Noise-induced properties of active dendrites.

Dendrites play an essential role in the integration of highly fluctuating input in vivo into neurons across all nervous systems. Yet, they are often studied under conditions where inputs to dendrites are sparse. The dynamic properties of active dendrites facing in vivo-like fluctuating input thus remain elusive. In this paper, we uncover dynamics in a canonical model of a dendritic compartment with active calcium channels, receiving in vivo-like fluctuating input. In a single-compartment model of the active dendrite with fast calcium activation, we show noise-induced nonmonotonic behavior in the relationship of the membrane potential output, and mean input emerges. In contrast, noise can induce bistability in the input-output relation in the system with slowly activating calcium channels. Both phenomena are absent in a noiseless condition. Furthermore, we show that timescales of the emerging stochastic bistable dynamics extend far beyond a deterministic system due to stochastic switching between the solutions. A numerical simulation of a multicompartment model neuron shows that in the presence of in vivo-like synaptic input, the bistability uncovered in our analysis persists. Our results reveal that realistic synaptic input contributes to sustained dendritic nonlinearities, and synaptic noise is a significant component of dendritic input integration.

Mechanisms underlying the response of mouse cortical networks to optogenetic manipulation.

GABAergic interneurons can be subdivided into three subclasses: parvalbumin positive (PV), somatostatin positive (SOM) and serotonin positive neurons. With principal cells (PCs) they form complex networks. We examine PCs and PV responses in mouse anterior lateral motor cortex (ALM) and barrel cortex (S1) upon PV photostimulation in vivo. In ALM layer five and S1, the PV response is paradoxical: photoexcitation reduces their activity. This is not the case in ALM layer 2/3. We combine analytical calculations and numerical simulations to investigate how these results constrain the architecture. Two-population models cannot explain the results. Four-population networks with V1-like architecture account for the data in ALM layer 2/3 and layer 5. Our data in S1 can be explained if SOM neurons receive inputs only from PCs and PV neurons. In both four-population models, the paradoxical effect implies not too strong recurrent excitation. It is not evidence for stabilization by inhibition.

Dynamics and orientation selectivity in a cortical model of rodent V1 with excess bidirectional connections.

Recent experiments have revealed fine structure in cortical microcircuitry. In particular, bidirectional connections are more prevalent than expected by chance. Whether this fine structure affects cortical dynamics and function has not yet been studied. Here we investigate the effects of excess bidirectionality in a strongly recurrent network model of rodent V1. We show that reciprocal connections have only a very weak effect on orientation selectivity. We find that excess reciprocity between inhibitory neurons slows down the dynamics and strongly increases the Fano factor, while for reciprocal connections between excitatory and inhibitory neurons it has the opposite effect. In contrast, excess bidirectionality within the excitatory population has a minor effect on the neuronal dynamics. These results can be explained by an effective delayed neuronal self-coupling which stems from the fine structure. Our work suggests that excess bidirectionality between inhibitory neurons decreases the efficiency of feature encoding in cortex by reducing the signal to noise ratio. On the other hand it implies that the experimentally observed strong reciprocity between excitatory and inhibitory neurons improves the feature encoding.

Fredholm theory for the mean first-passage time of integrate-and-fire oscillators with colored noise input.

We develop a method to investigate the effect of noise timescales on the first-passage time of nonlinear oscillators. Using Fredholm theory, we derive an exact integral equation for the mean event rate of a leaky integrate-and-fire oscillator that receives constant input and temporally correlated noise. Furthermore, we show that Fredholm theory provides a unified framework to determine the system scaling behavior for small and large noise timescales. In this framework, the leading-order and higher-order asymptotic corrections for slow and fast noise are naturally emerging. We show the scaling behavior in the both limits is not reciprocal. We discuss further how this approach can be extended to study the first-passage time in a general class of nonlinear oscillators driven by colored noise at arbitrary timescales.

Emergent Orientation Selectivity from Random Networks in Mouse Visual Cortex.

The connectivity principles underlying the emergence of orientation selectivity in primary visual cortex (V1) of mammals lacking an orientation map (such as rodents and lagomorphs) are poorly understood. We present a computational model in which random connectivity gives rise to orientation selectivity that matches experimental observations. The model predicts that mouse V1 neurons should exhibit intricate receptive fields in the two-dimensional frequency domain, causing a shift in orientation preferences with spatial frequency. We find evidence for these features in mouse V1 using calcium imaging and intracellular whole-cell recordings.

