Chemostat-cultivated Escherichia coli at high dilution rate: multiple steady states and drift

The representation of metabolic network reaction kinetics in a scaled, polynomial form can allow for the prediction of multiple steady states. The polynomial formalism is used to study chemostat-cultured Escherichia coli which has been observed to exhibit two multiple steady states under ammonium ion-limited growth conditions: a high cell density-low ammonium ion concentration steady state and a low cell density-high ammonium ion concentration steady state. Additionally, the low-cell-density steady state has been observed to drift to the high-cell-density steady state. Inspection of the steady-state rate expressions for the ammonium ion transport/assimilation network (in polynomial form) suggests that at low ammonium ion concentrations, two steady states are possible. One corresponds to heavy use of the glutamine synthetase-glutamate synthase (GLNS-GS) branch and the second to heavy use of the glutamate dehydrogenase (GDH) branch. Realization of the predicted intracellular steady states is also found to be dependent on the parameters of the transport process. Moreover, the two steady states differ in where their energy intensity lies. To explain the drift, GLNS, which is inducible under low ammonium ion concentrations, is suggested to be a "memory element." A chemostat-based model is developed to illustrate that perturbations in dilution rate can lead to drift between the two steady states provided that the disturbance in dilution rate is sufficiently large and/or long in duration.     

Dynamics and stability analysis of the growth and astaxanthin production system of Haematococcus pluvialis

This paper investigated high cell density cultivation of Haematococcus pluvialis for astaxanthin production in 3.7-L bioreactors. A biomass concentration of 2.74 g L⁻¹and an astaxanthin yield of 64.4 mg L⁻¹ were obtained. Based on the experimental results, a new and simple dynamic model is proposed, differing from Monod kinetics, to describe cell growth, product formation and substrate consumption. Good agreement was found between the model predictions and experimental data. The model revealed that there was cell growth inhibition on product formation and product feedback compensation for substrate consumption, but no substrate inhibition or product inhibition of cell growth. Stability analysis demonstrated that no multiplicity of steady states was observed; the unique positive steady state was locally asymptotically stable; and the effect of dilution rate on steady states was greater than that of the initial substrate concentration. Received 23 February 1999/ Accepted in revised form 08 June 1999     

Effect of wall growth on scale-up problems and dynamic operating characteristics of the biological reactor

If inhibitory substrates are being utilized in a well-stirred biological reactor, microbiological growth on the walls of the reactor can create a scale-up problem. A simple model is proposed which shows that without such growth, of the three existing steady states only one is stable and nontrivial, but with wall growth the trivial, stable, steady state (washout) is impossible. In addition, wall growth reduces the region over which three steady states are feasible and reduces the minimum residence time for which there is only one steady state that corresponds to a high conversion. Thus, a laboratory process with a high surface area to volume ratio can give an over optimistic prediction of both necessary residence; time and stability of the full scale process unless wall growth is accounted for.     

A model approach to the population dynamics of the rotifer Brachionus rubens in two-stage chemostat culture

Summary A model, based on energy-flow considerations, is presented which describes the population dynamics of Brachionus rubens in the second stage of a two-stage algalrotifer chemostat. The rotifers are foodlimited with substrate-inhibition occurring at high algal densities. The model shows two stable states: steady state with constant density of rotifers and washout of the animals. Which one of the stable states is reached depends on the initial conditions.Empirical data are in general agreement with the model. Deviations may be explained by the fact that the data underlying the model calculations are based on a different food alga (Chlorella vulgaris) than the one used in the experiments (Monoraphidium minutum).The observed population growth rate reaches a maximum value of 0.84 (1/day) at algal densities of 3–4. 10⁶ cells/ml. It decreases at higher algal densities. The egg ratio is related linearily to algal density without being reduced at high algal densities.This study is dedicated to the memory of Prof. Dr. Udo Halbach     

Positive Feedbacks in Seagrass Ecosystems: Implications for Success in Conservation and Restoration

