Pacemaker neurons and neuronal networks: an integrative view

Rhythmically active neuronal networks give rise to rhythmic motor activities but also to seemingly non-rhythmic behaviors such as sleep, arousal, addiction, memory and cognition. Many of these networks contain pacemaker neurons. The ability of these neurons to generate bursts of activity intrinsically lies in voltage- and time-dependent ion fluxes resulting from a dynamic interplay among ion channels, second messenger pathways and intracellular Ca2+ concentrations, and is influenced by neuromodulators and synaptic inputs. This complex intrinsic and extrinsic modulation of pacemaker activity exerts a dynamic effect on network activity. The nonlinearity of bursting activity might enable pacemaker neurons to facilitate the onset of excitatory states or to synchronize neuronal ensembles--an interactive process that is intimately regulated by synaptic and modulatory processes.     

An integrative and practical evolutionary optimization for a complex, dynamic model of biological networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Numerical optimization is the key to estimate the values of kinetic parameters so that the dynamic model reproduces the behaviors of the existing experimental data. It is required to develop general strategies for the optimization of complex biochemical networks with a huge space of search parameters, under the condition that kinetic and quantitative data are hardly available. We propose an integrative and practical strategy for optimizing a complex dynamic model by using qualitative and incomplete experimental data. The key technologies are the divide and conquer method for reducing the search space, handling of multiple objective functions representing different types of biological behaviors, and design of rule-based objective functions that are suitable for qualitative and error-prone experimental data. This strategy is applied to optimizing a dynamic model of the yeast cell cycle to demonstrate the feasibility of it.     

Variable neuronal participation in stereotypic motor programs

To what extent are motor networks underlying rhythmic behaviors rigidly hard-wired versus fluid and dynamic entities? Do the members of motor networks change from moment-to-moment or from motor program episode-to-episode? These are questions that can only be addressed in systems where it is possible to monitor the spiking activity of networks of neurons during the production of motor programs. We used large-scale voltage-sensitive dye (VSD) imaging followed by Independent Component Analysis spike-sorting to examine the extent to which the neuronal network underlying the escape swim behavior of Tritonia diomedea is hard-wired versus fluid from a moment-to-moment perspective. We found that while most neurons were dedicated to the swim network, a small but significant proportion of neurons participated in a surprisingly variable manner. These neurons joined the swim motor program late, left early, burst only on some cycles or skipped cycles of the motor program. We confirmed that this variable neuronal participation was not due to effects of the VSD by finding such neurons with intracellular recording in dye-free saline. Further, these neurons markedly varied their level of participation in the network from swim episode-to-episode. The generality of such unreliably bursting neurons was confirmed by their presence in the rhythmic escape networks of two other molluscan species, Tritonia festiva and Aplysia californica. Our observations support a view that neuronal networks, even those underlying rhythmic and stereotyped motor programs, may be more variable in structure than widely appreciated.     

Oscillations and Synchrony in Large-scale Cortical Network Models

Intrinsic neuronal and circuit properties control the responses of large ensembles of neurons by creating spatiotemporal patterns of activity that are used for sensory processing, memory formation, and other cognitive tasks. The modeling of such systems requires computationally efficient single-neuron models capable of displaying realistic response properties. We developed a set of reduced models based on difference equations (map-based models) to simulate the intrinsic dynamics of biological neurons. These phenomenological models were designed to capture the main response properties of specific types of neurons while ensuring realistic model behavior across a sufficient dynamic range of inputs. This approach allows for fast simulations and efficient parameter space analysis of networks containing hundreds of thousands of neurons of different types using a conventional workstation. Drawing on results obtained using large-scale networks of map-based neurons, we discuss spatiotemporal cortical network dynamics as a function of parameters that affect synaptic interactions and intrinsic states of the neurons.     

