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Understanding the genesis of shared trial-to-trial variability in neural activity within sensory cortex is critical to uncovering the biological basis of information processing in the brain. Shared variability is often a reflection of the structure of cortical connectivity since this variability likely arises, in part, from local circuit inputs. A series of experiments from segregated networks of (excitatory) pyramidal neurons in mouse primary visual cortex challenge this view. Specifically, the across-network correlations were found to be larger than predicted given the known weak cross-network connectivity. We aim to uncover the circuit mechanisms responsible for these enhanced correlations through biologically motivated cortical circuit models. Our central finding is that coupling each excitatory subpopulation with a specific inhibitory subpopulation provides the most robust network-intrinsic solution in shaping these enhanced correlations. This result argues for the existence of excitatory-inhibitory functional assemblies in early sensory areas which mirror not just response properties but also connectivity between pyramidal cells.

Recent experimental works have implicated astrocytes as a significant cell type underlying several neuronal processes in the mammalian brain, from encoding sensory information to neurological disorders. Despite this progress, it is still unclear how astrocytes are communicating with and driving their neuronal neighbors. While previous computational modeling works have helped propose mechanisms responsible for driving these interactions, they have primarily focused on interactions at the synaptic level, with microscale models of calcium dynamics and neurotransmitter diffusion. Since it is computationally infeasible to include the intricate microscale details in a network-scale model, little computational work has been done to understand how astrocytes may be influencing spiking patterns and synchronization of large networks. We overcome this issue by first developing an “effective” astrocyte that can be easily implemented to already established network frameworks. We do this by showing that the astrocyte proximity to a synapse makes synaptic transmission faster, weaker, and less reliable. Thus, our “effective” astrocytes can be incorporated by considering heterogeneous synaptic time constants, which are parametrized only by the degree of astrocytic proximity at that synapse. We then apply our framework to large networks of exponential integrate-and-fire neurons with various spatial structures. Depending on key parameters, such as the number of synapses ensheathed and the strength of this ensheathment, we show that astrocytes can push the network to a synchronous state and exhibit spatially correlated patterns.Author summaryIn many areas of the brain, glial cells called astrocytes wrap their processes around synapses – the points of contact between neurons. The number of wrapped synapses and the tightness of wrapping varies between brain areas and changes during some diseases, such as epilepsy. We investigate the effect that this synaptic ensheathment has on communication between neurons and the resulting collective dynamics of the neuronal network. We present a general, computationally-efficient way to include astrocytes in neuronal networks using an “effective astrocyte” representation derived from detailed microscopic scale models. The resulting hybrid networks allow us to emulate and observe the effect of ensheathment conditions corresponding to different brain areas and disease states. In particular, we find that it makes the networks more likely to switch into a highly correlated regime, contrary to predictions from the traditional neurons-only view. These results open a new perspective on neural network dynamics, where our understanding of conditions for generating correlated brain activity (e.g., rhythms associated with various brain functions, epileptic seizures) needs to be reevaluated.

Recurrent cortical activity sculpts visual perception by refining, amplifying, or suppressing incoming visual signals. Despite the importance of recurrent circuits for cortical processing, the basic rules that govern how nearby cortical neurons influence each other remains enigmatic. We used two-photon holographic optogenetics to activate ensembles of neurons in Layer 2/3 of the primary visual cortex (V1) in the absence of external stimuli to isolate the impact of local recurrence from external inputs. We find that the spatial arrangement and the stimulus feature preference of both the stimulated and the target ensemble jointly determine the net effect of recurrent activity, defining the cortical activity patterns that drive competition versus facilitation in L2/3 circuits. Computational modeling suggests that a combination of highly local recurrent excitatory connectivity and selective convergence onto inhibitory neurons give rise to these principles of recurrent activity. Our data and modeling reveal that recurrent activity can have varied impact, but a logic emerges through an understanding of the precise spatial distribution and feature preference of the multicellular pattern of activity.

