Theta Oscillations Gate the Transmission of Reliable Sequences in the Medial Entorhinal Cortex.

Stability and precision of sequential activity in the entorhinal cortex (EC) is crucial for encoding spatially guided behavior and memory. These sequences are driven by constantly evolving sensory inputs and persist despite a noisy background. In a realistic computational model of a medial EC (MEC) microcircuit, we show that intrinsic neuronal properties and network mechanisms interact with theta oscillations to generate reliable outputs. In our model, sensory inputs activate interneurons near their most excitable phase during each theta cycle. As the inputs change, different interneurons are recruited and postsynaptic stellate cells are released from inhibition. This causes a sequence of rebound spikes. The rebound time scale of stellate cells, because of an h-current, matches that of theta oscillations. This fortuitous similarity of time scales ensures that stellate spikes get relegated to the least excitable phase of theta and the network encodes the external drive but ignores recurrent excitation. In contrast, in the absence of theta, rebound spikes compete with external inputs and disrupt the sequence that follows. Further, the same mechanism where theta modulates the gain of incoming inputs, can be used to select between competing inputs to create transient functionally connected networks. Our results concur with experimental data that show, subduing theta oscillations disrupts the spatial periodicity of grid cell receptive fields. In the bat MEC where grid cell receptive fields persist even in the absence of continuous theta oscillations, we argue that other low frequency fluctuations play the role of theta.

Effect of Circuit Structure on Odor Representation in the Insect Olfactory System.

In neuroscience, the structure of a circuit has often been used to intuit function-an inversion of Louis Kahn's famous dictum, "Form follows function" (Kristan and Katz, 2006). However, different brain networks may use different network architectures to solve the same problem. The olfactory circuits of two insects, the locust, Schistocerca americana, and the fruit fly, Drosophila melanogaster, serve the same function-to identify and discriminate odors. The neural circuitry that achieves this shows marked structural differences. Projection neurons (PNs) in the antennal lobe innervate Kenyon cells (KCs) of the mushroom body. In locust, each KC receives inputs from ∼50% of PNs, a scheme that maximizes the difference between inputs to any two of ∼50,000 KCs. In contrast, in Drosophila, this number is only 5% and appears suboptimal. Using a computational model of the olfactory system, we show that the activity of KCs is sufficiently high-dimensional that it can separate similar odors regardless of the divergence of PN-KC connections. However, when temporal patterning encodes odor attributes, dense connectivity outperforms sparse connections. Increased separability comes at the cost of reliability. The disadvantage of sparse connectivity can be mitigated by incorporating other aspects of circuit architecture seen in Drosophila Our simulations predict that Drosophila and locust circuits lie at different ends of a continuum where the Drosophila gives up on the ability to resolve similar odors to generalize across varying environments, while the locust separates odor representations but risks misclassifying noisy variants of the same odor.

Optimality of sparse olfactory representations is not affected by network plasticity.

The neural representation of a stimulus is repeatedly transformed as it moves from the sensory periphery to deeper layers of the nervous system. Sparsening transformations are thought to increase the separation between similar representations, encode stimuli with great specificity, maximize storage capacity of associative memories, and provide an energy efficient instantiation of information in neural circuits. In the insect olfactory system, odors are initially represented in the periphery as a combinatorial code with relatively simple temporal dynamics. Subsequently, in the antennal lobe this representation is transformed into a dense and complex spatiotemporal activity pattern. Next, in the mushroom body Kenyon cells (KCs), the representation is dramatically sparsened. Finally, in mushroom body output neurons (MBONs), the representation takes on a new dense spatiotemporal format. Here, we develop a computational model to simulate this chain of olfactory processing from the receptor neurons to MBONs. We demonstrate that representations of similar odorants are maximally separated, measured by the distance between the corresponding MBON activity vectors, when KC responses are sparse. Sparseness is maintained across variations in odor concentration by adjusting the feedback inhibition that KCs receive from an inhibitory neuron, the Giant GABAergic neuron. Different odor concentrations require different strength and timing of feedback inhibition for optimal processing. Importantly, as observed in vivo, the KC-MBON synapse is highly plastic, and, therefore, changes in synaptic strength after learning can change the balance of excitation and inhibition, potentially leading to changes in the distance between MBON activity vectors of two odorants for the same level of KC population sparseness. Thus, what is an optimal degree of sparseness before odor learning, could be rendered sub-optimal post learning. Here, we show, however, that synaptic weight changes caused by spike timing dependent plasticity increase the distance between the odor representations from the perspective of MBONs. A level of sparseness that was optimal before learning remains optimal post-learning.

