Relating local connectivity and global dynamics in recurrent excitatory-inhibitory networks.

How the connectivity of cortical networks determines the neural dynamics and the resulting computations is one of the key questions in neuroscience. Previous works have pursued two complementary approaches to quantify the structure in connectivity. One approach starts from the perspective of biological experiments where only the local statistics of connectivity motifs between small groups of neurons are accessible. Another approach is based instead on the perspective of artificial neural networks where the global connectivity matrix is known, and in particular its low-rank structure can be used to determine the resulting low-dimensional dynamics. A direct relationship between these two approaches is however currently missing. Specifically, it remains to be clarified how local connectivity statistics and the global low-rank connectivity structure are inter-related and shape the low-dimensional activity. To bridge this gap, here we develop a method for mapping local connectivity statistics onto an approximate global low-rank structure. Our method rests on approximating the global connectivity matrix using dominant eigenvectors, which we compute using perturbation theory for random matrices. We demonstrate that multi-population networks defined from local connectivity statistics for which the central limit theorem holds can be approximated by low-rank connectivity with Gaussian-mixture statistics. We specifically apply this method to excitatory-inhibitory networks with reciprocal motifs, and show that it yields reliable predictions for both the low-dimensional dynamics, and statistics of population activity. Importantly, it analytically accounts for the activity heterogeneity of individual neurons in specific realizations of local connectivity. Altogether, our approach allows us to disentangle the effects of mean connectivity and reciprocal motifs on the global recurrent feedback, and provides an intuitive picture of how local connectivity shapes global network dynamics.

Recurrent networks endowed with structural priors explain suboptimal animal behavior.

The strategies found by animals facing a new task are determined both by individual experience and by structural priors evolved to leverage the statistics of natural environments. Rats quickly learn to capitalize on the trial sequence correlations of two-alternative forced choice (2AFC) tasks after correct trials but consistently deviate from optimal behavior after error trials. To understand this outcome-dependent gating, we first show that recurrent neural networks (RNNs) trained in the same 2AFC task outperform rats as they can readily learn to use across-trial information both after correct and error trials. We hypothesize that, although RNNs can optimize their behavior in the 2AFC task without any a priori restrictions, rats' strategy is constrained by a structural prior adapted to a natural environment in which rewarded and non-rewarded actions provide largely asymmetric information. When pre-training RNNs in a more ecological task with more than two possible choices, networks develop a strategy by which they gate off the across-trial evidence after errors, mimicking rats' behavior. Population analyses show that the pre-trained networks form an accurate representation of the sequence statistics independently of the outcome in the previous trial. After error trials, gating is implemented by a change in the network dynamics that temporarily decouple the categorization of the stimulus from the across-trial accumulated evidence. Our results suggest that the rats' suboptimal behavior reflects the influence of a structural prior that reacts to errors by isolating the network decision dynamics from the context, ultimately constraining the performance in a 2AFC laboratory task.

Dimensional reduction of emergent spatiotemporal cortical dynamics via a maximum entropy moment closure.

Modern electrophysiological recordings and optical imaging techniques have revealed a diverse spectrum of spatiotemporal neural activities underlying fundamental cognitive processing. Oscillations, traveling waves and other complex population dynamical patterns are often concomitant with sensory processing, information transfer, decision making and memory consolidation. While neural population models such as neural mass, population density and kinetic theoretical models have been used to capture a wide range of the experimentally observed dynamics, a full account of how the multi-scale dynamics emerges from the detailed biophysical properties of individual neurons and the network architecture remains elusive. Here we apply a recently developed coarse-graining framework for reduced-dimensional descriptions of neuronal networks to model visual cortical dynamics. We show that, without introducing any new parameters, how a sequence of models culminating in an augmented system of spatially-coupled ODEs can effectively model a wide range of the observed cortical dynamics, ranging from visual stimulus orientation dynamics to traveling waves induced by visual illusory stimuli. In addition to an efficient simulation method, this framework also offers an analytic approach to studying large-scale network dynamics. As such, the dimensional reduction naturally leads to mesoscopic variables that capture the interplay between neuronal population stochasticity and network architecture that we believe to underlie many emergent cortical phenomena.

A Mechanism for Synaptic Copy Between Neural Circuits.

Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking may be enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.

A coarse-graining framework for spiking neuronal networks: from strongly-coupled conductance-based integrate-and-fire neurons to augmented systems of ODEs.

