Computational models of neuronal biophysics and the characterization of potential neuropharmacological targets

Cell morphologies in the nervous system: Glia steal the limelight

Neurons and glia have distinct yet interactive functions but are both characterized by branching morphology. Dendritic trees have been digitally traced for over 40 years in many animal species, anatomical regions, and neuron types. Recently, long-range axons also are being reconstructed throughout the brain of many organisms from invertebrates to primates. In contrast, less attention has been paid until lately to glial morphology. Thus, although glia and neurons are similarly abundant in the nervous systems of humans and most animal models, glia have traditionally been much less represented than neurons in morphological reconstruction repositories such as NeuroMorpho.Org. This is rapidly changing with the advent of high-throughput glia tracing. NeuroMorpho.Org introduced glial cells in 2017 and today they constitute nearly a third of the database content. It took NeuroMorpho.Org 10 years to collect the first 40,000 neurons and now that amount of data can be produced in a single publication. This not only demonstrates the spectacular technological progress in data production, but also demands a corresponding advancement in informatics processing. At the same time, these publicly available data also open new opportunities for quantitative analysis and computational modeling to identify universal or cell-type-specific design principles in the cellular architecture of nervous systems. As a first application, we demonstrated that supervised machine learning of tree geometry classifies neurons and glia with practically perfect accuracy. Furthermore, we discovered a new morphometric biomarker capable of robustly separating these cell classes across multiple species, brain regions, and experimental preparations, with only sparse sampling of branch measurements.

The Human Body as a Super Network: Digital Methods to Analyze the Propagation of Aging

Biological aging is a complex process involving multiple biological processes. These can be understood theoretically though considering them as individual networks-e.g., epigenetic networks, cell-cell networks (such as astroglial networks), and population genetics. Mathematical modeling allows the combination of such networks so that they may be studied in unison, to better understand how the so-called "seven pillars of aging" combine and to generate hypothesis for treating aging as a condition at relatively early biological ages. In this review, we consider how recent progression in mathematical modeling can be utilized to investigate aging, particularly in, but not exclusive to, the context of degenerative neuronal disease. We also consider how the latest techniques for generating biomarker models for disease prediction, such as longitudinal analysis and parenclitic analysis can be applied to as both biomarker platforms for aging, as well as to better understand the inescapable condition. This review is written by a highly diverse and multi-disciplinary team of scientists from across the globe and calls for greater collaboration between diverse fields of research.

Distinct Functional Groups Emerge from the Intrinsic Properties of Molecularly Identified Entorhinal Interneurons and Principal Cells

Inhibitory interneurons are an important source of synaptic inputs that may contribute to network mechanisms for coding of spatial location by entorhinal cortex (EC). The intrinsic properties of inhibitory interneurons in the EC of the mouse are mostly undescribed. Intrinsic properties were recorded from known cell types, such as, stellate and pyramidal cells and 6 classes of molecularly identified interneurons (regulator of calcineurin 2, somatostatin, serotonin receptor 3a, neuropeptide Y neurogliaform (NGF), neuropeptide Y non-NGF, and vasoactive intestinal protein) in acute brain slices. We report a broad physiological diversity between and within cell classes. We also found differences in the ability to produce postinhibitory rebound spikes and in the frequency and amplitude of incoming EPSPs. To understand the source of this intrinsic variability we applied hierarchical cluster analysis to functionally classify neurons. These analyses revealed physiologically derived cell types in EC that mostly corresponded to the lines identified by biomarkers with a few unexpected and important differences. Finally, we reduced the complex multidimensional space of intrinsic properties to the most salient five that predicted the cellular biomolecular identity with 81.4% accuracy. These results provide a framework for the classification of functional subtypes of cortical neurons by their intrinsic membrane properties.

Design and implementation of multi-signal and time-varying neural reconstructions

Several efficient procedures exist to digitally trace neuronal structure from light microscopy, and mature community resources have emerged to store, share, and analyze these datasets. In contrast, the quantification of intracellular distributions and morphological dynamics is not yet standardized. Current widespread descriptions of neuron morphology are static and inadequate for subcellular characterizations. We introduce a new file format to represent multichannel information as well as an open-source Vaa3D plugin to acquire this type of data. Next we define a novel data structure to capture morphological dynamics, and demonstrate its application to different time-lapse experiments. Importantly, we designed both innovations as judicious extensions of the classic SWC format, thus ensuring full back-compatibility with popular visualization and modeling tools. We then deploy the combined multichannel/time-varying reconstruction system on developing neurons in live Drosophila larvae by digitally tracing fluorescently labeled cytoskeletal components along with overall dendritic morphology as they changed over time. This same design is also suitable for quantifying dendritic calcium dynamics and tracking arbor-wide movement of any subcellular substrate of interest.