Learning modifies odor mixture processing to improve detection of relevant components.

Honey bees have a rich repertoire of olfactory learning behaviors, and they therefore are an excellent model to study plasticity in olfactory circuits. Recent behavioral, physiological, and molecular evidence suggested that the antennal lobe, the first relay of the olfactory system in insects and analog to the olfactory bulb in vertebrates, is involved in associative and nonassociative olfactory learning. Here we use calcium imaging to reveal how responses across antennal lobe projection neurons change after association of an input odor with appetitive reinforcement. After appetitive conditioning to 1-hexanol, the representation of an odor mixture containing 1-hexanol becomes more similar to this odor and less similar to the background odor acetophenone. We then apply computational modeling to investigate how changes in synaptic connectivity can account for the observed plasticity. Our study suggests that experience-dependent modulation of inhibitory interactions in the antennal lobe aids perception of salient odor components mixed with behaviorally irrelevant background odors.

Excitatory local interneurons enhance tuning of sensory information.

Neurons in the insect antennal lobe represent odors as spatiotemporal patterns of activity that unfold over multiple time scales. As these patterns unspool they decrease the overlap between odor representations and thereby increase the ability of the olfactory system to discriminate odors. Using a realistic model of the insect antennal lobe we examined two competing components of this process -lateral excitation from local excitatory interneurons, and slow inhibition from local inhibitory interneurons. We found that lateral excitation amplified differences between representations of similar odors by recruiting projection neurons that did not receive direct input from olfactory receptors. However, this increased sensitivity also amplified noisy variations in input and compromised the ability of the system to respond reliably to multiple presentations of the same odor. Slow inhibition curtailed the spread of projection neuron activity and increased response reliability. These competing influences must be finely balanced in order to decorrelate odor representations.

Synaptic inhibition controls transient oscillatory synchronization in a model of the insect olfactory system.

In a variety of neuronal systems it has been hypothesized that inhibitory interneurons corral principal neurons into synchronously firing groups that encode sensory information and sub-serve behavior (Buzsáki and Chrobak, 1995; Buzsáki, 2008). This mechanism is particularly relevant to the olfactory system where spatiotemporal patterns of projection neuron (PN) activity act as robust markers of odor attributes (Laurent et al., 1996; Wehr and Laurent, 1996). In the insect antennal lobe (AL), a network of local inhibitory interneurons arborizes extensively throughout the AL (Leitch and Laurent, 1996) providing inhibitory input to the cholinergic PNs. Our theoretical work has attempted to elaborate the exact role of inhibition in the generation of odor specific PN responses (Bazhenov et al., 2001a,b; Assisi et al., 2011). In large-scale AL network models we characterized the inhibitory sub-network by its coloring (Assisi et al., 2011) and showed that it can entrain excitatory PNs to the odor specific patterns of transient synchronization. In this focused review, we further examine the dynamics of entrainment in more detail by simulating simple model networks in various parameter regimes. Our simulations in conjunction with earlier studies point to the key role played by lateral (between inhibitory interneurons) and feedback (from inhibitory interneurons to principal cells) inhibition in the generation of experimentally observed patterns of transient synchrony.

Using the structure of inhibitory networks to unravel mechanisms of spatiotemporal patterning.

Neuronal networks exhibit a rich dynamical repertoire, a consequence of both the intrinsic properties of neurons and the structure of the network. It has been hypothesized that inhibitory interneurons corral principal neurons into transiently synchronous ensembles that encode sensory information and subserve behavior. How does the structure of the inhibitory network facilitate such spatiotemporal patterning? We established a relationship between an important structural property of a network, its colorings, and the dynamics it constrains. Using a model of the insect antennal lobe, we show that our description allows the explicit identification of the groups of inhibitory interneurons that switch, during odor stimulation, between activity and quiescence in a coordinated manner determined by features of the network structure. This description optimally matches the perspective of the downstream neurons looking for synchrony in ensembles of presynaptic cells and allows a low-dimensional description of seemingly complex high-dimensional network activity.

Mode level cognitive subtraction (MLCS) quantifies spatiotemporal reorganization in large-scale brain topographies.

