Pseudomonas fluorescens «switchers », souches évolués artificiellement au Rainey Lab, sont un système modèle pour les switch phénotypiques. Ces populations sont typiquement caractérisées par les fréquences de deux phénotypes alternatifs liés à la production d’une capsule d’acide colanique autour de la paroi cellulaire. Bien qu'on s’attende que telles fréquences soient définies d’une manière univoque par le génotype, elles varient au long de la croissance de la population, ce qui indique une possible dépendance des taux de transition à l’égard de la démographie. J’ai développé un modèle mathématique où les cellules sont représentées comme systèmes bistables contrôlés par une concentration intracellulaire et où les taux de transition dépendent de l’état de la croissance de la population.Le modèle reproduit quantitativement la dynamique de la composition phénotypique de la population (dépendante de l’histoire), et fournie des prédictions à propos de son quasi équilibre en phase exponentielle en fonction du taux de croissance de la population - prédictions ensuite qualitativement confirmées par les résultats de mon travail expérimental.Pour conclure, on ne peux pas caractériser une population croissante de « switchers » que par l’état asymptotique des fréquences de ses phénotypes alternatifs, puisque le switch est étroitement lié à la démographie.Dans une perspective évolutive, la persistance transgénérationnelle du phénotype, influencée par des concentrations intracellulaires, pourrait être à l’origine de l’émergence de stratégies comme le « bet-hedging ». / Pseudomonas fluorescens “switchers”, artificially evolved in Rainey Lab, are a model system for phenotypic switching.Populations can be characterized by the frequencies of two alternative states related tothe production of a colanic acid capsule around the cell wall. Expected to be at an equilibrium underpinned by the genetic background, such frequencies vary during population growth, hinting to a dependence of the switching rates on demography, and appear to be dependent on the history of the preculture. I thus developed a mathematical model with individual cells as bistable systems controlled by an intracellular concentration, where transition rates depend on the growth state of the population.The model quantitatively reproduces the history-dependent dynamics of the phenotypic composition of the population, and provides qualitative predictions on its quasi-steady state in exponential phase as a function of the growth rate — then corroborated by the results of my experimental work. I conclude that agrowing population of switching cells cannot be fully characterized only by the asymptotic steady state of the phenotypes’ frequencies,because phenotypic switching is inextricably intertwined with demography. From an evolutionary perspective, trans-generational inheritance of the phenotype mediated by internal concentrations may be at the basis of the emergence of bet-hedging-like strategies.

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center. We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents' parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-Bӧtzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described.

