Ghanim Ullah

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.

The influence of sodium and potassium dynamics on excitability, seizures, and the stability of persistent states: II. Network and glial 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. We seek to study these dynamics with respect to the following compartments: neurons, glia, and extracellular space. We are particularly interested in the slower time-scale dynamics that determine overall excitability, and set the stage for transient episodes of persistent oscillations, working memory, or seizures. In this second of two companion papers, we present an ionic current network model composed of populations of Hodgkin–Huxley type excitatory and inhibitory neurons embedded within extracellular space and glia, in order to investigate the role of micro-environmental ionic dynamics on the stability of persistent activity. We show that these networks reproduce seizure-like activity if glial cells fail to maintain the proper micro-environmental conditions surrounding neurons, and produce several experimentally testable predictions. Our work suggests that the stability of persistent states to perturbation is set by glial activity, and that how the response to such perturbations decays or grows may be a critical factor in a variety of disparate transient phenomena such as working memory, burst firing in neonatal brain or spinal cord, up states, seizures, and cortical oscillations.

Unification of Neuronal Spikes, Seizures, and Spreading Depression

The pathological phenomena of seizures and spreading depression have long been considered separate physiological events in the brain. By incorporating conservation of particles and charge, and accounting for the energy required to restore ionic gradients, we extend the classic Hodgkin–Huxley formalism to uncover a unification of neuronal membrane dynamics. By examining the dynamics as a function of potassium and oxygen, we now account for a wide range of neuronal activities, from spikes to seizures, spreading depression (whether high potassium or hypoxia induced), mixed seizure and spreading depression states, and the terminal anoxic “wave of death.” Such a unified framework demonstrates that all of these dynamics lie along a continuum of the repertoire of the neuron membrane. Our results demonstrate that unified frameworks for neuronal dynamics are feasible, can be achieved using existing biological structures and universal physical conservation principles, and may be of substantial importance in enabling our understanding of brain activity and in the control of pathological states.

Assimilating seizure dynamics.

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics.

Intrinsic dependencies of CT radiomic features on voxel size and number of gray levels

Purpose: Many radiomics features were originally developed for non‐medical imaging applications and therefore original assumptions may need to be reexamined. In this study, we investigated the impact of slice thickness and pixel spacing (or pixel size) on radiomics features extracted from Computed Tomography (CT) phantom images acquired with different scanners as well as different acquisition and reconstruction parameters. The dependence of CT texture features on gray‐level discretization was also evaluated. Methods and materials: A texture phantom composed of 10 different cartridges of different materials was scanned on eight different CT scanners from three different manufacturers. The images were reconstructed for various slice thicknesses. For each slice thickness, the reconstruction Field Of View (FOV) was varied to render pixel sizes ranging from 0.39 to 0.98 mm. A fixed spherical region of interest (ROI) was contoured on the images of the shredded rubber cartridge and the 3D printed, 20% fill, acrylonitrile butadiene styrene plastic cartridge (ABS20) for all phantom imaging sets. Radiomic features were extracted from the ROIs using an in‐house program. Features categories were: shape (10), intensity (16), GLCM (24), GLZSM (11), GLRLM (11), and NGTDM (5), fractal dimensions (8) and first‐order wavelets (128), for a total of 213 features. Voxel‐size resampling was performed to investigate the usefulness of extracting features using a suitably chosen voxel size. Acquired phantom image sets were resampled to a voxel size of 1 × 1 × 2 mm3 using linear interpolation. Image features were therefore extracted from resampled and original datasets and the absolute value of the percent coefficient of variation (%COV) for each feature was calculated. Based on the %COV values, features were classified in 3 groups: (1) features with large variations before and after resampling (%COV >50); (2) features with diminished variation (%COV <30) after resampling; and (3) features that had originally moderate variation (%COV <50%) and were negligibly affected by resampling. Group 2 features were further studied by modifying feature definitions to include voxel size. Original and voxel‐size normalized features were used for interscanner comparisons. A subsequent analysis investigated feature dependency on gray‐level discretization by extracting 51 texture features from ROIs from each of the 10 different phantom cartridges using 16, 32, 64, 128, and 256 gray levels. Results: Out of the 213 features extracted, 150 were reproducible across voxel sizes, 42 improved significantly (%COV <30, Group 2) after resampling, and 21 had large variations before and after resampling (Group 1). Ten features improved significantly after definition modification effectively removed their voxel‐size dependency. Interscanner comparison indicated that feature variability among scanners nearly vanished for 8 of these 10 features. Furthermore, 17 out of 51 texture features were found to be dependent on the number of gray levels. These features were redefined to include the number of gray levels which greatly reduced this dependency. Conclusion: Voxel‐size resampling is an appropriate pre‐processing step for image datasets acquired with variable voxel sizes to obtain more reproducible CT features. We found that some of the radiomics features were voxel size and gray‐level discretization‐dependent. The introduction of normalizing factors in their definitions greatly reduced or removed these dependencies.

