Dynamics and Noise in Neural Networks

Cheng Ly

Virginia Commonwealth

"The Circuit Mechanisms that alter Spiking Statistics in Mammalian Olfactory Bulb Cells"

The olfactory bulb is one of the primary stages of odor processing, possessing a unique architecture hallmarked by fast dendro-dendritic synapses between all inhibitory cells (perioglomerular cells (PGC) and granule cells (GC)) connected to excitatory cells (mitral/tufted cells (MC)). Although there has been ample theoretical and experimental studies of the olfactory bulb (OB), dissecting the circuit mechanisms of modulation of the first and second order (MC) spiking statistics of populations is lacking. In particular, we analyze data from our (Shew) lab in spontaneous and odor-evoked states n vivo, with multi-electrode arrays that enable studying second order spiking statistics with simultaneous recordings. Based on a multicompartment large-scale biophysical model, we develop a reduced firing rate model that enables us to efficiently and accurately capture our data. We show that granule cell inhibition in particular helps decorrelate in the spontaneous state but is unlocked so that there is stimulus-induced correlation in the evoked state; this is in contrast to many cortical sensory systems where there is often stimulus-induced decorrelation. We also consider pharmacological drug applications to manipulate inhibitory synaptic strengths (both PGC and GC) that alter the spiking statistics. Our model qualitatively captures the statistically significant changes.

Kelsey Gasior

Florida State

"Mathematically Modeling Neuron Biophysics in Response to Ramped Input Current"

In the nervous system, olfactory bulb dopamine-secreting neurons (OBDA neurons) process different odors by inhibiting other downstream neurons. Recently, novel experiments were performed wherein current applied to individual neurons was continuously ramped to mimic biologically realistic neuronal input (at Florida State University, the Trombley lab performed) in comparison to previous standard protocols where current is applied in steps. However, this new stimulus protocol raises the questions of what is the proper way to interpret these data and how can mathematical analysis help? In this project, we have developed an integrated experimental-mathematical methodology to study transient dynamics in the electrical activity of single neurons while maintaining a close interdisciplinary collaboration with the biologists who carry out these electrophysiological experiments. One of the aims of our work is to create a positive feedback loop wherein experimental data informs the mathematical model, and in turn, the model directs future experiments. In particular, we are using bifurcation analysis to characterize the onset and offset of tonic spiking as well as the frequency of spiking in a neuron stimulated with both slow and fast applied current ramps. This work allows us to understand how different ion channels shape the transient response dynamics in OBDA neurons. Importantly, we have also developed mathematical tools that can be used to explore the behavior of other cell types as it is our belief that the ramping technique could be extended to study the single-neuron dynamics of all neuron types. The use of fast-slow analysis helps us to understand how the ramped applied current and the slow M-type Potassium channel influence tonic spiking behavior and frequency. Ultimately, this work helps close the gap between mathematical modeling and biological data in computational neuroscience.

Jan Kirchner

Max Planck Institute for Brain Research

"Local and global organization of synaptic inputs on cortical dendrites"

Synaptic inputs on cortical dendrites are organized with remarkable subcellular precision at the micron level. This organization emerges during early postnatal development through patterned spontaneous activity and manifests both locally where nearby synapses tend to share functional properties, and globally with distance to the soma. Recent experimental studies reveal species-specific differences in this organization between mouse, ferret and macaque visual cortex: While in the mouse, synapses are retinotopically organized along the proximal-distal axis of the dendrite, no such organization is present in the ferret or macaque. Instead, here synapses are organized into local clusters according to orientation preference. We propose a computational framework that combines activity derived from retinal waves with functional and structural plasticity to generate these different types of organization across species, as well as across scales by including attenuating backpropagating action potentials. Within this framework, a single anatomical factor -- the size of the visual cortex and the resulting magnification of visual space -- can explain the observed differences. This allows us to make predictions about the organization of synapses also in other species and indicates that the proximal-distal axis of a dendrite might be central in endowing a neuron with its powerful computational capacities.

Fereshteh Lagzi

University of Chicago

"Cell-type specific inhibitory plasticity can speed up assembly formation and slow down assembly degradation"

It is popular to ascribe distinct network functions to the different inhibitory neuron subtypes that makeup cortical circuits. Carving out functionally determined, cell-type specific circuit wiring is an essential component of this hypothesis. However, the plasticity rules for different interneuron subtypes, and how their interactions shape network dynamics are largely unexplored. We use in vitro patch clamp techniques paired with cell-specific optogenetic stimulation to measure the spike timing dependent plasticity (STDP) rules of the inhibitory inputs onto excitatory (E) pyramidal neurons from both Parvalbumin (PV) and Somatostatin (SOM) interneurons in mouse orbital frontal cortex (OFC). Consistent with past studies, PV inhibition shows a symmetric STDP that is often associated with the homeostatic control of excitatory firing rates. By contrast, SOM inhibition shows an asymmetric Hebbian STDP rule, so that recurrent SOM inhibition onto driving E neurons will ultimately depress. To understand the role of these different plasticity mechanisms in network dynamics we exploit large-scale network simulations of networks of spiking neuron model with plastic synapses, along with associated mean field theories of synaptic dynamics. We show that the asymmetric SOM plasticity rule promotes cross-inhibition between distinct E neuron assemblies, effectively providing a mechanism for competition between functionally grouped principle neurons. This competition will enhance computations where input comparisons must be made, as is often the case in decision task where the OFC is known to be essential. However, strong cross inhibition could lead to extreme (and unstable) winner-take-all assembly dynamics. Fortunately, the symmetric PV plasticity rule provides stability for the circuit, ensuring rich network dynamics. Finally, the increased correlations due to the asymmetric Hebbian learning for SOM connections to pyramidal cells can speed up assembly formation during training and slow assembly degradation post training.