Mathematical models for excitable cells are commonly based on cable theory, which considers a hom... more Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modelling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra-and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.
We review modeling of astrocyte ion dynamics with a specific focus on the implications of socalle... more We review modeling of astrocyte ion dynamics with a specific focus on the implications of socalled spatial potassium buffering where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. The chapter thus describes key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.
Computational modeling in neuroscience has largely focused on simulating the electrical activity ... more Computational modeling in neuroscience has largely focused on simulating the electrical activity of neurons, while ignoring other components of brain tissue, such as glial cells and the extracellular space. As such, most existing models can not be used to address pathological conditions, such as spreading depression, which involves dramatic changes in ion concentrations, large extracellular potential gradients, and glial buffering processes. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine multicompartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for neuronal somatic action potentials, and dendritic calcium spikes, (iii) contains a neuronal and glial home...
Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techni... more Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techniques for non-invasively studying cognition and disease in the human brain. These signals are known to originate from cortical neural activity, typically described in terms of current dipoles. While the link between cortical current dipoles and EEG/MEG signals is relatively well understood, surprisingly little is known about the link between different kinds of neural activity and the current dipoles themselves. Detailed biophysical modeling has played an important role in exploring the neural origin of intracranial electric signals, like extracellular spikes and local field potentials. However, this approach has not yet been taken full advantage of in the context of exploring the neural origin of the cortical current dipoles that are causing EEG/MEG signals.Here, we present a method for reducing arbitrary simulated neural activity to single current dipoles. We find that the method is appl...
Most neuronal models are based on the assumption that ion concentrations remain constant during t... more Most neuronal models are based on the assumption that ion concentrations remain constant during the simulated period, and do not account for possible effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials. Here, we present what is, to our knowledge, the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The model, which we refer to as the electrodiffusive Pinsky-Rinzel (edPR) model, is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron, where we have included homeostatic mechanisms and ion-specific leakage currents. Whereas the main dynamical variable in the original PR model is the transmembrane potential, the edPR model in addition keeps track of all ion c...
Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca 2+ concentr... more Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca 2+ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na + currents (I Na), high-voltage activated Ca 2+ currents (I Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I Na is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by I Ca. Unlike in rats, spontaneous I Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by I Na , and (3) the first pituitary cell model where the kinetics of the depolarizing currents, I Na and I Ca , are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire I Ca-based APs. We put a particular focus on how the big conductance K + current (I BK) modulates the AP shape. Interestingly, we find that I BK can prolong AP duration in models that fire I Ca-based APs, while it consistently shortens the duration of the predominantly I Na-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire I Na-mediated APs.
Visual signals originating in the retina pass through the dorsal geniculate nucleus (dLGN), the v... more Visual signals originating in the retina pass through the dorsal geniculate nucleus (dLGN), the visual part of thalamus, on the way to the visual cortex. This is however not a simple feedforward flow of information: there is a significant feedback from cortical cells back to both relay cells and interneurons in the dLGN. Despite four decades of experimental and theoretical studies, the functional role of this feedback is still debated. Here we use a firing-rate model, the extended difference-of-gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. For this model the responses are found by direct evaluation of two- or three-dimensional integrals allowing for fast and comprehensive studies of putative effects of different candidate organizations of the cortical feedback. Our analysis identifies a special mixed configuration of excitatory and inhibitory cortical feedback which seems to best account for available experimental data. This co...
Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the do... more Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the dorsal lateral geniculate nucleus (dLGN) in shaping the visual signals is not properly understood. Placed on route from retina to primary visual cortex in the early visual pathway, a striking feature of the dLGN circuit is that both the relay cells (RCs) and interneurons (INs) not only receive feedforward input from retinal ganglion cells, but also a prominent feedback from cells in layer 6 of visual cortex. This feedback has been proposed to affect synchronicity and other temporal properties of the RC firing. It has also been seen to affect spatial properties such as the center-surround antagonism of thalamic receptive fields, i.e., the suppression of the response to very large stimuli compared to smaller, more optimal stimuli. Here we explore the spatial effects of cortical feedback on the RC response by means of a a comprehensive network model with biophysically detailed, single-compartment and multicompartment neuron models of RCs, INs and a population of orientation-selective layer 6 simple cells, consisting of pyramidal cells (PY). We have considered two different arrangements of synaptic feedback from the ON and OFF zones in the visual cortex to the dLGN: phase-reversed ('push-pull') and phase-matched ('push-push'), as well as different spatial extents of the corticothalamic projection pattern. Our simulation results support that a phase-reversed arrangement provides a more effective way for cortical feedback to provide the increased center-surround antagonism seen in experiments both for flashing spots and, even more prominently, for patch gratings. This implies that ON-center RCs receive direct excitation from OFF-dominated cortical cells and indirect inhibitory feedback from ON-dominated cortical cells. The increased center-surround antagonism in the model is accompanied by spatial focusing, i.e., the maximum RC response occurs for smaller stimuli when feedback is present.
Many pathological conditions, such as seizures, stroke, and spreading depression, are associated ... more Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.
Computational models in neuroscience typically contain many parameters that are poorly constraine... more Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.
Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca2+ concentra... more Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca2+ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na+ currents (I_Na), high-voltage activated Ca2+ currents (I_Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I_Na is largely inactivated at the resting potential, and spontaneous APs are exclusively mediated by I_Ca. As a part of the previous modeling studies, a paradoxical role was identified for the big conductance K+ current (I_BK), which was found to prolong the duration of I_Ca-mediated APs, and sometimes give rise to pseudo-plateau bursts, contrary to what one would expect from a hyperpolarizing current. Unlike in rats, spontaneous I_Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species ...
Recent progress in electrophysiological and optical methods for neuronal recordings provides vast... more Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level. In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca2+ imaging. We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model. Our approach combines feat...
Recent studies have demonstrated the capacity of hippocampal sequences associated with theta osci... more Recent studies have demonstrated the capacity of hippocampal sequences associated with theta oscillation, to encode P160 The effect of progressive degradation of connectivity between brain areas on the brain network structure
Despite the widespread use of current-source density (CSD) analysis of extracellular potential re... more Despite the widespread use of current-source density (CSD) analysis of extracellular potential recordings in the brain, the physical mechanisms responsible for the generation of the signal are still debated. While the extracellular potential is thought to be exclusively generated by the transmembrane currents, recent studies suggest that extracellular diffusive, advective and displacement currents-traditionally neglected-may also contribute considerably toward extracellular potential recordings. Here, we first justify the application of the electro-quasistatic approximation of Maxwell's equations to describe the electromagnetic field of physiological origin. Subsequently, we perform spatial averaging of currents in neural tissue to arrive at the notion of the CSD and derive an equation relating it to the extracellular potential. We show that, in general, the extracellular potential is determined by the CSD of membrane currents as well as the gradients of the putative extracellular diffusion current. The diffusion current can contribute significantly to the extracellular potential at frequencies less than a few Hertz; in which case it must be subtracted to obtain correct CSD estimates. We also show that the advective and displacement currents in the extracellular space are negligible for physiological frequencies while, within cellular membrane, displacement current contributes toward the CSD as a capacitive current. Taken together, these findings elucidate the relationship between electric currents and the extracellular potential in brain tissue and form the necessary foundation for the analysis of extracellular recordings.
Neural circuits are notorious for the complexity of their organization. Part of this complexity i... more Neural circuits are notorious for the complexity of their organization. Part of this complexity is related to the number of different cell types that work together to encode stimuli. I will discuss theoretical results that point to functional advantages of splitting neural populations into subtypes, both in feedforward and recurrent networks. These results outline a framework for categorizing neuronal types based on their functional properties. Such classification scheme could augment classification schemes based on molecular, anatomical, and electrophysiological properties.
Mathematical models for excitable cells are commonly based on cable theory, which considers a hom... more Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modelling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra-and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.
