A unified physiological framework of transitions between seizures, sustained ictal activity and depolarization block at the single neuron level

The majority of seizures recorded in humans and experimental animal models can be described by a generic phenomenological mathematical model, the Epileptor. In this model, seizure-like events (SLEs) are driven by a slow variable and occur via saddle node (SN) and homoclinic bifurcations at seizure onset and offset, respectively. Here we investigated SLEs at the single cell level using a biophysically relevant neuron model including a slow/fast system of four equations. The two equations for the slow subsystem describe ion concentration variations and the two equations of the fast subsystem delineate the electrophysiological activities of the neuron. Using extracellular K+ as a slow variable, we report that SLEs with SN/homoclinic bifurcations can readily occur at the single cell level when extracellular K+ reaches a critical value. In patients and experimental models, seizures can also evolve into sustained ictal activity (SIA) and depolarization block (DB), activities which are also parts of the dynamic repertoire of the Epileptor. Increasing extracellular concentration of K+ in the model to values found during experimental status epilepticus and DB, we show that SIA and DB can also occur at the single cell level. Thus, seizures, SIA, and DB, which have been first identified as network events, can exist in a unified framework of a biophysical model at the single neuron level and exhibit similar dynamics as observed in the Epileptor.Author Summary: Epilepsy is a neurological disorder characterized by the occurrence of seizures. Seizures have been characterized in patients in experimental models at both macroscopic and microscopic scales using electrophysiological recordings. Experimental works allowed the establishment of a detailed taxonomy of seizures, which can be described by mathematical models. We can distinguish two main types of models. Phenomenological (generic) models have few parameters and variables and permit detailed dynamical studies often capturing a majority of activities observed in experimental conditions. But they also have abstract parameters, making biological interpretation difficult. Biophysical models, on the other hand, use a large number of variables and parameters due to the complexity of the biological systems they represent. Because of the multiplicity of solutions, it is difficult to extract general dynamical rules. In the present work, we integrate both approaches and reduce a detailed biophysical model to sufficiently low-dimensional equations, and thus maintaining the advantages of a generic model. We propose, at the single cell level, a unified framework of different pathological activities that are seizures, depolarization block, and sustained ictal activity.

Computational modelling and near-complete kinetochore tracking reveal how chromosome dynamics during cell division are co-ordinated in space and time

Mitotic chromosome segregation is a self-organising process that achieves high fidelity separation of 46 duplicated chromosomes into two daughter cells. Chromosomes must be captured by the microtubule-based spindle, aligned at the spindle equator where they undergo oscillatory motion (metaphase) and then pulled to opposite spindle poles (anaphase). These large and small-scale chromosome movements are driven by kinetochores, multi-protein machines, that link chromosomes to microtubules and generate directional forces. Through automated near-complete tracking of kinetochores at fine spatio-temporal resolution over long timescales, we produce a detailed atlas of kinetochore dynamics throughout metaphase and anaphase in human cells. We develop a hierarchical biophysical model of kinetochore dynamics and fit this model to 4D lattice light sheet experimental data using Bayesian inference. We demonstrate that location in the metaphase plate is the largest factor in the variation in kinetochore dynamics, exceeding the variation between cells, whilst within the spindle there is local spatio-temporal coordination between neighbouring kinetochores of directional switching events, kinetochore-fibre (K-fibre) polymerization/depolymerization state and the segregation of chromosomes. Thus, metaphase oscillations are robust to variation in the mechanical forces throughout the spindle, whilst the spindle environment couples kinetochore dynamics across the plate. Our methods provide a framework for detailed quantification of chromosome dynamics during mitosis in human cells.

Estimating potato crop wetness duration from agrometeorological data

Hourly meteorological observations over a potato crop field were used to validate a biophysical model and different thresholds of relative humidity (RH) to simulate the onset. cessation and total wetness duration (WD). The model showed the capability to simulate multiple wet and dry conditions as well as prolonged moist conditions with a mean absolute error of less than an hour. The deviation between measured and estimated onset and total WD was more pronounced when only RH was used. However, under the prevailing agroclimatic conditions of potato growing regions in India, 80% RH threshold may adequately be accurate to estimate WD for many weather-based disease management advisories.

Towards Biophysical Markers of Depression Vulnerability

A major difficulty with treating psychiatric disorders is their heterogeneity: different neural causes can lead to the same phenotype. To address this, we propose describing the underlying pathophysiology in terms of interpretable, biophysical parameters of a neural model derived from the electroencephalogram. We analyzed data from a small patient cohort of patients with depression and controls. We constructed biophysical models that describe neural dynamics in a cortical network activated during a task that is used to assess depression state. We show that biophysical model parameters are biomarkers, that is, variables that allow subtyping of depression at a biological level. They yield a low dimensional, interpretable feature space that allowed description of differences between individual patients with depressive symptoms. They capture internal heterogeneity/variance of depression state and achieve significantly better classification than commonly used EEG features. Our work is a proof of concept that a combination of biophysical models and machine learning may outperform earlier approaches based on classical statistics and raw brain data.

