Tatiana Kameneva

Brief paper: Robustness of quantized control systems with mismatch between coder/decoder initializations

This paper analyzes the stability of linear systems with quantized feedback in the presence of mismatch between the initial conditions at the coder and decoder. Under the assumption of the perfect channel, we show that using the scheme proposed in [Liberzon, D., & Nesic, D. (2007). Input-to-state stabilization of linear systems with quantized state measurements. Institute of Electrical and Electronic Engineers Transaction on Automatic Control, 52, 767-781] it is possible to achieve stability with exponential convergence of linear systems with quantized feedback when the coder and decoder are initialized at different initial conditions.

Modelling intrinsic electrophysiological properties of ON and OFF retinal ganglion cells

ON and OFF retinal ganglion cells (RGCs) display differences in their intrinsic electrophysiology: OFF cells maintain spontaneous activity in the absence of any input, exhibit subthreshold membrane potential oscillations, rebound excitation and burst firing; ON cells require excitatory input to drive their activity and display none of the aforementioned phenomena. The goal of this study was to identify and characterize ionic currents that explain these intrinsic electrophysiological differences between ON and OFF RGCs. A mathematical model of the electrophysiological properties of ON and OFF RGCs was constructed and validated using published patch-clamp data from isolated intact mouse retina. The model incorporates three ionic currents hypothesized to play a role in generating behaviors that are different between ON and OFF RGCs. These currents are persistent Na + , INaP, hyperpolarization-activated, Ih, and low voltage activated Ca2 + , IT, currents. Using computer simulations of Hodgkin-Huxley type neuron with a single compartment model we found two distinct sets of INaP, Ih, IT conductances that correspond to ON and OFF RGCs populations. Simulations indicated that special properties of IT explain the differences in intrinsic electrophysiology between ON and OFF RGCs examined here. The modelling shows that the maximum conductance of IT is higher in OFF than in ON cells, in agreement with recent experimental data.

On

This paper extends results from [D. Liberzon and D. Nesic, ldquoInput-to-state stabilization of linear systems with quantized feedback,rdquo IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767--781, May 2007], where input-to-state stabilization (ISS) of linear systems with quantized feedback was considered. In this paper, we show that, by using the same scheme and under the same conditions as in D. Liberzon and D. Nesic, ldquoInput-to-state stabilization of linear systems with quantized feedback,rdquo IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767-781, May 2007, it is also possible to achieve (nonlinear gain) l2 stabilization for linear systems. We also prove a new lemma on Kinfin functions that is interesting in its own right.

l_2

Retinal ganglion cells (RGCs) display differences in their morphology and intrinsic electrophysiology. The goal of this study is to characterize the ionic currents that explain the behavior of ON and OFF RGCs and to explore if all morphological types of RGCs exhibit the phenomena described in electrophysiological data. We extend our previous single compartment cell models of ON and OFF RGCs to more biophysically realistic multicompartment cell models and investigate the effect of cell morphology on intrinsic electrophysiological properties. The membrane dynamics are described using the Hodgkin - Huxley type formalism. A subset of published patch-clamp data from isolated intact mouse retina is used to constrain the model and another subset is used to validate the model. Two hundred morphologically distinct ON and OFF RGCs are simulated with various densities of ionic currents in different morphological neuron compartments. Our model predicts that the differences between ON and OFF cells are explained by the presence of the low voltage activated calcium current in OFF cells and absence of such in ON cells. Our study shows through simulation that particular morphological types of RGCs are capable of exhibiting the full range of phenomena described in recent experiments. Comparisons of outputs from different cells indicate that the RGC morphologies that best describe recent experimental results are ones that have a larger ratio of soma to total surface area.

Stabilization of Linear Systems With Quantized Control

Implantable electrode arrays are widely used in therapeutic stimulation of the nervous system (e.g. cochlear, retinal, and cortical implants). Currently, most neural prostheses use serial stimulation (i.e. one electrode at a time) despite this severely limiting the repertoire of stimuli that can be applied. Methods to reliably predict the outcome of multi-electrode stimulation have not been available. Here, we demonstrate that a linear-nonlinear model accurately predicts neural responses to arbitrary patterns of stimulation using in vitro recordings from single retinal ganglion cells (RGCs) stimulated with a subretinal multi-electrode array. In the model, the stimulus is projected onto a low-dimensional subspace and then undergoes a nonlinear transformation to produce an estimate of spiking probability. The low-dimensional subspace is estimated using principal components analysis, which gives the neuron’s electrical receptive field (ERF), i.e. the electrodes to which the neuron is most sensitive. Our model suggests that stimulation proportional to the ERF yields a higher efficacy given a fixed amount of power when compared to equal amplitude stimulation on up to three electrodes. We find that the model captures the responses of all the cells recorded in the study, suggesting that it will generalize to most cell types in the retina. The model is computationally efficient to evaluate and, therefore, appropriate for future real-time applications including stimulation strategies that make use of recorded neural activity to improve the stimulation strategy.

