Failure of Delayed Feedback Deep Brain Stimulation for Intermittent Pathological Synchronization in Parkinson's Disease

Suppression of excessively synchronous beta-band oscillatory activity in the brain is believed to suppress hypokinetic motor symptoms of Parkinson's disease. Recently, a lot of interest has been devoted to desynchronizing delayed feedback deep brain stimulation (DBS). This type of synchrony control was shown to destabilize the synchronized state in networks of simple model oscillators as well as in networks of coupled model neurons. However, the dynamics of the neural activity in Parkinson's disease exhibits complex intermittent synchronous patterns, far from the idealized synchronous dynamics used to study the delayed feedback stimulation. This study explores the action of delayed feedback stimulation on partially synchronized oscillatory dynamics, similar to what one observes experimentally in parkinsonian patients. We employ a model of the basal ganglia networks which reproduces experimentally observed fine temporal structure of the synchronous dynamics. When the parameters of our model are such that the synchrony is unphysiologically strong, the feedback exerts a desynchronizing action. However, when the network is tuned to reproduce the highly variable temporal patterns observed experimentally, the same kind of delayed feedback may actually increase the synchrony. As network parameters are changed from the range which produces complete synchrony to those favoring less synchronous dynamics, desynchronizing delayed feedback may gradually turn into synchronizing stimulation. This suggests that delayed feedback DBS in Parkinson's disease may boost rather than suppress synchronization and is unlikely to be clinically successful. The study also indicates that delayed feedback stimulation may not necessarily exhibit a desynchronization effect when acting on a physiologically realistic partially synchronous dynamics, and provides an example of how to estimate the stimulation effect.Comment: 19 pages, 8 figure

Complete synchronization in coupled Type-I neurons

For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of instantaneous frequency with the instantaneous phase of the stochastic inputs to each neuron matches exactly with that for the other in the event of CS of their outputs. Our observation can be exploited in practical situations to produce completely synchronized outputs in artificial devices. For excitatory-excitatory synaptic coupling, a functional dependence for the synchronization error on coupling and noise strengths is obtained. Finally we report an observation of noise-induced CS between non-identical neurons coupled bidirectionally through random non-zero couplings in an all-to- all way in a large neuronal ensemble.Comment: 24 pages, 9 figure

Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale

Synchronicity From Synchronized Chaos

The synchronization of loosely coupled chaotic oscillators, a phenomenon investigated intensively for the last two decades, may realize the philosophical notion of synchronicity. Effectively unpredictable chaotic systems, coupled through only a few variables, commonly exhibit a predictable relationship that can be highly intermittent. We argue that the phenomenon closely resembles the notion of meaningful synchronicity put forward by Jung and Pauli if one identifies "meaningfulness" with internal synchronization, since the latter seems necessary for synchronizability with an external system. Jungian synchronization of mind and matter is realized if mind is analogized to a computer model, synchronizing with a sporadically observed system as in meteorological data assimilation. Internal synchronization provides a recipe for combining different models of the same objective process, a configuration that may also describe the functioning of conscious brains. In contrast to Pauli's view, recent developments suggest a materialist picture of semi-autonomous mind, existing alongside the observed world, with both exhibiting a synchronistic order. Basic physical synchronicity is manifest in the non-local quantum connections implied by Bell's theorem. The quantum world resides on a generalized synchronization "manifold", a view that provides a bridge between nonlocal realist interpretations and local realist interpretations that constrain observer choice .Comment: 1) clarification regarding the connection with philosophical synchronicity in Section 2 and in the concluding section 2) reference to Maldacena-Susskind "ER=EPR" relation in discussion of role of wormholes in entanglement and nonlocality 3) length reduction and stylistic changes throughou

Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure $M_s$ by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure $M_s$ is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of $M_s$, we quantitatively characterize the stochastic spiking coherence, and find that $M_s$ reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure $M_s$ may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.Comment: 16 pages, 5 figures, to appear in the J. Comput. Neurosc

Information processing in biological complex systems: a view to bacterial and neural complexity

This thesis is a study of information processing of biological complex systems seen from the perspective of dynamical complexity (the degree of statistical independence of a system as a whole with respect to its components due to its causal structure). In particular, we investigate the influence of signaling functions in cell-to-cell communication in bacterial and neural systems. For each case, we determine the spatial and causal dependencies in the system dynamics from an information-theoretic point of view and we relate it with their physiological capabilities. The main research content is presented into three main chapters. First, we study a previous theoretical work on synchronization, multi-stability, and clustering of a population of coupled synthetic genetic oscillators via quorum sensing. We provide an extensive numerical analysis of the spatio-temporal interactions, and determine conditions in which the causal structure of the system leads to high dynamical complexity in terms of associated metrics. Our results indicate that this complexity is maximally receptive at transitions between dynamical regimes, and maximized for transient multi-cluster oscillations associated with chaotic behaviour. Next, we introduce a model of a neuron-astrocyte network with bidirectional coupling using glutamate-induced calcium signaling. This study is focused on the impact of the astrocyte-mediated potentiation on synaptic transmission. Our findings suggest that the information generated by the joint activity of the population of neurons is irreducible to its independent contribution due to the role of astrocytes. We relate these results with the shared information modulated by the spike synchronization imposed by the bidirectional feedback between neurons and astrocytes. It is shown that the dynamical complexity is maximized when there is a balance between the spike correlation and spontaneous spiking activity. Finally, the previous observations on neuron-glial signaling are extended to a large-scale system with community structure. Here we use a multi-scale approach to account for spatiotemporal features of astrocytic signaling coupled with clusters of neurons. We investigate the interplay of astrocytes and spiking-time-dependent-plasticity at local and global scales in the emergence of complexity and neuronal synchronization. We demonstrate the utility of astrocytes and learning in improving the encoding of external stimuli as well as its ability to favour the integration of information at synaptic timescales to exhibit a high intrinsic causal structure at the system level. Our proposed approach and observations point to potential effects of the astrocytes for sustaining more complex information processing in the neural circuitry