108 research outputs found
Flipping Biological Switches: Solving for Optimal Control: A Dissertation
Switches play an important regulatory role at all levels of biology, from molecular switches triggering signaling cascades to cellular switches regulating cell maturation and apoptosis. Medical therapies are often designed to toggle a system from one state to another, achieving a specified health outcome. For instance, small doses of subpathologic viruses activate the immune system’s production of antibodies. Electrical stimulation revert cardiac arrhythmias back to normal sinus rhythm. In all of these examples, a major challenge is finding the optimal stimulus waveform necessary to cause the switch to flip. This thesis develops, validates, and applies a novel model-independent stochastic algorithm, the Extrema Distortion Algorithm (EDA), towards finding the optimal stimulus. We validate the EDA’s performance for the Hodgkin-Huxley model (an empirically validated ionic model of neuronal excitability), the FitzHugh-Nagumo model (an abstract model applied to a wide range of biological systems that that exhibit an oscillatory state and a quiescent state), and the genetic toggle switch (a model of bistable gene expression). We show that the EDA is able to not only find the optimal solution, but also in some cases excel beyond the traditional analytic approaches. Finally, we have computed novel optimal stimulus waveforms for aborting epileptic seizures using the EDA in cellular and network models of epilepsy. This work represents a first step in developing a new class of adaptive algorithms and devices that flip biological switches, revealing basic mechanistic insights and therapeutic applications for a broad range of disorders
Nucleation of reaction-diffusion waves on curved surfaces
We study reaction-diffusion waves on curved two-dimensional surfaces, and
determine the influence of curvature upon the nucleation and propagation of
spatially localized waves in an excitable medium modelled by the generic
FitzHugh-Nagumo model. We show that the stability of propagating wave segments
depends crucially on the curvature of the surface. As they propagate, they may
shrink to the uniform steady state, or expand, depending on whether they are
smaller or larger, respectively, than a critical nucleus. This critical nucleus
for wave propagation is modified by the curvature acting like an effective
space-dependent local spatial coupling, similar to diffusion, thus extending
the regime of propagating excitation waves beyond the excitation threshold of
flat surfaces. In particular, a negative gradient of Gaussian curvature
, as on the outside of a torus surface (positive ), when the
wave segment symmetrically extends into the inside (negative ), allows
for stable propagation of localized wave segments remaining unchanged in size
and shape, or oscillating periodically in size
Stochastic neural network dynamics: synchronisation and control
Biological brains exhibit many interesting and complex behaviours. Understanding of the mechanisms behind brain behaviours is critical for continuing advancement in fields of research such as artificial intelligence and medicine. In particular, synchronisation of neuronal firing is associated with both improvements to and degeneration of the brain’s performance; increased synchronisation can lead to enhanced information-processing or neurological disorders such as epilepsy and Parkinson’s disease. As a result, it is desirable to research under which conditions synchronisation arises in neural networks and the possibility of controlling its prevalence. Stochastic ensembles of FitzHugh-Nagumo elements are used to model neural networks for numerical simulations and bifurcation analysis. The FitzHugh-Nagumo model is employed because of its realistic representation of the flow of sodium and potassium ions in addition to its advantageous property of allowing phase plane dynamics to be observed. Network characteristics such as connectivity, configuration and size are explored to determine their influences on global synchronisation generation in their respective systems. Oscillations in the mean-field are used to detect the presence of synchronisation over a range of coupling strength values. To ensure simulation efficiency, coupling strengths between neurons that are identical and fixed with time are investigated initially. Such networks where the interaction strengths are fixed are referred to as homogeneously coupled. The capacity of controlling and altering behaviours produced by homogeneously coupled networks is assessed through the application of weak and strong delayed feedback independently with various time delays. To imitate learning, the coupling strengths later deviate from one another and evolve with time in networks that are referred to as heterogeneously coupled. The intensity of coupling strength fluctuations and the rate at which coupling strengths converge to a desired mean value are studied to determine their impact upon synchronisation performance. The stochastic delay differential equations governing the numerically simulated networks are then converted into a finite set of deterministic cumulant equations by virtue of the Gaussian approximation method. Cumulant equations for maximal and sub-maximal connectivity are used to generate two-parameter bifurcation diagrams on the noise intensity and coupling strength plane, which provides qualitative agreement with numerical simulations. Analysis of artificial brain networks, in respect to biological brain networks, are discussed in light of recent research in sleep theor
