Bistable attractor dynamics in neuromorphic aVLSI chips

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2014

Relaxation times in a bistable system with parametric, white noise: Theory and experiment

We consider the effects of external, multiplicative white noise on the relaxation time of a general representation of a bistable system from the points of view provided by two, quite different, theoretical approaches: the classical Stratonovich decoupling of correlations and the new method due to Jung and Risken. Experimental results, obtained from a bistable electronic circuit, are compared to the theoretical predictions. We show that the phenomenon of critical slowing down appears as a function of the noise parameters, thereby providing a correct characterization of a noise-induced transition.

First-passage time in a bistable potential with colored noise

A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework.

Insight toward the first-passage time in a bistable potential with highly colored noise

The exponential coefficient in the first-passage-time problem for a bistable potential with highly colored noise is predicted to be (8/27 by all existing theories. On the other hand, we show herein that all existing numerical evidence seems to indicate that the coefficient is actually larger by about (4/3, i.e., that the numerical factor in the exponent is approximately (32/81. Existing data cover values of ¿V0/D up to ~20, where V0 is the barrier height, ¿ the correlation time of the noise, and D the noise intensity. We provide an explanation for the modified coefficinet, the explanation also being based on existing numerical simulations. Whether the value (8/27 predicted by all large-¿ theories is achieved for even larger values of ¿V0/D is unknown but appears questionable (except perhaps for enormously large, experimentally inaccessible values of this factor) in view of currently available results.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.

Pulse propagation sustained by noise in arrays of bistable electronic circuits

One-dimensional arrays of nonlinear electronic circuits are shown to support propagation of pulses when operating in a locally bistable regime, provided the circuits are under the influence of a global noise. These external random fluctuations are applied to the parameter that controls the transition between bistable and monostable dynamics in the individual circuits. As a result, propagating fronts become destabilized in the presence of noise, and the system self-organizes to allow the transmission of pulses. The phenomenon is also observed in weakly coupled arrays, when propagation failure arises in the absence of noise.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.

