Network Self-Organization Explains the Statistics and Dynamics of Synaptic Connection Strengths in Cortex

The information processing abilities of neural circuits arise from their synaptic connection patterns. Understanding the laws governing these connectivity patterns is essential for understanding brain function. The overall distribution of synaptic strengths of local excitatory connections in cortex and hippocampus is long-tailed, exhibiting a small number of synaptic connections of very large efficacy. At the same time, new synaptic connections are constantly being created and individual synaptic connection strengths show substantial fluctuations across time. It remains unclear through what mechanisms these properties of neural circuits arise and how they contribute to learning and memory. In this study we show that fundamental characteristics of excitatory synaptic connections in cortex and hippocampus can be explained as a consequence of self-organization in a recurrent network combining spike-timing-dependent plasticity (STDP), structural plasticity and different forms of homeostatic plasticity. In the network, associative synaptic plasticity in the form of STDP induces a rich-get-richer dynamics among synapses, while homeostatic mechanisms induce competition. Under distinctly different initial conditions, the ensuing self-organization produces long-tailed synaptic strength distributions matching experimental findings. We show that this self-organization can take place with a purely additive STDP mechanism and that multiplicative weight dynamics emerge as a consequence of network interactions. The observed patterns of fluctuation of synaptic strengths, including elimination and generation of synaptic connections and long-term persistence of strong connections, are consistent with the dynamics of dendritic spines found in rat hippocampus. Beyond this, the model predicts an approximately power-law scaling of the lifetimes of newly established synaptic connection strengths during development. Our results suggest that the combined action of multiple forms of neuronal plasticity plays an essential role in the formation and maintenance of cortical circuits.     

Modeling the Seasonal Adaptation of Circadian Clocks by Changes in the Network Structure of the Suprachiasmatic Nucleus

The dynamics of circadian rhythms needs to be adapted to day length changes between summer and winter. It has been observed experimentally, however, that the dynamics of individual neurons of the suprachiasmatic nucleus (SCN) does not change as the seasons change. Rather, the seasonal adaptation of the circadian clock is hypothesized to be a consequence of changes in the intercellular dynamics, which leads to a phase distribution of electrical activity of SCN neurons that is narrower in winter and broader during summer. Yet to understand this complex intercellular dynamics, a more thorough understanding of the impact of the network structure formed by the SCN neurons is needed. To that effect, we propose a mathematical model for the dynamics of the SCN neuronal architecture in which the structure of the network plays a pivotal role. Using our model we show that the fraction of long-range cell-to-cell connections and the seasonal changes in the daily rhythms may be tightly related. In particular, simulations of the proposed mathematical model indicate that the fraction of long-range connections between the cells adjusts the phase distribution and consequently the length of the behavioral activity as follows: dense long-range connections during winter lead to a narrow activity phase, while rare long-range connections during summer lead to a broad activity phase. Our model is also able to account for the experimental observations indicating a larger light-induced phase-shift of the circadian clock during winter, which we show to be a consequence of higher synchronization between neurons. Our model thus provides evidence that the variations in the seasonal dynamics of circadian clocks can in part also be understood and regulated by the plasticity of the SCN network structure.     

The assessment of the strength of the interaction between neurons of the cat motor cortex in a conditioned reflex to time]

The work was conducted on cats with recording multineuronal activity of the motor cortex at the elaboration of conditioned reflex to time. Strength of interaction was estimated between the adjacent and remote neurones in the limits of 0.5 m. The dynamics of strengths of interneuronal interaction in most cases did not correlate with the dynamics of impulses frequency of the studied neurones. Changes of strengths of interaction between mutually remote neurones at CRT were met more frequently than between the adjacent ones, what may serve as one more evidence of the hypothesis on more strict structure of connections within microsystems and greater plasticity of connections between microsystems.     