A reanalysis of "Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons".

Neuronal activity in the central nervous system varies strongly in time and across neuronal populations. It is a longstanding proposal that such fluctuations generically arise from chaotic network dynamics. Various theoretical studies predict that the rich dynamics of rate models operating in the chaotic regime can subserve circuit computation and learning. Neurons in the brain, however, communicate via spikes and it is a theoretical challenge to obtain similar rate fluctuations in networks of spiking neuron models. A recent study investigated spiking balanced networks of leaky integrate and fire (LIF) neurons and compared their dynamics to a matched rate network with identical topology, where single unit input-output functions were chosen from isolated LIF neurons receiving Gaussian white noise input. A mathematical analogy between the chaotic instability in networks of rate units and the spiking network dynamics was proposed. Here we revisit the behavior of the spiking LIF networks and these matched rate networks. We find expected hallmarks of a chaotic instability in the rate network: For supercritical coupling strength near the transition point, the autocorrelation time diverges. For subcritical coupling strengths, we observe critical slowing down in response to small external perturbations. In the spiking network, we found in contrast that the timescale of the autocorrelations is insensitive to the coupling strength and that rate deviations resulting from small input perturbations rapidly decay. The decay speed even accelerates for increasing coupling strength. In conclusion, our reanalysis demonstrates fundamental differences between the behavior of pulse-coupled spiking LIF networks and rate networks with matched topology and input-output function. In particular there is no indication of a corresponding chaotic instability in the spiking network.

Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events.

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.

Renewal Approach to the Analysis of the Asynchronous State for Coupled Noisy Oscillators.

We develop a framework in which the activity of nonlinear pulse-coupled oscillators is posed within the renewal theory. In this approach, the evolution of the interevent density allows for a self-consistent calculation that determines the asynchronous state and its stability. This framework can readily be extended to the analysis of systems with more state variables and provides a population density treatment to evolve them in their thermodynamical limits. To demonstrate this we study a nonlinear pulse-coupled system, where couplings are dynamic and activity dependent. We investigate its stability and numerically study the nonequilibrium behavior of the system after the bifurcation. We show that this system undergoes a supercritical Hopf bifurcation to collective synchronization.

Pulvinar thalamic nucleus allows for asynchronous spike propagation through the cortex.

We create two multilayered feedforward networks composed of excitatory and inhibitory integrate-and-fire neurons in the balanced state to investigate the role of cortico-pulvino-cortical connections. The first network consists of ten feedforward levels where a Poisson spike train with varying firing rate is applied as an input in layer one. Although the balanced state partially avoids spike synchronization during the transmission, the average firing-rate in the last layer either decays or saturates depending on the feedforward pathway gain. The last layer activity is almost independent of the input even for a carefully chosen intermediate gain. Adding connections to the feedforward pathway by a nine areas Pulvinar structure improves the firing-rate propagation to become almost linear among layers. Incoming strong pulvinar spikes balance the low feedforward gain to have a unit input-output relation in the last layer. Pulvinar neurons evoke a bimodal activity depending on the magnitude input: synchronized spike bursts between 20 and 80 Hz and an asynchronous activity for very both low and high frequency inputs. In the first regime, spikes of last feedforward layer neurons are asynchronous with weak, low frequency, oscillations in the rate. Here, the uncorrelated incoming feedforward pathway washes out the synchronized thalamic bursts. In the second regime, spikes in the whole network are asynchronous. As the number of cortical layers increases, long-range pulvinar connections can link directly two or more cortical stages avoiding their either saturation or gradual activity falling. The Pulvinar acts as a shortcut that supplies the input-output firing-rate relationship of two separated cortical areas without changing the strength of connections in the feedforward pathway.

Linear summation of outputs in a balanced network model of motor cortex.

