Complex sequencing rules of birdsong can be explained by simple hidden Markov processes

Complex sequencing rules observed in birdsongs provide an opportunity to investigate the neural mechanism for generating complex sequential behaviors. To relate the findings from studying birdsongs to other sequential behaviors, it is crucial to characterize the statistical properties of the sequencing rules in birdsongs. However, the properties of the sequencing rules in birdsongs have not yet been fully addressed. In this study, we investigate the statistical propertiesof the complex birdsong of the Bengalese finch (Lonchura striata var. domestica). Based on manual-annotated syllable sequences, we first show that there are significant higher-order context dependencies in Bengalese finch songs, that is, which syllable appears next depends on more than one previous syllable. This property is shared with other complex sequential behaviors. We then analyze acoustic features of the song and show that higher-order context dependencies can be explained using first-order hidden state transition dynamics with redundant hidden states. This model corresponds to hidden Markov models (HMMs), well known statistical models with a large range of application for time series modeling. The song annotation with these models with first-order hidden state dynamics agreed well with manual annotation, the score was comparable to that of a second-order HMM, and surpassed the zeroth-order model (the Gaussian mixture model (GMM)), which does not use context information. Our results imply that the hierarchical representation with hidden state dynamics may underlie the neural implementation for generating complex sequences with higher-order dependencies

A compact statistical model of the song syntax in Bengalese finch

Songs of many songbird species consist of variable sequences of a finite number of syllables. A common approach for characterizing the syntax of these complex syllable sequences is to use transition probabilities between the syllables. This is equivalent to the Markov model, in which each syllable is associated with one state, and the transition probabilities between the states do not depend on the state transition history. Here we analyze the song syntax in a Bengalese finch. We show that the Markov model fails to capture the statistical properties of the syllable sequences. Instead, a state transition model that accurately describes the statistics of the syllable sequences includes adaptation of the self-transition probabilities when states are repeatedly revisited, and allows associations of more than one state to the same syllable. Such a model does not increase the model complexity significantly. Mathematically, the model is a partially observable Markov model with adaptation (POMMA). The success of the POMMA supports the branching chain network hypothesis of how syntax is controlled within the premotor song nucleus HVC, and suggests that adaptation and many-to-one mapping from neural substrates to syllables are important features of the neural control of complex song syntax

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

The Actin Associated Protein Palladin Is Important for the Early Smooth Muscle Cell Differentiation

Palladin, an actin associated protein, plays a significant role in regulating cell adhesion and cell motility. Palladin is important for development, as knockdown in mice is embryonic lethal, yet its role in the development of the vasculature is unknown. We have shown that palladin is essential for the expression of smooth muscle cells (SMC) marker genes and force development in response to agonist stimulation in palladin deficient SMCs. The goal of the study was to determine the molecular mechanisms underlying palladin's ability to regulate the expression of SMC marker genes. Results showed that palladin expression was rapidly induced in an A404 cell line upon retinoic acid (RA) induced differentiation. Suppression of palladin expression with siRNAs inhibited the expression of RA induced SMC differentiation genes, SM α-actin (SMA) and SM22, whereas over-expression of palladin induced SMC gene expression. Chromatin immunoprecipitation assays provided evidence that palladin bound to SMC genes, whereas co-immunoprecipitation assays also showed binding of palladin to myocardin related transcription factors (MRTFs). Endogenous palladin was imaged in the nucleus, increased with leptomycin treatment and the carboxyl-termini of palladin co-localized with MRTFs in the nucleus. Results support a model wherein palladin contributes to SMC differentiation through regulation of CArG-SRF-MRTF dependent transcription of SMC marker genes and as previously published, also through actin dynamics. Finally, in E11.5 palladin null mouse embryos, the expression of SMA and SM22 mRNA and protein is decreased in the vessel wall. Taken together, our findings suggest that palladin plays a key role in the differentiation of SMCs in the developing vasculature

Time-reversed adapted-perturbation (TRAP) optical focusing onto dynamic objects inside scattering media

The ability to steer and focus light inside scattering media has long been sought for a multitude of applications. At present, the only feasible strategy to form optical foci inside scattering media is to guide photons by using either implanted or virtual guide stars, which can be inconvenient and limits the potential applications. Here we report a scheme for focusing light inside scattering media by employing intrinsic dynamics as guide stars. By adaptively time-reversing the perturbed component of the scattered light, we show that it is possible to focus light to the origin of the perturbation. Using this approach, we demonstrate non-invasive dynamic light focusing onto moving targets and imaging of a time-variant object obscured by highly scattering media. Anticipated applications include imaging and photoablation of angiogenic vessels in tumours, as well as other biomedical uses

