A model for oscillatory kinetic systems

A kinetic model is proposed for oscillatory kinetic phenomena. The exact analytic solution is exhibited and shown to account for several features exhibited by oscillatory chemical and biological systems.     

A simple kinetic model for dynein oscillatory activity

A kinetic model for dynein, a molecular motor, complexed with microtubule fragments, is considered. The model explains the experimental observations of oscillatory movements in surprisingly simple axonemal fragments perfused by the ATP solution. The model explains at first time the oscillatory dynein activity as a phenomenon induced by two dynein heads cooperative interaction in the axoneme. The oscillation form, frequency, and amplitude, observed for the model, are close to these experimental characteristics. Kinetic parameters, used in the model, are close to the known experimental parameters.     

A simple kinetic model for dynein oscillatory activity

A kinetic model was proposed for dynein, a motor protein, complexed with microtubule fragments. The model explains the experimental observations of oscillatory movements in surprisingly simple axoneme fragments perfused with an ATP solution. This is the first model explaining the oscillatory activity of dynein as determined by a cooperative interaction of two dynein heads in the axoneme. The oscillation shape, frequency, and amplitude obtained for the model are close to the corresponding parameters determined experimentally.     

A model with 'growth retardation' for the kinetic heterogeneity of tumour cell populations

In the present paper we propose a continuous cell population model based on Shackney's idea of growth retardation. Cells are characterized by two state variables: the cell maturity x, 0 < or = x < or = 1, and a state variable T that identifies the rate of maturation along cell cycle. During their life span, cells can change T at random by jump transitions to T values corresponding to slower maturation rates, while at each jump the maturity x is conserved. Both the time evolution of the population and the exponential stationary solution are numerically computed. The distribution of the cell cycle transit time in asynchronous exponential growth is investigated by Monte Carlo simulation. An approximated formula for the distribution of cell cycle time is also provided.     

Modeling of oscillatory scenarios of the coexistence of competing populations

The scenarios of the formation of population distributions have been analyzed for a system of nonlinear reaction–diffusion–advection equations to describe the spatiotemporal distribution of predators and prey. The conditions that must be fulfilled for the model to belong to the class of cosymmetric systems were identified using an analytical approach. Computer simulations of a system with prey and two predators showed that the emergence of families of stationary distributions and oscillatory modes is possible when these conditions are met. The initial distributions of predators were shown to determine the character of the scenario (stationary or non-stationary) at certain combinations of parameters.     

Effect of high substrate concentration and cell feedback on kinetic behavior of heterogeneous populations in completely mixed systems

Growth kinetics of heterogeneous populations of sewage origin were studied in completely mixed reactors of the once-through type at a high concentration of incoming substrate, 3000 mg/l glucose, and in systems employing cell feedback or sludge recycle at an incoming substrate concentration of 1000 mg/1 glucose. The recycle flow rate employed was 25% of the incoming feed flow, and the concentration of cells in the recycle was maintained as closely as possible at 150% of the cell concentration in the reactor. Studies were made at various dilution rates. Throughout these studies, batch experiments using cells grown at the various dilution rates were made to determine k_s and μ_m values. As in previous studios using heterogeneous populations, the relationship between specific growth rates μ and substrate concentration S was represented better by the Monod equation than by any other which was tested. The growth “constants” μ_m, k_s, and Y were found to fall in the same general range as those determined in previous studies in once-through systems operated at 1000 mg/l glucose. It was observed that cell recycle, even at the relatively low concentration factor employed in these studies, greatly enhanced the flocculating and settling characteristics of the cells.     

