(c) was not as strongly related to PCr, Cr, PCr/Cr, and ADP (r < 0.77, P < 0.001-0.18) and was significantly influenced by end-exercise pH (r = -0.43, P < 0.01). These findings suggest that end-exercise PCr and Cr should be taken into consideration when PCr recovery kinetics is used as an indicator of mitochondrial respiration and that the initial PCr resynthesis rate is a more reliable indicator of mitochondrial respiration compared with the PCr T(c).     

ATP synthesis and proton handling in muscle during short periods of exercise and subsequent recovery.

We used (31)P-magnetic resonance spectroscopy to study proton buffering in finger flexor muscles of eight healthy men (25-45 yr), during brief (18-s) voluntary finger flexion exercise (0.67-Hz contraction at 10% maximum voluntary contraction; 50/50 duty cycle) and 180-s recovery. Phosphocreatine (PCr) concentration fell 19 +/- 2% during exercise and then recovered with half time = 0.24 +/- 0.01 min. Cell pH rose by 0.058 +/- 0.003 units during exercise as a result of H(+) consumption by PCr splitting, which (assuming no lactate production or H(+) efflux) implies a plausible non-P(i) buffer capacity of 20 +/- 3 mmol. l intracellular water(-1). pH unit(-1). There was thus no evidence of significant glycogenolysis to lactate during exercise. Analysis of PCr kinetics as a classic linear response suggests that oxidative ATP synthesis reached 48 +/- 2% of ATP demand by the end of exercise; the rest was met by PCr splitting. Postexercise pH recovery was faster than predicted, suggesting "excess proton" production, with a peak value of 0.6 +/- 0.2 mmol/l intracellular water at 0.45 min of recovery, which might be due to, e.g., proton influx driven by cellular alkalinization, or a small glycolytic contribution to PCr resynthesis in recovery.     

Spontaneous aggregation of the mitochondrial natural ATPase inhibitor in salt solutions as demonstrated by gel filtration and neutron scattering. Application to the concomitant purification of the ATPase inhibitor and F1-ATPase

(1) The natural ATPase inhibitor (IF1) from beef heart mitochondria has a tendency to form aggregates in aqueous solutions. The extent of aggregation and the structure of the aggregates were assessed by gel filtration and small-angle neutron scattering. IF1 polymerization was found to depend on the salt concentrations, pH of the medium and concentration of IF1. The higher the salt concentration, the lower the aggregation state. Aggregation of IF1 was decreased at slightly acidic pH. It increased with the concentration of IF1 as expected from the law of mass action. (2) Neutron scattering showed the aggregation of IF1 in 2 M ammonium sulfate solutions. The predominant species is the dimer which has a somewhat elongated shape. (3) The Sephadex G-50 chromatography that is supposed to deprive beef heart submitochondrial particles of loosely bound IF1 (Racker, E. and Horstman, L.L. (1967) J. Biol. Chem. 242, 2547-2551) was shown to have a limited effectiveness as a trap for IF1. The reason was that IF1 released from the particles formed high molecular weight aggregates that were not separated from the membrane vesicles by Sephadex G-50 chromatography. (4) The above observations provide the basis for a simple method of purification of beef heart IF1 which combines the recovery of the supernatant from submitochondrial particles with the last three steps of the IF1 preparation described by Horstman and Racker (J. Biol. Chem. (1970) 265, 1336-1344). The particles recovered in the sediment were deprived of IF1 and could therefore be used for preparation of F1-ATPase. The advantage of this method is that both IF1 and F1-ATPase can be prepared from the same batch of mitochondria.     

Cellular energetics analysis by a mathematical model of energy balance: estimation of parameters in human skeletal muscle

Cellularenergy balance requires that the physiological demands by ATP-utilizingfunctions be matched by ATP synthesis to sustain muscle activity. Wedevised a new method of analysis of these processes in data from singleindividuals. Our approach is based on the logic of current informationon the major mechanisms involved in this energy balance and canquantify not directly measurable parameters that govern thosemechanisms. We use a mathematical model that simulates by ordinary,nonlinear differential equations three components of cellularbioenergetics (cellular ATP flux, mitochondrial oxidativephosphorylation, and creatine kinase kinetics). We incorporate dataunder resting conditions, during the transition toward a steady stateof stimulation and during the transition during recovery back to theoriginal resting state. Making use of prior information about thekinetic parameters, we fitted the model to previously published dynamicphosphocreatine (PCr) and inorganic phosphate (P_i) dataobtained in normal subjects with an activity-recovery protocol using³¹P nuclear magnetic resonance spectroscopy. The experimentconsisted of a baseline phase, an ischemic phase (during which musclestimulation and PCr utilization occurred), and an aerobic recoveryphase. The model described satisfactorily the kinetics of the changes in PCr and P_i and allowed estimation of the maximalvelocity of oxidative phosphorylation and of the net ATP flux inindividuals both at rest and during stimulation. This work lays thefoundation for a quantitative, model-based approach to the study of invivo muscle energy balance in intact muscle systems, including human muscle.