Support for a synaptic chain model of neuronal sequence generation

In songbirds, the remarkable temporal precision of song is generated by a sparse sequence of bursts in the premotor nucleus HVC. To distinguish between two possible classes of models of neural sequence generation, we carried out intracellular recordings of HVC neurons in singing zebra finches (Taeniopygia guttata). We found that the subthreshold membrane potential is characterized by a large, rapid depolarization 5–10 ms before burst onset, consistent with a synaptically connected chain of neurons in HVC. We found no evidence for the slow membrane potential modulation predicted by models in which burst timing is controlled by subthreshold dynamics. Furthermore, bursts ride on an underlying depolarization of ~10-ms duration, probably the result of a regenerative calcium spike within HVC neurons that could facilitate the propagation of activity through a chain network with high temporal precision. Our results provide insight into the fundamental mechanisms by which neural circuits can generate complex sequential behaviours.National Institutes of Health (U.S.) (Grant MH067105)National Institutes of Health (U.S.) (Grant DC009280)National Science Foundation (U.S.) (IOS-0827731)Alfred P. Sloan Foundation (Research Fellowship

Natural Changes in Brain Temperature Underlie Variations in Song Tempo during a Mating Behavior

The song of a male zebra finch is a stereotyped motor sequence whose tempo varies with social context – whether or not the song is directed at a female bird – as well as with the time of day. The neural mechanisms underlying these changes in tempo are unknown. Here we show that brain temperature recorded in freely behaving male finches exhibits a global increase in response to the presentation of a female bird. This increase strongly correlates with, and largely explains, the faster tempo of songs directed at a female compared to songs produced in social isolation. Furthermore, we find that the observed diurnal variations in song tempo are also explained by natural variations in brain temperature. Our findings suggest that brain temperature is an important variable that can influence the dynamics of activity in neural circuits, as well as the temporal features of behaviors that some of these circuits generate

The Temporal Winner-Take-All Readout

How can the central nervous system make accurate decisions about external stimuli at short times on the basis of the noisy responses of nerve cell populations? It has been suggested that spike time latency is the source of fast decisions. Here, we propose a simple and fast readout mechanism, the temporal Winner-Take-All (tWTA), and undertake a study of its accuracy. The tWTA is studied in the framework of a statistical model for the dynamic response of a nerve cell population to an external stimulus. Each cell is characterized by a preferred stimulus, a unique value of the external stimulus for which it responds fastest. The tWTA estimate for the stimulus is the preferred stimulus of the cell that fired the first spike in the entire population. We then pose the questions: How accurate is the tWTA readout? What are the parameters that govern this accuracy? What are the effects of noise correlations and baseline firing? We find that tWTA sensitivity to the stimulus grows algebraically fast with the number of cells in the population, N, in contrast to the logarithmic slow scaling of the conventional rate-WTA sensitivity with N. Noise correlations in first-spike times of different cells can limit the accuracy of the tWTA readout, even in the limit of large N, similar to the effect that has been observed in population coding theory. We show that baseline firing also has a detrimental effect on tWTA accuracy. We suggest a generalization of the tWTA, the n-tWTA, which estimates the stimulus by the identity of the group of cells firing the first n spikes and show how this simple generalization can overcome the detrimental effect of baseline firing. Thus, the tWTA can provide fast and accurate responses discriminating between a small number of alternatives. High accuracy in estimation of a continuous stimulus can be obtained using the n-tWTA

A Neural Correlate of the Processing of Multi-Second Time Intervals in Primate Prefrontal Cortex

Several areas of the brain are known to participate in temporal processing. Neurons in the prefrontal cortex (PFC) are thought to contribute to perception of time intervals. However, it remains unclear whether the PFC itself can generate time intervals independently of external stimuli. Here we describe a group of PFC neurons in area 9 that became active when monkeys recognized a particular elapsed time within the range of 1–7 seconds. Another group of area 9 neurons became active only when subjects reproduced a specific interval without external cues. Both types of neurons were individually tuned to recognize or reproduce particular intervals. Moreover, the injection of muscimol, a GABA agonist, into this area bilaterally resulted in an increase in the error rate during time interval reproduction. These results suggest that area 9 may process multi-second intervals not only in perceptual recognition, but also in internal generation of time intervals