Modeling of an aerobic biofilm reactor with double-limiting substrate kinetics: bifurcational and dynamical analysis

A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behavior of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. is extended to embody key features of the phenomenology of the granular‐supported biofilm: biofilm growth and detachment, gas–liquid oxygen transport, phenol, and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady‐state conditions and stability, and local dynamic behavior have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gas–liquid mass transfer coefficient, biofilm detachment rate, and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady‐state scenario with transcritical and saddle‐node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is <10% of the saturation level, the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011     

Spatio-temporal modelling explains the effect of reduced plasma membrane Ca2+ efflux on intracellular Ca2+ oscillations in hepatocytes

In many non-excitable eukaryotic cells, including hepatocytes, Ca²⁺ oscillations play a key role in intra- and intercellular signalling, thus regulating many cellular processes from fertilisation to death. Therefore, understanding the mechanisms underlying these oscillations, and consequently understanding how they may be regulated, is of great interest. In this paper, we study the influence of reduced Ca²⁺ plasma membrane efflux on Ca²⁺ oscillations in hepatocytes. Our previous experiments with carboxyeosin show that a reduced plasma membrane Ca²⁺ efflux increases the frequency of Ca²⁺ oscillations, but does not affect the duration of individual transients. This phenomenon can be best explained by taking into account not only the temporal, but also the spatial dynamics underlying the generation of Ca²⁺ oscillations in the cell. Here we divide the cell into a grid of elements and treat the Ca²⁺ dynamics as a spatio-temporal phenomenon. By converting an existing temporal model into a spatio-temporal one, we obtain theoretical predictions that are in much better agreement with the experimental observations.     

Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

Modeling temporal and spatial colony-site dynamics in a long-lived seabird

We studied the determinants of colony site dynamics in Audouin's gull, Larus audouinii, breeding in a small archipelago of the western Mediterranean. Data on island occupation were available for a series of 25 years, since first colonization of the archipelago in 1973. Group behavior was studied in relation to the components of dispersal: permanence or abandonment (extinction) on an island previously occupied and permanence or occupation (colonization) of another island. Generalized Linear Mixed Models (GLMMs) were used to identify the relative contribution of each explanatory variable to the probability of colony abandonment. Gulls showed a low probability (3%) of abandoning one of the islands (Grossa I.), especially when the colony was increasing in numbers from time t_i-1 to t_i. However, the probability of abandoning Grossa increased up to 31% when the colony was declining. The probability of island abandonment was very high for all other islands (range 66–99%) when the colony was declining, but much lower (range 36–82%) when it was increasing. Hence, we suggest that island abandonment by Audouin's gull is at least a two-step process. The first step (dispersal of a portion of the colony) probably takes place at random, as an evolutionary load typical of a species evolved in unstable habitats. The second step, a further loss of breeding pairs, seems to feedback on the first loss of members of the colony (public information), likely perceived as a loss of colony quality. Colonization of islands by gulls abandoning Grossa I. was marginally and negatively affected by the density of breeding yellow-legged gulls, a predatory species. Results apply to conservation ecology since they highlight the need to protect not only occupied patches but also those empty at present.     

Modeling of a propagation mechanism of infectious prion protein; a hexamer as the minimum infectious unit

To construct a new model of the propagation mechanism of infectious scrapie-type prion protein (PrP(Sc)), here we conducted a disruption simulation of a PrP(Sc) nonamer using structure-based molecular dynamics simulation method based on a hypothetical PrP(Sc) model structure. The simulation results showed that the nonamer disrupted in cooperative manners into monomers via two significant intermediate states: (1) a nonamer with a partially unfolded surface trimer and (2) a hexamer and three monomers. Dimers and trimers were rarely observed. Then, we propose a new PrP(Sc) propagation mechanism where a hexamer plays an essential role as a minimum infectious unit.     

Modeling of ATP-mediated signal transduction and wave propagation in astrocytic cellular networks

Astrocytes, a special type of glial cells, were considered to have supporting role in information processing in the brain. However, several recent studies have shown that they can be chemically stimulated by neurotransmitters and use a form of signaling, in which ATP acts as an extracellular messenger. Pathological conditions, such as spreading depression, have been linked to abnormal range of wave propagation in astrocytic cellular networks. Nevertheless, the underlying intra- and inter-cellular signaling mechanisms remain unclear. Motivated by the above, we constructed a model to understand the relationship between single-cell signal transduction mechanisms and wave propagation and blocking in astrocytic networks. The model incorporates ATP-mediated IP3 production, the subsequent Ca2+ release from the ER through IP3R channels and ATP release into the extracellular space. For the latter, two hypotheses were tested: Ca2+- or IP3-dependent ATP release. In the first case, single astrocytes can exhibit excitable behavior and frequency-encoded oscillations. Homogeneous, one-dimensional astrocytic networks can propagate waves with infinite range, while in two dimensions, spiral waves can be generated. However, in the IP3-dependent ATP release case, the specific coupling of the driver ATP-IP3 system with the driven Ca2+ subsystem leads to one- and two-dimensional wave patterns with finite range of propagation.     