We review modeling of astrocyte ion dynamics with a specific focus on the implications of socalle... more We review modeling of astrocyte ion dynamics with a specific focus on the implications of socalled spatial potassium buffering where excess potassium in the extracellular space (ECS) is transported away to prevent pathological neural spiking. The recently introduced Kirchoff-Nernst-Planck (KNP) scheme for modeling ion dynamics in astrocytes (and brain tissue in general) is outlined and used to study such spatial buffering. We next describe how the ion dynamics of astrocytes may regulate microscopic liquid flow by osmotic effects and how such microscopic flow can be linked to whole-brain macroscopic flow. The chapter thus describes key elements in a putative multiscale theory with astrocytes linking neural activity on a microscopic scale to macroscopic fluid flow.
Computational modeling in neuroscience has largely focused on simulating the electrical activity ... more Computational modeling in neuroscience has largely focused on simulating the electrical activity of neurons, while ignoring other components of brain tissue, such as glial cells and the extracellular space. As such, most existing models can not be used to address pathological conditions, such as spreading depression, which involves dramatic changes in ion concentrations, large extracellular potential gradients, and glial buffering processes. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine multicompartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for neuronal somatic action potentials, and dendritic calcium spikes, (iii) contains a neuronal and glial home...
Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techni... more Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techniques for non-invasively studying cognition and disease in the human brain. These signals are known to originate from cortical neural activity, typically described in terms of current dipoles. While the link between cortical current dipoles and EEG/MEG signals is relatively well understood, surprisingly little is known about the link between different kinds of neural activity and the current dipoles themselves. Detailed biophysical modeling has played an important role in exploring the neural origin of intracranial electric signals, like extracellular spikes and local field potentials. However, this approach has not yet been taken full advantage of in the context of exploring the neural origin of the cortical current dipoles that are causing EEG/MEG signals.Here, we present a method for reducing arbitrary simulated neural activity to single current dipoles. We find that the method is appl...
Most neuronal models are based on the assumption that ion concentrations remain constant during t... more Most neuronal models are based on the assumption that ion concentrations remain constant during the simulated period, and do not account for possible effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials. Here, we present what is, to our knowledge, the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The model, which we refer to as the electrodiffusive Pinsky-Rinzel (edPR) model, is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron, where we have included homeostatic mechanisms and ion-specific leakage currents. Whereas the main dynamical variable in the original PR model is the transmembrane potential, the edPR model in addition keeps track of all ion c...
Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca 2+ concentr... more Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca 2+ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na + currents (I Na), high-voltage activated Ca 2+ currents (I Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I Na is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by I Ca. Unlike in rats, spontaneous I Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by I Na , and (3) the first pituitary cell model where the kinetics of the depolarizing currents, I Na and I Ca , are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire I Ca-based APs. We put a particular focus on how the big conductance K + current (I BK) modulates the AP shape. Interestingly, we find that I BK can prolong AP duration in models that fire I Ca-based APs, while it consistently shortens the duration of the predominantly I Na-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire I Na-mediated APs.
Visual signals originating in the retina pass through the dorsal geniculate nucleus (dLGN), the v... more Visual signals originating in the retina pass through the dorsal geniculate nucleus (dLGN), the visual part of thalamus, on the way to the visual cortex. This is however not a simple feedforward flow of information: there is a significant feedback from cortical cells back to both relay cells and interneurons in the dLGN. Despite four decades of experimental and theoretical studies, the functional role of this feedback is still debated. Here we use a firing-rate model, the extended difference-of-gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. For this model the responses are found by direct evaluation of two- or three-dimensional integrals allowing for fast and comprehensive studies of putative effects of different candidate organizations of the cortical feedback. Our analysis identifies a special mixed configuration of excitatory and inhibitory cortical feedback which seems to best account for available experimental data. This co...
Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the do... more Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the dorsal lateral geniculate nucleus (dLGN) in shaping the visual signals is not properly understood. Placed on route from retina to primary visual cortex in the early visual pathway, a striking feature of the dLGN circuit is that both the relay cells (RCs) and interneurons (INs) not only receive feedforward input from retinal ganglion cells, but also a prominent feedback from cells in layer 6 of visual cortex. This feedback has been proposed to affect synchronicity and other temporal properties of the RC firing. It has also been seen to affect spatial properties such as the center-surround antagonism of thalamic receptive fields, i.e., the suppression of the response to very large stimuli compared to smaller, more optimal stimuli. Here we explore the spatial effects of cortical feedback on the RC response by means of a a comprehensive network model with biophysically detailed, single-compartment and multicompartment neuron models of RCs, INs and a population of orientation-selective layer 6 simple cells, consisting of pyramidal cells (PY). We have considered two different arrangements of synaptic feedback from the ON and OFF zones in the visual cortex to the dLGN: phase-reversed ('push-pull') and phase-matched ('push-push'), as well as different spatial extents of the corticothalamic projection pattern. Our simulation results support that a phase-reversed arrangement provides a more effective way for cortical feedback to provide the increased center-surround antagonism seen in experiments both for flashing spots and, even more prominently, for patch gratings. This implies that ON-center RCs receive direct excitation from OFF-dominated cortical cells and indirect inhibitory feedback from ON-dominated cortical cells. The increased center-surround antagonism in the model is accompanied by spatial focusing, i.e., the maximum RC response occurs for smaller stimuli when feedback is present.
Many pathological conditions, such as seizures, stroke, and spreading depression, are associated ... more Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.
Computational models in neuroscience typically contain many parameters that are poorly constraine... more Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.
Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca2+ concentra... more Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca2+ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na+ currents (I_Na), high-voltage activated Ca2+ currents (I_Ca), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where I_Na is largely inactivated at the resting potential, and spontaneous APs are exclusively mediated by I_Ca. As a part of the previous modeling studies, a paradoxical role was identified for the big conductance K+ current (I_BK), which was found to prolong the duration of I_Ca-mediated APs, and sometimes give rise to pseudo-plateau bursts, contrary to what one would expect from a hyperpolarizing current. Unlike in rats, spontaneous I_Na-mediated APs are consistently seen in pituitary cells of several other animal species, including several species ...
Recent progress in electrophysiological and optical methods for neuronal recordings provides vast... more Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level. In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca2+ imaging. We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model. Our approach combines feat...
Recent studies have demonstrated the capacity of hippocampal sequences associated with theta osci... more Recent studies have demonstrated the capacity of hippocampal sequences associated with theta oscillation, to encode P160 The effect of progressive degradation of connectivity between brain areas on the brain network structure
Despite the widespread use of current-source density (CSD) analysis of extracellular potential re... more Despite the widespread use of current-source density (CSD) analysis of extracellular potential recordings in the brain, the physical mechanisms responsible for the generation of the signal are still debated. While the extracellular potential is thought to be exclusively generated by the transmembrane currents, recent studies suggest that extracellular diffusive, advective and displacement currents-traditionally neglected-may also contribute considerably toward extracellular potential recordings. Here, we first justify the application of the electro-quasistatic approximation of Maxwell's equations to describe the electromagnetic field of physiological origin. Subsequently, we perform spatial averaging of currents in neural tissue to arrive at the notion of the CSD and derive an equation relating it to the extracellular potential. We show that, in general, the extracellular potential is determined by the CSD of membrane currents as well as the gradients of the putative extracellular diffusion current. The diffusion current can contribute significantly to the extracellular potential at frequencies less than a few Hertz; in which case it must be subtracted to obtain correct CSD estimates. We also show that the advective and displacement currents in the extracellular space are negligible for physiological frequencies while, within cellular membrane, displacement current contributes toward the CSD as a capacitive current. Taken together, these findings elucidate the relationship between electric currents and the extracellular potential in brain tissue and form the necessary foundation for the analysis of extracellular recordings.
Neural circuits are notorious for the complexity of their organization. Part of this complexity i... more Neural circuits are notorious for the complexity of their organization. Part of this complexity is related to the number of different cell types that work together to encode stimuli. I will discuss theoretical results that point to functional advantages of splitting neural populations into subtypes, both in feedforward and recurrent networks. These results outline a framework for categorizing neuronal types based on their functional properties. Such classification scheme could augment classification schemes based on molecular, anatomical, and electrophysiological properties.
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Papers by Geir Halnes