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

Microbial fuel cell compared to a chemostat

Microbial Fuel Cells (MFCs) represent a green and sustainable energy conversion system that integrate bacterial biofilms within an electrochemical two-electrode set-up to produce electricity from organic waste. In this review, we focus on a novel exploratory model, regarding "thin" biofilms forming on highly perfusable (non-diffusible) anodes in small-scale, continuous flow MFCs due to the unique properties of the electroactive biofilm. We discuss how this type of MFC can behave as a chemostat in fulfilling common properties including steady state growth and multiple steady states within the limit of biological physicochemical conditions imposed by the external environment. With continuous steady state growth, there is also continuous metabolic rate and continuous electrical power production, which like the chemostat can be controlled. The model suggests that in addition to controlling growth rate and power output by changing the external resistive load, it will be possible instead to change the flow rate/dilution rate.

Discovery, development and exploitation of steady-state biofilms

Early in vitro biofilm models go back even beyond the invention of the word 'biofilm'. In the dental field, biofilms were simply known as dental plaque and many of the first in vitro models were termed 'artificial mouth microcosm plaques'. The purpose of this review is to highlight important elements of research from over the years regarding in vitro biofilm models, including data from our own laboratories. This helps us to interpret the models and point the way to the future development of biofilm testing. Many hypotheses regarding biofilm phenomena, particularly ecology, metabolism and physiology of volatile sulphur compounds (VSCs) and volatile organic compound (VOC) production could potentially be supported or disproved. In this way, the methods we use for screening biologically active agents including inhibitors, biocides and antimicrobial compounds in general can be improved. Hopefully, any lessons learnt in the past may be of value for the future. In this review, we focus around the need for growth rate controlled long-term biofilms; being continuously monitored using recent technical advances in bioluminescence, selective real-time electrodes, pH electrodes and continuous on-line analysis of the gas phase (both qualitatively and quantitatively). These features allow for accurate determination of growth rate and/or metabolic rate as well as pave the way towards automated assays and fine control of metabolism; impossible to achieve according to conventional biofilm theory. We also attempt to address the questions; can biofilm systems be improved to maintain long term 'real' or 'true' steady states over weeks or months, or are we limited to quasi-steady state systems for a limited period of time.

Marching along to an Offbeat Drum: Entrainment of Synthetic Gene Oscillators by a Noisy Stimulus

Modulation of biological oscillations by stimuli lies at the root of many phenomena, including maintenance of circadian rhythms, propagation of neural signals, and somitogenesis. While it is well established that regular periodic modulation can entrain an oscillator, an aperiodic (noisy) modulation can also robustly entrain oscillations. This latter scenario may describe, for instance, the effect of irregular weather patterns on circadian rhythms, or why irregular neural stimuli can still reliably transmit information. A synthetic gene oscillator approach has already proven to be useful in understanding the entrainment of biological oscillators by periodic signaling, mimicking the entrainment of a number of noisy oscillating systems. We similarly seek to use synthetic biology as a platform to understand how aperiodic signals can strongly correlate the behavior of cells. This study should lead to a deeper understanding of how fluctuations in our environment and even within our body may promote substantial synchrony among our cells. Specifically, we investigate experimentally and theoretically the entrainment of a synthetic gene oscillator in E. coli by a noisy stimulus. This phenomenon was experimentally studied and verified by a combination of microfluidics and microscopy using the real synthetic circuit. Stochastic simulation of an associated model further supports that the synthetic gene oscillator can be strongly entrained by aperiodic signals, especially telegraph noise. Finally, widespread applicability of aperiodic entrainment beyond the synthetic gene oscillator is supported by results derived from both a model for a natural oscillator in D. discoideum and a model for predator-prey oscillations.

Competition between two microbial populations in a sequencing fed-batch reactor: theory, experimental verification, and implications for waste treatment applications

Competition between two microbial populations for a single pollutant (phenol) was studied in a sequencing fed-batch reactor (SFBR). A mathematical model describing this system was developed and tested experimentally. It is based on specific growth rate expressions revealed from pure culture batch experiments. The species employed were Pseudomonas putida (ATCC 17514) and Pseudomonas resinovorans (ATCC 14235). It was found that both species biodegrade phenol following inhibitory kinetics which can be described by Andrews' expression. The model predicts that the dynamics of a SFBR, and the kinetics of biodegradation, result in a complex set of operating regimes in which neither species, only one species, or both species can survive at steady cycle. The model also predicts the existence of multiple outcomes, achievable from different start-up conditions, in some domains of the operating parameter space. Experimental results confirmed the model predictions. There was excellent agreement between predicted and measured concentrations of phenol, total biomass, and the biomass of each individual species. This study shows how serious discrepancies can arise in scale-up of biodegradation data if population dynamics are not taken into account. It also further confirms experimentally the theory of microbial competition in periodically forced bioreactors.

