Jokubas Ziburkus

The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics

In these companion papers, we study how the interrelated dynamics of sodium and potassium affect the excitability of neurons, the occurrence of seizures, and the stability of persistent states of activity. In this first paper, we construct a mathematical model consisting of a single conductance-based neuron together with intra- and extracellular ion concentration dynamics. We formulate a reduction of this model that permits a detailed bifurcation analysis, and show that the reduced model is a reasonable approximation of the full model. We find that competition between intrinsic neuronal currents, sodium-potassium pumps, glia, and diffusion can produce very slow and large-amplitude oscillations in ion concentrations similar to what is seen physiologically in seizures. Using the reduced model, we identify the dynamical mechanisms that give rise to these phenomena. These models reveal several experimentally testable predictions. Our work emphasizes the critical role of ion concentration homeostasis in the proper functioning of neurons, and points to important fundamental processes that may underlie pathological states such as epilepsy.

Erratum to: The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: I. Single neuron dynamics

The original version of this article contains a few typographical errors. These do not affect the results and conclusions that we originally reported. However, to assist readers interested in reproducing our results, we list below several corrections in order to accurately reflect the equations that were used to generate the published figures. Some errors are consequential, and others are less so; we list them all for completeness. Code containing the correct equations is available at ModelDB (http://senselab.med.yale.edu/modeldb). Equation (2) should appear as follows:

From Molecular Circuit Dysfunction to Disease Case Studies in Epilepsy, Traumatic Brain Injury, and Alzheimer’s Disease

Complex circuitry with feed-forward and feed-back systems regulate neuronal activity throughout the brain. Cell biological, electrical, and neurotransmitter systems enable neural networks to process and drive the entire spectrum of cognitive, behavioral, and motor functions. Simultaneous orchestration of distinct cells and interconnected neural circuits relies on hundreds, if not thousands, of unique molecular interactions. Even single molecule dysfunctions can be disrupting to neural circuit activity, leading to neurological pathology. Here, we sample our current understanding of how molecular aberrations lead to disruptions in networks using three neurological pathologies as exemplars: epilepsy, traumatic brain injury (TBI), and Alzheimer’s disease (AD). Epilepsy provides a window into how total destabilization of network balance can occur. TBI is an abrupt physical disruption that manifests in both acute and chronic neurological deficits. Last, in AD progressive cell loss leads to devastating cognitive consequences. Interestingly, all three of these neurological diseases are interrelated. The goal of this review, therefore, is to identify molecular changes that may lead to network dysfunction, elaborate on how altered network activity and circuit structure can contribute to neurological disease, and suggest common threads that may lie at the heart of molecular circuit dysfunction.

Kalman filter tracking of intracellular neuronal voltage and current

The nervous system encodes and processes information with the activities of neurons. The response of a single neuron is complex and depends on the interactions between its previous state, its intrinsic properties, and the stimuli it receives. Experimentally, we utilize the patch clamp technique to monitor neural membrane voltages, but the underlying stimuli, including the external current or synaptic current from other neurons, cannot be fully observed. In this paper, we used computational models as an alternative to tackle these challenges. We employed an ensemble Kalman filter to reconstruct unobserved intracellular variables and parameters only from measured membrane potentials in a CA1 pyramidal neuron model that follows Hodgkin-Huxley dynamics. We found that the tracking of intracellular neuronal voltage and current was close to their true values whether the observations are from model generated data or real experimental data. In addition, we retrieved the experimentally inaccessible dynamics of the neuron, such as the changes of sodium and potassium gating variables, which helps to understand their roles in generating action potentials. Our study provides a powerful framework for observing dynamics underlying neural activity and seeking better real-time neuronal control.

Ion concentration dynamics: mechanisms for bursting and seizing

Address: 1Department of Physics & Astronomy and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia, 22030, USA, 2Department of Engineering Sciences and Mechanics, The Pennsylvania State University, University Park, Pennsylvania, 16802, USA, 3Department of Biology and Biochemistry, The University of Houston, Houston, Texas, USA and 4Departments of Neurosurgery and Physics, The Pennsylvania State University, University Park, Pennsylvania, 16802, USA

Robust Cell Detection for Large-Scale 3D Microscopy Using GPU-Accelerated Iterative Voting

High-throughput imaging techniques, such as Knife-Edge Scanning Microscopy (KESM),are capable of acquiring three-dimensional whole-organ images at sub-micrometer resolution. These images are challenging to segment since they can exceed several terabytes (TB) in size, requiring extremely fast and fully automated algorithms. Staining techniques are limited to contrast agents that can be applied to large samples and imaged in a single pass. This requires maximizing the number of structures labeled in a single channel, resulting in images that are densely packed with spatial features. In this paper, we propose a three-dimensional approach for locating cells based on iterative voting. Due to the computational complexity of this algorithm, a highly efficient GPU implementation is required to make it practical on large data sets. The proposed algorithm has a limited number of input parameters and is highly parallel.

Slow potassium dynamics and seizure evolution

Seizures involve dynamics on a wide range of temporal scales, from spike times on the order of milliseconds to the large depolarizations seen in single cells that can last several tens of seconds. At the longest time scales, these events modify the cellular environment, altering oxygen, potassium, sodium and other electrolyte concentrations to produce a durable but transient modification of the network dynamics. In order to investigate these slow dynamics we have developed a highly simplified model that monitors the changes in ionic concentrations in and around highly active cells, while disregarding the fast dynamics responsible for action potential generation. We model the time-dependent potassium concentration in and around a cell resulting from flow through voltage-gated channels, pumps, and the surrounding glial network. The flow through voltage-gated channels is determined by time-averaging simulated potassium currents in a Hodgkin-Huxley conductance-based neuron. The current is a function of both intra- and extracellular potassium concentrations and responds to changes in the concentration gradient over a duration that is long compared to the time associated with spiking events. On the other hand, this response time, which can be as slow as a fraction of a second, is still short compared to the lifetime of a network seizure and can be considered instantaneous. Therefore we disregard the response time and approximate the model as a pair of differential equations which are amenable to a complete phase plane analysis. We report on the results of this phase plane analysis and show comparisons with results from in vitro experiments.