Bursting dynamics remarkably improve the performance of neural networks on liquid computing

Burst firings are functionally important behaviors displayed by neural circuits, which plays a primary role in reliable transmission of electrical signals for neuronal communication. However, with respect to the computational capability of neural networks, most of relevant studies are based on the spiking dynamics of individual neurons, while burst firing is seldom considered. In this paper, we carry out a comprehensive study to compare the performance of spiking and bursting dynamics on the capability of liquid computing, which is an effective approach for intelligent computation of neural networks. The results show that neural networks with bursting dynamic have much better computational performance than those with spiking dynamics, especially for complex computational tasks. Further analysis demonstrate that the fast firing pattern of bursting dynamics can obviously enhance the efficiency of synaptic integration from pre-neurons both temporally and spatially. This indicates that bursting dynamic can significantly enhance the complexity of network activity, implying its high efficiency in information processing.     

Working Memory Cells' Behavior May Be Explained by Cross-Regional Networks with Synaptic Facilitation

Neurons in the cortex exhibit a number of patterns that correlate with working memory. Specifically, averaged across trials of working memory tasks, neurons exhibit different firing rate patterns during the delay of those tasks. These patterns include: 1) persistent fixed-frequency elevated rates above baseline, 2) elevated rates that decay throughout the tasks memory period, 3) rates that accelerate throughout the delay, and 4) patterns of inhibited firing (below baseline) analogous to each of the preceding excitatory patterns. Persistent elevated rate patterns are believed to be the neural correlate of working memory retention and preparation for execution of behavioral/motor responses as required in working memory tasks. Models have proposed that such activity corresponds to stable attractors in cortical neural networks with fixed synaptic weights. However, the variability in patterned behavior and the firing statistics of real neurons across the entire range of those behaviors across and within trials of working memory tasks are typical not reproduced. Here we examine the effect of dynamic synapses and network architectures with multiple cortical areas on the states and dynamics of working memory networks. The analysis indicates that the multiple pattern types exhibited by cells in working memory networks are inherent in networks with dynamic synapses, and that the variability and firing statistics in such networks with distributed architectures agree with that observed in the cortex.     

Connecting the dots in ethology: applying network theory to understand neural and animal collectives

A major goal shared by neuroscience and collective behavior is to understand how dynamic interactions between individual elements give rise to behaviors in populations of neurons and animals, respectively. This goal has recently become within reach, thanks to techniques providing access to the connectivity and activity of neuronal ensembles as well as to behaviors among animal collectives. The next challenge using these datasets is to unravel network mechanisms generating population behaviors. This is aided by network theory, a field that studies structure–function relationships in interconnected systems. Here we review studies that have taken a network view on modern datasets to provide unique insights into individual and collective animal behaviors. Specifically, we focus on how analyzing signal propagation, controllability, symmetry, and geometry of networks can tame the complexity of collective system dynamics. These studies illustrate the potential of network theory to accelerate our understanding of behavior across ethological scales.     

Biological modeling of complex chemotaxis behaviors for C. elegans under speed regulation—a dynamic neural networks approach

In this paper, the modeling of several complex chemotaxis behaviors of C. elegans is explored, which include food attraction, toxin avoidance, and locomotion speed regulation. We first model the chemotaxis behaviors of food attraction and toxin avoidance separately. Then, an integrated chemotaxis behavioral model is proposed, which performs the two chemotaxis behaviors simultaneously. The novelty and the uniqueness of the proposed chemotaxis behavioral models are characterized by several attributes. First, all the chemotaxis behavioral model sare on biological basis, namely, the proposed chemotaxis behavior models are constructed by extracting the neural wire diagram from sensory neurons to motor neurons, where sensory neurons are specific for chemotaxis behaviors. Second, the chemotaxis behavioral models are able to perform turning and speed regulation. Third, chemotaxis behaviors are characterized by a set of switching logic functions that decide the orientation and speed. All models are implemented using dynamic neural networks (DNN) and trained using the real time recurrent learning (RTRL) algorithm. By incorporating a speed regulation mechanism, C. elegans can stop spontaneously when approaching food source or leaving away from toxin. The testing results and the comparison with experiment results verify that the proposed chemotaxis behavioral models can well mimic the chemotaxis behaviors of C. elegans in different environments.     

