The complexity of dynamics in small neural circuits

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise. Here we introduce a study of the dynamics of a small firing-rate network with excitatory and inhibitory populations, in terms of local and global bifurcations of the neural activity. Our approach is analytically tractable in many respects, and sheds new light on the finite-size effects of the system. In particular, we focus on the formation of multiple branching solutions of the neural equations through spontaneous symmetry-breaking, since this phenomenon increases considerably the complexity of the dynamical behavior of the network. For these reasons, branching points may reveal important mechanisms through which neurons interact and process information, which are not accounted for by the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of figures 8 and 9 fixed, results unchange

Integration of continuous-time dynamics in a spiking neural network simulator

Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here supports the combination of the two for multi-scale modeling approaches, the quantitative validation of mean-field approaches by spiking network simulations, and an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most efficient spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. We further demonstrate the broad applicability of the framework by considering various examples from the literature ranging from random networks to neural field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation

Coordination dynamics in the sensorimotor loop

The last two decades have witnessed radical changes of perspective about the nature of intelligence and cognition, leaving behind some of the assumptions of computational functionalism. From the myriad of approaches seeking to substitute the old rule-based symbolic perception of mind, we are especially interested in two of them. The first is Embodied and Situated Cognition, where the advances in modeling complex adaptive systems through computer simulations have reconfigured the way in which mechanistic, embodied and interactive explanations can conceptualize the mind. We are particularly interested in the concept of sensorimotor loop, which brings a new perspective about what is needed for a meaningful interaction with the environment, emphasizing the role of the coordination of effector and sensor activities while performing a concrete task. The second one is the framework of Coordination Dynamics, which has been developed as a result of the increasing focus of neuroscience on self-organized oscillatory brain dynamics. It provides formal tools to study the mechanisms through which complex biological systems stabilize coordination states under conditions in which they would otherwise become unstable. We will merge both approaches and define coordination in the sensorimotor loop as the main phenomena behind the emergence of cognitive behavior. At the same time, we will provide methodological tools and concepts to address this hypothesis. Finally, we will present two case studies based on the proposed approach: 1. We will study the phenomenon known as “intermittent behavior”, which is observed in organisms at different levels (from microorganisms to higher animals). We will propose a model that understands intermittent behavior as a general strategy of biologica organization when an organism has to adapt to complex changing environments, and would allow to establish effective sensorimotor loops even in situations of instable engagement with the world. 2. We will perform a simulation of a phonotaxis task performed by an agent with an oscillator network as neural controller. The objective will be to characterize robust adaptive coupling between perceptive activity and the environmental dynamics just through phase information processing. We will observe how the robustness of the coupling crucially depends of how the sensorimotor loop structures and constrains both the emergent neural and behavioral patterns. We will hypothesize that this structuration of the sensorimotor space, in which only meaningful behavioral patterns can be stabilized, is a key ingredient for the emergence of higher cognitive abilities

Pulse shape and voltage-dependent synchronization in spiking neuron networks

Pulse-coupled spiking neural networks are a powerful tool to gain mechanistic insights into how neurons self-organize to produce coherent collective behavior. These networks use simple spiking neuron models, such as the $\theta$-neuron or the quadratic integrate-and-fire (QIF) neuron, that replicate the essential features of real neural dynamics. Interactions between neurons are modeled with infinitely narrow pulses, or spikes, rather than the more complex dynamics of real synapses. To make these networks biologically more plausible, it has been proposed that they must also account for the finite width of the pulses, which can have a significant impact on the network dynamics. However, the derivation and interpretation of these pulses is contradictory and the impact of the pulse shape on the network dynamics is largely unexplored. Here, I take a comprehensive approach to pulse-coupling in networks of QIF and $\theta$-neurons. I argue that narrow pulses activate voltage-dependent synaptic conductances and show how to implement them in QIF neurons such that their effect can last through the phase after the spike. Using an exact low-dimensional description for networks of globally coupled spiking neurons, I prove for instantaneous interactions that collective oscillations emerge due to an effective coupling through the mean voltage. I analyze the impact of the pulse shape by means of a family of smooth pulse functions with arbitrary finite width and symmetric or asymmetric shapes. For symmetric pulses, the resulting voltage-coupling is little effective in synchronizing neurons, but pulses that are slightly skewed to the phase after the spike readily generate collective oscillations. The results unveil a voltage-dependent spike synchronization mechanism in neural networks, which is facilitated by pulses of finite width and complementary to traditional synaptic transmission.Comment: 38 pages, 11 figure