Evidence and control of bifurcations in a respiratory system

Multifractal analysis of birdsong and its correlation structure

The time series recordings of typical songs of songbirds exhibit highly complex and structured behavior, which is characteristic of their species and stage of development, and need to be analyzed by methods that can uncover their correlation structure. Here we analyze a typical song of a canary using Hurst exponents and multifractal analysis, which uncovers the correlation structure of typical song segments. These are then compared with the corresponding quantities from shuffled data, which destroys the temporal correlations and iterative amplitude-adjusted Fourier transform (IAAFT) data. It is seen that temporal correlations are responsible for the multifractal behavior seen in the data and that two-point correlations, which are preserved by the transform, are important in the high-fluctuation regime. Higher-order correlations and intersyllabic gaps dominate the behavior of the low-fluctuation regime. These observations are supported by the simplicial characterization of the corresponding time series networks. Complexity measures are also used to analyze the amplitude envelope time series. These indicate that intersyllabic gaps contribute a significant fraction to the complexity of the birdsong. Our method provides a detailed characterization of the data, which can enable the comparison of real and synthetic birdsong and comparisons across stages of development and species. A brief comparison with the song of the zebra finch supports this.

Nonlinear dynamics in the study of birdsong

Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.

Temperature manipulation of neuronal dynamics in a forebrain motor control nucleus

Different neuronal types within brain motor areas contribute to the generation of complex motor behaviors. A widely studied songbird forebrain nucleus (HVC) has been recognized as fundamental in shaping the precise timing characteristics of birdsong. This is based, among other evidence, on the stretching and the “breaking” of song structure when HVC is cooled. However, little is known about the temperature effects that take place in its neurons. To address this, we investigated the dynamics of HVC both experimentally and computationally. We developed a technique where simultaneous electrophysiological recordings were performed during temperature manipulation of HVC. We recorded spontaneous activity and found three effects: widening of the spike shape, decrease of the firing rate and change in the interspike interval distribution. All these effects could be explained with a detailed conductance based model of all the neurons present in HVC. Temperature dependence of the ionic channel time constants explained the first effect, while the second was based in the changes of the maximal conductance using single synaptic excitatory inputs. The last phenomenon, only emerged after introducing a more realistic synaptic input to the inhibitory interneurons. Two timescales were present in the interspike distributions. The behavior of one timescale was reproduced with different input balances received form the excitatory neurons, whereas the other, which disappears with cooling, could not be found assuming poissonian synaptic inputs. Furthermore, the computational model shows that the bursting of the excitatory neurons arises naturally at normal brain temperature and that they have an intrinsic delay at low temperatures. The same effect occurs at single synapses, which may explain song stretching. These findings shed light on the temperature dependence of neuronal dynamics and present a comprehensive framework to study neuronal connectivity. This study, which is based on intrinsic neuronal characteristics, may help to understand emergent behavioral changes.

The study of the neuronal mechanisms that give rise to the complex behavior of singing in birds has been hotly debated lately. Many models have been tested and novel tools have been developed to try to understand the role of a key brain nucleus in the song pathway: HVC. It is believed that it is highly responsible for generating the precise timing of songs, and this has been tested by manipulating it with temperature. Results showed that cooling can stretch, but that it can also restructure or “break” the song syllables. However, single neuronal mechanisms are not yet described. To better understand this, we cooled HVC in canaries and measured spontaneous activity electrophysiologically. We found three effects: spike shape widening, spike rate reduction and changes in inter-spike-interval (ISI) distributions. To explain them, we built a computational model with a detailed description of ion channel conductances and temperature dependency. We could explain the first effect with a single neuron model. The second, could be explained adding single synapses. Finally, we showed similar ISI modifications of one of the timescales present by means of multiple stochastic inputs. In addition, we found that excitatory neurons show natural bursting behavior at normal brain temperatures and that synaptic delays are the main candidates to explain song stretching at low temperatures.

Nonlinear resonances and multi-stability in simple neural circuits

This article describes a numerical procedure designed to tune the parameters of periodically driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic solutions available to the system within a range of the parameters that define the driving. The procedure is applied to a problem of interest in computational neuroscience: a circuit composed of two interacting populations of neurons under external periodic forcing. Depending on the parameters that define the circuit, such as the weights of the connections between the populations, the response of the circuit to the driving can be strikingly rich and diverse. The procedure is employed to find circuits that, when driven by external input, exhibit multiple stable patterns of periodic activity organized in complex tuning diagrams and signatures of low dimensional chaos.

A circular model for song motor control in Serinus canaria

Song production in songbirds is controlled by a network of nuclei distributed across several brain regions, which drives respiratory and vocal motor systems to generate sound. We built a model for birdsong production, whose variables are the average activities of different neural populations within these nuclei of the song system. We focus on the predictions of respiratory patterns of song, because these can be easily measured and therefore provide a validation for the model. We test the hypothesis that it is possible to construct a model in which (1) the activity of an expiratory related (ER) neural population fits the observed pressure patterns used by canaries during singing, and (2) a higher forebrain neural population, HVC, is sparsely active, simultaneously with significant motor instances of the pressure patterns. We show that in order to achieve these two requirements, the ER neural population needs to receive two inputs: a direct one, and its copy after being processed by other areas of the song system. The model is capable of reproducing the measured respiratory patterns and makes specific predictions on the timing of HVC activity during their production. These results suggest that vocal production is controlled by a circular network rather than by a simple top-down architecture.