A data-driven model of a modal gated ion channel: The inositol 1,4,5-trisphosphate receptor in insect Sf9 cells

The inositol 1,4,5-trisphosphate (IP3) receptor (IP3R) channel is crucial for the generation and modulation of intracellular Ca2+ signals in animal cells. To gain insight into the complicated ligand regulation of this ubiquitous channel, we constructed a simple quantitative continuous-time Markov-chain model from the data. Our model accounts for most experimentally observed gating behaviors of single native IP3R channels from insect Sf9 cells. Ligand (Ca2+ and IP3) dependencies of channel activity established six main ligand-bound channel complexes, where a complex consists of one or more states with the same ligand stoichiometry and open or closed conformation. Channel gating in three distinct modes added one complex and indicated that three complexes gate in multiple modes. This also restricted the connectivity between channel complexes. Finally, latencies of channel responses to abrupt ligand concentration changes defined a model with specific network topology between 9 closed and 3 open states. The model with 28 parameters can closely reproduce the equilibrium gating statistics for all three gating modes over a broad range of ligand concentrations. It also captures the major features of channel response latency distributions. The model can generate falsifiable predictions of IP3R channel gating behaviors and provide insights to both guide future experiment development and improve IP3R channel gating analysis. Maximum likelihood estimates of the model parameters and of the parameters in the De Young–Keizer model yield strong statistical evidence in favor of our model. Our method is simple and easily applicable to the dynamics of other ion channels and molecules.

Oxygen and seizure dynamics: II. Computational modeling

Electrophysiological recordings show intense neuronal firing during epileptic seizures leading to enhanced energy consumption. However, the relationship between oxygen metabolism and seizure patterns has not been well studied. Recent studies have developed fast and quantitative techniques to measure oxygen microdomain concentration during seizure events. In this article, we develop a biophysical model that accounts for these experimental observations. The model is an extension of the Hodgkin-Huxley formalism and includes the neuronal microenvironment dynamics of sodium, potassium, and oxygen concentrations. Our model accounts for metabolic energy consumption during and following seizure events. We can further account for the experimental observation that hypoxia can induce seizures, with seizures occurring only within a narrow range of tissue oxygen pressure. We also reproduce the interplay between excitatory and inhibitory neurons seen in experiments, accounting for the different oxygen levels observed during seizures in excitatory vs. inhibitory cell layers. Our findings offer a more comprehensive understanding of the complex interrelationship among seizures, ion dynamics, and energy metabolism.

