Comparison of Langevin and Markov channel noise models for neuronal signal generation

The stochastic opening and closing of voltage-gated ion channels produces noise in neurons. The effect of this noise on the neuronal performance has been modelled using either approximate or Langevin model, based on stochastic differential equations or an exact model, based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produced by the Markov model remains unclear. Here we present a comparison between Langevin and Markov models of channel noise in neurons using single compartment Hodgkin-Huxley models containing either $Na^{+}$ and $K^{+}$, or only $K^{+}$ voltage-gated ion channels. The performance of the Langevin and Markov models was quantified over a range of stimulus statistics, membrane areas and channel numbers. We find that in comparison to the Markov model, the Langevin model underestimates the noise contributed by voltage-gated ion channels, overestimating information rates for both spiking and non-spiking membranes. Even with increasing numbers of channels the difference between the two models persists. This suggests that the Langevin model may not be suitable for accurately simulating channel noise in neurons, even in simulations with large numbers of ion channels

Locally embedded presages of global network bursts

Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially non-bursting network state is not fully understood. In this study, we develop a new state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during non-bursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean field activity for predicting future global bursts. Moreover, the inter-cell variability in the burst predictability is found to reflect the network structure realized in the non-bursting periods. These findings demonstrate the deterministic mechanisms underlying the locally concentrated early-warnings of the global state transition in self-organized networks

Photogenetic Retinal Prosthesis

The last few decades have witnessed an immense effort to develop working retinal implants for patients suffering from retinal degeneration diseases such as retinitis pigmentosa. However, it is becoming apparent that this approach is unable to restore levels of vision that will be sufficient to offer significant improvement in the quality of life of patients. Herein, a new type of retinal prosthesis that is based on genetic expression of microbial light sensitive ion channel, Chanelrhodopsin-2 (ChR2), and a remote light stimulation is examined. First, the dynamics of the ChR2 stimulation is characterized and it is shown that (1) the temporal resolution of ChR2-evoked spiking is limited by a continuous drop in its depolarization efficiency that is due to (a) frequency-independent desensitization process and (b) slow photocurrent shutting, which leads to a frequency-dependent post-spike depolarization and (2) the ChR2 response to light can be accurately reproduced by a four-state model consisting of two interconnected branches of open and close states. Then, a stimulation prototype is developed and its functionality is demonstrated in-vitro. The prototype uses a new micro-emissive matrix which enables generating of two-dimensional stimulation patterns with enhanced resolution compared to the conventional retinal implants. Finally, based on the micro-emitters matrix, a new technique for sub-cellular and network-level neuroscience experimentations is shown. The capacity to excite sub-cellular compartments is demonstrated and an example utility to fast map variability in dendrites conductance is shown. The outcomes of this thesis present an outline and a first proof-of-concept for a future photogenetic retinal prosthesis. In addition, they provide the emerging optogenetic technology with a detailed analysis of its temporal resolution and a tool to expand its spatial resolution, which can have immediate high impact applications in modulating the activity of sub-cellular compartments, mapping neuronal networks and studying synchrony and plasticity effects

Physiological synaptic signals initiate sequential spikes at soma of cortical pyramidal neurons

The neurons in the brain produce sequential spikes as the digital codes whose various patterns manage well-organized cognitions and behaviors. A source for the physiologically integrated synaptic signals to initiate digital spikes remains unknown, which we studied at pyramidal neurons of cortical slices. In dual recordings from the soma vs. axon, the signals recorded in vivo induce somatic spikes with higher capacity, which is associated with lower somatic thresholds and shorter refractory periods mediated by voltage-gated sodium channels. The introduction of these parameters from the soma and axon into NEURON model simulates sequential spikes being somatic in origin. Physiological signals integrated from synaptic inputs primarily trigger the soma to encode neuronal digital spikes

Development of axon-carrying dendrite cells in murine hippocampus and primary somatosensory cortex

In some neurons, axons originate from a basal dendrite, resulting in an axon-carrying dendrite (AcD) branch with unique functional features. Initial observations showed that the AcD has a privileged position, allowing circumvention of somatic inhibition and providing a highly efficient synaptic input channel, resulting in potentially distinct functional implications for overall network activity. Although AcD neurons have been described in numerous anatomical regions across species, their developmental profile and putative ability to remodel their axonal onset throughout their lifetime remains largely unknown. Therefore, this project investigated the early maturation profile of AcD neurons in comparison to nonAcD neurons in the murine ventral hippocampus (vHC) and primary somatosensory (S1) cortex, using a transgenic mouse line (Thy1-GFP-M). Additionally, to investigate large-scale morphological plasticity, I used immunofluorescence and live-cell imaging of neurons from the mouse primary somatosensory cortex in organotypic slice cultures. In a second approach, I employed an established in vivo paradigm to manipulate sensory input to layer V pyramidal cells in the barrel cortex. This study demonstrates that the proportion of AcD neurons peaks in juvenile mice and that Nav1.6 is clustered more distally in the axon initial segment of AcD neurons than in nonAcD neurons. Furthermore, neurons are indeed capable of changing the onset of their axon origin from somatic to dendritic and vice versa within a few days in vitro. Furthermore, the manipulation of sensory input drives large-scale morphological plasticity especially with regard to the axon onset in vivo. Altogether, the study contributes to the understanding of developmental and activity-dependent plasticity of a functionally important variant of mammalian pyramidal neurons