Nichtlineare multistabile Systeme unter dem Einfluss von Rauschen weisen vielschichtige dynamische Eigenschaften auf. <br /> Ein mittleres Rauschlevel zeitigt ein Springen zwischen den metastabilen Zustaenden. <br /> Dieser “attractor-hopping” Prozess ist gekennzeichnet durch laminare Bewegung in der Naehe von Attraktoren und erratische Bewegung, die sich auf chaotischen Satteln abspielt, welche in die fraktalen Einzugsgebietsgrenzen eingebettet sind. Er hat rauschinduziertes Chaos zur Folge. <br /> Bei der Untersuchung der dissipativen Standardabbildung wurde das Phaenomen der Praeferenz von Attraktoren durch die Wirkung des Rauschens gefunden. Dies bedeutet, dass einige Attraktoren eine groessere Wahrscheinlichkeit erhalten aufzutreten, als dies fuer das rauschfreie System der Fall waere. Bei einer bestimmten Rauschstaerke ist diese Bevorzugung maximal. <br /> Andere Attraktoren werden aufgrund des Rauschens weniger oft angelaufen. Bei einer entsprechend hohen Rauschstaerke werden sie komplett ausgeloescht. <br /> Die Komplexitaet des Sprungprozesses wird fuer das Modell zweier gekoppelter logistischer Abbildungen mit symbolischer Dynamik untersucht. <br /> Bei Variation eines Parameters steigt an einem bestimmten Wert des Parameters die topologische Entropie steil an, die neben der Shannon Entropie als Komplexitaetsmass verwendet wird. Dieser Anstieg wird auf eine neuartige Bifurkation von chaotischen Satteln zurueckgefuehrt, die in einem Verschmelzen zweier Sattel besteht und durch einen “Snap-back”-Repellor vermittelt wird. <br /> Skalierungsgesetze sowohl der Verweilzeit auf einem der zuvor getrennten Teile des Sattels als auch des Wachsens der fraktalen Dimension des entstandenen Sattels beschreiben diese neuartige Bifurkation genauer. <br /> Wenn ein chaotischer Sattel eingebettet in der offenen Umgebung eines Einzugsgebietes eines metastabilen Zustandes liegt, fuehrt das zu einer deutlichen Senkung der Schwelle des rauschinduzierten Tunnelns. <br /> Dies wird anhand der Ikeda-Abbildung, die ein Lasersystem mit einer zeitverzoegerden Interferenz beschreibt, demonstriert. Dieses Resultat wird unter Verwendung der Theorie der Quasipotentiale erzielt. <br /> Sowohl dieser Effekt, die Senkung der Schwelle für rauschinduziertes Tunneln aus einem metastabilen Zustand durch einen chaotischen Sattel, als auch die beiden Skalierungsgesteze sind von experimenteller Relevanz. / Nonlinear multistable systems under the influence of noise exhibit a plethora of interesting dynamical properties. A medium noise level causes hopping between the metastable states. This attractorhopping process is characterized through laminar motion in the vicinity of the attractors and erratic motion taking place on chaotic saddles, which are embedded in the fractal basin boundary. This leads to noise-induced chaos. The investigation of the dissipative standard map showed the phenomenon of preference of attractors through the noise. It means, that some attractors get a larger probability of occurrence than in the noisefree system. For a certain noise level this prefernce achieves a maximum. Other attractors are occur less often. For sufficiently high noise they are completely extinguished. The complexity of the hopping process is examined for a model of two coupled logistic maps employing symbolic dynamics. With the variation of a parameter the topological entropy, which is used together with the Shannon entropy as a measure of complexity, rises sharply at a certain value. This increase is explained by a novel saddle merging bifurcation, which is mediated by a snapback repellor. Scaling laws of the average time spend on one of the formerly disconnected parts and of the fractal dimension of the connected saddle describe this bifurcation in more detail. If a chaotic saddle is embedded in the open neighborhood of the basin of attraction of a metastable state, the required escape energy is lowered. This enhancement of noise-induced escape is demonstrated for the Ikeda map, which models a laser system with time-delayed feedback. The result is gained using the theory of quasipotentials. This effect, as well as the two scaling laws for the saddle merging bifurcation, are of experimental relevance.

Networks of neurons, which form central pattern generators (CPGs), are important for controlling animal behaviors. Of special interest are configurations or CPG motifs composed of reciprocally inhibited neurons, such as half-center oscillators (HCOs). Bursting rhythms of HCOs are shown to include stable synchrony or in-phase bursting. This in-phase bursting can co-exist with anti-phase bursting, commonly expected as the single stable state in HCOs that are connected with fast non-delayed synapses. The finding contrasts with the classical view that reciprocal inhibition has to be slow or time-delayed to synchronize such bursting neurons. Phase-locked rhythms are analyzed via Lyapunov exponents estimated with variational equations, and through the convergence rates estimated with Poincar\'e return maps. A new mechanism underlying multistability is proposed that is based on the spike interactions, which confer a dual property on the fast non-delayed reciprocal inhibition; this reveals the role of spikes in generating multiple co-existing phase-locked rhythms. In particular, it demonstrates that the number and temporal characteristics of spikes determine the number and stability of the multiple phase-locked states in weakly coupled HCOs. The generality of the multistability phenomenon is demonstrated by analyzing diverse models of bursting networks with various inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, the Purkinje neuron model and Fitzhugh-Rinzel phenomenological model. Finally, hypothetical and experiment-based CPGs composed of HCOs are investigated. This study is relevant for various applications that use CPGs such as robotics, prosthetics, and artificial intelligence.

The co-existence of bursting activity and silence is a common property of various neuronal models. We describe a novel mechanism explaining the co-existence of and the transition between these two regimes. It is based on the specific homoclinic and Andronov-Hopf bifurcations of the hyper- and depolarized steady states that determine the co-existence domain in the parameter space of the leech heart interneuron models: canonical and simplified. We found that a sub-critical Andronov-Hopf bifurcation of the hyperpolarized steady state gives rise to small amplitude sub-threshold oscillations terminating through the secondary homoclinic bifurcation. Near the corresponding boundary the system can exhibit long transition from bursting oscillations into silence, as well as the bi-stability where the observed regime is determined by the initial state of the neuron. The mechanism found is shown to be generic for the simplified 4D and the original 14D leech heart interneuron models.