Semi-empirical power-law scaling of new infection rate to model epidemic dynamics with inhomogeneous mixing

The expected number of new infections per day per infectious person during an epidemic has been found to exhibit power-law scaling with respect to the susceptible fraction of the population. This is in contrast to the linear scaling assumed in traditional epidemiologic modeling. Based on simulated epidemic dynamics in synthetic populations representing Los Angeles, Chicago, and Portland, we find city-dependent scaling exponents in the range of 1.7-2.06. This scaling arises from variations in the strength, duration, and number of contacts per person. Implementation of power-law scaling of the new infection rate is quite simple for SIR, SEIR, and histogram-based epidemic models. Treatment of the effects of the social contact structure through this power-law formulation leads to significantly lower predictions of final epidemic size than the traditional linear formulation.     

Modeling for the optimal biodegradation of toxic wastewater in a discontinuous reactor

The degradation of toxic compounds in Sequencing Batch Reactors (SBRs) poses inhibition problems. Time Optimal Control (TOC) methods may be used to avoid such inhibition thus exploiting the maximum capabilities of this class of reactors. Biomass and substrate online measurements, however, are usually unavailable for wastewater applications, so TOC must use only related variables as dissolved oxygen and volume. Although the standard mathematical model to describe the reaction phase of SBRs is good enough for explaining its general behavior in uncontrolled batch mode, better details are needed to model its dynamics when the reactor operates near the maximum degradation rate zone, as when TOC is used. In this paper two improvements to the model are suggested: to include the sensor delay effects and to modify the classical Haldane curve in a piecewise manner. These modifications offer a good solution for a reasonable complexification tradeoff. Additionally, a new way to look at the Haldane K-parameters (micro(o),K(I),K(S)) is described, the S-parameters (micro*,S*,S(m)). These parameters do have a clear physical meaning and, unlike the K-parameters, allow for the statistical treatment to find a single model to fit data from multiple experiments.     

Modeling of glycerol production by fermentation in different reactor states

A kinetic model of glycerol production by fermentation with the osmophilic yeast Candida krusei was studied firstly by analogies to published works. Considering that the glycerol produced competes with glucose, as a second carbon source for energy maintenance, mathematical models of glucose utilization and glycerol accumulation were modified further. By adjusting only two variable macrokinetic parameters, K_S and β, the model simulations could fit experimental data well when the reactor was changed from Airlift Loop Reactor in different scale or airlift mode to Stirred Vessel. To avoid a significant reduction in glycerol production in the latter fermentation stage, the final condition of the fermentation, determined by the concentration ratio of glycerol to glucose, was also investigated in four different Reactor States. The kinetic models and simulation results can provide certain reference for scale up of glycerol production by fermentation.     

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.     

中国潜在植被NPP的空间分布模拟

在对1980年以来气候要素进行空间化的基础上,利用分类回归树模型CART计算中国的潜在归一化植被指数(NDVI),采用改进的光能利用率模型(CASA)和潜在NDVI数据对中国的潜在植被净初级生产力(NPP)进行模拟。结果表明:中国潜在NDVI和潜在NPP均呈现出南高北低、东高西低的格局,低值多分布在沙漠、戈壁等干旱地带,高值多出现在低、中山平原区; 400 mm等降水量线是潜在NDVI和潜在NPP高值与低值的分界线;全国潜在NDVI和潜在NPP的平均值分别为0.396和319.31 g C·m-2;夏季潜在NPP的平均值最大,其次是春季,冬季最小;依据潜在NPP与2015年现实NPP的差异,可将中国植被恢复区划分为西部高潜力区、北部低潜力区和南部非潜力区3部分;潜在NDVI和潜在NPP的空间模拟可以将人类活动对自然生态系统的直接影响与气候变化的影响分离,量化了外界压力下真实的生态状况和潜在生态状况的差异,为制定差别化的生态恢复对策提供了科学依据。     

Modeling of hollow-fiber capillary reactor for the production of L-Alanine with coenzyme regeneration

