Direct experimental evidence for alternative stable states: a review

A large number of studies have presented empirical arguments for the existence of alternative stable states (ASS) in a wide range of ecological systems. However, most of these studies have used non-manipulative, indirect methods, which findings remain open for alternative explanations. Here, we review the direct evidence for ASS resulting from manipulation experiments. We distinguish four conclusive experimental approaches which test for predictions made by the hysteresis effect: (1) discontinuity in the response to an environmental driving parameter, (2) lack of recovery potential after a perturbation, (3) divergence due to different initial conditions and (4) random divergence. Based on an extensive literature search we found 35 corresponding experiments. We assessed the ecological stability of the reported contrasting states using the minimum turnover of individuals in terms of life span and classified the studies according to 4 categories: (1) experimental system, (2) habitat type, (3) involved organisms and (4) theoretical framework. 13 experiments have directly demonstrated the existence of alternative stable states while 8 showed the absence of ASS in other cases. 14 experiments did not fulfil the requirements of a conclusive test, mostly because they applied a too short time scale. We found a bias towards laboratory experiments compared to field experiments in demonstrating bistability. There was no clear pattern of the distribution of ASS over categories. The absence of ASS in 38% of the tested systems indicates that ASS are just one possibility of how ecological systems can behave. The relevance of the concept of ASS for natural systems is discussed, in particular under consideration of the observed laboratory bias, perturbation frequency and variable environments. It is argued, that even for a permanently transient system, alternative attractors may still be of relevance.     

Representational switching by dynamical reorganization of attractor structure in a network model of the prefrontal cortex

The prefrontal cortex (PFC) plays a crucial role in flexible cognitive behavior by representing task relevant information with its working memory. The working memory with sustained neural activity is described as a neural dynamical system composed of multiple attractors, each attractor of which corresponds to an active state of a cell assembly, representing a fragment of information. Recent studies have revealed that the PFC not only represents multiple sets of information but also switches multiple representations and transforms a set of information to another set depending on a given task context. This representational switching between different sets of information is possibly generated endogenously by flexible network dynamics but details of underlying mechanisms are unclear. Here we propose a dynamically reorganizable attractor network model based on certain internal changes in synaptic connectivity, or short-term plasticity. We construct a network model based on a spiking neuron model with dynamical synapses, which can qualitatively reproduce experimentally demonstrated representational switching in the PFC when a monkey was performing a goal-oriented action-planning task. The model holds multiple sets of information that are required for action planning before and after representational switching by reconfiguration of functional cell assemblies. Furthermore, we analyzed population dynamics of this model with a mean field model and show that the changes in cell assemblies' configuration correspond to those in attractor structure that can be viewed as a bifurcation process of the dynamical system. This dynamical reorganization of a neural network could be a key to uncovering the mechanism of flexible information processing in the PFC.     

On the dynamical properties of a model of cell differentiation

One of the major challenges in complex systems biology is that of providing a general theoretical framework to describe the phenomena involved in cell differentiation, i.e., the process whereby stem cells, which can develop into different types, become progressively more specialized. The aim of this study is to briefly review a dynamical model of cell differentiation which is able to cover a broad spectrum of experimentally observed phenomena and to present some novel results.     

Fenamin stereotypy as a stable rhythmic process

In cats with amphetamine stereotypy, the rate of horizontal head movements ranges rhythmically in time. Marked stereotypy is in agreement with more regular and low amplitude waves on the total activity curve. During amphetamine effect abatement, the curve gets stabilized as regards the amplitude and period. According to the results of separate evaluation of the temporary dynamics of the number of the left- and right-handed head movements, stereotypy is marked by an increase in the period duration when the rate of the movements changes differently. Natural or neuroleptic-induced abatement of stereotypy is accompanied by an increase in the duration of unidirectional (synchronized) shifts of the rate of the head movements.     

A designed RNA selection: establishment of a stable complex between a target and selectant RNA via two coordinated interactions

In this paper, we describe a new method for selecting RNA aptamers that cooperatively bind to two specific sites within a target RNA. We designed a selection system in which two RNAs, a target RNA and a RNA pool, were assembled by employing a pre-organized GAAA tetraloop-11-nt receptor interaction. This allows us to select the binding sequence against a targeted internal loop as well as a linker region optimized for binding of the two binding sites. After the selection, the aptamers bound with dissociation constants in the nanomolar range, thereby forming a stable complex with the target RNA. Thus this method enables identification of aptamers for a specific binding site together with a linker for cooperative binding of the two RNAs. It appears that our new method can be applied generally to select RNAs that adhere tightly to a target RNA via two specific sites. The method can also be applicable for further engineering of both natural and artificial RNAs.     