Abstract Seagrasses are threatened by human activity in many locations around the world. Their decline is often characterized by sudden ecosystem collapse from a vegetated to a bare state. In the 1930s, such a dramatic event happened in the Dutch Wadden Sea. Before the shift, large seagrass beds (Zostera marina) were present in this area. After the construction of a large dam and an incidence of the “wasting disease” in the early 1930s, these meadows became virtually extinct and never recovered despite restoration attempts. We investigated whether this shift could be explained as a critical transition between alternative stable states, and whether the lack of recovery could be due to the high resilience of the new turbid state. We analyzed the depth distribution of the historical meadows, a long-term dataset of key factors determining turbidity and a minimal model based on these data. Results demonstrate that recovery was impossible because turbidity related to suspended sediment was too high, probably because turbidity was no longer reduced by seagrass itself. Model simulations on the positive feedback suggest indeed the robust occurrence of alternative stable states and a high resilience of the current turbid state. As positive feedbacks are common in seagrasses, our findings may explain both the worldwide observed collapses and the low success rate of restoration attempts of seagrass habitats. Therefore, appreciation of ecosystem resilience may be crucial in seagrass ecosystem management.     

Major disturbances test resilience at a long‐term boreal forest monitoring site

相似文献   

The role of disturbance in the co‐existence of the evergreen Quercus ilex and the deciduous Quercus cerrioides

Question: Which is the response of the evergreen Quercus ilex and the deciduous Q. cerrioides to repeated disturbances? Location: central Catalonia (northeastern Spain), in the areas affected by two of the largest historically recorded wildfires in NE Spain: the Bages‐Berguedà fire (24 300 ha forested area burned in July 1994), and the Solsonès fire (14 300 ha burned in 1998). Methods: Survival and growth of individuals of Quercus ilex and Q. cerrioides were evaluated in plants subjected to different fire histories and experimental disturbances (burning, cutting or clipping) applied either before or after summer. Results: Survival was high (> 99%), with both species showing a similar high resistance to disturbances. Growth after experimental disturbance was positively related to the size of the individual before the latest forest fire occurred. Fire history had a large effect on resprout growth, as the repeated incidence of disturbances lowered the capacity of individuals to grow. The type and season of experimental disturbance experienced by plants had a large effect. Individuals that experienced total above‐ground loss had lower growth rates than those with partial loss. A similar pattern was observed in individuals disturbed after the summer in relation to those disturbed before summer. Conclusions: The larger growth rates recorded in Q. cerrioides across all fire histories and experimental treatments, and the higher vulnerability of Q. ilex to increased fire frequency, intensity of experimental disturbance, and disturbance season, provide evidence for the relatively high susceptibility of the latter to repeated disturbances. This view disagrees with the larger resilience of this species compared to co‐existing deciduous oaks, as reported.     

Why the Lysogenic State of Phage λ Is So Stable: A Mathematical Modeling Approach

We develop a mathematical model of the phage λ lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state corresponds to the lysogenic state. When the CI degradation rate (γ_cI) is slightly increased from its normal value (γ_cI 0.0 min⁻¹), two additional steady states appear (through a saddle-node bifurcation) in addition to the lysogenic state. One of these new steady states is stable and corresponds to the lytic state. The other steady state is an (unstable) saddle node. The coexistence these two globally stable steady states (the lytic and lysogenic states) is maintained with further increases of γ_cI until γ_cI 0.35 min⁻¹, when the lysogenic steady state and the saddle node collide and vanish (through a reverse saddle node bifurcation) leaving only the lytic state surviving. These results allow us to understand the high degree of stability of the lysogenic state because, normally, it is the only steady state. Further implications of these results for the stability of the phage λ switch are discussed, as well as possible experimental tests of the model.     

Multiple steady states in a continuous stirred tank reactor: an experimental case study for hydrolysis of sucrose by invertase

The purpose of this work was to validate experimentally that multiple steady states may be achieved in a continuous stirred tank reactor (CSTR) during hydrolysis of sucrose by invertase. Experiments were done with four initial sucrose concentrations (0.1, 0.175, 0.584 and 1 M) to study their effect on residual sucrose and reaction rate at steady state. Two different steady states (S=0.7 M, r=9×10⁻⁴ mol/l min and S=0.135 M, r=1.54×10⁻³ mol/l min) were found depending on initial concentration of sucrose in the reactor. Two stable steady states were possible in a CSTR using invertase for the hydrolysis of sucrose. A third possible steady state can be derived theoretically, but it should be a metastable condition because any small disturbance in the system will result in transitory states stabilizing at sugar concentrations of either 0.135 or 0.7 M.     