Peripheral sensory organ damage leads to compensatory cortical plasticity that supports a remarkable recovery of perceptual capabilities. A major knowledge gap is the lack of precise mechanisms that explain how this plasticity is implemented and distributed over a diverse collection of excitatory and inhibitory cortical neurons. Here, we explored these mechanisms in mouse A1. After peripheral damage, we found recovered sound-evoked activity of excitatory principal neurons (PNs) and parvalbumin (PVs) interneurons (INs), reduced activity in somatostatin-INs (SOMs), and recovered activity in vasoactive intestinal peptide-INs (VIPs). Given the sequentially organized cortical network where VIPs inhibit INs, SOMs inhibit PVs and PNs, and PVs inhibit PNs, our results suggest that PVs contribute to PN stability, SOMs allow for increased PN and PV activity, and VIPs enable the PN and PV recovery by inhibiting SOMs. These results highlight a strategic, cooperative, and cell-type-specific plasticity program that restores cortical sound processing after peripheral damage.

Gamma band synchronization can facilitate local and long-range communication in neural circuits. In the primary visual cortex (V1) the strength of synchronization on the local level is strongly tuned to the contrast, size and center/surround orientation of grating stimuli. On the global level, the synchronization of gamma oscillations across the retinotopic map crucially depends on matched stimulus properties in the corresponding locations in the visual field. Although these features of V1 gamma rhythms are likely to be crucial for how they might support cortico-cortical communication and visual perception, their neural basis remains largely unknown. We hypothesized VIP disinhibitory interneurons, which shape other tuning properties in V1 by inhibiting SST neurons, may be responsible for tuning local gamma band power and global gamma synchronization. To test these ideas, we combined multi-electrode electrophysiology, cell-type specific optogenetic suppression of VIP neurons and computational modeling. Contrary to expectations, our data show that on the local level, VIP activity has no role in tuning gamma power to stimulus properties; rather, it scales the gain of gamma oscillations linearly across stimulus space and across behavioral state. Conversely, on the global level, VIP neurons specifically suppress gamma synchronization (as measured by spectral coherence) between spatially separated cortical ensembles when they are processing non-matched stimulus features. A straightforward computational model of V1 shows that like-to-like connectivity across retinotopic space, and specific, but powerful VIP➔SST inhibition are sufficient to capture these seemingly opposed effects. These data demonstrate how VIP neurons differentially impact local and global properties of gamma rhythms depending on the global statistics of the retinal image. VIP neurons may thus construct temporal filters in the gamma band for spatially continuous image features, such as contours, to facilitate the downstream generation of coherent visual percepts.

From nutrient uptake, to chemoreception, to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules since, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many particle stochastic system., 26 pages, 5 figures

We consider n particles diffusing freely in a domain. The boundary contains absorbing escape regions, where the particles can escape, and traps, where the particles can be captured. Modeled after biological examples such as receptors in the synaptic cleft and ambush predators waiting for prey, these traps, or capture regions, must recharge between captures. We are interested in characterizing the time courses of the number of particles remaining in the domain, the number of cumulative captures, and the number of available capture regions. We find that under certain conditions, the number of cumulative captures increases linearly in time with a slope and duration determined explicitly by the recharge rate of the capture regions. This recharge rate also determines the mean and variance of the clearance time, defined as the time it takes for all particles to leave the domain. Further, we find that while a finite recharge rate will always result in a lower number of captured particles when compared to instantaneous recharging, it can either increase or decrease the amount of variability. Lastly, we extend the model to partially absorbing traps in order to investigate the dynamics of receptor activation within an idealized synaptic cleft. We find that the width of the domain controls the amount of time that these receptors are activated, while the number of receptors controls the amplitude of activation. Our mathematical results are derived from considering this system in several ways: as a full spatial diffusion process with recharging traps, as a continuous-time Markov process on a discrete state space, and as a system of ordinary differential equations in a mean-field approximation.

We study evoked calcium dynamics in astrocytes, a major cell type in the mammalian brain. Experimental evidence has shown that such dynamics are highly variable between different trials, cells, and cell subcompartments. Here we present a qualitative analysis of a recent mathematical model of astrocyte calcium responses. We show how the major response types are generated in the model as a result of the underlying bifurcation structure. By varying key channel parameters, mimicking blockers used by experimentalists, we manipulate this underlying bifurcation structure and predict how the distributions of responses can change. We find that store-operated calcium channels, plasma membrane bound channels with little activity during calcium transients, have a surprisingly strong effect, underscoring the importance of considering these channels in both experiments and mathematical settings. Variation in the maximum flow in different calcium channels is also shown to determine the range of stable oscillations, as well as set the range of frequencies of the oscillations. Further, by conducting a randomized search through the parameter space and recording the resulting calcium responses, we create a database that can be used by experimentalists to help estimate the underlying channel distribution of their cells.

