Emergence of co-tuning in inhibitory neurons as a network phenomenon mediated by randomness, correlations, and homeostatic plasticity.

Cortical excitatory neurons show clear tuning to stimulus features, but the tuning properties of inhibitory interneurons are ambiguous. While inhibitory neurons have been considered to be largely untuned, some studies show that some parvalbumin-expressing (PV) neurons do show feature selectivity and participate in co-tuned subnetworks with pyramidal neurons. In this study, we first use mean-field theory to demonstrate that a combination of homeostatic plasticity governing the synaptic dynamics of the connections from PV to excitatory neurons, heterogeneity in the excitatory postsynaptic potentials that impinge on PV neurons, and shared correlated input from layer 4 results in the functional and structural self-organization of PV subnetworks. Second, we show that structural and functional feature tuning of PV neurons emerges more clearly at the network level, i.e., that population-level measures identify functional and structural co-tuning of PV neurons that are not evident in pairwise individual-level measures. Finally, we show that such co-tuning can enhance network stability at the cost of reduced feature selectivity.

A mathematical model of neuroimmune interactions in epileptogenesis for discovering treatment strategies.

The development of epilepsy (epileptogenesis) involves a complex interplay of neuronal and immune processes. Here, we present a first-of-its-kind mathematical model to better understand the relationships among these processes. Our model describes the interaction between neuroinflammation, blood-brain barrier disruption, neuronal loss, circuit remodeling, and seizures. Formulated as a system of nonlinear differential equations, the model reproduces the available data from three animal models. The model successfully describes characteristic features of epileptogenesis such as its paradoxically long timescales (up to decades) despite short and transient injuries or the existence of qualitatively different outcomes for varying injury intensity. In line with the concept of degeneracy, our simulations reveal multiple routes toward epilepsy with neuronal loss as a sufficient but non-necessary component. Finally, we show that our model allows for in silico predictions of therapeutic strategies, revealing injury-specific therapeutic targets and optimal time windows for intervention.

Bifurcation analysis of the dynamics of interacting subnetworks of a spiking network.

We analyze the collective dynamics of hierarchically structured networks of densely connected spiking neurons. These networks of sub-networks may represent interactions between cell assemblies or different nuclei in the brain. The dynamical activity pattern that results from these interactions depends on the strength of synaptic coupling between them. Importantly, the overall dynamics of a brain region in the absence of external input, so called ongoing brain activity, has been attributed to the dynamics of such interactions. In our study, two different network scenarios are considered: a system with one inhibitory and two excitatory subnetworks, and a network representation with three inhibitory subnetworks. To study the effect of synaptic strength on the global dynamics of the network, two parameters for relative couplings between these subnetworks are considered. For each case, a bifurcation analysis is performed and the results have been compared to large-scale network simulations. Our analysis shows that Generalized Lotka-Volterra (GLV) equations, well-known in predator-prey studies, yield a meaningful population-level description for the collective behavior of spiking neuronal interaction, which have a hierarchical structure. In particular, we observed a striking equivalence between the bifurcation diagrams of spiking neuronal networks and their corresponding GLV equations. This study gives new insight on the behavior of neuronal assemblies, and can potentially suggest new mechanisms for altering the dynamical patterns of spiking networks based on changing the synaptic strength between some groups of neurons.

Dynamics of Competition between Subnetworks of Spiking Neuronal Networks in the Balanced State.