Given the non-linearities of the neural circuitry's elements, we would expect cortical circuits to respond non-linearly when activated. Surprisingly, when two points in the motor cortex are activated simultaneously, the EMG responses are the linear sum of the responses evoked by each of the points activated separately. Additionally, the corticospinal transfer function is close to linear, implying that the synaptic interactions in motor cortex must be effectively linear. To account for this, here we develop a model of motor cortex composed of multiple interconnected points, each comprised of reciprocally connected excitatory and inhibitory neurons. We show how non-linearities in neuronal transfer functions are eschewed by strong synaptic interactions within each point. Consequently, the simultaneous activation of multiple points results in a linear summation of their respective outputs. We also consider the effects of reduction of inhibition at a cortical point when one or more surrounding points are active. The network response in this condition is linear over an approximately two- to three-fold decrease of inhibitory feedback strength. This result supports the idea that focal disinhibition allows linear coupling of motor cortical points to generate movement related muscle activation patterns; albeit with a limitation on gain control. The model also explains why neural activity does not spread as far out as the axonal connectivity allows, whilst also explaining why distant cortical points can be, nonetheless, functionally coupled by focal disinhibition. Finally, we discuss the advantages that linear interactions at the cortical level afford to motor command synthesis.

Pointing to oneself: active versus passive proprioception revisited and implications for internal models of motor system function.

We re-examined the issue of active versus passive proprioception to more fully characterize the accuracy afforded by proprioceptive information in natural, unconstrained, movements in 3-dimensions. Subjects made pointing movements with their non-dominant arm to various locations with eyes closed. They then proprioceptively localized the tip of its index finger with a prompt pointing movement of their dominant arm, thereby bringing the two indices in apposition. Subjects performed this task with remarkable accuracy. More remarkably, the same subjects were equally accurate at localizing the index finger when the arm was passively moved and maintained in its final position by an experimenter. Two subjects were also tested with eyes open, and they were no more accurate than with eyes closed. We also found that the magnitude of the error did not depend on movement duration, which is contrary to a key observation in support of the existence of an internal forward model-based state-reconstruction scheme. Three principal conclusions derive from this study. First, in unconstrained movements, proprioceptive information provides highly accurate estimates of limb position. Second, so-called active proprioception does not provide better estimates of limb position than passive proprioception. Lastly, in the active movement condition, an internal model-based estimation of limb position should, according to that hypothesis, have occurred throughout the movement. If so, it did not lead to a better estimate of final limb position, or lower variance of the estimate, casting doubt on the necessity to invoke this hypothetical construct.

On the functional organization and operational principles of the motor cortex.

Recent studies on the functional organization and operational principles of the motor cortex (MCx), taken together, strongly support the notion that the MCx controls the muscle synergies subserving movements in an integrated manner. For example, during pointing the shoulder, elbow and wrist muscles appear to be controlled as a coupled functional system, rather than singly and separately. The recurrent pattern of intrinsic synaptic connections between motor cortical points is likely part of the explanation for this operational principle. So too is the reduplicated, non-contiguous and intermingled representation of muscles in the MCx. A key question addressed in this article is whether the selection of movement related muscle synergies is a dynamic process involving the moment to moment functional linking of a variety of motor cortical points, or rather the selection of fixed patterns embedded in the MCx circuitry. It will be suggested that both operational principles are probably involved. We also discuss the neural mechanisms by which cortical points may be dynamically linked to synthesize movement related muscle synergies. Separate corticospinal outputs sum linearly and lead to a blending of the movements evoked by activation of each point on its own. This operational principle may simplify the synthesis of motor commands. We will discuss two possible mechanisms that may explain linear summation of outputs. We have observed that the final posture of the arm when pointing to a given spatial location is relatively independent of its starting posture. From this observation and the recurrent nature of the MCx intrinsic connectivity we hypothesize that the basic mode of operation of the MCx is to associate spatial location to final arm posture. We explain how the recurrent network connectivity operates to generate the muscle activation patterns (synergies) required to move the arm and hold it in its final position.

Impact of spike train autostructure on probability distribution of joint spike events.