The inositol 1,4,5-trisphosphate (IP(3)) receptor is a Ca(2+) channel located in the endoplasmic reticulum and is regulated by IP(3) and Ca(2+). This channel is critical to calcium signaling in cell types as varied as neurons and pancreatic beta cells to mast cells. De Young and Keizer (1992) created an eight-state, nine-variable model of the IP(3) receptor. In their model, they accounted for three binding sites, a site for IP(3), activating Ca(2+), and deactivating Ca(2+). The receptor is only open if IP(3) and activating Ca(2+) is bound. Li and Rinzel followed up this paper in 1994 by introducing a reduction that made it into a two variable system. A recent publication by Rossi et al. (2009) studied the effect of introducing IP(3)-like molecules, referred to as partial agonists (PA), into the cell to determine the structure-function relationship between IP(3) and its receptor. Initial results suggest a competitive model, where IP(3) and PA fight for the same binding site. We extend the original eight-state model to a 12-state model in order to illustrate this competition, and perform a similar reduction to that of Li and Rinzel in the first modeling study we are aware of considering PA effect on an IP(3) receptor. Using this reduction we solve for the equilibrium open probability for calcium release in the model. We replicate graphs provided by the Rossi paper, and find that optimizing the subunit affinities for IP(3) and PA yields a good fit to the data. We plug our extended reduced model into a full cell model, in order to analyze the effects PA have on whole cell properties specifically the propagation of calcium waves in two dimensions. We conclude that PA creates qualitatively different calcium dynamics than would simply reducing IP(3), but that effectively PA can act as an IP(3) knockdown.

In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. In this work, we give conditions that are necessary and sufficient for the true class-conditional distributions to be identifiable. These conditions are weaker than those analyzed previously, and allow for the classes to be nonseparable and the noise levels to be asymmetric and unknown. The conditions essentially state that a majority of the observed labels are correct and that the true class-conditional distributions are “mutually irreducible,” a concept we introduce that limits the similarity of the two distributions. For any label noise problem, there is a unique pair of true class-conditional distributions satisfying the proposed conditions, and we argue that this pair corresponds in a certain sense to maximal denoising of the observed distributions. ¶ Our results are facilitated by a connection to “mixture proportion estimation,” which is the problem of estimating the maximal proportion of one distribution that is present in another. We establish a novel rate of convergence result for mixture proportion estimation, and apply this to obtain consistency of a discrimination rule based on surrogate loss minimization. Experimental results on benchmark data and a nuclear particle classification problem demonstrate the efficacy of our approach.

International audience; In many real-world classification problems, the labels of training examples are randomly corrupted. Thus, the set of training examples for each class is contaminated by examples of the other class. Previous theoretical work on this problem assumes that the two classes are separable, that the label noise is independent of the true class label, or that the noise proportions for each class are known. We introduce a general framework for classification with label noise that eliminates these assumptions. Instead, we give assumptions ensuring identifiability and the existence of a consistent estimator of the optimal risk, with associated estimation strategies. For any arbitrary pair of contaminated distributions, there is a unique pair of non-contaminated distributions satisfying the proposed assumptions, and we argue that this solution corresponds in a certain sense to maximal denoising. In particular, we find that learning in the presence of label noise is possible even when the class-conditional distributions overlap and the label noise is not symmetric. A key to our approach is a universally consistent estimator of the maximal proportion of one distribution that is present in another, a problem we refer to as "mixture proportion estimation." This work is motivated by a problem in nuclear particle classification.

We present experimental results of applying various nature-inspired optimization techniques to real-world problems from the areas of diagnosis, configuration, planning, and pathfinding. The optimization techniques we investigate include the traditional Genetic Algorithm (GA), discrete (binary and integer-based) Particle Swarm Optimization (DPSO), relatively new Extremal Optimization (EO), and recently developed Raindrop Optimization (RO); all inspired by different aspects of the natural world. We present algorithm setup, issues with adapting the various optimization methods to the selected problems, and the emerging results produced by the methods.We consider the GA to be the baseline technique because of its robustness and widespread application. The major contribution of this chapter deals with the fact that DPSO, EO, and RO have never been applied to the majority of these selected problems, making this the first time most of these results have appeared in the literature.