Baseline Shift in Neuronal Oscillations and Its Implications for the Interpretation of Evoked Activity Obtained with EEG/MEG

Oscillations and evoked responses are two types of neuronal activity recorded non-invasively with EEG/MEG. Although typically studied separately, they might in fact represent the same process. One possibility to unite them is to demonstrate that neuronal oscillations have non-zero mean which would indicate that stimulus-relating amplitude modulation of neuronal oscillations should lead to the generation of evoked responses. We validated this mechanism using computational modelling and analysis of a large EEG data set. With a biophysical model generating alpha rhythm, we indeed demonstrated that the oscillatory mean is nonzero for a large range of model-parameter values. In EEG data we detected non-zero mean alpha oscillations in about 96% of the participants. Furthermore, using neuronal-ensemble modelling, we provided an explanation for the often observed discrepancies between amplitude modulation and baseline shifts. Overall, our results provide strong support for the unification of neuronal oscillations and evoked responses.

Closed-loop Controller Based on Reference Signal Tracking for Absence Seizures

Deep brain stimulation (DBS) targeting thalamus reticular nucleus (TRN) brain regions has been proven to play an irreplaceable role in the treatment of absence seizures. Compared with open-loop DBS, closed-loop DBS has been recognized by researchers for its advantages of significantly inhibiting seizures and having fewer side effects. However, due to the complexity of the nervous system, the mechanism of DBS control epilepsy is still unclear, which hinders the study of closed-loop DBS. In our study, based on the biophysical model jointly constituted by cortical, thalamic, and basal ganglia, we selected the 2-4 Hz spike and wave discharges (SWDs) of the cortical region as a biomarker for response to absence epilepsy, and the mean firing rate (MFR) of substantia nigra pars reticulata (SNr) was used as a reference signal for modulation of closed-loop DBS. Moreover, to obtain the linear relationship between the stimulus and the response, we adopted an algorithm that combines controlled auto-regressive (CAR) and recursive least squares (RLS), and we built a proportional integral (PI) controller to make the DBS stimulus parameters self-update to control the seizures. The numerical simulation results show that the closed-loop DBS controllers based on frequency modulation and amplitude modulation respectively not only successfully track the firing rate (FR) of SNr, but also significantly destroy the SWDs of cerebral cortex and restore it to the other two normal discharge modes.

Probing ion channel functional architecture and domain recombination compatibility by massively parallel domain insertion profiling

Protein domains are the basic units of protein structure and function. Comparative analysis of genomes and proteomes showed that domain recombination is a main driver of multidomain protein functional diversification and some of the constraining genomic mechanisms are known. Much less is known about biophysical mechanisms that determine whether protein domains can be combined into viable protein folds. Here, we use massively parallel insertional mutagenesis to determine compatibility of over 300,000 domain recombination variants of the Inward Rectifier K+ channel Kir2.1 with channel surface expression. Our data suggest that genomic and biophysical mechanisms acted in concert to favor gain of large, structured domain at protein termini during ion channel evolution. We use machine learning to build a quantitative biophysical model of domain compatibility in Kir2.1 that allows us to derive rudimentary rules for designing domain insertion variants that fold and traffic to the cell surface. Positional Kir2.1 responses to motif insertion clusters into distinct groups that correspond to contiguous structural regions of the channel with distinct biophysical properties tuned towards providing either folding stability or gating transitions. This suggests that insertional profiling is a high-throughput method to annotate function of ion channel structural regions.

Modelling the effect of ephaptic coupling on spike propagation in peripheral nerve fibres

Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of identical axons, whereas realistic peripheral nerve bundles contain numerous axons with different diameters. Here, we present a computationally efficient spike propagation model, which captures the essential features of propagating spikes and their ephaptic interaction, and facilitates the theoretical investigation of spike volleys in large, heterogeneous fibre bundles. The spike propagation model describes an action potential, or spike, by its position on the axon, and its velocity. The velocity is primarily defined by intrinsic features of the axons, such as diameter and myelination status, but it is also modulated by changes in the extracellular potential. These changes are due to transmembrane currents that occur during the generation of action potentials. The resulting change in the velocity is appropriately described by a linearised coupling function, which is calibrated with a biophysical model. We first lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model based on Hodgkin-Huxley dynamics. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that with increasing level of heterogeneity the ephaptic coupling strength has to increase to achieve full synchronisation between spikes. Another result of this study is that in the absence of full synchronisation, a subset of spikes on axons with similar diameter can form synchronised clusters. These findings may help interpret the results of noninvasive experiments on the electrophysiology of peripheral nerves.