Homogeneously structured, fluctuation-driven networks of spiking neurons can exhibit a wide variety of dynamical behaviors, ranging from homogeneity to synchrony. We extend our partitioned-ensemble average (PEA) formalism proposed in Zhang et al. (Journal of Computational Neuroscience, 37(1), 81-104, 2014a) to systematically coarse grain the heterogeneous dynamics of strongly coupled, conductance-based integrate-and-fire neuronal networks. The population dynamics models derived here successfully capture the so-called multiple-firing events (MFEs), which emerge naturally in fluctuation-driven networks of strongly coupled neurons. Although these MFEs likely play a crucial role in the generation of the neuronal avalanches observed in vitro and in vivo, the mechanisms underlying these MFEs cannot easily be understood using standard population dynamic models. Using our PEA formalism, we systematically generate a sequence of model reductions, going from Master equations, to Fokker-Planck equations, and finally, to an augmented system of ordinary differential equations. Furthermore, we show that these reductions can faithfully describe the heterogeneous dynamic regimes underlying the generation of MFEs in strongly coupled conductance-based integrate-and-fire neuronal networks.

Analysis of Six ß-Lactam Residues in Milk and Egg by Micellar Electrokinetic Chromatography with Large-Volume Sample Stacking and Polarity Switching.

A new micellar electrokinetic chromatography method with large-volume sample stacking and polarity switching was developed to analyze amoxicllin, cephalexin, oxacillin, penicillin G, cefazolin, and cefoperazone in milk and egg. The important parameters influencing separation and enrichment factors were optimized. The optimized running buffer consisted of 10 mM phosphate and 22 mM SDS at pH 6.7. The sample size was 1.47 kPa × 690 s, the reverse voltage was 20 kV, and the electric current recovery was 95%. Under these optimum conditions, the enrichment factors of six ß-lactams were 193-601. Their LODs were <0.26 ng/g, and LOQs were all 2 ng/g, which was only 1/50-1/2 of the maximum residual limits demanded by U.S. and Japanese regulations. The intraday and interday RSDs of method were lower than 3.70 and 3.91%, respectively. The method can be applied to determine these six antibiotic residues in egg and milk.

Determination of eight triazine herbicide residues in cereal and vegetable by micellar electrokinetic capillary chromatography with on-line sweeping.

A new method was developed for the determination of eight triazine herbicide residues in cereal and vegetable samples by on-line sweeping technique in micellar electrokinetic capillary chromatography (MEKC). Some factors affecting analyte enrichment and separation efficiency were examined. The optimum buffer was composed of 25 mM borate, 15 mM phosphate, 40 mM sodium dodecylsulfate (SDS) and 3% (v/v) of 1-propanol at pH 6.5. The separation voltage was 20 kV and the sample was injected at 0.5 psi for 240 s. The detection wavelength was set at 220 nm with the capillary temperature being at 25 °C. Under the optimized conditions, the enrichment factors were achieved from 479 to 610. The limits of detection (LODs, S/N = 3) ranged from 0.02 to 0.04 ng/g and the limits of quantification (LOQs) of eight triazine herbicides were all 0.1 ng/g. The average recoveries of spiked samples were 82.8-96.8%. This method has been successfully applied to the determination of the triazine herbicide residues in cereal and vegetable samples.

On-line preconcentration and determination of six sulfonylurea herbicides in cereals by MEKC with large-volume sample stacking and polarity switching.

A new MEKC method with large-volume sample stacking and polarity switching was developed for on-line preconcentration and detection of sulfonylurea herbicide (SUH) residues in cereals, including nicosulfuron (NS), thifensulfuon (methyl) (TFM), tribenuron-methly (TBM), sulfometuron-methyl (SMM), pyrazosulfuron-ethyl (PSE), and chlorimuron-ethyl (CME). In order to achieve a high resolution and enrichment factor, several parameters were optimized, such as the pH of the running buffer, the concentration of the BGE and the SDS, the separate voltage, the sample size, the pH, and the electrolyte concentration of the sample. The optimal running buffer was composed of 30 mM borate and 80 mM SDS at pH 7.0. The borate concentration in the sample was 30 mM and the pH value of the sample was the same as that of the running buffer. The concentrating voltage and the separating voltage were -15 kV and 15 kV, respectively. The sample size was 1.455 kPa × 780 s (33.11 cm). Under the optimum conditions, for NS, TFM, TBM, SMM, PSE, and CME, the enrichment factors were 613, 642, 835, 570, 709, and 599; the LODs were 0.29-0.50 ng/g, 0.22-0.36 ng/g, 0.60-0.89 ng/g, 0.39-0.72 ng/g, 0.28-0.56 ng/g, and 0.31-0.57 ng/g; the LOQs of six SUHs were all 5 ng/g; the average recoveries of the spiked sample were 86.68-92.99%, 80.73-93.65%, 81.49-94.40%, 82.97-95.1%, 82.96-98.84%, and 80.41-92.94%, respectively.