Molecular fingerprinting of principal neurons in the rodent hippocampus: A neuroinformatics approach

Neurons are often classified by their morphological and molecular properties. The online knowledge base Hippocampome.org primarily defines neuron types from the rodent hippocampal formation based on their main neurotransmitter (glutamate or GABA) and the spatial distributions of their axons and dendrites. For each neuron type, this open-access resource reports any and all published information regarding the presence or absence of known molecular markers, including calcium-binding proteins, neuropeptides, receptors, channels, transcription factors, and other molecules of biomedical relevance. The resulting chemical profile is relatively sparse: even for the best studied neuron types, the expression or lack thereof of fewer than 70 molecules has been firmly established to date. The mouse genome-wide in situ hybridization mapping of the Allen Brain Atlas provides a wealth of data that, when appropriately analyzed, can substantially augment the molecular marker knowledge in Hippocampome.org. Here we focus on the principal cell layers of dentate gyrus (DG), CA3, CA2, and CA1, which together contain approximately 90% of hippocampal neurons. These four anatomical parcels are densely packed with somata of mostly excitatory projection neurons. Thus, gene expression data for those layers can be justifiably linked to the respective principal neuron types: granule cells in DG and pyramidal cells in CA3, CA2, and CA1. In order to enable consistent interpretation across genes and regions, we screened the whole-genome dataset against known molecular markers of those neuron types. The resulting threshold values allow over 6000 very-high confidence (>99.5%) expressed/not-expressed assignments, expanding the biochemical information content of Hippocampome.org more than five-fold. Many of these newly identified molecular markers are potential pharmacological targets for major neurological and psychiatric conditions. Furthermore, our approach yields reasonable expression/non-expression estimates for every single gene in each of these four neuron types with >90% average confidence, providing a considerably complete genetic characterization of hippocampal principal neurons.

Post-Inhibitory Rebound Spikes in Rat Medial Entorhinal Layer II/III Principal Cells: In Vivo, In Vitro, and Computational Modeling Characterization

Medial entorhinal cortex Layer-II stellate cells (mEC-LII-SCs) primarily interact via inhibitory interneurons. This suggests the presence of alternative mechanisms other than excitatory synaptic inputs for triggering action potentials (APs) in stellate cells during spatial navigation. Our intracellular recordings show that the hyperpolarization-activated cation current (Ih) allows post-inhibitory-rebound spikes (PIRS) in mEC-LII-SCs. In vivo, strong inhibitory-post-synaptic potentials immediately preceded most APs shortening their delay and enhancing excitability. In vitro experiments showed that inhibition initiated spikes more effectively than excitation and that more dorsal mEC-LII-SCs produced faster and more synchronous spikes. In contrast, PIRS in Layer-II/III pyramidal cells were harder to evoke, voltage-independent, and slower in dorsal mEC. In computational simulations, mEC-LII-SCs morphology and Ih homeostatically regulated the dorso-ventral differences in PIRS timing and most dendrites generated PIRS with a narrow range of stimulus amplitudes. These results suggest inhibitory inputs could mediate the emergence of grid cell firing in a neuronal network.

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N_2a, N_2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

Distinct and synergistic feedforward inhibition of pyramidal cells by basket and bistratified interneurons

Feedforward inhibition (FFI) enables pyramidal cells in area CA1 of the hippocampus (CA1PCs) to remain easily excitable while faithfully representing a broad range of excitatory inputs without quickly saturating. Despite the cortical ubiquity of FFI, its specific function is not completely understood. FFI in CA1PCs is mediated by two physiologically and morphologically distinct GABAergic interneurons: fast-spiking, perisomatic-targeting basket cells and regular-spiking, dendritic-targeting bistratified cells. These two FFI pathways might create layer-specific computational sub-domains within the same CA1PC, but teasing apart their specific contributions remains experimentally challenging. We implemented a biophysically realistic model of CA1PCs using 40 digitally reconstructed morphologies and constraining synaptic numbers, locations, amplitude, and kinetics with available experimental data. First, we validated the model by reproducing the known combined basket and bistratified FFI of CA1PCs at the population level. We then analyzed how the two interneuron types independently affected the CA1PC spike probability and timing as a function of inhibitory strength. Separate FFI by basket and bistratified respectively modulated CA1PC threshold and gain. Concomitant FFI by both interneuron types synergistically extended the dynamic range of CA1PCs by buffering their spiking response to excitatory stimulation. These results suggest testable hypotheses on the precise effects of GABAergic diversity on cortical computation.