The relationship between kinetics of substrate-limited transitions and steady-state growth in continuous cultures ofAquaspirillum autotrophicum limited by pyruvate

Heterotrophic growth at steady state and during transient states caused by the sudden change of the concentration of the limiting factor in the feed medium was investigated experimentally for continuous cultures ofAquaspirillum autotrophicum limited by pyruvate. A model for describing the growth at steady state was selected from three unstructured models after statistical tests of the data. This model postulates that the growth yield increases linearly with the growth rate. Growth during transitions where the substrate remained limiting at all times was fitted with first-order kinetics. Theoretical predictions of these kinetics were derived from the unstructured models used to describe steady state. The predicted rate coefficients of the transients were compared to the experimental coefficients. It appeared that the model which best described steady-state growth also provided the best predictions for growth during the transient state. It is a widespread opinion that unstructured models are adequate to describe growth under steady-state conditions but not to predict transitions in continuous culture. However, for the particular case studied here, no higher degree of complexity was required to describe transitions, provided the growth of the culture was always limited by the substrate.     

Are Large, Infrequent Disturbances Qualitatively Different from Small, Frequent Disturbances?

In this article, we develop a heuristic model of ecosystem-disturbance dynamics that illustrates a range of responses of disturbance impact to gradients of increasing disturbance extent, intensity, or duration. Three general kinds of response are identified and illustrated: (a) threshold response, (b) scale-independent response, and (c) continuous response. Threshold responses are those in which the response curve shows a discontinuity or a sudden change in slope along the axis of increasing disturbance extent, intensity, or duration. The response threshold occurs at a point where the force of the disturbance exceeds the capacity of internal mechanisms to resist disturbance, or where new mechanisms of recovery become involved. Within this conceptual framework, we find that some unusually large or intense disturbances, but not all, produce qualitatively different responses compared with similar disturbances of lesser magnitude. If disturbance impact does not increase with increasing disturbance extent, intensity, or duration, or if the response curve changes monotonically, then large disturbances are not qualitatively different from small ones. For example, jack pine tends to become reestablished after stand-replacing fire in boreal forests, regardless of fire size, because its serotinous cones provide an adequate seed source throughout the burned area. Thus, large fires are not qualitatively different from small fires in terms of jack pine reproduction. However, if disturbance impact does increase abruptly at some point with increasing disturbance extent, intensity, or duration, often because of thresholds in the capacity of internal mechanisms to resist or respond to disturbance impact, then large disturbances are qualitatively different from small ones, at least for some parameters of ecological response. For example, balsam fir and white cedar can recolonize a small burned patch of boreal forest in close proximity to surviving individuals of these species, but they will be eliminated from a large burn because of their susceptibility to fire-caused mortality and their inability to disperse their seeds over long distances. The conceptual framework presented here permits some new insights into the dynamics of natural systems and may provide a useful tool with which managers can assess the potential for catastrophic damages resulting from large, infrequent disturbances. Received 14 July 1998; accepted 29 September 1998     

Parameterization and prediction of community interaction models using stable-state assumptions and computational techniques: an example from the high rocky intertidal

Many ecological communities exist in a stable state where, if undisturbed, no net change will occur in the populations or in the interactions between the component parts of the system. In this paper we present computational methods (evolutionary algorithms and random searches) to parameterize mathematical models that describe communities in stable states. The initial parameterization of the model requires only "best guess" estimates for parameters and can therefore be used in data-poor situations. The technique locates the stable state that occurs with minimum deviation from these parameters. Alternative stable states in which the community may exist after a disturbance event can also be assessed using this technique, even though the number of alternative states may be large. Using available but incomplete data from an intertidal grazer/biofilm community, we created a prediction of the dynamics of both a pre- and post-disturbance community. Using limited data, we then predicted the most likely post-disturbance community, which proved to be a good match to experimental data, indicating the usefulness of this technique as a predictive tool.     