An ecosystem analysis of the activated sludge microbial community

This study was undertaken (i) to investigate the interactions of the activated sludge microbial community in a chemostat with the "environment", such as the substrate composition and variations, (ii) to investigate how these interactions affect the quality of the treated effluent and (iii) to determine the limits or applicability conditions to the indicators and to the prediction potential of the treated effluent quality. This work presents (a) the experimental results obtained from a reactor fed municipal wastewater (Data Set2-DS2) concerning the reactor's operating conditions and the microbial community of the sludge (b) comparisons between DS2 and an older Data Set (DS1) obtained when the reactor was fed synthetic substrate, all other experimental conditions being identical, and (c) simulation results and sensitivity analyses of two model runs (R1 and R2, corresponding to DS1 and DS2). The first trophic level (P(1)) of the DS2 microbial community consisted of bacteria, the second trophic level (P(2)) of bacteria-eating protozoa, rotifers and nematodes and the third trophic level (P(3)) of carnivorous protozoa and arthropods. Rotifers were an important constituent of the DS2 microbial community. The DS1 and DS1 communities differed in total size, trophic level sizes and species composition. Correlations between the major microbial groups of DS2 community and either loading rates or effluent quality attributes were generally low, but the correlation of bacteria with SVI and ammonia in the effluent was better. Also, the ratio of rotifers to protozoa in P(2) was correlated to BOD in the effluent. The results of this work indicate that predictions of the treated effluent quality based only on protozoa may not be safe. Sensitivity analysis of R2 run indicate that, when variation in Y and K(d) biokinetic coefficients of the sludge are combined with fluctuations in composition and quality of municipal wastewater entering the reactor, then sufficient significant prediction of bacteria in the aeration tank is not possible. In order to avoid erroneous oversimplifications regarding phenomena taking place in the sludge and to understand "unexplained" process failures, more ecologically sound methods for studying wastewater treatment (WWT) processes are needed, since WWT are primarily ecosystems interacting with technological systems.

Peak-to-peak dynamics in food chain models

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the forecast concerns the population at the top of the food chain and that peaks variability often increases from bottom to top. All these findings bring naturally to the conclusion that top populations should be sampled in order to have higher chances to detect peak-to-peak dynamics. The analysis is carried out by studying ditrophic food chain models with seasonally varying parameters, tritrophic food chain models with constant parameters, and more complex food chain and food web models.

Resistance of a food chain to invasion by a top predator

We study the invasion of a top predator into a food chain in a chemostat. For each trophic level, a bioenergetic model is used in which maintenance and energy reserves are taken into account. Bifurcation analysis is performed on the set of nonlinear ordinary differential equations which describe the dynamic behaviour of the food chain. In this paper, we analyse how the ability of a top predator to invade the food chain depends on the values of two control parameters: the dilution rate and the concentration of the substrate in the input. We investigate invasion by studying the long-term behaviour after introduction of a small amount of top predator. To that end we look at the stability of the boundary attractors; equilibria, limit cycles as well as chaotic attractors using bifurcation analysis. It will be shown that the invasibility criterion is the positiveness of the Lyapunov exponent associated with the change of the biomass of the top predator. It appears that the region in the control parameter space where a predator can invade increases with its growth rate. The resulting system becomes more resistant to further invasion when the top predator grows faster. This implies that short food chains with moderate growth rate of the top predator are liable to be invaded by fast growing invaders which consume the top predator. There may be, however, biological constraints on the top predator's growth rate. Predators are generally larger than prey while larger organisms commonly grow slower. As a result, the growth rate generally decreases with the trophic level. This may enable short food chains to be resistant to invaders. We will relate these results to ecological community assembly and the debate on the length of food chains in nature.

Consequences of population models for the dynamics of food chains

A class of bioenergetic ecological models is studied for the dynamics of food chains with a nutrient at the base. A constant influx rate of the nutrient and a constant efflux rate for all trophic levels is assumed. Starting point is a simple model where prey is converted into predator with a fixed efficiency. This model is extended by the introduction of maintenance and energy reserves at all trophic levels, with two state variables for each trophic level, biomass and reserve energy. Then the dynamics of each population are described by two ordinary differential equations. For all models the bifurcation diagram for the bi-trophic food chain is simple. There are three important regions; a region where the predator goes to extinction, a region where there is a stable equilibrium and a region where a stable limit cycle exists. Bifurcation diagrams for tritrophic food chains are more complicated. Flip bifurcation curves mark regions where complex dynamic behaviour (higher periodic limit cycles as well as chaotic attractors) can occur. We show numerically that Shil'nikov homoclinic orbits to saddle-focus equilibria exists. The codimension 1 continuations of these orbits form a 'skeleton' for a cascade of flip and tangent bifurcations. The bifurcation analysis facilitates the study of the consequences of the population model for the dynamic behaviour of a food chain. Although the predicted transient dynamics of a food chain may depend sensitively on the underlying model for the populations, the global picture of the bifurcation diagram for the different models is about the same.