Sustained oscillations in extended genetic oscillatory systems

Various dynamic cellular behaviors have been successfully modeled in terms of elementary circuitries showing particular characteristics such as negative feedback loops for sustained oscillations. Given, however, the increasing evidences indicating that cellular components do not function in isolation but form a complex interwoven network, it is still unclear to what extent the conclusions drawn from the elementary circuit analogy hold for systems that are highly interacting with surrounding environments. In this article, we consider a specific example of genetic oscillator systems, the so-called repressilator, as a starting point toward a systematic investigation into the dynamic consequences of the extension through interlocking of elementary biological circuits. From in silico analyses with both continuous and Boolean dynamics approaches to the four-node extension of the repressilator, we found that 1), the capability of sustained oscillation depends on the topology of extended systems; and 2), the stability of oscillation under the extension also depends on the coupling topology. We then deduce two empirical rules favoring the sustained oscillations, termed the coherent coupling and the homogeneous regulation. These simple rules will help us prioritize candidate patterns of network wiring, guiding both the experimental investigations for further physiological verification and the synthetic designs for bioengineering.     

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.     

A general kinetic model for biological nutrient removal activated sludge systems: model development

In this article, a kinetic model is developed and presented for biological nutrient removal (BNR) activated sludge (BNRAS) systems in general, but for external nitrification (EN) BNRAS (ENBNRAS) systems in particular. The model is based on the UCTPHO model, but includes some significant modifications, such as anoxic P uptake and associated denitrification by phosphorus accumulating organisms (PAOs). Some key features of the model are described and discussed before the model is presented. Model evaluation will be addressed in another article (Hu et al., 2007).     

A general kinetic model for biological nutrient removal activated sludge systems: model evaluation

Hu et al. (2007) presented a general kinetic model for biological nutrient removal (BNR) activated sludge (AS) systems in general, but for external nitrification (EN) BNRAS (ENBNRAS) systems in particular. In this article, this model is evaluated against a large number of experimental data sets. In this evaluation, the model is first used to simulate a wide variety of conventional internal nitrification (IN) BNRAS systems to evaluate its predictions and also evaluate the model parameters suggested by Hu et al. (2007), and to calibrate those constants for which values are not available in the literature. Simulation results indicate that the model, with appropriately calibrated parameters, is capable of predicting COD removal, nitrification and denitrification and two types of biological excess phosphorus removal (BEPR), namely aerobic and anoxic/aerobic P uptake BEPR. The model is then used to simulate the ENBNRAS systems to evaluate its capacity of simulating the behaviour of this system. Simulation results show that the model is capable of simulating the behaviour of the ENBNRAS systems, including COD, nitrification, denitrification and BEPR, particularly anoxic P uptake BEPR, with the values of kinetic and stoichiometric parameters obtained in modelling conventional BNRAS systems, except for micro(NIT), K(MP), eta(PAO) and eta(H) which required calibration.     

A parsimonious oscillatory model of handwriting

We propose an oscillatory model that is theoretically parsimonious, empirically efficient and biologically plausible. Building on Hollerbach’s (Biol Cybern 39:139–156, 1981) model, our Parsimonious Oscillatory Model of Handwriting (POMH) overcomes the latter’s main shortcomings by making it possible to extract its parameters from the trace itself and by reinstating symmetry between the \(x\) and \(y\) coordinates. The benefit is a capacity to autonomously generate a smooth continuous trace that reproduces the dynamics of the handwriting movements through an extremely sparse model, whose efficiency matches that of other, more computationally expensive optimizing methods. Moreover, the model applies to 2D trajectories, irrespective of their shape, size, orientation and length. It is also independent of the endeffectors mobilized and of the writing direction.     

A systems model and computer simulation of the green rice leafhopper populations in control programmes

A simulation model of the green rice leafhopper-spiders system was presented. The validity of this model for simulation purpose was tested by comparing the calculated values with observed ones (Fig. 4). The effectiveness of various control measures against leafhoppers was evaluated by computer simulations. The computer simulation demonstrated that the wrong use of selective insecticide, contrary to expectation, brought an increase in the pest density, i. e., that the egg densities of leafhoppers in the 2nd and 3rd generations are increased by the insecticidal application in February, while they are decreased by the July application (Table 2). To obtain satisfactory control by sterile-male release, 320,000 sterile-male per square kilometer should be released even in the combined use with insecticides (Fig. 5). The escape of leafhoppers from predation by spiders was demonstrated by the simulation. It is suggested that spiders are able to suppress the leafhopper populations at a low density when there is a very favorable balance between spiders and leafhoppers, and this condition may be realized by sophisticated use of selective insecticides (Fig. 6). Factors and/or processes which have to be involved in a more improved systems model are discussed.     