Computational study of resting state network dynamics
Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le più importanti proprietà della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cos’è il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nell’analisi dell’attività cerebrale, per poi evidenziare la differenza tra connettività strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio ‘bottom-up’, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il ‘connettoma’ adoperato. Successivamente vengono mostrati i risultati dell’analisi svolta sui dati ricavati, dai quali si mostra come la criticità e il rumore svolgano un ruolo chiave nell'emergenza di questa attività di fondo del cervello. Questi risultati vengono poi confrontati con le più importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilità di virtualizzare l’attività cerebrale
Dynamical principles in neuroscience
Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA
Nonlinear Dynamics, Synchronisation and Chaos in Coupled FHN Cardiac and Neural Cells
Physiological systems are amongst the most challenging systems to investigate from a
mathematically based approach. The eld of mathematical biology is a relatively recent
one when compared to physics. In this thesis I present an introduction to the physiological
aspects needed to gain access to both cardiac and neural systems for a researcher trained
in a mathematically based discipline. By using techniques from nonlinear dynamical
systems theory I show a number of results that have implications for both neural and
cardiac cells. Examining a reduced model of an excitable biological oscillator I show how
rich the dynamical behaviour of such systems can be when coupled together. Quantifying
the dynamics of coupled cells in terms of synchronisation measures is treated at length.
Most notably it is shown that for cells that themselves cannot admit chaotic solutions,
communication between cells be it through electrical coupling or synaptic like coupling,
can lead to the emergence of chaotic behaviour. I also show that in the presence of
emergent chaos one nds great variability in intervals of activity between the constituent
cells. This implies that chaos in both cardiac and neural systems can be a direct result
of interactions between the constituent cells rather than intrinsic to the cells themselves.
Furthermore the ubiquity of chaotic solutions in the coupled systems may be a means of
information production and signaling in neural systems
Neuronal oscillations: from single-unit activity to emergent dynamics and back
L’objectiu principal d’aquesta tesi és avançar en la comprensió del processament d’informació en xarxes neuronals en presència d’oscil lacions subumbrals. La majoria de neurones propaguen la seva activitat elèctrica a través de sinapsis quÃmiques que són activades, exclusivament, quan el corrent elèctric que les travessa supera un cert llindar. És per aquest motiu que les descà rregues rà pides i intenses produïdes al soma neuronal, els anomenats potencials d’acció, són considerades la unitat bà sica d’informació neuronal, és a dir, el senyal mÃnim i necessari per a iniciar la comunicació entre dues neurones. El codi neuronal és entès, doncs, com un llenguatge binari que expressa qualsevol missatge (estÃmul sensorial, memòries, etc.) en un tren de potencials d’acció. Tanmateix, cap funció cognitiva rau en la dinà mica d’una única neurona. Circuits de milers de neurones connectades entre sà donen lloc a determinats ritmes, palesos en registres d’activitat colectiva com els electroencefalogrames (EEG) o els potencials de camp local (LFP). Si els potencials d’acció de cada cèl lula, desencadenats per fluctuacions estocà stiques de les corrents sinà ptiques, no assolissin un cert grau de sincronia, no apareixeria aquesta periodicitat a nivell de xarxa.
Per tal de poder entendre si aquests ritmes intervenen en el codi neuronal hem estudiat tres situacions. Primer, en el CapÃtol 2, hem mostrat com una
cadena oberta de neurones amb un potencial de membrana intrÃnsecament oscil latori filtra un senyal periòdic arribant per un dels extrems. La resposta
de cada neurona (pulsar o no pulsar) depèn de la seva fase, de forma que cada una d’elles rep un missatge filtrat per la precedent. A més, cada potencial
d’acció presinà ptic provoca un canvi de fase en la neurona postsinà ptica que depèn de la seva posició en l’espai de fases. Els perÃodes d’entrada capaços de sincronitzar les oscil lacions subumbrals són aquells que mantenen la fase d’arribada dels potencials d’acció fixa al llarg de la cadena. Per tal de què el missatge arribi intacte a la darrera neurona cal, a més a més, que aquesta fase permeti la descà rrega del voltatge transmembrana.