A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along bursting orbits. Using computer assisted analysis, we examine stability, bifurcations of attractors, and transformations of their basins in the phase plane. These structures determine the global bursting rhythms emitted by the CPG. By varying the coupling synaptic strength, we examine the dynamics and patterns produced by inhibitory networks.

Made available in DSpace on 2016-12-12T20:15:53Z (GMT). No. of bitstreams: 1 Elementos Pre-Textuais.pdf: 7374343 bytes, checksum: e9469c7859d60daa5c005889409ff1ee (MD5) Previous issue date: 2011-02-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Hénon map is a paradigmatic two-dimensional discrete-time dynamical system, which was originally proposed as a model to the Poincaré section of the continuous-time Lorenz system, and has been extensively investigated in the last years. Apart from its theoretical importance, some practical applications are possible. As an example, it can be used to model CO2 lasers in the limit of strong dissipation. The Hénon map is characterized by two parameters, namely the nonlinearity and the dissipativity. In this work we consider a situation where these two parameters of one Hénon map are linearly modulated by the solution of another Hénon map whose parameters are constants in time, but which can be adjusted. We investigate periodic and chaotic modulations of the first Hénon map, due to the second, and show that method is able to destroy or create attractors in the phase-space. More specifically, the modulation is able to control the multistability (bistability in the considered case) present in the Hénon map, leading the system to monostability. Finally, we investigate the dynamics of the Hénon map when its parameters are modulated by another Hénon map in a regime close to the conservative limit and in a regime close to the dissipative limit. Lyapunov exponents, bifurcation diagrams, basins of attraction, parameter space and phase-space diagrams are used to characterize the dynamics of the modulated system. / O mapa de Hénon é um sistema dinâmico bidimensional a tempo discreto, originalmente proposto como um modelo para a seção de Poincaré do sistema de Lorenz a tempo contínuo, e tem sido extensivamente investigado nos últimos anos. Além da sua grande importância teórica, algumas aplicações práticas são possíveis. Como por exemplo, pode ser usado para modelar lasers de CO2 no limite de forte dissipação. O mapa de Hénon é caracterizado por dois parâmetros, o de não linearidade e o de dissipação. Neste trabalho nós consideramos a situação onde estes dois parâmetros do mapa de Hénon são linearmente modulados pela solução de outro mapa de Hénon, cujos parâmetros são constantes no tempo, mas que podem ser ajustados. Investigamos modulações periódicas e caóticas do primeiro mapa de Hénon devido ao segundo, e mostramos que este método pode destruir ou criar atratores no espaço de fases, bem como produzir mudanças na localização dos pontos onde ocorrem as bifurcações. Mais especificamente, a modulação permite controlar a multiestabilidade (biestabilidade, nos casos considerados) presente no mapa de Hénon, conduzindo o sistema a monoestabilidade. Por fim, investigamos a dinâmica do mapa de Hénon quando seus parâmetros são modulados por um outro mapa de Hénon em um regime próximo ao limite conservativo e em um regime de alta dissipação. Expoentes de Lyapunov, diagramas de bifurcação, bacias de atração, diagramas do espaço de parâmetros e do espaço de fases são utilizados para caracterizar a dinâmica do sistema modulado.