Do Brain Networks Evolve by Maximizing Their Information Flow Capacity?

We propose a working hypothesis supported by numerical simulations that brain networks evolve based on the principle of the maximization of their internal information flow capacity. We find that synchronous behavior and capacity of information flow of the evolved networks reproduce well the same behaviors observed in the brain dynamical networks of Caenorhabditis elegans and humans, networks of Hindmarsh-Rose neurons with graphs given by these brain networks. We make a strong case to verify our hypothesis by showing that the neural networks with the closest graph distance to the brain networks of Caenorhabditis elegans and humans are the Hindmarsh-Rose neural networks evolved with coupling strengths that maximize information flow capacity. Surprisingly, we find that global neural synchronization levels decrease during brain evolution, reflecting on an underlying global no Hebbian-like evolution process, which is driven by no Hebbian-like learning behaviors for some of the clusters during evolution, and Hebbian-like learning rules for clusters where neurons increase their synchronization.     

Noise-Driven Neocortical Interaction: A Simple Generation Mechanism for Complex Neuron Spiking

We discuss a generic scenario along which complex spiking behavior evolves in biologically realistic neural networks. Our nonlinear dynamics approach is based directly on rat neocortical in vitro recordings. Using this experimental data, we obtain a full overview on the possible spiking behaviors of pyramidal neurons that are engaged in binary interactions. Universality arguments imply that the observed spiking behaviors are largely independent from the specific properties of individual neurons; theoretical arguments and numerical experiments indicate that they should be observable in in vivo neocortical neuron networks.     

Contagion of Cooperation in Static and Fluid Social Networks

Cooperation is essential for successful human societies. Thus, understanding how cooperative and selfish behaviors spread from person to person is a topic of theoretical and practical importance. Previous laboratory experiments provide clear evidence of social contagion in the domain of cooperation, both in fixed networks and in randomly shuffled networks, but leave open the possibility of asymmetries in the spread of cooperative and selfish behaviors. Additionally, many real human interaction structures are dynamic: we often have control over whom we interact with. Dynamic networks may differ importantly in the goals and strategic considerations they promote, and thus the question of how cooperative and selfish behaviors spread in dynamic networks remains open. Here, we address these questions with data from a social dilemma laboratory experiment. We measure the contagion of both cooperative and selfish behavior over time across three different network structures that vary in the extent to which they afford individuals control over their network ties. We find that in relatively fixed networks, both cooperative and selfish behaviors are contagious. In contrast, in more dynamic networks, selfish behavior is contagious, but cooperative behavior is not: subjects are fairly likely to switch to cooperation regardless of the behavior of their neighbors. We hypothesize that this insensitivity to the behavior of neighbors in dynamic networks is the result of subjects’ desire to attract new cooperative partners: even if many of one’s current neighbors are defectors, it may still make sense to switch to cooperation. We further hypothesize that selfishness remains contagious in dynamic networks because of the well-documented willingness of cooperators to retaliate against selfishness, even when doing so is costly. These results shed light on the contagion of cooperative behavior in fixed and fluid networks, and have implications for influence-based interventions aiming at increasing cooperative behavior.     