Multiscale model of dynamic neuromodulation integrating neuropeptide-induced signaling pathway activity with membrane electrophysiology

We developed a multiscale model to bridge neuropeptide receptor-activated signaling pathway activity with membrane electrophysiology. Typically, the neuromodulation of biochemical signaling and biophysics have been investigated separately in modeling studies. We studied the effects of Angiotensin II (AngII) on neuronal excitability changes mediated by signaling dynamics and downstream phosphorylation of ion channels. Experiments have shown that AngII binding to the AngII receptor type-1 elicits baseline-dependent regulation of cytosolic Ca(2+) signaling. Our model simulations revealed a baseline Ca(2+)-dependent response to AngII receptor type-1 activation by AngII. Consistent with experimental observations, AngII evoked a rise in Ca(2+) when starting at a low baseline Ca(2+) level, and a decrease in Ca(2+) when starting at a higher baseline. Our analysis predicted that the kinetics of Ca(2+) transport into the endoplasmic reticulum play a critical role in shaping the Ca(2+) response. The Ca(2+) baseline also influenced the AngII-induced excitability changes such that lower Ca(2+) levels were associated with a larger firing rate increase. We examined the relative contributions of signaling kinases protein kinase C and Ca(2+)/Calmodulin-dependent protein kinase II to AngII-mediated excitability changes by simulating activity blockade individually and in combination. We found that protein kinase C selectively controlled firing rate adaptation whereas Ca(2+)/Calmodulin-dependent protein kinase II induced a delayed effect on the firing rate increase. We tested whether signaling kinetics were necessary for the dynamic effects of AngII on excitability by simulating three scenarios of AngII-mediated KDR channel phosphorylation: (1), an increased steady state; (2), a step-change increase; and (3), dynamic modulation. Our results revealed that the kinetics emerging from neuromodulatory activation of the signaling network were required to account for the dynamical changes in excitability. In summary, our integrated multiscale model provides, to our knowledge, a new approach for quantitative investigation of neuromodulatory effects on signaling and electrophysiology.

Effects of low frequency electric fields on synaptic integration in hippocampal CA1 pyramidal neurons: implications for power line emissions

The possible cognitive effects of low frequency external electric fields (EFs), such as those generated by power lines, are poorly understood. Their functional consequences for mechanisms at the single neuron level are very difficult to study and identify experimentally, especially in vivo. The major open problem is that experimental investigations on humans have given inconsistent or contradictory results, making it difficult to estimate the possible effects of external low frequency electric fields on cognitive functions. Here we investigate this issue with realistic models of hippocampal CA1 pyramidal neurons. Our findings suggest how and why EFs, with environmentally observed frequencies and intensities far lower than what is required for direct neural activation, can perturb dendritic signal processing and somatic firing of neurons that are crucially involved in cognitive tasks such as learning and memory. These results show that individual neuronal morphology, ion channel dendritic distribution, and alignment with the electric field are major determinants of overall effects, and provide a physiologically plausible explanation of why experimental findings can appear to be small and difficult to reproduce, yet deserve serious consideration.

Effects of SKF83959 on the excitability of hippocampal CA1 pyramidal neurons: a modeling study

AIM

3-Methyl-6-chloro-7,8-hydroxy-1-(3-methylphenyl)-2,3,4,5-tetrahydro-1H-3-benzazepine (SKF83959) have been shown to affect several types of voltage-dependent channels in hippocampal pyramidal neurons. The aim of this study was to determine how modulation of a individual type of the channels by SKF83959 contributes to the overall excitability of CA1 pyramidal neurons during either direct current injections or synaptic activation.

METHODS

Rat hippocampal slices were prepared. The kinetics of voltage-dependent Na(+) channels and neuronal excitability and depolarization block in CA1 pyramidal neurons were examined using whole-cell recording. A realistic mathematical model of hippocampal CA1 pyramidal neuron was used to simulate the effects of SKF83959 on neuronal excitability.