Dynamics of pattern formation in lateral-inhibition type neural fields

The dynamics of pattern formation is studied for lateral-inhibition type homogeneous neural fields with general connections. Neural fields consisting of single layer are first treated, and it is proved that there are five types of pattern dynamics. The type of the dynamics of a field depends not only on the mutual connections within the field but on the level of homogeneous stimulus given to the field. An example of the dynamics is as follows: A fixed size of localized excitation, once evoked by stimulation, can be retained in the field persistently even after the stimulation vanishes. It moves until it finds the position of the maximum of the input stimulus. Fields consisting of an excitatory and an inhibitory layer are next analyzed. In addition to stationary localized excitation, fields have such pattern dynamics as production of oscillatory waves, travelling waves, active and dual active transients, etc.This research was supported in part by a Sloan Foundation grant to the Center for Systems Neuroscience, University of Massachusetts at AmherstOn sabbatical leave from the University of Tokyo     

Oscillatory activity in the neural networks of spiking elements

We study the dynamics of activity in the neural networks of enhanced integrate-and-fire elements (with random noise, refractory periods, signal propagation delay, decay of postsynaptic potential, etc.). We consider the networks composed of two interactive populations of excitatory and inhibitory neurons with all-to-all or random sparse connections. It is shown by computer simulations that the regime of regular oscillations is very stable in a broad range of parameter values. In particular, oscillations are possible even in the case of very sparse and randomly distributed inhibitory connections and high background activity. We describe two scenarios of how oscillations may appear which are similar to Andronov-Hopf and saddle-node-on-limit-cycle bifurcations in dynamical systems. The role of oscillatory dynamics for information encoding and processing is discussed.     

Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity.     

Beyond connectivity: how the structure of dispersal influences metacommunity dynamics

Dispersal within metacommunities can play a major role in species persistence by promoting asynchrony between communities. Understanding this role is crucial both for explaining species coexistence and managing landscapes that are increasingly fragmented by human activities. Here, we demonstrate that spatial patterning of dispersal connections can drastically alter both the tendency toward asynchrony and the effect of asynchrony on metacommunity dynamics commonly used to infer the potential for persistence. We also demonstrate that changes in dispersal connections in strictly homogeneous predator-prey metacommunities can generate an extremely rich variety of dynamics even when previously investigated properties of connectivity such as the magnitude and distribution of dispersal among patches are held constant. Furthermore, the dynamics we observe depend strongly on initial conditions. Our results illustrate the effectiveness of measures of spatial structure for predicting asynchrony and its effects on community dynamics, providing a deeper understanding of the relationship between spatial structure and species persistence in metacommunities.     

Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs. Received: 27 April 1998 / Accepted in revised form: 16 March 1999     

Faraway,so close! Functions of Endoplasmic reticulum–Endosome contacts

Eukaryotic cells are partitioned into functionally distinct organelles. Long considered as independent units in the cytosol, organelles are actually in constant and direct interaction with each other, mostly through the establishment of physical connections named membrane contact sites. Membrane contact sites constitute specific active regions involved in organelle dynamics, inter-organelle exchanges and communications. The endoplasmic reticulum (ER), which spreads throughout the cytosol, forms an extensive network that has many connections with the other organelles of the cell. Ample connections between the ER and endocytic organelles are observed in many cell types, highlighting their prominent physiological roles. Even though morphologically similar – a contact is a contact –, the identity of ER-Endosome contacts is defined by their specific molecular composition, which in turn determines the function of the contact. Here, we review the molecular mechanisms of ER-Endosome contact site formation and their associated cellular functions.This article is part of a Special Issue entitled Endoplasmic reticulum platforms for lipid dynamics edited by Shamshad Cockcroft and Christopher Stefan.     