The effect of morphology upon electrophysiological responses of retinal ganglion cells: simulation results

This paper extends results from (D. Liberzon et al., 2005), where input-to-state stabilization (ISS) of linear systems with quantized feedback was considered. In this paper, we show that using the scheme proposed in (D. Liberzon et al., 2005) it is also possible to achieve (nonlinear gain) l2 stabilization for linear systems.

A Simple and Accurate Model to Predict Responses to Multi-electrode Stimulation in the Retina.

Epilepsy is one of the most common neurological disorders and is characterized by recurrent seizures. We use theoretical neuroscience tools to study brain dynamics during seizures. We derive and simulate a computational model of a network of hippocampal neuronal populations. Each population within the network is based on a model that has been shown to replicate the electrophysiological dynamics observed during seizures. The results provide insights into possible mechanisms for seizure spread. We observe that epileptiform activity remains localized to a pathological region when a global connectivity parameter is less than a critical value. After establishing the critical value for seizure spread, we explored how to correct the effect by altering particular synaptic gains. The spreading of seizures is quantified using numerical methods for seizure detection. The results from this study provide a new avenue of exploration for seizure control.

Further results on robustness of linear control systems with quantized feedback

Energy-based bond graph modelling of biomolecular systems is extended to include chemoelectrical transduction thus enabling integrated thermodynamically-compliant modelling of chemoelectrical systems in general and excitable membranes in particular. Our general approach is illustrated by recreating a well-known model of an excitable membrane. This model is used to investigate the energy consumed during a membrane action potential thus contributing to the current debate on the trade-off between the speed of an action potential event and energy consumption. The influx of Na+ is often taken as a proxy for energy consumption; in contrast, this paper presents an energy based model of action potentials. As the energy based approach avoids the assumptions underlying the proxy approach it can be directly used to compute energy consumption in both healthy and diseased neurons. These results are illustrated by comparing the energy consumption of healthy and degenerative retinal ganglion cells using both simulated and in vitro data.

Neural mass models as a tool to investigate neural dynamics during seizures

OBJECTIVE Retinal ganglion cells (RGCs) demonstrate a large range of variation in their ionic channel properties and morphologies. Cell-specific properties are responsible for the unique way RGCs process synaptic inputs, as well as artificial electrical signals such as that from a visual prosthesis. A cell-specific computational modelling approach allows us to examine the functional significance of regional membrane channel expression and cell morphology. APPROACH In this study, an existing RGC ionic model was extended by including a hyperpolarization activated non-selective cationic current as well as a T-type calcium current identified in recent experimental findings. Biophysically-defined model parameters were simultaneously optimized against multiple experimental recordings from ON and OFF RGCs. MAIN RESULTS With well-defined cell-specific model parameters and the incorporation of detailed cell morphologies, these models were able to closely reconstruct and predict ON and OFF RGC response properties recorded experimentally. SIGNIFICANCE The resulting models were used to study the contribution of different ion channel properties and spatial structure of neurons to RGC activation. The techniques of this study are generally applicable to other excitable cell models, increasing the utility of theoretical models in accurately predicting the response of real biological neurons.

Bond graph modelling of chemoelectrical energy transduction

OBJECTIVE ON and OFF retinal ganglion cells (RGCs) are known to have non-monotonic responses to increasing amplitudes of high frequency (2 kHz) biphasic electrical stimulation. That is, an increase in stimulation amplitude causes an increase in the cells spike rate up to a peak value above which further increases in stimulation amplitude cause the cell to decrease its activity. The peak response for ON and OFF cells occurs at different stimulation amplitudes, which allows differential stimulation of these functional cell types. In this study, we investigate the mechanisms underlying the non-monotonic responses of ON and OFF brisk-transient RGCs and the mechanisms underlying their differential responses. APPROACH Using in vitro patch-clamp recordings from rat RGCs, together with simulations of single and multiple compartment Hodgkin-Huxley models, we show that the non-monotonic response to increasing amplitudes of stimulation is due to depolarization block, a change in the membrane potential that prevents the cell from generating action potentials. MAIN RESULTS We show that the onset for depolarization block depends on the amplitude and frequency of stimulation and reveal the biophysical mechanisms that lead to depolarization block during high frequency stimulation. Our results indicate that differences in transmembrane potassium conductance lead to shifts of the stimulus currents that generate peak spike rates, suggesting that the differential responses of ON and OFF cells may be due to differences in the expression of this current type. We also show that the length of the axons high sodium channel band (SOCB) affects non-monotonic responses and the stimulation amplitude that leads to the peak spike rate, suggesting that the length of the SOCB is shorter in ON cells. SIGNIFICANCE This may have important implications for stimulation strategies in visual prostheses.