The discussion whether temporally coordinated spiking activity really exists and whether it is relevant has been heated over the past few years. To investigate this issue, several approaches have been taken to determine whether synchronized events occur significantly above chance, that is, whether they occur more often than expected if the neurons fire independently. Most investigations ignore or destroy the autostructure of the spiking activity of individual cells or assume Poissonian spiking as a model. Such methods that ignore the autostructure can significantly bias the coincidence statistics. Here, we study the influence of the autostructure on the probability distribution of coincident spiking events between tuples of mutually independent non-Poisson renewal processes. In particular, we consider two types of renewal processes that were suggested as appropriate models of experimental spike trains: a gamma and a log-normal process. For a gamma process, we characterize the shape of the distribution analytically with the Fano factor (FFc). In addition, we perform Monte Carlo estimations to derive the full shape of the distribution and the probability for false positives if a different process type is assumed as was actually present. We also determine how manipulations of such spike trains, here dithering, used for the generation of surrogate data change the distribution of coincident events and influence the significance estimation. We find, first, that the width of the coincidence count distribution and its FFc depend critically and in a nontrivial way on the detailed properties of the structure of the spike trains as characterized by the coefficient of variation CV. Second, the dependence of the FFc on the CV is complex and mostly nonmonotonic. Third, spike dithering, even if as small as a fraction of the interspike interval, can falsify the inference on coordinated firing.

The role of pulvinar in the transmission of information in the visual hierarchy.

VISUAL RECEPTIVE FIELD (RF) ATTRIBUTES IN VISUAL CORTEX OF PRIMATES HAVE BEEN EXPLAINED MAINLY FROM CORTICAL CONNECTIONS: visual RFs progress from simple to complex through cortico-cortical pathways from lower to higher levels in the visual hierarchy. This feedforward flow of information is paired with top-down processes through the feedback pathway. Although the hierarchical organization explains the spatial properties of RFs, is unclear how a non-linear transmission of activity through the visual hierarchy can yield smooth contrast response functions in all level of the hierarchy. Depending on the gain, non-linear transfer functions create either a bimodal response to contrast, or no contrast dependence of the response in the highest level of the hierarchy. One possible mechanism to regulate this transmission of visual contrast information from low to high level involves an external component that shortcuts the flow of information through the hierarchy. A candidate for this shortcut is the Pulvinar nucleus of the thalamus. To investigate representation of stimulus contrast a hierarchical model network of ten cortical areas is examined. In each level of the network, the activity from the previous layer is integrated and then non-linearly transmitted to the next level. The arrangement of interactions creates a gradient from simple to complex RFs of increasing size as one moves from lower to higher cortical levels. The visual input is modeled as a Gaussian random input, whose width codes for the contrast. This input is applied to the first area. The output activity ratio among different contrast values is analyzed for the last level to observe sensitivity to a contrast and contrast invariant tuning. For a purely cortical system, the output of the last area can be approximately contrast invariant, but the sensitivity to contrast is poor. To account for an alternative visual processing pathway, non-reciprocal connections from and to a parallel pulvinar like structure of nine areas is coupled to the system. Compared to the pure feedforward model, cortico-pulvino-cortical output presents much more sensitivity to contrast and has a similar level of contrast invariance of the tuning.

Bistability and spatiotemporal irregularity in neuronal networks with nonlinear synaptic transmission.

We present a mean-field theory for spiking networks operating in the balanced excitation-inhibition regime, with synapses displaying short-term plasticity. The theory reveals a novel mechanism for bistability which relies on the nonlinearity of the synaptic interactions. As synaptic nonlinearity is mainly controlled by the spiking rates, the different states are stabilized by dynamically generated changes in the noise level. Thus, in both states, the network operates in the fluctuation-driven regime, producing activity patterns characterized by strong spatiotemporal irregularity.

The mechanism of orientation selectivity in primary visual cortex without a functional map.

Neurons in primary visual cortex (V1) display substantial orientation selectivity even in species where V1 lacks an orientation map, such as in mice and rats. The mechanism underlying orientation selectivity in V1 with such a salt-and-pepper organization is unknown; it is unclear whether a connectivity that depends on feature similarity is required, or a random connectivity suffices. Here we argue for the latter. We study the response to a drifting grating of a network model of layer 2/3 with random recurrent connectivity and feedforward input from layer 4 neurons with random preferred orientations. We show that even though the total feedforward and total recurrent excitatory and inhibitory inputs all have a very weak orientation selectivity, strong selectivity emerges in the neuronal spike responses if the network operates in the balanced excitation/inhibition regime. This is because in this regime the (large) untuned components in the excitatory and inhibitory contributions approximately cancel. As a result the untuned part of the input into a neuron as well as its modulation with orientation and time all have a size comparable to the neuronal threshold. However, the tuning of the F0 and F1 components of the input are uncorrelated and the high-frequency fluctuations are not tuned. This is reflected in the subthreshold voltage response. Remarkably, due to the nonlinear voltage-firing rate transfer function, the preferred orientation of the F0 and F1 components of the spike response are highly correlated.

