Insights from models of rhythmic motor systems

Choice-relevant information transformation along a ventrodorsal axis in the medial prefrontal cortex

Choice-relevant brain regions in prefrontal cortex may progressively transform information about options into choices. Here, we examine responses of neurons in four regions of the medial prefrontal cortex as macaques performed two-option risky choices. All four regions encode economic variables in similar proportions and show similar putative signatures of key choice-related computations. We provide evidence to support a gradient of function that proceeds from areas 14 to 25 to 32 to 24. Specifically, we show that decodability of twelve distinct task variables increases along that path, consistent with the idea that regions that are higher in the anatomical hierarchy make choice-relevant variables more separable. We also show progressively longer intrinsic timescales in the same series. Together these results highlight the importance of the medial wall in choice, endorse a specific gradient-based organization, and argue against a modular functional neuroanatomy of choice.

Dynamics and computation in mixed networks containing neurons that accelerate towards spiking

Networks in the brain consist of different types of neurons. Here we investigate the influence of neuron diversity on the dynamics, phase space structure, and computational capabilities of spiking neural networks. We find that already a single neuron of a different type can qualitatively change the network dynamics and that mixed networks may combine the computational capabilities of ones with a single-neuron type. We study inhibitory networks of concave leaky (LIF) and convex "antileaky" (XIF) integrate-and-fire neurons that generalize irregularly spiking nonchaotic LIF neuron networks. Endowed with simple conductance-based synapses for XIF neurons, our networks can generate a balanced state of irregular asynchronous spiking as well. We determine the voltage probability distributions and self-consistent firing rates assuming Poisson input with finite-size spike impacts. Further, we compute the full spectrum of Lyapunov exponents (LEs) and the covariant Lyapunov vectors (CLVs) specifying the corresponding perturbation directions. We find that there is approximately one positive LE for each XIF neuron. This indicates in particular that a single XIF neuron renders the network dynamics chaotic. A simple mean-field approach, which can be justified by properties of the CLVs, explains the finding. As an application, we propose a spike-based computing scheme where our networks serve as computational reservoirs and their different stability properties yield different computational capabilities.

Brian 2, an intuitive and efficient neural simulator

Brian 2 allows scientists to simply and efficiently simulate spiking neural network models. These models can feature novel dynamical equations, their interactions with the environment, and experimental protocols. To preserve high performance when defining new models, most simulators offer two options: low-level programming or description languages. The first option requires expertise, is prone to errors, and is problematic for reproducibility. The second option cannot describe all aspects of a computational experiment, such as the potentially complex logic of a stimulation protocol. Brian addresses these issues using runtime code generation. Scientists write code with simple and concise high-level descriptions, and Brian transforms them into efficient low-level code that can run interleaved with their code. We illustrate this with several challenging examples: a plastic model of the pyloric network, a closed-loop sensorimotor model, a programmatic exploration of a neuron model, and an auditory model with real-time input.

Reactive oxygen species regulate activity-dependent neuronal plasticity in Drosophila

Reactive oxygen species (ROS) have been extensively studied as damaging agents associated with ageing and neurodegenerative conditions. Their role in the nervous system under non-pathological conditions has remained poorly understood. Working with the Drosophila larval locomotor network, we show that in neurons ROS act as obligate signals required for neuronal activity-dependent structural plasticity, of both pre- and postsynaptic terminals. ROS signaling is also necessary for maintaining evoked synaptic transmission at the neuromuscular junction, and for activity-regulated homeostatic adjustment of motor network output, as measured by larval crawling behavior. We identified the highly conserved Parkinson’s disease-linked protein DJ-1β as a redox sensor in neurons where it regulates structural plasticity, in part via modulation of the PTEN-PI3Kinase pathway. This study provides a new conceptual framework of neuronal ROS as second messengers required for neuronal plasticity and for network tuning, whose dysregulation in the ageing brain and under neurodegenerative conditions may contribute to synaptic dysfunction.

Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.

Robust design of polyrhythmic neural circuits

Neural circuit motifs producing coexistent rhythmic patterns are treated as building blocks of multifunctional neuronal networks. We study the robustness of such a motif of inhibitory model neurons to reliably sustain bursting polyrhythms under random perturbations. Without noise, the exponential stability of each of the coexisting rhythms increases with strengthened synaptic coupling, thus indicating an increased robustness. Conversely, after adding noise we find that noise-induced rhythm switching intensifies if the coupling strength is increased beyond a critical value, indicating a decreased robustness. We analyze this stochastic arrhythmia and develop a generic description of its dynamic mechanism. Based on our mechanistic insight, we show how physiological parameters of neuronal dynamics and network coupling can be balanced to enhance rhythm robustness against noise. Our findings are applicable to a broad class of relaxation-oscillator networks, including Fitzhugh-Nagumo and other Hodgkin-Huxley-type networks.

Setting the pace: new insights into central pattern generator interactions in box jellyfish swimming

Central Pattern Generators (CPGs) produce rhythmic behaviour across all animal phyla. Cnidarians, which have a radially symmetric nervous system and pacemaker centres in multiples of four, provide an interesting comparison to bilaterian animals for studying the coordination between CPGs. The box jellyfish Tripedalia cystophora is remarkable among cnidarians due to its most elaborate visual system. Together with their ability to actively swim and steer, they use their visual system for multiple types of behaviour. The four swim CPGs are directly regulated by visual input. In this study, we addressed the question of how the four pacemaker centres of this radial symmetric cnidarian interact. We based our investigation on high speed camera observations of the timing of swim pulses of tethered animals (Tripedalia cystophora) with one or four rhopalia, under different simple light regimes. Additionally, we developed a numerical model of pacemaker interactions based on the inter pulse interval distribution of animals with one rhopalium. We showed that the model with fully resetting coupling and hyperpolarization of the pacemaker potential below baseline fitted the experimental data best. Moreover, the model of four swim pacemakers alone underscored the proportion of long inter pulse intervals (IPIs) considerably. Both in terms of the long IPIs as well as the overall swim pulse distribution, the simulation of two CPGs provided a better fit than that of four. We therefore suggest additional sources of pacemaker control than just visual input. We provide guidelines for future research on the physiological linkage of the cubozoan CPGs and show the insight from bilaterian CPG research, which show that pacemakers have to be studied in their bodily and nervous environment to capture all their functional features, are also manifest in cnidarians.