A model of the oscillatory metabolism of activated neutrophils

We present a two-compartment model to explain the oscillatory behavior observed experimentally in activated neutrophils. Our model is based mainly on the peroxidase-oxidase reaction catalyzed by myeloperoxidase with melatonin as a cofactor and NADPH oxidase, a major protein in the phagosome membrane of the leukocyte. The model predicts that after activation of a neutrophil, an increase in the activity of the hexose monophosphate shunt and the delivery of myeloperoxidase into the phagosome results in oscillations in oxygen and NAD(P)H concentration. The period of oscillation changes from >200 s to 10-30 s. The model is consistent with previously reported oscillations in cell metabolism and oxidant production. Key features and predictions of the model were confirmed experimentally. The requirement of the hexose monophosphate pathway for 10 s oscillations was verified using 6-aminonicotinamide and dexamethasone, which are inhibitors of glucose-6-phosphate dehydrogenase. The role of the NADPH oxidase in promoting oscillations was confirmed by dose-response studies of the effect of diphenylene iodonium, an inhibitor of the NADPH oxidase. Moreover, the model predicted an increase in the amplitude of NADPH oscillations in the presence of melatonin, which was confirmed experimentally. Successful computer modeling of complex chemical dynamics within cells and their chemical perturbation will enhance our ability to identify new antiinflammatory compounds.     

Instability and oscillatory behavior of membrane-chemical reaction systems

The stability problem of a chemical system consisting of reversible reactions is analyzed with the aid of computer calculations. The system is based on the model proposed by Edelstein and exhibits oscillations of chemical species. The analysis shows that the oscillatory character is of limit cycle type. The results are applied to the construction of a membrane-chemical reaction system, which shows characteristic instability behavior. This is useful as a model of cell division.     

A new model for interacting populations—I: Two-species systems

The exact solvable model presented here describes two interacting species whose populations oscillate periodically in time in the absence of self-interaction and attain saturation with fluctuations if self-interactions are included. While sharing broad features of the classical Volterra system, the model proposed here has the advantage of possessing exact solutions. The model thus provides a testing ground for general principles employed in the study of dynamics of populations.     

An oscillatory correlation model of auditory streaming

We present a neurocomputational model for auditory streaming, which is a prominent phenomenon of auditory scene analysis. The proposed model represents auditory scene analysis by oscillatory correlation, where a perceptual stream corresponds to a synchronized assembly of neural oscillators and different streams correspond to desynchronized oscillator assemblies. The underlying neural architecture is a two-dimensional network of relaxation oscillators with lateral excitation and global inhibition, where one dimension represents time and another dimension frequency. By employing dynamic connections along the frequency dimension and a random element in global inhibition, the proposed model produces a temporal coherence boundary and a fissure boundary that closely match those from the psychophysical data of auditory streaming. Several issues are discussed, including how to represent physical time and how to relate shifting synchronization to auditory attention.     

Effect of the larynx on oscillatory flow in the central airways: a model study

Measurements were made of the effect of the larynx on the oscillatory flow profiles in a 3:1 scale model of the human central airways. A fixed glottic aperture corresponding to the shape and size at midinspiration was used. Oscillatory airflows at peak Reynolds numbers, similar to those obtained during spontaneous breathing and panting, were studied. The flow distribution to the five lobar bronchi was maintained by distally placed linear resistors. A hot-wire anemometer probe was used to measure the local velocity along two perpendicular diameters at six stations distributed through the model. Near the proximal end of the trachea, the flat velocity profiles at the beginning of the flow cycle peaked at maximum flow because of the jet created by the glottic aperture. This peaked structure was conserved during the latter half of the inspiratory cycle. Close to the carina, the jet had almost dissipated and the entry conditions into the main bronchi corresponded to those in the absence of the laryngeal model. The effect of the glottic aperture on the mean velocity was not felt beyond the carina, and the characteristic skewed profiles seen in oscillatory flows, in the absence of the larynx, were present in the main and lobar bronchi.