Regulation of bistable ICEclc transfer in pseudomonas knackmussii B13

L'élément génétique intégratif et conjugatif auto-transférable de 103 kb qui se trouve dans le génome de Pseudomonas knackmussii B13 (ICEc/c) confère la capacité de dégrader le 3-chlorobenzoate et le 2-aminophénol. L'élément ICE c/c peut être transféré par conjugaison de la souche B13 à diverses bêta- et gamma- protéobactéries. Seule une sous-population de 3 à 5% des cellules transfère l'élément, les cellules dites "compétentes pour le transfert". L'acquisition de la compétence pour le transfert est vraisemblablement la conséquence d'une régulation bistable, conduisant une partie des cellules au transfert de l'élément ICE c/c tandis que, dans les autres, l'élément reste quiescent et ne se transfère pas. À ce jour, les mécanismes et les acteurs moléculaires qui régulent l'activation bistable de l'élément sont restés inconnus. Mon travail de doctorat visait à identifier les éléments bistables du régulon de la compétence pour le transfert et d'analyser les fondements moléculaires de la bistabilité de l'élément ICE c/c chez P. knackmussii. Le premier chapitre introduit le thème du transfert génétique horizontal avec un accent particulier sur les éléments intégratifs et conjugatifs (ICE) et ICEcIc. L'état actuel des connaissances sur l'organisation génétique, la régulation, l'intégration et le transfert de différents modèles de ICEs est exposé en détail. En outre, je m'étends sur les phénomènes d'hétérogénéité et de bistabilité phénotyplques, qu'on peut distinguer dans une population isogénique dans des conditions de culture homogènes, et qui sont susceptibles de jouer un rôle dans le transfert de l'élément ICE c/c, dans la mesure où il ne s'active et n'est transférable que dans une très petite sous-population de cellules. Dans le chapitre 2, je présente une analyse globale des régions promotrices minimales des gènes appartenant au régulon de la compétence pour le transfert de l'élément ICE c/c. Nous avons étudié les caractéristiques d'expression des promoteurs et, s'ils s'avéraient bistables, leur activation dans le temps par comparaison avec le mutant lntB13. Pour ce faire, nous avons utilisé des fusions de promoteurs avec des gènes rapporteurs et testé l'expression bistable chez P. knackmussii par microscopie à épifluorescence. Pour six promoteurs présentant une expression bistable, nous avons employé de la microscopie temporelle pour déterminer la chronologie de leur expression par rapport à Pint et PinR. Parmi eux, nous avons identifié deux gènes exprimés précocement et trois gènes exprimés tardivement dans le processus d'acquisition de la compétence de transfert. Dans le chapitre 3, j'expose une analyse d'expression génétique pour l'un des groupes de gènes dont la transcription est la plus élevée dans la région conservée de ICE c/c, les gènes orf81655-orf68241 contenus dans une région de 14 kb. Nous montrons d'abord que cet opéron fait partie du même régulon bistable que intB13 et inrR et analysons les caractéristiques génétiques qui conduisent à une transcription élevée. Nous étudions les fonctions biologiques de ce groupe de gènes par des délétlons ciblées et montrons que certaines d'entre elles empêchent le transfert de l'élément. Nous approfondissons la caractérlsatlon de I'orf8l655 en construisant une fusion transcrlptionnelle avec le gène codant pour la protéine fluorescente verte (egfp) (en utilisant le système minl-Tn5). L'expression de Vorf81655 dans des cellules individuelles est comparée au signal mesuré par hybridation in situ en fluorescence (FISH) sur le ARN messager du gène. En utilisant FISH, des délétlons du promoteur et de l'analyse directe de transcription, nous avons localisé la région promotrice du groupe de gènes. En outre, nous avons utilisé des mutations dirigées pour comprendre la bistabilité de cette région promotrice, caractérisée par une transcription très élevée et une traduction lente de l'ARN messager.  Dans le chapitre 4, nous nous efforçons de comprendre comment la bistabilité est générée au sein du régulon te de l'élément ICE c/c. Pour ce faire, nous avons tenté de reconstituer une expression bistable, dans un hôte qui ne présente pas de bistabilité naturellement, à partir d'éléments génétiques individuels. L'hôte choisi est Pseudomonas putida dans lequel nous avons introduit une copie unique de Pint, PinR ou PaipA fusionnés à la egfp, construits qui permettent d'observer l'apparition de bistabilité. Nous avons ensuite construit différents assemblages de composants génétiques de l'élément ICE c/c, en nous concentrant sur la région parA-inrR. En effet, nous avons pu démontrer qu'une expression bistable apparaît dans P. putida grâce à ces éléments en l'absence de l'élément ICE c/c complet. À noter que la plupart des construits génétiques activent PaipA ou P|,,R, mais qu'un seul recrée la bistabilité de Pint, ce qui suggère que la région parA-inrR permet à la fois d'engendrer la bistabilité et d'opérer la transition entre les promoteurs précoces et les promoteurs tardifs du régulon de la bistabilité. Dans le chapitre 5, nous concluons sur une discussion de la pertinence de nos résultats et sur de futures perspectives de recherche. -- The 103-kb self-transmissible integrative and conjugative element (ICE) of Pseudomonas knackmussii B13 (ICEc/c) confers the capacity to degrade 3- chlorobenzoate and 2-aminophenol. ICEc/c can be conjugated from strain B13 to a variety of Beta- and Gammaproteobacteria. Interestingly, ICE c/c transfer is observed in a subpopulatlon of cells (3-5%) only, the so-called 'transfer competent' cells. The formation of transfer competence (tc) is thought to be the consequence of a 'bistable' decision, which forces those cells to follow the developmental path which leads to ICEc/c transfer, whereas in others ICE c/c remains silent and does not transfer. So far, the mechanisms and molecular partners generating this bistable transfer activation in cells of P. knackmussii B13 remain mostly unidentified. This thesis aimed at understanding the extent of the tc bistability regulon and to dissect the molecular basis of bistabillty formation of ICEc/c in P. knackmussii. The first chapter is a general Introduction on horizontal gene transfer (HGT) with particular emphasis on ICEs and ICE c/c. The emphasis is made on the current knowledge about the HGT gene organization, regulation and specific integration and transfer aspects of the different ICEs models. Furthermore, I focus on the phenomena of phenotypic heterogeneity and bistability (the property of two distinguishable phenotypes existing within an isogenic population under homogeneous conditions), which may play a particular role in ICEc/c behaviour, since ICE activation and transfer only occurs in a very small subpopulation of cells. In Chapter Two, I focus on a global analysis of the different core promoters that might belong to the ICEc/c tc pathway regulon. We studied both expression patterns of ICEc/c promoters and, once being identified as "bistable", their temporal activation compared to that of intB13. In order to do this, we used promoter reporter fusions and tested blstability expression in P. knackmussii using epifluorescence microscopy. For the 6 promoters that showed bistable expression, we used time-lapse microscopy to study the timing of promoter expression in comparison to that of P,,,t or PlnR. We could establish two "early" and 3 "late" phase promoters in the process of transfer competence. In Chapter Three, I focused my attention on analysis of gene expression of one of the most highly transcribed gene clusters in the conserved core region of ICEc/c, a 14-kb gene cluster formed by the genes orf81655-orf68241. First we showed that this operon is part of the same bistability 'regulon' as intB13 and inrR, and analysed the genetic features that lead to high transcription. We studied the potential biological function of this cluster for ICE c/c by making specific gene deletions, showing that some interrupt ICEc/c transfer. We further analysed the orfdl655 promoter by constructing transcriptional egfp fusion reporter strains using the miniTn5 delivery system. Expression of the orf81655 promoter in single cells was compared to signals measured by Fluorescence In Situ Hybridization (FISH) on orfSl655 mRNA. We localized the promoter region of the gene cluster using FISH, promoter deletions, and by direct transcript analysis. We further used site-directed mutagenesis to understand the bistability character of the promoter region and the extremely high transcription but low translation from this mRNA. In Chapter Four, we set out to understand how bistability is generated in the tc pathway of ICEc/c. For this we tried rebuilding bistable expression from ICEc/c individual gene components in a host, which normally does not display bistability. As host we used P. putida without ICEc/c but with a single copy Pint-, PlnR- or PalpA- egfp fusion that enabled us to verify bistability formation. Subsequently, we built different assemblages of ICEc/c gene components, focusing on the parA-inrR region. Indeed, we found that bistable expression can be build from those components in P. putida without ICEc/c. Interestingly, most genetic constructs activated PaipA or PlnR, but only one resulted in bistable activation of PinT. This suggests that the parA-inrR region acts as a bistability "generator", but also as a bistability "relay" from early to late promoters in the tc pathway hierarchy. In the final fifth chapter, we conclude with a discussion of the relevance of the present thesis and the resulting perspectives for future studies.