A simple sequential-binding model for calcium puffs

Calcium puffs describe the transient release of Ca(2+) ions into the cytosol, through small clusters of 1,4,5-inositol triphosphate (IP(3)) receptors, present on internal stores such as the endoplasmic reticulum. Statistical properties of puffs, such as puff amplitudes and durations, have been well characterized experimentally. We model calcium puffs using a simple, sequential-binding model for the IP(3) receptor in conjunction with a computationally inexpensive point-source approximation. We follow two different protocols, a sequential protocol and a renewal protocol. In the sequential protocol, puffs are generated successively by the same cluster; in the renewal protocol, the system is reset after each puff. In both cases for a single set of parameters our results are in excellent agreement with experimental results for puff amplitudes and durations but indicate puff-to-puff correlations for the sequential protocol, consistent with recent experimental findings [H. J. Rose, S. Dargan, J. W. Shuai, and I. Parker, Biophys. J. 91, 4024 (2006)]. The model is then used to test the consistency of the hypothesized steep Ca(2+) gradients around single channels with the experimentally observed features of puff durations and amplitudes. A three-dimensional implementation of our point-source model suggests that a peak Ca(2+) concentration of the order of 10 muM at the cluster site (not channel) is consistent with the statistical features of observed calcium puffs.

The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization.

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics. By incorporating cell swelling together with dynamic ion concentrations and oxygen supply into Hodgkin-Huxley type spiking dynamics, we demonstrate the spontaneous transition between epileptic seizure and spreading depression states as the cell swells and contracts in response to changes in osmotic pressure. Our use of volume as an order parameter further revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from spreading depression, as well as predicted a second ceiling that demarcates spreading depression from anoxic depolarization. Our model highlights the neuroprotective role of glial K buffering against seizures and spreading depression, and provides novel insights into anoxic depolarization and the relevant cell swelling during ischemia. We argue that the dynamics of seizures, spreading depression, and anoxic depolarization lie along a continuum of the repertoire of the neuron membrane that can be understood only when the dynamic ion concentrations, oxygen homeostasis,and cell swelling in response to osmotic pressure are taken into consideration. Our results demonstrate the feasibility of a unified framework for a wide range of neuronal behaviors that may be of substantial importance in the understanding of and potentially developing universal intervention strategies for these pathological states.

Permeant calcium ion feed-through regulation of single inositol 1,4,5-trisphosphate receptor channel gating

The ubiquitous inositol 1,4,5-trisphosphate (InsP3) receptor (InsP3R) Ca2+ release channel plays a central role in the generation and modulation of intracellular Ca2+ signals, and is intricately regulated by multiple mechanisms including cytoplasmic ligand (InsP3, free Ca2+, free ATP4−) binding, posttranslational modifications, and interactions with cytoplasmic and endoplasmic reticulum (ER) luminal proteins. However, regulation of InsP3R channel activity by free Ca2+ in the ER lumen ([Ca2+]ER) remains poorly understood because of limitations of Ca2+ flux measurements and imaging techniques. Here, we used nuclear patch-clamp experiments in excised luminal-side-out configuration with perfusion solution exchange to study the effects of [Ca2+]ER on homotetrameric rat type 3 InsP3R channel activity. In optimal [Ca2+]i and subsaturating [InsP3], jumps of [Ca2+]ER from 70 nM to 300 µM reduced channel activity significantly. This inhibition was abrogated by saturating InsP3 but restored when [Ca2+]ER was raised to 1.1 mM. In suboptimal [Ca2+]i, jumps of [Ca2+]ER (70 nM to 300 µM) enhanced channel activity. Thus, [Ca2+]ER effects on channel activity exhibited a biphasic dependence on [Ca2+]i. In addition, the effect of high [Ca2+]ER was attenuated when a voltage was applied to oppose Ca2+ flux through the channel. These observations can be accounted for by Ca2+ flux driven through the open InsP3R channel by [Ca2+]ER, raising local [Ca2+]i around the channel to regulate its activity through its cytoplasmic regulatory Ca2+-binding sites. Importantly, [Ca2+]ER regulation of InsP3R channel activity depended on cytoplasmic Ca2+-buffering conditions: it was more pronounced when [Ca2+]i was weakly buffered but completely abolished in strong Ca2+-buffering conditions. With strong cytoplasmic buffering and Ca2+ flux sufficiently reduced by applied voltage, both activation and inhibition of InsP3R channel gating by physiological levels of [Ca2+]ER were completely abolished. Collectively, these results rule out Ca2+ regulation of channel activity by direct binding to the luminal aspect of the channel.