En segon cas, hem estudiat una xarxa neuronal amb connexions tant a veïns propers com de llarg abast, on les oscil lacions subumbrals emergeixen de
l’activitat col lectiva reflectida en els corrents sinà ptics (o equivalentment en el LFP). Les neurones inhibidores aporten un ritme a l’excitabilitat de la
xarxa, és a dir, que els episodis en què la inhibició és baixa, la probabilitat d’una descà rrega global de la població neuronal és alta. En el CapÃtol 3
mostrem com aquest ritme implica l’aparició d’una bretxa en la freqüència de descà rrega de les neurones: o bé polsen espaiadament en el temps o bé
en rà fegues d’elevada intensitat. La fase del LFP determina l’estat de la xarxa neuronal codificant l’activitat de la població: els mÃnims indiquen la
descà rrega simultà nia de moltes neurones que, ocasionalment, han superat el llindar d’excitabilitat degut a un decreixement global de la inhibició, mentre
que els mà xims indiquen la coexistència de rà fegues en diferents punts de la xarxa degut a decreixements locals de la inhibició en estats globals d’excitació. Aquesta dinà mica és possible grà cies al domini de la inhibició sobre l’excitació. En el CapÃtol 4 considerem acoblament entre dues xarxes neuronals per tal d’estudiar la interacció entre ritmes diferents. Les oscil lacions indiquen recurrència en la sincronització de l’activitat col lectiva, de manera que durant aquestes finestres temporals una població optimitza el seu impacte en una xarxa diana. Quan el ritme de la població receptora i el de l’emissora difereixen significativament, l’eficiència en la comunicació decreix, ja que les fases de mà xima resposta de cada senyal LFP no mantenen una diferència constant entre elles.
Finalment, en el CapÃtol 5 hem estudiat com les oscil lacions col lectives pròpies de l’estat de son donen lloc al fenomen de coherència estocà stica.
Per a una intensitat òptima del soroll, modulat per l’excitabilitat de la xarxa, el LFP assoleix una regularitat mà xima donant lloc a un perÃode refractari de
la població neuronal.
En resum, aquesta Tesi mostra escenaris d’interacció entre els potencials d’acció, caracterÃstics de la dinà mica de neurones individuals, i les oscil lacions
subumbrals, fruit de l’acoblament entre les cèl lules i ubiqües en la dinà mica de poblacions neuronals. Els resultats obtinguts aporten funcionalitat a aquests
ritmes emergents, agents sincronitzadors i moduladors de les descà rregues neuronals i reguladors de la comunicació entre xarxes neuronals.The main objective of this thesis is to better understand information processing in neuronal networks in the presence of subthreshold oscillations. Most neurons propagate their electrical activity via chemical synapses, which are only activated when the electric current that passes through them surpasses a certain threshold. Therefore, fast and intense discharges produced at the neuronal soma (the action potentials or spikes) are considered the basic unit of neuronal information. The neuronal code is understood, then, as a binary language that expresses any message (sensory stimulus, memories, etc.) in a train of action potentials. Circuits of thousands of interconnected neurons give rise to certain rhythms, revealed in collective activity measures such as electroencephalograms (EEG) and local field potentials (LFP). Synchronization of action potentials of each cell, triggered by stochastic fluctuations of the synaptic currents, cause this periodicity at the network level.To understand whether these rhythms are involved in the neuronal code we studied three situations. First, in Chapter 2, we showed how an open chain of neurons with an intrinsically oscillatory membrane potential filters a periodic signal coming from one of its ends. The response of each neuron (to spike or not) depends on its phase, so that each cell receives a message filtered by the preceding one. Each presynaptic action potential causes a phase change in the postsynaptic neuron, which depends on its position in the phase space. Those incoming periods that are able to synchronize the subthreshold oscillations, keep the phase of arrival of action potentials fixed along the chain. The original message reaches intact the last neuron provided that this phase allows the discharge of the transmembrane voltage.I the second case, we studied a neuronal network with connections to both long range and close neighbors, in which the subthreshold oscillations emerge from the collective activity apparent in the synaptic currents. The inhibitory neurons provide a rhythm to the excitability of the network. When inhibition is low, the likelihood of a global discharge of the neuronal population is high. In Chapter 3 we show how this rhythm causes a gap in the discharge frequency of neurons: either they pulse single spikes or they fire bursts of high intensity. The LFP phase determines the state of the neuronal network, coding the activity of the population: its minima indicate the simultaneous discharge of many neurons, while its maxima indicate the coexistence of bursts due to local decreases of inhibition at global states of excitation. In