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

An Efficient Steady-State Analysis Method for Large Boolean Networks with High Maximum Node Connectivity

Boolean networks have been widely used to model biological processes lacking detailed kinetic information. Despite their simplicity, Boolean network dynamics can still capture some important features of biological systems such as stable cell phenotypes represented by steady states. For small models, steady states can be determined through exhaustive enumeration of all state transitions. As the number of nodes increases, however, the state space grows exponentially thus making it difficult to find steady states. Over the last several decades, many studies have addressed how to handle such a state space explosion. Recently, increasing attention has been paid to a satisfiability solving algorithm due to its potential scalability to handle large networks. Meanwhile, there still lies a problem in the case of large models with high maximum node connectivity where the satisfiability solving algorithm is known to be computationally intractable. To address the problem, this paper presents a new partitioning-based method that breaks down a given network into smaller subnetworks. Steady states of each subnetworks are identified by independently applying the satisfiability solving algorithm. Then, they are combined to construct the steady states of the overall network. To efficiently apply the satisfiability solving algorithm to each subnetwork, it is crucial to find the best partition of the network. In this paper, we propose a method that divides each subnetwork to be smallest in size and lowest in maximum node connectivity. This minimizes the total cost of finding all steady states in entire subnetworks. The proposed algorithm is compared with others for steady states identification through a number of simulations on both published small models and randomly generated large models with differing maximum node connectivities. The simulation results show that our method can scale up to several hundreds of nodes even for Boolean networks with high maximum node connectivity. The algorithm is implemented and available at http://cps.kaist.ac.kr/∼ckhong/tools/download/PAD.tar.gz.     

Intracellular CHO Cell Metabolite Profiling Reveals Steady‐State Dependent Metabolic Fingerprints in Perfusion Culture

Perfusion cell culture processes allow the steady‐state culture of mammalian cells at high viable cell density, which is beneficial for overall product yields and homogeneity of product quality in the manufacturing of therapeutic proteins. In this study, the extent of metabolic steady state and the change of the metabolite profile between different steady states of an industrial Chinese hamster ovary (CHO) cell line producing a monoclonal antibody (mAb) was investigated in stirred tank perfusion bioreactors. Matrix‐assisted laser desorption/ionization time of flight mass spectrometry (MALDI‐TOF‐MS) of daily cell extracts revealed more than a hundred peaks, among which 76 metabolites were identified by tandem MS (MS/MS) and high resolution Fourier transform ion cyclotron resonance (FT‐ICR) MS. Nucleotide ratios (Uridine (U)‐ratio, nucleotide triphosphate (NTP)‐ratio and energy charge (EC)) and multivariate analysis of all features indicated a consistent metabolite profile for a stable culture performed at 40 × 10⁶ cells/mL over 26 days of culture. Conversely, the reactor was operated continuously so as to reach three distinct steady states one after the other at 20, 60, and 40 × 10⁶ cells/mL. In each case, a stable metabolite profile was achieved after an initial transient phase of approximately three days at constant cell density when varying between these set points. Clear clustering according to cell density was observed by principal component analysis, indicating steady‐state dependent metabolite profiles. In particular, varying levels of nucleotides, nucleotide sugar, and lipid precursors explained most of the variance between the different cell density set points. © 2016 American Institute of Chemical Engineers Biotechnol. Prog., 33:879–890, 2017     

Grassland responses to multiple disturbances on the New England Tablelands in NSW,Australia

Disturbances have played a significant role in shaping vegetation patterns following European settlement and agricultural development in Australia, particularly over the last 100 years. However, little is known about the temporal dynamics of plant communities in relation to disturbances and their interactions. In this study we examined the response and recovery of temperate grassland communities to disturbance, using a multi-factorial experiment involving grazing exclusion (absent and present), fire (absent and present), soil cultivation (none, 5 and 20 cm) and soil amendment (none, fertiliser and fertiliser plus clover seeds) on the New England Tablelands in NSW, Australia. Temporal patterns of plant communities were analysed using detrended correspondence analysis for eight surveys over 24 months. Vegetation patterns at each survey were analysed using principal components analysis. The effects of treatments on malleability (Bray–Curtis dissimilarity) of plant communities were analysed using a linear mixed model, and the relationships between malleability and plant species groups were depicted using a generalised additive model and further analysed using a linear model. Perennial native grasses and a non-native forb (Hypochaeris radicata) initially dominated the vegetation, but after the disturbances H. radicata and other non-native species dominated. Compositional changes from the initial states were greatest in the first spring (7 months after treatment application), and then the vegetation tended to recover towards its original state. Soil cultivation resulted in the greatest deviation in community composition, followed by soil amendment, fire, with grazing exclusion the least. The recovery process and rate of recovery varied with treatment reflecting the dominance of soil cultivation and its interactions with other forms of disturbances. Soil amendment and grazing exclusion tended to reduce the effects of soil cultivation. Malleability was negatively related to perennial native grasses; positively to other non-native species, annual native grasses and perennial native sedges/rushes; and negatively to H. radicata when its cover was below 18%, but positively when above 18%. The degree of malleability reflected the high resilience of the vegetation to disturbance, and was mainly due to the recovery of perennial native grasses and H. radicata. This resilience demonstrated that the small-scale disturbances did not cause vegetation to cross an ecological threshold and that the present vegetation is resilient to common disturbances occurring at small scales. The results also suggest (1) that the present vegetation has developed mechanisms to adapt to these disturbances, (2) the importance of disturbance scale or (3) that the ecological threshold had already been crossed and the present vegetation is in a degraded state compared with its original state before the end of the 19th century.     