Continuous production of L-alanine with conjugated enzyme systems of alanine dehydrogenase (AlaDH) and lactate dehydrogenase (LDH) or alcohol dehydrogenase (ADH) was carried out with NAD regeneration in an ultrafiltration hollow-fiber capillary reactor (HFCR) which was proposed as a test bioreactor with very small scale. In the AlaDH/LDH system, pyruvate is the intermediate product for L-alanine so that an optimal point existed in pyruvate concentration for the production rate of L-alanine. NAD cycling number of 4850 and L-alanine productivity of 61.7 mmol/L h were obtained at the best condition. In the AlaDH/ADH system, however, the substrate inhibition in the AlaDH reaction by pyruvate should be considered and the best results of NAD cycling number and (L)-alanine productivity were 2700 and 13.5 mmol/L h, respectively. In consideration of concentration distribution and mixing in the axial direction on an HFCR, performance of the reactor was theoretically analyzed with a multistage stirred tank reactor model combined with the kinetic model based on all the elementary reactions involved. Although quantitative discrepancy existed in some cases, the present theoretical model could explain experimental results and is expected to be generally applicable to standard hollow fiber reactors.     

Numerical simulation of wave propagation in a realistic model of the human external ear

In this study, a numerical investigation is performed to evaluate the effects of high-pressure sinusoidal and blast wave's propagation around and inside of a human external ear. A series of computed tomography images are used to reconstruct a realistic three-dimensional (3D) model of a human ear canal and the auricle. The airflow field is then computed by solving the governing differential equations in the time domain using a computational fluid dynamics software. An unsteady algorithm is used to obtain the high-pressure wave propagation throughout the ear canal which is validated against the available analytical and numerical data in literature. The effects of frequency, wave shape, and the auricle on pressure distribution are then evaluated and discussed. The results clearly indicate that the frequency plays a key role on pressure distribution within the ear canal. At 4 kHz frequency, the pressure magnitude is much more amplified within the ear canal than the frequencies of 2 and 6 kHz, for the incident wave angle of 90° investigated in this study, attributable to the ‘4-kHz notch’ in patients with noise-induced hearing loss. According to the results, the pressure distribution patterns at the ear canal are very similar for both sinusoidal pressure waveform with the frequency of 2 kHz and blast wave. The ratio of the peak pressure value at the eardrum to that at the canal entrance increases from about 8% to 30% as the peak pressure value of the blast wave increases from 5 to 100 kPa for the incident wave angle of 90° investigated in this study. Furthermore, incorporation of the auricle to the ear canal model is associated with centerline pressure magnitudes of about 50% and 7% more than those of the ear canal model without the auricle throughout the ear canal for sinusoidal and blast waves, respectively, without any significant effect on pressure distribution pattern along the ear canal for the incident wave angle of 90° investigated in this study.     

Modeling the spatial and temporal dynamics of riparian vegetation induced by river flow fluctuation

River flow fluctuation has an important influence on riparian vegetation dynamics. A temporally segmented stochastic model focusing on a same‐aged population is developed for the purpose of describing both spatial and temporal dynamics of riparian vegetation. In the model, the growth rate of population, rather than carrying capacity, is modeled as the random variable. This model has explicit physical meaning. The model deduces a process‐based solution. From the solution process, the probability density of spatial distribution can be derived; therefore, the spatial distribution of population abundance can be described. The lifespan of a same‐aged population and the age structure of the species‐specific population can also be studied with the aid of this temporally segmented model. The influence of correlation time of river flow fluctuation is also quantified according to the model. The calibration of model parameters and model application are discussed. The model provides a computer‐aided method to simulate and predict vegetation dynamics during river flow disturbances. Meanwhile, the model is open and allows for more accurate and concrete modeling of growth rate. Because of the Markov property involved in the process‐based solution, the model also has the ability to deal with cases of nonstationary disturbances.     

碱化草地群落恢复演替空间格局动态分析

对松嫩平原碱化草地1989年开始围栏封育的1hm^2样地9a间的空间格局进行了分析,结果表明：（1）不同物种斑块空间格局动态不同,在恢复演替各个阶段中的地位与作用也不同。（2）结论基本上支持了斑块化－稳定性假说。     

Evolution of cooperation in spatial public goods games with common resource dynamics

Investment in a common resource shared by all players is difficult to evolve despite higher returns because a non-investor (free-rider) always receives more than an investor (altruist). This situation is referred to as the Tragedy of the Commons and is often observed in various biological systems including environmental problems of human society. Punishment and reputation are effective mechanisms but require cooperator's ability to identify free-riders. Volunteering can work in anonymous public goods games but this requires voluntary participation, which is not always the case. Here, we show that the evolution of altruism is possible in anonymous and obligate public goods games if we consider the spatiotemporal dynamics of the common resource that incorporate spatial diffusion and internal dynamics of the commons. The investors' strategy to counter free-riders is to increase population density and to outnumber them with the common resource level kept as low as that of the free-riders.     