We explore and analyze the nonlinear switching dynamics of neuronal networks with non-homogeneous connectivity. The general significance of such transient dynamics for brain function is unclear; however, for instance decision-making processes in perception and cognition have been implicated with it. The network under study here is comprised of three subnetworks of either excitatory or inhibitory leaky integrate-and-fire neurons, of which two are of the same type. The synaptic weights are arranged to establish and maintain a balance between excitation and inhibition in case of a constant external drive. Each subnetwork is randomly connected, where all neurons belonging to a particular population have the same in-degree and the same out-degree. Neurons in different subnetworks are also randomly connected with the same probability; however, depending on the type of the pre-synaptic neuron, the synaptic weight is scaled by a factor. We observed that for a certain range of the "within" versus "between" connection weights (bifurcation parameter), the network activation spontaneously switches between the two sub-networks of the same type. This kind of dynamics has been termed "winnerless competition", which also has a random component here. In our model, this phenomenon is well described by a set of coupled stochastic differential equations of Lotka-Volterra type that imply a competition between the subnetworks. The associated mean-field model shows the same dynamical behavior as observed in simulations of large networks comprising thousands of spiking neurons. The deterministic phase portrait is characterized by two attractors and a saddle node, its stochastic component is essentially given by the multiplicative inherent noise of the system. We find that the dwell time distribution of the active states is exponential, indicating that the noise drives the system randomly from one attractor to the other. A similar model for a larger number of populations might suggest a general approach to study the dynamics of interacting populations of spiking networks.

A Markov model for the temporal dynamics of balanced random networks of finite size.

The balanced state of recurrent networks of excitatory and inhibitory spiking neurons is characterized by fluctuations of population activity about an attractive fixed point. Numerical simulations show that these dynamics are essentially nonlinear, and the intrinsic noise (self-generated fluctuations) in networks of finite size is state-dependent. Therefore, stochastic differential equations with additive noise of fixed amplitude cannot provide an adequate description of the stochastic dynamics. The noise model should, rather, result from a self-consistent description of the network dynamics. Here, we consider a two-state Markovian neuron model, where spikes correspond to transitions from the active state to the refractory state. Excitatory and inhibitory input to this neuron affects the transition rates between the two states. The corresponding nonlinear dependencies can be identified directly from numerical simulations of networks of leaky integrate-and-fire neurons, discretized at a time resolution in the sub-millisecond range. Deterministic mean-field equations, and a noise component that depends on the dynamic state of the network, are obtained from this model. The resulting stochastic model reflects the behavior observed in numerical simulations quite well, irrespective of the size of the network. In particular, a strong temporal correlation between the two populations, a hallmark of the balanced state in random recurrent networks, are well represented by our model. Numerical simulations of such networks show that a log-normal distribution of short-term spike counts is a property of balanced random networks with fixed in-degree that has not been considered before, and our model shares this statistical property. Furthermore, the reconstruction of the flow from simulated time series suggests that the mean-field dynamics of finite-size networks are essentially of Wilson-Cowan type. We expect that this novel nonlinear stochastic model of the interaction between neuronal populations also opens new doors to analyze the joint dynamics of multiple interacting networks.

The effect of proprioceptive training on multisensory perception under visual uncertainty.

Most previous studies on multisensory integration concern mandatory integration. Moreover, no study has evaluated the effect of modality training on the result of integration. The purpose of this study is to evaluate the effect of training on visual-proprioceptive integration; i.e., we investigate the effect of proprioceptive modality training on the hand location estimation, when visual feedback exists. To achieve this goal, the effect of visual uncertainty on the estimation of hand position in visual-proprioceptive integration is studied in two groups: trained proprioception and untrained proprioception. The visual uncertainty is provided by an unpredictable spatial shift between visual and proprioceptive sensory feedbacks. The experiment was performed on nine subjects with trained proprioception and 11 subjects without proprioception training. The experiment had three phases: "familiarization", to draw participant's attention to a modality, "proprioception test", to estimate the hand position using only proprioception, and "vision-proprioception test", to investigate the effect of the visual uncertainty (bias) on hand position estimation. Our results indicate that: (i) modality training increases the subject reliance on the proprioceptive sensory information (i.e., bias decrement in sensory integration); and (ii) increasing the discrepancy between the modalities leads to more uncertainty (i.e., variance) in the estimation of hand position, but the variance of the final estimate is less than the variance of the proprioceptive estimate. This result confirms the theory that both senses contribute to the multisensory perception and in contrast to some studies, the dominant sense does not fully override the non-dominant one in the range of applied shift between the sensory sources.