Perceptual bi/multi-stability—the phenomenon in which perceptual awareness switches between alternative interpretations of a stimulus—can be elicited by a large range of stimuli. The phenomenon is explored in vision, audition, touch, and even olfaction. The degree to which perceptual switching across visual and auditory bi/multi-stable paradigms depends on common or separate mechanisms remains unanswered. This main question was addressed in the current work by using four ambiguous tasks that give rise to bi/multi-stability and which are thought to involve rivalry at different levels of cognitive processing: auditory streaming and ambiguous-structure-from-motion (low- level tasks), and verbal transformations and ambiguous figures (high-level tasks). It was also investigated if individual differences in executive function (inhibitory control and set-shifting), creativity and personality traits have common relationships with perceptual switching in adults and children. A series of five experiments (four studies) were conducted. In Study 1 (two experiments), perceptual switching behaviour of adult participants was examined in the four perceptual tasks mentioned above. In Experiment 1, participants reported higher switching rates for the ambiguous figure and verbal transformations than for ambiguous motion and auditory streaming. However, in Experiment 2 participants had a higher switching rate in verbal transformations than in auditory streaming, while the switching rates in the two visual tasks did not differ significantly. The correlations between visual and auditory switching rates were similarly inconclusive: in Experiment 1, no cross-modal correlations emerged, while in Experiment 2 there were correlations between ambiguous figure and verbal transformations and between ambiguous motion and verbal transformation. Furthermore, inhibitory control, set-shifting, and creativity correlated with perceptual ii switching rates in some of the perceptual tasks, although not in a consistent manner. In Study 2, the development of perceptual switching was investigated in children in the same four tasks used in Study 1. Findings showed that the number of switches increased with age in all four perceptual tasks, indicating general maturational developments. Executive functions and creativity were not associated with the ongoing perceptual switching, which was similar to what was found in adults. In Study 3, a neuroscientific perturbation approach was used to investigate whether the superior parietal cortex is causally involved in both visual and auditory multistability as a top-down mechanism. Transcranial magnetic stimulation on the anterior and posterior superior parietal cortex did not increase or decrease the median phase durations in response to the ambiguous motion and auditory streaming. These regions were not causally involved in either visual or auditory multistability. Perceptual switching across modalities correlated nevertheless, indicating common perceptual mechanisms. In Study 4, the effects of attentional control and instructions were further investigated in ambiguous motion and auditory streaming. There were strong correlations between perceptual switching in the two tasks, confirming that there are common mechanisms. However, the effects of voluntary attention did not explain the commonalities found. Possibly the commonalities found reflect similar functionalities at more low-level sensorial mechanisms. In conclusion, perceptual switching in vision and audition share common mechanisms. These commonalities do not seem to be due to the same neural underpinning in parietal cortex. Moreover, attentional control does not explain the commonalities found, indicating a more low-level common mechanism or functionality. Perceptual switching across all ages is task-specific, more than modality specific. No central influence of inhibitory control and creativity was constantly associated with perceptual switching regardless of task/modality, supporting the distributed mechanisms hypothesis.

Magnetic shape memory alloys are active materials which deform under the application of a magnetic field or an external stress. Due to their internal friction, recognizable from the strain-stress hysteresis, this new material technology allows the design of multistable actuators. This paper describes and characterizes an innovative airflow control valve whose aperture is proportional to the deformation of the active material and thus controllable by the input voltage. The multistability of the material is partially exploited within an airflow control loop to reduce the energy losses of the valve when a specific airflow value must be hold.

abstract: Synthetic gene networks have evolved from simple proof-of-concept circuits to complex therapy-oriented networks over the past fifteen years. This advancement has greatly facilitated expansion of the emerging field of synthetic biology. Multistability is a mechanism that cells use to achieve a discrete number of mutually exclusive states in response to environmental inputs. However, complex contextual connections of gene regulatory networks in natural settings often impede the experimental establishment of the function and dynamics of each specific gene network. In this work, diverse synthetic gene networks are rationally designed and constructed using well-characterized biological components to approach the cell fate determination and state transition dynamics in multistable systems. Results show that unimodality and bimodality and trimodality can be achieved through manipulation of the signal and promoter crosstalk in quorum-sensing systems, which enables bacterial cells to communicate with each other. Moreover, a synthetic quadrastable circuit is also built and experimentally demonstrated to have four stable steady states. Experiments, guided by mathematical modeling predictions, reveal that sequential inductions generate distinct cell fates by changing the landscape in sequence and hence navigating cells to different final states. Circuit function depends on the specific protein expression levels in the circuit. We then establish a protein expression predictor taking into account adjacent transcriptional regions’ features through construction of ~120 synthetic gene circuits (operons) in Escherichia coli. The predictor’s utility is further demonstrated in evaluating genes’ relative expression levels in construction of logic gates and tuning gene expressions and nonlinear dynamics of bistable gene networks. These combined results illustrate applications of synthetic gene networks to understand the cell fate determination and state transition dynamics in multistable systems. A protein-expression predictor is also developed to evaluate and tune circuit dynamics. / Dissertation/Thesis / Doctoral Dissertation Biomedical Engineering 2017