A statistical analysis of the functional connections between the neurons of the visual and motor cortex in different forms of conditioned-reflex behavior]

In experiments on cats with elaboration of delayed alimentary operant reflexes to light organization was studied of interneuronal cortical connections. By means of cross-correlation analysis the dynamics of intra- and interstructural neuronal network was revealed at the level of cortical projections (visual and motor) of cats brain zones at three forms of behaviour: CR realization, in intersignal period with the presence and absence of operant movements. Depending on the forms of behaviour, predominance of "informational" or "motivational" interneuronal connections was observed.     

Optimal Information Representation and Criticality in an Adaptive Sensory Recurrent Neuronal Network

Recurrent connections play an important role in cortical function, yet their exact contribution to the network computation remains unknown. The principles guiding the long-term evolution of these connections are poorly understood as well. Therefore, gaining insight into their computational role and into the mechanism shaping their pattern would be of great importance. To that end, we studied the learning dynamics and emergent recurrent connectivity in a sensory network model based on a first-principle information theoretic approach. As a test case, we applied this framework to a model of a hypercolumn in the visual cortex and found that the evolved connections between orientation columns have a "Mexican hat" profile, consistent with empirical data and previous modeling work. Furthermore, we found that optimal information representation is achieved when the network operates near a critical point in its dynamics. Neuronal networks working near such a phase transition are most sensitive to their inputs and are thus optimal in terms of information representation. Nevertheless, a mild change in the pattern of interactions may cause such networks to undergo a transition into a different regime of behavior in which the network activity is dominated by its internal recurrent dynamics and does not reflect the objective input. We discuss several mechanisms by which the pattern of interactions can be driven into this supercritical regime and relate them to various neurological and neuropsychiatric phenomena.     

Persistent activity in neural networks with dynamic synapses

Persistent activity states (attractors), observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity—symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.     

Nonuniformity in the linear network model of the oculomotor integrator produces approximately fractional-order dynamics and more realistic neuron behavior

The oculomotor integrator is a network that is composed of neurons in the medial vestibular nuclei and nuclei prepositus hypoglossi in the brainstem. Those neurons act approximately as fractional integrators of various orders, converting eye velocity commands into signals that are intermediate between velocity and position. The oculomotor integrator has been modeled as a network of linear neural elements, the time constants of which are lengthened by positive feedback through reciprocal inhibition. In this model, in which each neuron reciprocally inhibits its neighbors with the same Gaussian profile, all model neurons behave as identical, first-order, low-pass filters with dynamics that do not match the variable, approximately fractional-order dynamics of the neurons that compose the actual oculomotor integrator. Fractional-order integrators can be approximated by weighted sums of first-order, low-pass filters with diverse, broadly distributed time constants. Dynamic systems analysis reveals that the model integrator indeed has many broadly distributed time constants. However, only one time constant is expressed in the model due to the uniformity of its network connections. If the model network is made nonuniform by removing the reciprocal connections to and from a small number of neurons, then many more time constants are expressed. The dynamics of the neurons in the nonuniform network model are variable, approximately fractional-order, and resemble those of the neurons that compose the actual oculomotor integrator. Completely removing the connections to and from a neuron is equivalent to eliminating it, an operation done previously to demonstrate the robustness of the integrator network model. Ironically, the resulting nonuniform network model, previously supposed to represent a pathological integrator, may in fact represent a healthy integrator containing neurons with realistically variable, approximately fractional-order dynamics. Received: 8 August 1997 / Accepted in revised form: 18 June 1998     

Linear-nonlinear cascades capture synaptic dynamics

Short-term synaptic dynamics differ markedly across connections and strongly regulate how action potentials communicate information. To model the range of synaptic dynamics observed in experiments, we have developed a flexible mathematical framework based on a linear-nonlinear operation. This model can capture various experimentally observed features of synaptic dynamics and different types of heteroskedasticity. Despite its conceptual simplicity, we show that it is more adaptable than previous models. Combined with a standard maximum likelihood approach, synaptic dynamics can be accurately and efficiently characterized using naturalistic stimulation patterns. These results make explicit that synaptic processing bears algorithmic similarities with information processing in convolutional neural networks.     