Alternative community compositional and dynamical states: the dual consequences of assembly history

1. Much work on ecological consequences of community assembly history has focused on the formation of history-induced alternative stable equilibria. We hypothesize that assembly history may affect not only community composition but also population dynamics, with assembled communities differing in species composition potentially residing in different dynamical states. 2. We provided an empirical test of the aforementioned hypothesis using a laboratory microcosm experiment that manipulated both the colonization order of three bacterivorous protist species in the presence of a protist predator and environmental productivity. 3. Both priority effects and random divergence emerged, resulting in two different community compositional states: one characterized by the dominance of one prey species and the other by the extinction of the same prey. While communities in the former state exhibited noncyclic dynamics, the majority of communities in the latter state exhibited cyclic dynamics driven by the interaction between another prey and the predator. 4. Temporal variability of total prey community biovolume consequently differed among communities with different histories. 5. Changing productivity altered priority effects on the structure and dynamics of communities experiencing only certain histories. 6. Our results support the dual (compositional and dynamical) consequences of assembly history and emphasize the importance of incorporating the dynamical view into the field of community assembly.     

Transitions and new dynamical states induced by noise in a multiply regulated biochemical system

Noise-induced transitions between coexisting states, and the emergence of a new oscillatory state, are examined in a model for a multiply regulated biochemical system. For the undisturbed system, three oscillatory states, I, II, and III, coexist. It is found that noise above a critical amplitude can cause a transition between states III and II and between states III or II and state I, whereas a transition from state I to either states II or III is never observed. This indicates that the relative stability under noise perturbations is greatest for state I, and progressively less for states II and III. In addition to this transition behaviour, a purely noise-induced state is found. Under noise perturbations, the average concentration of metabolites may depend on both the time duration and amplitude of the superimposed noise. The implications of these results for understanding the in vivo behaviour of complex biochemical systems are discussed.     

Synthetic studies towards a novel, chemical stable, abasic site analogue of DNA

We synthesized the phosphinate 7 via photoaddition of methanol to the alpha, beta unsaturated deoxyribono lactone as the key step, followed by an Arbusov reaction for the introduction of phosphorous. Precursor 7 serves for the synthesis and incorporation into DNA of a novel chemically stable abasic site analogue that might act as an inhibitor for DNA glycosylases.     

Alternative stable states in eutrophic,shallow freshwater systems: A minimal model

A simple mathematical model was constructed, describing the relationships between pike, bream, aquatic macrophytes and the nutrient loading of shallow lakes. The model is analyzed with the use of zero-isoclines. It is concluded that, over a certain range of nutrient concentrations, the ecological relations incorporated in the model can give rise to the existence of two alternative stable equilibria;viz. a turbid bream-dominated one, and a clear state in which pike and aquatic vegetation are abundant. Under oligotrophic conditions, the clear-water state represents the only stable equilibrium; however, at high nutrient levels, the clear state is absent, or only locally stable. The response of the model to both increase and decrease of the nutrient level is characterised by hysteresis. The results indicate that manipulation of fish densities as a measure to improve water quality is only likely to produce long-term results when the nutrient level is below a certain threshold.     

Ventilatory support: a dynamical systems approach

Misunderstanding of the dynamical behavior of the ventilatory system, especially under assisted ventilation, may explain the problems encountered in ventilatory support monitoring. Proportional assist ventilation (PAV) that theoretically gives a breath by breath assistance presents instability with high levels of assistance. We have constructed a mathematical model of interactions between three objects: the central respiratory pattern generator modelled by a modified Van der Pol oscillator, the mechanical respiratory system which is the passive part of the system and a controlled ventilator that follows its own law. The dynamical study of our model shows the existence of two crucial behaviors, i.e. oscillations and damping, depending on only two parameters, namely the time constant of the mechanical respiratory system and a cumulative interaction index. The same result is observed in simulations of spontaneous breathing as well as of PAV. In this last case, increasing assistance leads first to an increase of the tidal volume (V_T), a further increase in assistance inducing a decrease in V_T, ending in damping of the whole system to an attractive fixed point. We conclude that instabilities observed in PAV may be explained by the different possible dynamical behaviors of the system rather than changes in mechanical characteristics of the respiratory system.     

Absolute stability and transitions in ecosystems with a multiplicity of stable states and dispersal

The principle that for a large class of spatially extended dynamic systems with several locally stable states there exists at most one absolutely stable state is applied to population dynamical models with diffusive spatial dispersal. The basic concepts and methods to characterize absolute stability and its limits are presented. Some interesting results concerning the significance of dispersal ability in competing and mutualistic systems are found. The concepts appear of practical importance since only absolutely stable states are resilient against all localized fluctuations and disturbances.