Attenuation of flow disturbances in tapered arterial grafts

Flow disturbances in tapered arterial grafts of angles of taper between 0.5 and 1.0 deg were measured in vitro using a pulsed ultrasound Doppler velocimeter. The increase in transition Reynolds numbers with angle of taper and axial distance was determined for steady flow. The instantaneous centerline velocities were measured distal to a 50 percent area stenosis (as a model of a proximal anastomosis), in steady and pulsatile flow, from which the disturbance intensities were calculated. A significant reduction in post-stenotic disturbance intensity was recorded in the tapered grafts, relative to a conventional cylindrical graft. In pulsatile flow with a large backflow component, however, there was an increase in disturbance intensity due to diverging flow during flow reversal. This was observed only in the 1.0 deg tapered graft. These findings indicate that taper is an important consideration in the design of vascular prostheses.     

Dissipation and maintenance of stable states in an enzymatic system: analysis and simulation

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. An essential assumption for constraint-based analysis is the formation of a stable steady state. This work investigates dissipation and maintenance of stable states in a simple reversible enzymatic reaction with substrate inhibition. Under mass-action kinetics, the conditions under which the reaction maintains a stable steady state are analytically derived and numerically confirmed. It is shown that, in order to maintain a steady state in the regulated reaction, maximal enzyme activity must be much higher than input rate. Moreover, it is revealed that requirements for large enzyme activity are due to substrate inhibition. It is suggested that high activities of enzymes may play a vital role in protecting a stable state from its catastrophic collapse, giving an additional explanation to an intriguing problem—why the activities of some enzymes greatly exceed the flux capacity of a pathway. In addition, dissipation of the enzymatic reaction is analysed. It is shown that the collapse of stable states is always associated with a point at which dissipation is the highest. Therefore, in order to maintain a stable state, dissipation of the reaction must be less than a critical value. Moreover, although external forcing may not change net mass flow, it may lead to collapse of stable states. Furthermore, when stable states collapse at a critical forcing amplitude and period, dissipation also reaches a highest value. It is concluded that collapse of stable steady state in the enzyme system with substrate inhibition always corresponds to critical points at which dissipation is highest, regardless if the reaction is forced or not. Therefore, for the substrate inhibited reaction, maintenance of stable states is intrinsically related to level of dissipation.     

Interpreting woody cover data in tropical and subtropical areas: Comparison between the equilibrium and the non-equilibrium assumption

We compared two basic assumptions about the woody cover distribution in tropical and subtropical areas: the equilibrium (woody cover always reaches a long-term steady state) vs the non-equilibrium assumption (woody cover fluctuates in response to fire disturbances). We considered two models each one representative of one of the two assumptions: an equilibrium and a non-equilibrium model. The equilibrium model considered fire as an a priori determined parameter, whereas the non-equilibrium model assumed fires as stochastic events whose probability increased with grass density. We compared the results of the models with large datasets containing woody cover values sampled at the continental and at the global scale. In particular, we focused on two evidences shown by data. The first evidence is that woody cover is limited by water scarcity for low rainfall values and by fire for high rainfall values (arid–moist savanna distinction). The second evidence is the bimodality of woody cover data observed for high rainfall values. The equilibrium model gave a static interpretation of the data. The non-equilibrium model, instead, gave a more general interpretation of the data. In particular, the non-equilibrium model detected the arid–moist savanna distinction as emergent along a rainfall gradient and demonstrated that the bimodality observed in the woody cover data could be obtained in the woody cover values exhibited by a vegetation system in different times. Thus, woody cover data do not necessarily represent steady states. Rather, they could represent snapshots of a vegetation system in certain time instants.