Highly nonrandom features of synaptic connectivity in local cortical circuits

How different is local cortical circuitry from a random network? To answer this question, we probed synaptic connections with several hundred simultaneous quadruple whole-cell recordings from layer 5 pyramidal neurons in the rat visual cortex. Analysis of this dataset revealed several nonrandom features in synaptic connectivity. We confirmed previous reports that bidirectional connections are more common than expected in a random network. We found that several highly clustered three-neuron connectivity patterns are overrepresented, suggesting that connections tend to cluster together. We also analyzed synaptic connection strength as defined by the peak excitatory postsynaptic potential amplitude. We found that the distribution of synaptic connection strength differs significantly from the Poisson distribution and can be fitted by a lognormal distribution. Such a distribution has a heavier tail and implies that synaptic weight is concentrated among few synaptic connections. In addition, the strengths of synaptic connections sharing pre- or postsynaptic neurons are correlated, implying that strong connections are even more clustered than the weak ones. Therefore, the local cortical network structure can be viewed as a skeleton of stronger connections in a sea of weaker ones. Such a skeleton is likely to play an important role in network dynamics and should be investigated further.     

Modifiers of solid RNP granules control normal RNP dynamics and mRNA activity in early development

Ribonucleoproteins (RNPs) often coassemble into supramolecular bodies with regulated dynamics. The factors controlling RNP bodies and connections to RNA regulation are unclear. During Caenorhabditis elegans oogenesis, cytoplasmic RNPs can transition among diffuse, liquid, and solid states linked to mRNA regulation. Loss of CGH-1/Ddx6 RNA helicase generates solid granules that are sensitive to mRNA regulators. Here, we identified 66 modifiers of RNP solids induced by cgh-1 mutation. A majority of genes promote or suppress normal RNP body assembly, dynamics, or metabolism. Surprisingly, polyadenylation factors promote RNP coassembly in vivo, suggesting new functions of poly(A) tail regulation in RNP dynamics. Many genes carry polyglutatmine (polyQ) motifs or modulate polyQ aggregation, indicating possible connections with neurodegenerative disorders induced by CAG/polyQ expansion. Several RNP body regulators repress translation of mRNA subsets, suggesting that mRNAs are repressed by multiple mechanisms. Collectively, these findings suggest new pathways of RNP modification that control large-scale coassembly and mRNA activity during development.     

Segregation and mixing in degenerate diffusion in population dynamics

 We study the qualitative properties of degenerate diffusion equations used to describe dispersal processes in population dynamics. For systems of interacting populations, the forms of the diffusion models used determine if the population will intermix or remain disjoint (segregated). The dynamics and stability of segregation boundaries between competing populations is analyzed. General population models with segregation and mixing interactions are derived and connections to behavior in fluid mechanical systems are addressed. Received 19 January 1996; received in revised form 4 April 1996     

Role of structural inhomogeneities in resting-state brain dynamics

Brain imaging methods allow a non-invasive assessment of both structural and functional connectivity. However, the mechanism of how functional connectivity arises in a structured network of interacting neural populations is as yet poorly understood. Here we use a modeling approach to explore the way in which functional correlations arise from underlying structural connections taking into account inhomogeneities in the interactions between the brain regions of interest. The local dynamics of a neural population is assumed to be of phase-oscillator type. The considered structural connectivity patterns describe long-range anatomical connections between interacting neural elements. We find a dependence of the simulated functional connectivity patterns on the parameters governing the dynamics. We calculate graph-theoretic measures of the functional network topology obtained from numerical simulations. The effect of structural inhomogeneities in the coupling term on the observed network state is quantified by examining the relation between simulated and empirical functional connectivity. Importantly, we show that simulated and empirical functional connectivity agree for a narrow range of coupling strengths. We conclude that identification of functional connectivity during rest requires an analysis of the network dynamics.