Modulation of circuits underlying rhythmic behaviors

Summary What have we learned about behavior from neuromodulatory studies of the crustacean stomatogastric system? The emphasis of this paper has been on the analysis of one single class of behaviors (rhythmic) in terms of microcircuitry (synaptic connections between identified neurons). But in the general case, all behaviors result from the generation of spatio-temporal patterns by the central nervous system. How individual nerve cells interact with each other to produce such patterns is of fundamental interest. We know from work on simple networks that it is possible to link the circuitry of the nervous system with behavior in a precise way, and that instead of a large number of dedicated circuits, behaviors can be altered by chemically adjusting the functional properties of the neuronal elements. One circuit can be configured to perform a variety of different behaviors by activating neurons which contain neuromodulatory substances or in response to neurohormones circulating in the hemolymph. At present we know only a few of the ways neuromodulatory neurons are triggered to release their contents onto the neurons making up CPGs.The findings described here raise many questions. What are the parameters which control the distribution of neuromodulatory substances throughout the nervous system? What happens when more than one neuromodulator is present? At the cellular level, what mechanisms are involved in transforming each neuron from one functional state to another, and then how does the entire constellation of changes give rise to a new output? It is important to answer such questions in reduced networks, because there are presently no techniques available to answer them in the more complex networks of the brain. While there is no question that modulatory activity occurs in the brain, whether or not the principles which have been discovered by using simple invertebrate circuits scale up to vertebrate circuits remains an intriguing question.     

The functional role of different neural activation profiles during precision grip: An artificial neural network approach

A dynamic and recurrent artificial neural network was used to investigate the functional properties of firing patterns observed in the primary motor (M1) and the primary somatosensory (S1) cortex of the behaving monkey during control of precision grip force. In the behaving monkey it was found that neurons in M1 and in S1 increase their firing activity with increasing grip force, as do the intrinsic and extrinsic hand muscles implicated in the task. However, some neurons also decreased their activity as a function of increasing force. The functional implication of these latter neurons is not clear and has not been elucidated so far. In order to explore their functional implication, we therefore simulated patterns of neural activity in artificial neural networks that represent cortical, spinal and afferent neural populations and tested whether particular activity profiles would emerge as a function of the input and of the connectivity of these networks. The functional implication of units with emergent or imposed decreasing activity was then explored.Decreasing patterns of activity in M1 units did not emerge from the networks. However, the same networks generated decreasing activity if imposed as target patterns. As indicated by the emerging weight space, M1 projection units with decreasing patterns are functionally less involved in driving alpha motoneurons than units with increasing profiles. Furthermore, these units did not provide significant fusimotor drive, whereas those with increasing profiles did. Fusimotor drive was a function of the (imposed) form of muscle spindle afferent activity: with gamma (fusimotor) drive, muscle spindle afferents provided signals other than muscle length (as observed experimentally). The network solutions thus predict a functional dichotomy between increasing and decreasing M1 neurons: the former primarily drive alpha and gamma motoneurons, the latter only weakly alpha motoneurons.     

Neural mechanism of dynamic responses of neurons in inferior temporal cortex in face perception

Understanding the neural mechanisms of object and face recognition is one of the fundamental challenges of visual neuroscience. The neurons in inferior temporal (IT) cortex have been reported to exhibit dynamic responses to face stimuli. However, little is known about how the dynamic properties of IT neurons emerge in the face information processing. To address this issue, we made a model of IT cortex, which performs face perception via an interaction between different IT networks. The model was based on the face information processed by three resolution maps in early visual areas. The network model of IT cortex consists of four kinds of networks, in which the information about a whole face is combined with the information about its face parts and their arrangements. We show here that the learning of face stimuli makes the functional connections between these IT networks, causing a high spike correlation of IT neuron pairs. A dynamic property of subthreshold membrane potential of IT neuron, produced by Hodgkin–Huxley model, enables the coordination of temporal information without changing the firing rate, providing the basis of the mechanism underlying face perception. We show also that the hierarchical processing of face information allows IT cortex to perform a “coarse-to-fine” processing of face information. The results presented here seem to be compatible with experimental data about dynamic properties of IT neurons.     

Network reconfiguration and neuronal plasticity in rhythm-generating networks

Neuronal networks are highly plastic and reconfigure in a state-dependent manner. The plasticity at the network level emerges through multiple intrinsic and synaptic membrane properties that imbue neurons and their interactions with numerous nonlinear properties. These properties are continuously regulated by neuromodulators and homeostatic mechanisms that are critical to maintain not only network stability and also adapt networks in a short- and long-term manner to changes in behavioral, developmental, metabolic, and environmental conditions. This review provides concrete examples from neuronal networks in invertebrates and vertebrates, and illustrates that the concepts and rules that govern neuronal networks and behaviors are universal.     