Chaos and peak-to-peak dynamics in a plankton-fish model

A plankton-fish model, comprising phosphorus, algae, zooplankton, and young fish, with light intensity and water temperature varying periodically with the seasons, is analyzed in this paper. For realistic values of the parameters the model behaves chaotically, but its dynamics within the strange attractor can be described by a few one-dimensional maps that allow one to forecast the next yearly peak of plankton or fish from the last peaks. This property is an unambiguous mark of a special form of chaos. Unfortunately, the estimate of such peak-to-peak maps from field data is possible only if plankton or young fish biomass has been sampled accurately and frequently for a paramount number of years. In conclusion, the analysis shows that it might be that plankton dynamics are characterized by an interesting and peculiar form of chaos, but that inferences from recorded data on the existence of these forms of chaos are premature.

Biodegradation of mixed wastes in continuously operated cyclic reactors

The problem of simultaneous biodegradation of two dissimilar substrates in a continuously operated cyclic reactor was studied both at the theoretical and experimental levels using a simple model system. The system involved media containing mixtures of glucose and phenol as carbon sources. A pure culture of Pseudomonas putida (ATCC 17514) was employed. Independent kinetic experiments have revealed that glucose and phenol are involved in a crossinhibitory uncompetitive kinetic interaction. The dynamics of a cyclically operated reactor were analyzed using the principles of bifurcation theory for forced systems. Experimental results have confirmed the theoretical predictions. Implications of the results for the design of waste-treating facilities are discussed.

Coexistence of three competing microbial populations in a chemostat with periodically varying dilution rate

Coexistence of three microbial populations engaged in pure and simple competition is not possible in a chemostat with time-invariant operating conditions under any circumstances. It is shown that by periodic variation of the chemostat dilution rate it is possible to obtain a stable coexistence state of all three populations in the chemostat. This is accomplished by performing a numerical bifurcation analysis of a mathematical model of the system and by determining its dynamic behavior with respect to its operating parameters. The coexistence state obtained in the periodically operated chemostat is usually periodic, but cases of quasi-periodic and chaotic behavior are also observed.

Microbial predation in coupled chemostats: a global study of two coupled nonlinear oscillators

Predator-prey systems in continuously operated chemostats exhibit sustained oscillations over a wide range of operating conditions. When two such chemostats interact through flow exchange, the interplay of the oscillation frequencies gives rise to a wealth of dynamic behavior patterns. Using numerical bifurcation techniques, we perform a detailed computational study of these patterns and the transitions between them as the coupling strength and relative frequencies of the two chemostats vary. We concentrate on certain strong resonance phenomena between the two frequencies as well as their mutual extinction and provide a representative sampling of possible phase portraits for our model system. Our observations corroborate recent mathematical results and case studies of coupled nonlinear chemical oscillators in which regions of mutual extinction as well as the Arnol'd structure for two-parameter families of maps of the plane have been observed. We highlight certain unexpected features of the operating diagram discovered through our computational study and discuss their implication for the dynamic response of the chemostat system.

Periodic, quasi-periodic, and chaotic coexistence of two competing microbial populations in a periodically operated chemostat

It is well known that when two microbial populations competing for a single rate-limiting nutrient are grown in a chemostat with time-invariant inputs, with competition being the only interaction between them, they cannot coexist, but eventually one of the two populations prevails and the other becomes extinct. It has been suggested that periodic variation of one of the chemostat's operating parameters can stabilize the coexistence state of the two microbial populations. A systematic numerical study of the model equations describing microbial competition in a chemostat with periodically varying dilution rate is performed, and it is shown that coexistence of the competing microbial populations is obtained for a wide range of operating conditions. The coexistence state is usually in the form of limit cycle oscillations. However, cases of chaotic behavior resulting from successive period doublings and quasi-periodicity are also observed.

Chaos in a periodically forced predator-prey ecosystem model

We subject to periodic forcing the classical Volterra predator-prey ecosystem model, which in its unforced state has a globally stable focus as its equilibrium. The periodic forcing is effected by assuming a periodic variation in the intrinsic growth rate of the prey. In nondimensional form the forced system contains four control parameters, including the forcing amplitude and forcing frequency. Numerical experiments carried out over sections of the parameter space reveal an abundance of steady-state chaotic solutions. We graph Poincaré maps and calculate Lyapunov exponents and fractal dimensions for a representative selection of strange attractors. The transitions to chaos were found to be either via a Feigenbaum cascade of period-doubling bifurcations or via frequency locking.