Modeling and manufacturability assessment of bistable quantum-dot cells

We have investigated the behavior of bistable cells made up of four quantum dots and occupied by two electrons, in the presence of realistic confinement potentials produced by depletion gates on top of a GaAs/AlGaAs heterostructure. Such a cell represents the basic building block for logic architectures based on the concept of quantum cellular automata (QCA) and of ground state computation, which have been proposed as an alternative to traditional transistor-based logic circuits. We have focused on the robustness of the operation of such cells with respect to asymmetries derived from fabrication tolerances. We have developed a two-dimensional model for the calculation of the electron density in a driven cell in response to the polarization state of a driver cell. Our method is based on the one-shot configuration-interaction technique, adapted from molecular chemistry. From the results of our simulations, we conclude that an implementation of QCA logic based on simple ¿hole arrays¿ is not feasible, because of the extreme sensitivity to fabrication tolerances. As an alternative, we propose cells defined by multiple gates, where geometrical asymmetries can be compensated for by adjusting the bias voltages. Even though not immediately applicable to the implementation of logic gates and not suitable for large scale integration, the proposed cell layout should allow an experimental demonstration of a chain of QCA cells.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

The Fokker-Planck equation for a bistable potential

The Fokker-Planck equation is studied through its relation to a Schrodinger-type equation. The advantage of this combination is that we can construct the probability distribution of the Fokker-Planck equation by using well-known solutions of the Schrodinger equation. By making use of such a combination, we present the solution of the Fokker-Planck equation for a bistable potential related to a double oscillator. Thus, we can observe the temporal evolution of the system describing its dynamic properties such as the time tau to overcome the barrier. By calculating the rates k = 1/tau as a function of the inverse scaled temperature 1/D, where D is the diffusion coefficient, we compare the aspect of the curve k x 1/D, with the ones obtained from other studies related to four different kinds of activated process. We notice that there are similarities in some ranges of the scaled temperatures, where the different processes follow the Arrhenius behavior. We propose that the type of bistable potential used in this study may be used, qualitatively, as a simple model, whose rates share common features with the rates of some single rate-limited thermally activated processes. (C) 2014 Elsevier B.V. All rights reserved.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

