Biomedical subjects

Todd W Troyer

Publications and source records attributed to Todd W Troyer.

5 recordsLinked to original sources

PubMed2006

Factors affecting phase synchronization in integrate-and-fire oscillators.

Step changes in input current are known to induce partial phase synchrony in ensembles of leaky integrate-and-fire neurons operating in the oscillatory or "regular firing" regime. An analysis of this phenomenon in the absence of noise is presented based on the probability flux within an ensemble of generalized integrate-and-fire neurons. It is shown that the induction of phase synchrony by a step input can be determined by calculating the ratio of the voltage densities obtained from fully desynchronized ensembles firing at the pre and post-step firing rates. In the limit of low noise and in the absence of phase synchrony, the probability density as a function of voltage is inversely proportional to the time derivative along the voltage trajectory. It follows that the magnitude of phase synchronization depends on the degree to which a change in input leads to a uniform multiplication of the voltage derivative over the range from reset to spike threshold. This analysis is used to investigate several factors affecting phase synchronization including high firing rates, inputs modeled as conductances rather than currents, peri-threshold sodium currents, and spike-triggered potassium currents. Finally, we show that without noise, the equilibrium ensemble density is proportional to the phase response curve commonly used to analyze oscillatory systems.

Action Potentials↗

PubMed2006

Temporal structure in zebra finch song: implications for motor coding.

Adult zebra finch songs consist of stereotyped sequences of syllables. Although some behavioral and physiological data suggest that songs are structured hierarchically, there is also evidence that they are driven by nonhierarchical, clock-like bursting in the premotor nucleus HVC (used as a proper name). In this study, we developed a semiautomated template-matching algorithm to identify repeated sequences of syllables and a modified dynamic time-warping algorithm to make fine-grained measurements of the temporal structure of song. We find that changes in song length are expressed across the song as a whole rather than resulting from an accumulation of independent variance during singing. Song length changes systematically over the course of a day and is related to the general level of bird activity as well as the presence of a female. The data also show patterns of variability that suggest distinct mechanisms underlying syllable and gap lengths: as tempo varies, syllables stretch and compress proportionally less than gaps, whereas syllable-syllable and gap-gap correlations are significantly stronger than syllable-gap correlations. There is also increased temporal variability at motif boundaries and especially strong positive correlations between the same syllables sung in different motifs. Finally, we find evidence that syllable onsets may have a special role in aligning syllables with global song structure. Generally, the timing data support a hierarchical view in which song is composed of smaller syllable-based units and provide a rich set of constraints for interpreting the results of physiological recordings.

Animals↗

PubMed2005

Temporal correlations in stochastic models of double bursting during simulated locomotion.

The output of the spinal central pattern generator for locomotion falls into two broad categories: alternation between antagonistic muscles and double bursting within muscles acting on multiple joints. We first model an alternating half-center and then present two different models of double bursting. The first double-bursting model consists of a central clock with an explicit one-to-one mapping between interneuron activity and model output. The second double-bursting model consists of a half-center with an added feedback neuron. Models are built using rate-coded leaky integrator neurons with slow self-inhibition. Structure-function relationships are explored by the addition of noise. The interaction of noise with the dynamics of each network creates a unique pattern of correlation between phases of the simulated cycle. The effects of noise can be explained by perturbation of deterministic versions of the networks. Three basic results were obtained: slow self-inhibitory currents lead to correlations between parts of the step cycle that are separated in time and network relative; model outputs are most sensitive to perturbations presented just before competitive switches in network activity, and clock-like models possess substantial symmetries within the correlation structure of burst durations, whereas the correlation structure of feedback models are asymmetric. Our models suggest that variability in burst length durations can be analyzed to make inferences about the structure of the spinal networks for locomotion. In particular, correlation patterns within double-bursting outputs may yield important clues regarding the interaction between more central, clock-like networks and feedback from more peripheral interneurons.

Animals↗

PubMed2002

Neural noise can explain expansive, power-law nonlinearities in neural response functions.

Many phenomenological models of the responses of simple cells in primary visual cortex have concluded that a cell's firing rate should be given by its input raised to a power greater than one. This is known as an expansive power-law nonlinearity. However, intracellular recordings have shown that a different nonlinearity, a linear-threshold function, appears to give a good prediction of firing rate from a cell's low-pass-filtered voltage response. Using a model based on a linear-threshold function, Anderson et al. showed that voltage noise was critical to converting voltage responses with contrast-invariant orientation tuning into spiking responses with contrast-invariant tuning. We present two separate results clarifying the connection between noise-smoothed linear-threshold functions and power-law nonlinearities. First, we prove analytically that a power-law nonlinearity is the only input-output function that converts contrast-invariant input tuning into contrast-invariant spike tuning. Second, we examine simulations of a simple model that assumes instantaneous spike rate is given by a linear-threshold function of voltage and voltage responses include significant noise. We show that the resulting average spike rate is well described by an expansive power law of the average voltage (averaged over multiple trials), provided that average voltage remains less than about 1.5 SDs of the noise above threshold. Finally, we use this model to show that the noise levels recorded by Anderson et al. are consistent with the degree to which the orientation tuning of spiking responses is more sharply tuned relative to the orientation tuning of voltage responses. Thus neuronal noise can robustly generate power-law input-output functions of the form frequently postulated for simple cells.

Action Potentials↗

PubMed2002

LGN input to simple cells and contrast-invariant orientation tuning: an analysis.

We develop a new analysis of the lateral geniculate nucleus (LGN) input to a cortical simple cell, demonstrating that this input is the sum of two terms, a linear term and a nonlinear term. In response to a drifting grating, the linear term represents the temporal modulation of input, and the nonlinear term represents the mean input. The nonlinear term, which grows with stimulus contrast, has been neglected in many previous models of simple cell response. We then analyze two scenarios by which contrast-invariance of orientation tuning may arise. In the first scenario, at larger contrasts, the nonlinear part of the LGN input, in combination with strong push-pull inhibition, counteracts the nonlinear effects of cortical spike threshold, giving the result that orientation tuning scales with contrast. In the second scenario, at low contrasts, the nonlinear component of LGN input is negligible, and noise smooths the nonlinearity of spike threshold so that the input-output function approximates a power-law function. These scenarios can be combined to yield contrast-invariant tuning over the full range of stimulus contrast. The model clarifies the contribution of LGN nonlinearities to the orientation tuning of simple cells and demonstrates how these nonlinearities may impact different models of contrast-invariant tuning.

Animals↗