A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity

A half-center oscillator (HCO) is a common circuit building block of central pattern generator networks that produce rhythmic motor patterns in animals. Here we constructed an efficient relational database table with the resulting characteristics of the Hill et al.'s (J Comput Neurosci 10:281-302, 2001) HCO simple conductance-based model. The model consists of two reciprocally inhibitory neurons and replicates the electrical activity of the oscillator interneurons of the leech heartbeat central pattern generator under a variety of experimental conditions. Our long-range goal is to understand how this basic circuit building block produces functional activity under a variety of parameter regimes and how different parameter regimes influence stability and modulatability. By using the latest developments in computer technology, we simulated and stored large amounts of data (on the order of terabytes). We systematically explored the parameter space of the HCO and corresponding isolated neuron models using a brute-force approach. We varied a set of selected parameters (maximal conductance of intrinsic and synaptic currents) in all combinations, resulting in about 10 million simulations. We classified these HCO and isolated neuron model simulations by their activity characteristics into identifiable groups and quantified their prevalence. By querying the database, we compared the activity characteristics of the identified groups of our simulated HCO models with those of our simulated isolated neuron models and found that regularly bursting neurons compose only a small minority of functional HCO models; the vast majority was composed of spiking neurons.

Computational approaches to neuronal network analysis

Computational modelling is an approach to neuronal network analysis that can complement experimental approaches. Construction of useful neuron and network models is often complicated by a variety of factors and unknowns, most notably the considerable variability of cellular and synaptic properties and electrical activity characteristics found even in relatively 'simple' networks of identifiable neurons. This chapter discusses the consequences of biological variability for network modelling and analysis, describes a way to embrace variability through ensemble modelling and summarizes recent findings obtained experimentally and through ensemble modelling.

Action and behavior: a free-energy formulation

We have previously tried to explain perceptual inference and learning under a free-energy principle that pursues Helmholtz's agenda to understand the brain in terms of energy minimization. It is fairly easy to show that making inferences about the causes of sensory data can be cast as the minimization of a free-energy bound on the likelihood of sensory inputs, given an internal model of how they were caused. In this article, we consider what would happen if the data themselves were sampled to minimize this bound. It transpires that the ensuing active sampling or inference is mandated by ergodic arguments based on the very existence of adaptive agents. Furthermore, it accounts for many aspects of motor behavior; from retinal stabilization to goal-seeking. In particular, it suggests that motor control can be understood as fulfilling prior expectations about proprioceptive sensations. This formulation can explain why adaptive behavior emerges in biological agents and suggests a simple alternative to optimal control theory. We illustrate these points using simulations of oculomotor control and then apply to same principles to cued and goal-directed movements. In short, the free-energy formulation may provide an alternative perspective on the motor control that places it in an intimate relationship with perception.

Reinforcement learning or active inference?

This paper questions the need for reinforcement learning or control theory when optimising behaviour. We show that it is fairly simple to teach an agent complicated and adaptive behaviours using a free-energy formulation of perception. In this formulation, agents adjust their internal states and sampling of the environment to minimize their free-energy. Such agents learn causal structure in the environment and sample it in an adaptive and self-supervised fashion. This results in behavioural policies that reproduce those optimised by reinforcement learning and dynamic programming. Critically, we do not need to invoke the notion of reward, value or utility. We illustrate these points by solving a benchmark problem in dynamic programming; namely the mountain-car problem, using active perception or inference under the free-energy principle. The ensuing proof-of-concept may be important because the free-energy formulation furnishes a unified account of both action and perception and may speak to a reappraisal of the role of dopamine in the brain.

Spinal cord injury: present and future therapeutic devices and prostheses

A range of passive and active devices are under development or are already in clinical use to partially restore function after spinal cord injury (SCI). Prosthetic devices to promote host tissue regeneration and plasticity and reconnection are under development, comprising bioengineered bridging materials free of cells. Alternatively, artificial electrical stimulation and robotic bridges may be used, which is our focus here. A range of neuroprostheses interfacing either with CNS or peripheral nervous system both above and below the lesion are under investigation and are at different stages of development or translation to the clinic. In addition, there are orthotic and robotic devices which are being developed and tested in the laboratory and clinic that can provide mechanical assistance, training or substitution after SCI. The range of different approaches used draw on many different aspects of our current but limited understanding of neural regeneration and plasticity, and spinal cord function and interactions with the cortex. The best therapeutic practice will ultimately likely depend on combinations of these approaches and technologies and on balancing the combined effects of these on the biological mechanisms and their interactions after injury. An increased understanding of plasticity of brain and spinal cord, and of the behavior of innate modular mechanisms in intact and injured systems, will likely assist in future developments. We review the range of device designs under development and in use, the basic understanding of spinal cord organization and plasticity, the problems and design issues in device interactions with the nervous system, and the possible benefits of active motor devices.