Stochastic models and dynamic measures for the characterization of bistable circuits

During the last few years, a great deal of interest has risen concerning the applications of stochastic methods to several biochemical and biological phenomena. Phenomena like gene expression, cellular memory, bet-hedging strategy in bacterial growth and many others, cannot be described by continuous stochastic models due to their intrinsic discreteness and randomness. In this thesis I have used the Chemical Master Equation (CME) technique to modelize some feedback cycles and analyzing their properties, including experimental data. In the first part of this work, the effect of stochastic stability is discussed on a toy model of the genetic switch that triggers the cellular division, which malfunctioning is known to be one of the hallmarks of cancer. The second system I have worked on is the so-called futile cycle, a closed cycle of two enzymatic reactions that adds and removes a chemical compound, called phosphate group, to a specific substrate. I have thus investigated how adding noise to the enzyme (that is usually in the order of few hundred molecules) modifies the probability of observing a specific number of phosphorylated substrate molecules, and confirmed theoretical predictions with numerical simulations. In the third part the results of the study of a chain of multiple phosphorylation-dephosphorylation cycles will be presented. We will discuss an approximation method for the exact solution in the bidimensional case and the relationship that this method has with the thermodynamic properties of the system, which is an open system far from equilibrium.In the last section the agreement between the theoretical prediction of the total protein quantity in a mouse cells population and the observed quantity will be shown, measured via fluorescence microscopy.

Investigation of the Design of a Bistable Micro-Chemical-Mechanical Device Utilizing Lateral Buckling

The Gracias Laboratory at Johns Hopkins University has developed microgrippers which utilize chemically-actuated joints to be used in micro-surgery. These grippers, however, take up to thirty minutes to close fully when activated biochemicals in the human body. This is very problematic and could limit the use of the devices in surgery. It is the goal of this research to develop a gripper that uses theGracias Laboratory's existing joints in conjunction with mechanical components to decrease the closing time. The purpose of including the mechanical components is to induce a state of instability at which time a small perturbation would cause the joint to close fully.The main concept of the research was to use the lateral buckling of a triangular gripper geometry and use a toggle mechanism to decrease the closure time of the device. This would create a snap-action device mimicking the quick closure of a Venus flytrap. All developed geometries were tested using finite element analysis to determine ifloading conditions produced the desired buckled shape. This research examines lateral buckling on the micro-scale and the possibility ofusing this phenomenon in a micro-gripper. Although a final geometry with the required deformed shaped was not found, this document contains suggestions for future geometries that may produce the correct deformed shape. It was determined through this work that in order to obtain the desired deformed shape, polymeric sections need to be added to the geometry. This simplifies the analysis and allows the triangular structure to buckle in the appropriate way due to the added joints. Future work for this project will be completed by undergraduate students at Bucknell University. Fabrication and testing of devices will be done at Johns Hopkins University in the Gracias Laboratory.

Interhemispheric connections shape subjective experience of bistable motion

The right and left visual hemifields are represented in different cerebral hemispheres and are bound together by connections through the corpus callosum. Much has been learned on the functions of these connections from split-brain patients [1-4], but little is known about their contribution to conscious visual perception in healthy humans. We used diffusion tensor imaging and functional magnetic resonance imaging to investigate which callosal connections contribute to the subjective experience of a visual motion stimulus that requires interhemispheric integration. The "motion quartet" is an ambiguous version of apparent motion that leads to perceptions of either horizontal or vertical motion [5]. Interestingly, observers are more likely to perceive vertical than horizontal motion when the stimulus is presented centrally in the visual field [6]. This asymmetry has been attributed to the fact that, with central fixation, perception of horizontal motion requires integration across hemispheres whereas perception of vertical motion requires only intrahemispheric processing [7]. We are able to show that the microstructure of individually tracked callosal segments connecting motion-sensitive areas of the human MT/V5 complex (hMT/V5+; [8]) can predict the conscious perception of observers. Neither connections between primary visual cortex (V1) nor other surrounding callosal regions exhibit a similar relationship.