Stability Analysis of Phase-Locked Bursting in Inhibitory Neuron Networks

Networks of neurons, which form central pattern generators (CPGs), are important for controlling animal behaviors. Of special interest are configurations or CPG motifs composed of reciprocally inhibited neurons, such as half-center oscillators (HCOs). Bursting rhythms of HCOs are shown to include stable synchrony or in-phase bursting. This in-phase bursting can co-exist with anti-phase bursting, commonly expected as the single stable state in HCOs that are connected with fast non-delayed synapses. The finding contrasts with the classical view that reciprocal inhibition has to be slow or time-delayed to synchronize such bursting neurons. Phase-locked rhythms are analyzed via Lyapunov exponents estimated with variational equations, and through the convergence rates estimated with Poincar\\u27e return maps. A new mechanism underlying multistability is proposed that is based on the spike interactions, which confer a dual property on the fast non-delayed reciprocal inhibition; this reveals the role of spikes in generating multiple co-existing phase-locked rhythms. In particular, it demonstrates that the number and temporal characteristics of spikes determine the number and stability of the multiple phase-locked states in weakly coupled HCOs. The generality of the multistability phenomenon is demonstrated by analyzing diverse models of bursting networks with various inhibitory synapses; the individual cell models include the reduced leech heart interneuron, the Sherman model for pancreatic beta cells, the Purkinje neuron model and Fitzhugh-Rinzel phenomenological model. Finally, hypothetical and experiment-based CPGs composed of HCOs are investigated. This study is relevant for various applications that use CPGs such as robotics, prosthetics, and artificial intelligence

Modeling Rhythm Generation in Swim Central Pattern Generator of Melibe Leonina

Central pattern generators (CPGs) are neural networks to produce a rich multiplicity of rhythmic activity types like walking, breathing and swim locomotion. Basis principles of the underlying mechanisms of rhythm generation in CPGs remain yet insufficiently understood. Interactive pairing experimental and modeling studies have proven to be vital to unlocking insights into operational and dynamical principles of CPGs and support the consensus that the most of essential structural and functional elements in vertebrate and invertebrate nervous systems are shared. We have developed a family of highly-detailed, biologically plausible CPG models using the extensive data intracellularly recorded from constituent interneurons of the swim CPG of the sea slug {\it Melibe leonina}. We also have deduced fundamental properties needed for the devised Hodgkin-Huxley type neuronal models with specific slow-fast dynamics to become qualitatively and quantitatively similar to biological CPG interneurons and their responses to parameter and external perturbations. We have studied the onset and robustness of rhythmogenesis of network bursting the CPG circuits comprised of tonic spiking interneurons coupled with mixed inhibitory/excitatory, slow chemical synapses. We have shown that the mathematical CPG model can be reduced functionally from an 8-cell circuit to a 4-cell one using the calibration of timing and weights of synaptic coupling between CPG core interneurons. We demonstrate that the developed mathematical network meets all the experimental fact-checks obtained for the biological Melibe swim CPG from a variety of state-of-the-art experimental studies including dynamic-clamp recordings, external pulses perturbations as well as from its forced behaviors under applications of neuro-blockers such as curare and TTX. Our model and developed mathematical approaches and computational methodology allow for laying down theoretical foundations necessary for devising new detailed and phenomenological models of neural circuits and for making testable predictions of dynamics of rhythmic neural networks from diverse species

A point process framework for modeling electrical stimulation of the auditory nerve

Model-based studies of auditory nerve responses to electrical stimulation can provide insight into the functioning of cochlear implants. Ideally, these studies can identify limitations in sound processing strategies and lead to improved methods for providing sound information to cochlear implant users. To accomplish this, models must accurately describe auditory nerve spiking while avoiding excessive complexity that would preclude large-scale simulations of populations of auditory nerve fibers and obscure insight into the mechanisms that influence neural encoding of sound information. In this spirit, we develop a point process model of the auditory nerve that provides a compact and accurate description of neural responses to electric stimulation. Inspired by the framework of generalized linear models, the proposed model consists of a cascade of linear and nonlinear stages. We show how each of these stages can be associated with biophysical mechanisms and related to models of neuronal dynamics. Moreover, we derive a semi-analytical procedure that uniquely determines each parameter in the model on the basis of fundamental statistics from recordings of single fiber responses to electric stimulation, including threshold, relative spread, jitter, and chronaxie. The model also accounts for refractory and summation effects that influence the responses of auditory nerve fibers to high pulse rate stimulation. Throughout, we compare model predictions to published physiological data and explain differences in auditory nerve responses to high and low pulse rate stimulation. We close by performing an ideal observer analysis of simulated spike trains in response to sinusoidally amplitude modulated stimuli and find that carrier pulse rate does not affect modulation detection thresholds.Comment: 1 title page, 27 manuscript pages, 14 figures, 1 table, 1 appendi