Finite-size and correlation-induced effects in mean-field dynamics

The brain’s activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system.     

Flux module decomposition for parameter estimation in a multiple-feedback loop model of biochemical networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Since few quantitative values are measured in vivo, the values for unmeasured parameters should be estimated so that the simulation agrees with the experimental data. Considering the sparsity and error rates of experimentally measured data, the first thing is not to find a numerically exact and global solution but to explore a variety of the plausible parameter solutions. To find many plausible parameter solutions without any biases, we developed the two-phase search (TPS) method. However, calculation complexity makes it hard for TPS to optimize a large-scale dynamic model. In this study divide-and-conquer methods are used to solve this problem. The flux module decomposition (FMD) is first proposed that separates a complex, large-scale dynamic model into multiple flux modules without deteriorating its basic control architectures. FMD is combined with TPS, named FMD-TPS, to find many plausible parameter solutions for a dynamic model. To demonstrate the feasibility of FMD-TPS, it is applied to the E. coli ammonia assimilation system that consists of multiple-feedback loops. The variability of the solutions is verified by measuring the space distribution of the parameter solution vectors and by defining the binary vectors checking the consistency with biological behaviors. Compared with non-decomposition methods, FMD-TPS efficiently explored a variety of plausible parameter solutions that reproduce the dynamic behaviors in vivo.     

Short-term memory of motor network performance via activity-dependent potentiation of Na+/K+ pump function

Brain networks memorize previous performance to adjust their output in light of past experience. These activity-dependent modifications generally result from changes in synaptic strengths or ionic conductances, and ion pumps have only rarely been demonstrated to play a dynamic role. Locomotor behavior is produced by central pattern generator (CPG) networks and modified by sensory and descending signals to allow for changes in movement frequency, intensity, and duration, but whether or how the CPG networks recall recent activity is largely unknown. In Xenopus frog tadpoles, swim bout duration correlates linearly with interswim interval, suggesting that the locomotor network retains a short-term memory of previous output. We discovered an ultraslow, minute-long afterhyperpolarization (usAHP) in network neurons following locomotor episodes. The usAHP is mediated by an activity- and sodium spike-dependent enhancement of electrogenic Na(+)/K(+) pump function. By integrating spike frequency over time and linking the membrane potential of spinal neurons to network performance, the usAHP plays a dynamic role in short-term motor memory. Because Na(+)/K(+) pumps are ubiquitously expressed in neurons of all animals and because sodium spikes inevitably accompany network activity, the usAHP may represent a phylogenetically conserved but largely overlooked mechanism for short-term memory of neural network function.     

Complementary molecular models of learning and memory.

The functional capabilities of the brain are formally characterizable interms of a finite system along with a memory space which it can manipulate. Two types of learning are possible: (1) modification-based learning, associated with alternate realizations of the finite system; (2) memory-based learning, associated with the assimilation, manipulation, and retrieval of memories. Constructive models which fulfill these conditions and which at the same time operate on the basis of molecular information processing principles have certain general features. We describe these features in terms of two interfaced submodels, the first for the finite system and the second for the memory space. The finite system may be realized by networks of neurons in which the specificity of enzyme molecules controls the nerve impulse. Such a realization is amenable to modification-based learning mediated by processes analogous to those of natural evolution and selective theories of antibody synthesis. The memory space is realizable by networks of neurons in which the conformation of dendritic receptor molecules controls the nerve impulse. In this case certain neurons firing in response to an external input undergo sensitization at the dendrites and in such a way that they are loadable and later callable by reference neurons, thereby allowing for reconstruction of manipulation of the firing pattern associated with this input. The overall construction makes a large number of biochemical, anatomical, physiological, and psychological predictions which are either testable or in good agreement with fact.