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

Energy efficiency of information transmission by electrically coupled neurons

The generation of spikes by neurons is energetically a costly process. This paper studies the consumption of energy and the information entropy in the signalling activity of a model neuron both when it is supposed isolated and when it is coupled to another neuron by an electrical synapse. The neuron has been modelled by a four dimensional Hindmarsh-Rose type kinetic model for which an energy function has been deduced. For the isolated neuron values of energy consumption and information entropy at different signalling regimes have been computed. For two neurons coupled by a gap junction we have analyzed the roles of the membrane and synapse in the contribution of the energy that is required for their organized signalling. Computational results are provided for cases of identical and nonidentical neurons coupled by unidirectional and bidirectional gap junctions. One relevant result is that there are values of the coupling strength at which the organized signalling of two neurons induced by the gap junction takes place at relatively low values of energy consumption and the ratio of mutual information to energy consumption is relatively high. Therefore, communicating at these coupling values could be energetically the most efficient option

Adaptive and Phase Selective Spike Timing Dependent Plasticity in Synaptically Coupled Neuronal Oscillators

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits

Pattern Turnover within Synaptically Perturbed Neural Systems

AbstractA critical level of synaptic perturbation within a trained, artificial neural system induces the nucleation of novel activation patterns, many of which could qualify as viable ideas or action plans. In building massively parallel connectionist architectures requiring myriad, coupled neural modules driven to ideate in this manner, the need has arisen to shift the attention of computational critics to only those portions of the neural “real estate” generating sufficiently novel activation patterns. The search for a suitable affordance to guide such attention has revealed that the rhythm of pattern generation by synaptically perturbed neural nets is a quantitative indicator of the novelty of their conceptual output, that cadence in turn characterized by a frequency and a corresponding temporal clustering that is discernible through fractal dimension. Anticipating that synaptic fluctuations are tantamount in effect to volume neurotransmitter release within cortex, a novel theory of both cognition and consciousness arises that is reliant upon the rate of transitions within cortical activation topologies

A mathematical model of sleep-wake cycles: the role of hypocretin/orexin in homeostatic regulation and thalamic synchronization

Sleep is vital to our health and well-being. Yet, we do not have answers to such fundamental questions as “why do we sleep?” and “what are the mechanisms of sleep regulation?”. Better understanding of these issues can open new perspectives not only in basic neurophysiology but also in different pathological conditions that are going along with sleep disorders and/or disturbances of sleep, e.g. in mental or neurological diseases. A generally accepted concept that explains regulation of sleep was proposed in 1982 by Alexander Borb´ely. It postulates that sleep-wake transitions result from the interaction between a circadian and a homeostatic sleep processes. The circadian process is ascribed to a “genetic clock” in the neurons of the suprachiasmatic nucleus of the hypothalamus. The mechanisms of the homeostatic process are still unclear. In this study a novel concept of hypocretin (orexin) - based control of sleep homeostasis is presented. The neuropeptide hypocretin is a synaptic co-transmitter of neurons in the lateral hypothalamus. It was discovered in 1998 independently by two different groups, therefore, obtaining two names, hypocretin and orexin. This neuropeptide is required to maintain wakefulness. Dysfunction in the hypocretin system leads to the sleep disorder narcolepsy, which, among other symptoms, is characterized by severe disturbances of sleep-wake cycles with sudden sleep-attacks in the wake period and interruptions of the sleep phase. On the other hand injection of hypocretin promotes wakefulness and improves the performance of sleep deprived subjects. The major proposals of the present study are the following: 1) the homeostatic regulation of sleep depends on the dynamics of a neuropeptide hypocretin; 2) ongoing impulse generation of the hypocretin neurons during wakefulness is sustained by reciprocal excitatory connections with other neurons, including local glutamate interneurons; 3) the transition to a silent state (sleep) is going along with an activity-dependent weakening of the hypocretin synaptic efficacy; 4) during the silent state (sleep) synaptic efficacy recovers and firing (wakefulness) can be reinstalled due to the circadian or other input. This concept is realized in a mathematical model of sleep-wake cycles which is built up on a physiology-based, although simplified Hodgkin-Huxley-type approach. In the proposed model a hypocretin neuron is reciprocally connected with a local interneuron via excitatory glutamate synapses. The hypocretin neuron additionally releases the neuropeptide hypocretin as co-transmitter. Besides of the local glutamate interneurons hypocretin neuron excites two gap junction coupled thalamic neurons. The functionally relevant changes are introduced via activity-dependent alterations of the synaptic efficacy of hypocretin. It is decreasing with each action potential generated by the hypocretin neuron. This effect is superimposed by a slow, continuous recovery process. The decreasing synaptic efficacy during the active wake state introduces an increasing sleep pressure. Ist dissipation during the silent sleep state results from the synaptic recovery. The model data demonstrate that the proposed mechanisms can account for typical alterations of homeostatic changes in sleep and wake states, including the effects of an alarm clock, napping and sleep deprivation. In combination with a circadian input, the model mimics the experimentally demonstrated transitions between different activity states of hypothalamic and thalamic neurons. In agreement with sleep-wake cycles, the activity of hypothalamic neurons changes from silence to firing, and the activity of thalamic neurons changes from synchronized bursting to unsynchronized single-spike discharges. These simulation results support the proposed concept of state-dependent alterations of hypocretin effects as an important homeostatic process in sleep-wake regulation, although additional mechanisms may be involved

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