Contemporary brain theories of cognitive function posit spatial, temporal and spatiotemporal reorganization as mechanisms for neural information processing. Corresponding brain imaging results underwrite this perspective of large-scale reorganization. As we show here, a suitable choice of experimental control tasks allows the disambiguation of the spatial and temporal components of reorganization to a quantifiable degree of certainty. When using electro- or magnetoencephalography (EEG or MEG), our approach relies on the identification of lower dimensional spaces obtained from the high dimensional data of suitably chosen control task conditions. Encephalographic data from task conditions are reconstructed within these control spaces. We show that the residual signal (part of the task signal not captured by the control spaces) allows the quantification of the degree of spatial reorganization, such as recruitment of additional brain networks.

Adaptive regulation of sparseness by feedforward inhibition.

In the mushroom body of insects, odors are represented by very few spikes in a small number of neurons, a highly efficient strategy known as sparse coding. Physiological studies of these neurons have shown that sparseness is maintained across thousand-fold changes in odor concentration. Using a realistic computational model, we propose that sparseness in the olfactory system is regulated by adaptive feedforward inhibition. When odor concentration changes, feedforward inhibition modulates the duration of the temporal window over which the mushroom body neurons may integrate excitatory presynaptic input. This simple adaptive mechanism could maintain the sparseness of sensory representations across wide ranges of stimulus conditions.

Multisensory integration for timing engages different brain networks.

How does the brain integrate information from different senses into a unitary percept? What factors influence such multisensory integration? Using a rhythmic behavioral paradigm and functional magnetic resonance imaging, we identified networks of brain regions for perceptions of physically synchronous and asynchronous auditory-visual events. Measures of behavioral performance revealed the existence of three distinct perceptual states. Perception of asynchrony activated a network of the primary sensory, prefrontal, and inferior parietal cortices, perception of synchrony disengaged the inferior parietal cortex and further recruited the superior colliculus, and when no clear percept was established, only the residual areas comprised of prefrontal and sensory areas were active. These results indicate that distinct percepts arise within specific brain sub-networks, the components of which are differentially engaged and disengaged depending on the timing of environmental signals.

Dynamics of multifrequency coordination using parametric driving: theory and experiment.

The coupling of movement behavior and environmental signals has been extensively studied within the domain of rhythmic coordination tasks. However, in contrast to most traditional coordination studies, here we drive the coupled sensorimotor system far beyond the frequency regime in which these signals may be synchronized. Our goal is to identify the properties of the coupling between the human subject and the environment. Earlier studies have shown that the environmental signal may be parametrically coupled to the effectors. A necessary feature of parametrically driven oscillators is the existence of stable 1:1 and 1:2 coordination modes. Here, we test this prediction experimentally using a coordination paradigm in which subjects were asked to coincide peak finger flexion with an auditory metronome beat. The rate of the metronome was increased in steps of 0.5 Hz from 2.5 Hz to 12 Hz. It was observed that the subjects shifted involuntarily from a 1:1 to a 1:2 coordination mode at high driving frequencies, as predicted. These results are examined in the context of an extended form of the Haken-Kelso-Bunz (Haken et al. 1985) model (HKB) for bimanual coordination, which includes a parametric driving term (Jirsa et al. 2000). Unimanual coordination is treated as a special case of this extended model. An important feature of the HKB model is bistability and the presence of a phase transition from an anti-phase mode to in-phase mode of coordination. Our description of unimanual coordination leads to a mechanism for phase transitions that is distinct from that seen in the HKB model. The transition is mediated by the dynamics of both the amplitude and the phase of the oscillator. More generally, we propose the existence of two types of transitions in our extended theory, that is, phase-mediated and amplitude-mediated transitions. Both have characteristic features; in particular, their transients are mutually orthogonal in the plane spanned by the amplitude and phase of the oscillator. The analytical and numerical results of our theoretical model are demonstrated to compare favorably with our experimental results.

Synchrony and clustering in heterogeneous networks with global coupling and parameter dispersion.

Networks with nonidentical nodes and global coupling may display a large variety of dynamic behaviors, such as phase clustered solutions, synchrony, and oscillator death. The network dynamics is a function of the parameter dispersion and may be captured by conventional mean field approaches if it is close to the completely synchronous state. In this Letter we introduce a novel method based on a mode decomposition in the parameter space, which provides a low-dimensional network description for more complex dynamic behaviors and captures the mean field approach as a special case. The example of globally coupled Fitzhugh-Nagumo neurons is discussed.