Chapter 4 we consider coupling between two neural networks in order to study the interaction between different rhythms. The oscillations indicate recurrence in the synchronization of collective activity, so that during these time windows a population optimizes its impact on a target network. When the rhythm of the emitter and receiver population differ significantly, the communication efficiency decreases as the phases of maximum response of each LFP signal do not maintain a constant difference between them.Finally, in Chapter 5 we studied how oscillations typical of the collective sleep state give rise to stochastic coherence. For an optimal noise intensity, modulated by the excitability of the network, the LFP reaches a maximal regularity leading to a refractory period of the neuronal population.In summary, this Thesis shows scenarios of interaction between action potentials, characteristics of the dynamics of individual neurons, and the subthreshold oscillations, outcome of the coupling between the cells and ubiquitous in the dynamics of neuronal populations . The results obtained provide functionality to these emerging rhythms, triggers of synchronization and modulator agents of the neuronal discharges and regulators of the communication between neuronal networks
Locomotor Network Dynamics Governed By Feedback Control In Crayfish Posture And Walking
Sensorimotor circuits integrate biomechanical feedback with ongoing motor activity to produce behaviors that adapt to unpredictable environments. Reflexes are critical in modulating motor output by facilitating rapid responses. During posture, resistance reflexes generate negative feedback that opposes perturbations to stabilize a body. During walking, assistance reflexes produce positive feedback that facilitates fast transitions between swing and stance of each step cycle.
Until recently, sensorimotor networks have been studied using biomechanical feedback based on external perturbations in the presence or absence of intrinsic motor activity. Experiments in which biomechanical feedback driven by intrinsic motor activity is studied in the absence of perturbation have been limited. Thus, it is unclear whether feedback plays a role in facilitating transitions between behavioral states or mediating different features of network activity independent of perturbation. These properties are important to understand because they can elucidate how a circuit coordinates with other neural networks or contributes to adaptable motor output.
Computational simulations and mathematical models have been used extensively to characterize interactions of negative and positive feedback with nonlinear oscillators. For example, neuronal action potentials are generated by positive and negative feedback of ionic currents via a membrane potential. While simulations enable manipulation of system parameters that are inaccessible through biological experiments, mathematical models ascertain mechanisms that help to generate biological hypotheses and can be translated across different systems.
Here, a three-tiered approach was employed to determine the role of sensory feedback in a crayfish locomotor circuit involved in posture and walking. In vitro experiments using a brain-machine interface illustrated that unperturbed motor output of the circuit was changed by closing the sensory feedback loop. Then, neuromechanical simulations of the in vitro experiments reproduced a similar range of network activity and showed that the balance of sensory feedback determined how the network behaved. Finally, a reduced mathematical model was designed to generate waveforms that emulated simulation results and demonstrated how sensory feedback can control the output of a sensorimotor circuit. Together, these results showed how the strengths of different approaches can complement each other to facilitate an understanding of the mechanisms that mediate sensorimotor integration
Memristors
This Edited Volume Memristors - Circuits and Applications of Memristor Devices is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Engineering. The book comprises single chapters authored by various researchers and edited by an expert active in the physical sciences, engineering, and technology research areas. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on physical sciences, engineering, and technology,and open new possible research paths for further novel developments
18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings
Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I
Table of Contents ........................ Page III
Symposium Committees .............. Page IV
Special Thanks ............................. Page V
Conference program (incl. page numbers of papers)
................... Page VI
Conference papers
Invited talks ................................ Page 1
Regular Papers ........................... Page 14
Wednesday, May 26th, 2010 ......... Page 15
Thursday, May 27th, 2010 .......... Page 110
Friday, May 28th, 2010 ............... Page 210
Author index ............................... Page XII
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