Deciphering the effect of climate warming on an emerging poplar pest using spatial extrapolation of population parameters

1. The woolly poplar aphid Phloeomyzus passerinii Signoret (Aphididae: Phloeomyzinae) is a major pest of poplar plantations. We hypothesized that recent temperature increases may have contributed to the emergence and subsequent northward expansion of outbreaks in France.
2. We reared P. passerinii at four temperatures to estimate its thermal requirements. We used experimental data to parametrize a mechanistic and temperature-driven physiologically-based demographic model. The model was used to simulate the effect of temperature on aphid dynamics and to assess the role of climate warming on the spatiotemporal dynamics of outbreaks.
3. The lower developmental threshold was estimated at 6.4 °C and the development degree-days at 171.
4. Our model supports the hypothesis that recent warming may have promoted outbreaks in northern France. During recent exceptionally warm years, more than 70% of the northern poplar area was favourable for outbreaks.
5. Our model suggests that climate warming is not the sole factor involved. The dominance of resistant poplar genotypes such as ‘Robusta’ or ‘Beaupré’ may have preserved plantations from outbreaks before 1996 in southern France and until 2000 in the central part. Other factors, including biological characteristics, biotic interactions, or precipitation should be investigated.

     

Modeling association among demographic parameters in analysis of open population capture-recapture data

We present a hierarchical extension of the Cormack-Jolly-Seber (CJS) model for open population capture-recapture data. In addition to recaptures of marked animals, we model first captures of animals and losses on capture. The parameter set includes capture probabilities, survival rates, and birth rates. The survival rates and birth rates are treated as a random sample from a bivariate distribution, thus the model explicitly incorporates correlation in these demographic rates. A key feature of the model is that the likelihood function, which includes a CJS model factor, is expressed entirely in terms of identifiable parameters; losses on capture can be factored out of the model. Since the computational complexity of classical likelihood methods is prohibitive, we use Markov chain Monte Carlo in a Bayesian analysis. We describe an efficient candidate-generation scheme for Metropolis-Hastings sampling of CJS models and extensions. The procedure is illustrated using mark-recapture data for the moth Gonodontis bidentata.     

Calcium wave propagation in pancreatic acinar cells: functional interaction of inositol 1,4,5-trisphosphate receptors, ryanodine receptors, and mitochondria

In pancreatic acinar cells, inositol 1,4,5-trisphosphate (InsP(3))-dependent cytosolic calcium ([Ca(2+)](i)) increases resulting from agonist stimulation are initiated in an apical "trigger zone," where the vast majority of InsP(3) receptors (InsP(3)R) are localized. At threshold stimulation, [Ca(2+)](i) signals are confined to this region, whereas at concentrations of agonists that optimally evoke secretion, a global Ca(2+) wave results. Simple diffusion of Ca(2+) from the trigger zone is unlikely to account for a global [Ca(2+)](i) elevation. Furthermore, mitochondrial import has been reported to limit Ca(2+) diffusion from the trigger zone. As such, there is no consensus as to how local [Ca(2+)](i) signals become global responses. This study therefore investigated the mechanism responsible for these events. Agonist-evoked [Ca(2+)](i) oscillations were converted to sustained [Ca(2+)](i) increases after inhibition of mitochondrial Ca(2+) import. These [Ca(2+)](i) increases were dependent on Ca(2+) release from the endoplasmic reticulum and were blocked by 100 microM ryanodine. Similarly, "uncaging" of physiological [Ca(2+)](i) levels in whole-cell patch-clamped cells resulted in rapid activation of a Ca(2+)-activated current, the recovery of which was prolonged by inhibition of mitochondrial import. This effect was also abolished by ryanodine receptor (RyR) blockade. Photolysis of d-myo InsP(3) P(4(5))-1-(2-nitrophenyl)-ethyl ester (caged InsP(3)) produced either apically localized or global [Ca(2+)](i) increases in a dose-dependent manner, as visualized by digital imaging. Mitochondrial inhibition permitted apically localized increases to propagate throughout the cell as a wave, but this propagation was inhibited by ryanodine and was not seen for minimal control responses resembling [Ca(2+)](i) puffs. Global [Ca(2+)](i) rises initiated by InsP(3) were also reduced by ryanodine, limiting the increase to a region slightly larger than the trigger zone. These data suggest that, while Ca(2+) release is initially triggered through InsP(3)R, release by RyRs is the dominant mechanism for propagating global waves. In addition, mitochondrial Ca(2+) import controls the spread of Ca(2+) throughout acinar cells by modulating RyR activation.