On the distribution of firing rates in networks of cortical neurons.

The distribution of in vivo average firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of the in vivo f-I curve. During in vivo conditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of the f-I curve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of the f-I curve and, by extension, on the distribution of firing rates in randomly connected networks.

Neural mechanism of activity spread in the cat motor cortex and its relation to the intrinsic connectivity.

Motor cortical points are linked by intrinsic horizontal connections having a recurrent network topology. However, it is not known whether neural activity can propagate over the area covered by these intrinsic connections and whether there are spatial anisotropies of synaptic strength, as opposed to synaptic density. Moreover, the mechanisms by which activity spreads have yet to be determined. To address these issues, an 8 × 8 microelectrode array was inserted in the forelimb area of the cat motor cortex (MCx). The centre of the array had a laser etched hole ∼500 µm in diameter. A microiontophoretic pipette, with a tip diameter of 2-3 µm, containing bicuculline methiodide (BIC) was inserted in the hole and driven to a depth of 1200-1400 µm from the cortical surface. BIC was ejected for ∼2min from the tip of the micropipette with positive direct current ranging between 20 and 40 nA in different experiments. This produced spontaneous nearly periodic bursts (0.2-1.0 Hz) of multi-unit activity in a radius of about 400 µm from the tip of the micropipette. The bursts of neural activity spread at a velocity of 0.11-0.24 ms⁻¹ (mean=0.14 mm ms⁻¹, SD=0.05)with decreasing amplitude.The area activated was on average 7.22 mm² (SD=0.91 mm²), or ∼92% of the area covered by the recording array. The mode of propagation was determined to occur by progressive recruitment of cortical territory, driven by a central locus of activity of some 400 µm in radius. Thus, activity did not propagate as a wave. Transection of the connections between the thalamus and MCx did not significantly alter the propagation velocity or the size of the recruited area, demonstrating that the bursts spread along the routes of intrinsic cortical connectivity. These experiments demonstrate that neural activity initiated within a small motor cortical locus (≤ 400 µm in radius) can recruit a relatively large neighbourhood in which a variety of muscles acting at several forelimb joints are represented. These results support the hypothesis that the MCx controls the forelimb musculature in an integrated and anticipatory manner based on a recurrent network topology

Power-law input-output transfer functions explain the contrast-response and tuning properties of neurons in visual cortex.

We develop a unified model accounting simultaneously for the contrast invariance of the width of the orientation tuning curves (OT) and for the sigmoidal shape of the contrast response function (CRF) of neurons in the primary visual cortex (V1). We determine analytically the conditions for the structure of the afferent LGN and recurrent V1 inputs that lead to these properties for a hypercolumn composed of rate based neurons with a power-law transfer function. We investigate what are the relative contributions of single neuron and network properties in shaping the OT and the CRF. We test these results with numerical simulations of a network of conductance-based model (CBM) neurons and we demonstrate that they are valid and more robust here than in the rate model. The results indicate that because of the acceleration in the transfer function, described here by a power-law, the orientation tuning curves of V1 neurons are more tuned, and their CRF is steeper than those of their inputs. Last, we show that it is possible to account for the diversity in the measured CRFs by introducing heterogeneities either in single neuron properties or in the input to the neurons. We show how correlations among the parameters that characterize the CRF depend on these sources of heterogeneities. Comparison with experimental data suggests that both sources contribute nearly equally to the diversity of CRF shapes observed in V1 neurons.

On the nature of the intrinsic connectivity of the cat motor cortex: evidence for a recurrent neural network topology.

The details and functional significance of the intrinsic horizontal connections between neurons in the motor cortex (MCx) remain to be clarified. To further elucidate the nature of this intracortical connectivity pattern, experiments were done on the MCx of three cats. The anterograde tracer biocytin was ejected iontophoretically in layers II, III, and V. Some 30-50 neurons within a radius of approximately 250 microm were thus stained. The functional output of the motor cortical point at which biocytin was injected, and of the surrounding points, was identified by microstimulation and electromyographic recordings. The axonal arborizations of the stained neurons were traced under camera lucida. The axon collaterals were extensive, reaching distances of