RESULTS

SKF83959 (50 μmol/L) shifted the inactivation curve of Na(+) current by 10.3 mV but had no effect on the activation curve in CA1 pyramidal neurons. The effects of SKF83959 on passive membrane properties, including a decreased input resistance and depolarized resting potential, predicted by our simulations were in agreement with the experimental data. The simulations showed that decreased excitability of the soma by SKF83959 (examined with current injection at the soma) was only observed when the membrane potential was compensated to the control levels, whereas the decreased dendritic excitability (examined with current injection at the dendrite) was found even without membrane potential compensation, which led to a decreased number of action potentials initiated at the soma. Moreover, SKF83959 significantly facilitated depolarization block in CA1 pyramidal neurons. SKF83959 decreased EPSP temporal summation and, of physiologically greater relevance, the synaptic-driven firing frequency.

CONCLUSION

SKF83959 decreased the excitability of CA1 pyramidal neurons even though the drug caused the membrane potential depolarization. The results may reveal a partial mechanism for the drug's anti-Parkinsonian effects and may also suggest that SKF83959 has a potential antiepileptic effect.

Reaction-diffusion in the NEURON simulator

In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library.

Functional impact of dendritic branch-point morphology

Cortical pyramidal cells store multiple features of complex synaptic input in individual dendritic branches and independently regulate the coupling between dendritic and somatic spikes. Branch points in apical trees exhibit wide ranges of sizes and shapes, and the large diameter ratio between trunk and oblique dendrites exacerbates impedance mismatch. The morphological diversity of dendritic bifurcations could thus locally tune neuronal excitability and signal integration. However, these aspects have never been investigated. Here, we first quantified the morphological variability of branch points from two-photon images of rat CA1 pyramidal neurons. We then investigated the geometrical features affecting spike initiation, propagation, and timing with a computational model validated by glutamate uncaging experiments. The results suggest that even subtle membrane readjustments at branch points could drastically alter the ability of synaptic input to generate, propagate, and time action potentials.

Neuronal morphology goes digital: a research hub for cellular and system neuroscience

The importance of neuronal morphology in brain function has been recognized for over a century. The broad applicability of "digital reconstructions" of neuron morphology across neuroscience subdisciplines has stimulated the rapid development of numerous synergistic tools for data acquisition, anatomical analysis, three-dimensional rendering, electrophysiological simulation, growth models, and data sharing. Here we discuss the processes of histological labeling, microscopic imaging, and semiautomated tracing. Moreover, we provide an annotated compilation of currently available resources in this rich research "ecosystem" as a central reference for experimental and computational neuroscience.

Modeling of the nervous system: from modulation of glutamatergic and gabaergic molecular dynamics to neuron spiking activity

One of the fundamental characteristics of the brain is its hierarchical and temporal organization: scales in both space and time must be considered to fully grasp the system's underlying mechanisms and their impact on brain function. Complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. These integrations across hierarchies of the nervous system are sufficiently complex to have impeded the development of routine multi-level modeling methodologies. The present study describes an example of our multiscale efforts to rise from the biomolecular level to the neuron level. We more specifically describe how we integrate biomolecular mechanisms taking place at glutamatergic and gabaergic synapses and integrate them to study the impact of these modifications on spiking activity of a CA1 pyramidal cell in the hippocampus.

Progressive effect of beta amyloid peptides accumulation on CA1 pyramidal neurons: a model study suggesting possible treatments

Several independent studies show that accumulation of β-amyloid (Aβ) peptides, one of the characteristic hallmark of Alzheimer's Disease (AD), can affect normal neuronal activity in different ways. However, in spite of intense experimental work to explain the possible underlying mechanisms of action, a comprehensive and congruent understanding is still lacking. Part of the problem might be the opposite ways in which Aβ have been experimentally found to affect the normal activity of a neuron; for example, making a neuron more excitable (by reducing the A- or DR-type K⁺ currents) or less excitable (by reducing synaptic transmission and Na⁺ current). The overall picture is therefore confusing, since the interplay of many mechanisms makes it difficult to link individual experimental findings with the more general problem of understanding the progression of the disease. This is an important issue, especially for the development of new drugs trying to ameliorate the effects of the disease. We addressed these paradoxes through computational models. We first modeled the different stages of AD by progressively modifying the intrinsic membrane and synaptic properties of a realistic model neuron, while accounting for multiple and different experimental findings and by evaluating the contribution of each mechanism to the overall modulation of the cell's excitability. We then tested a number of manipulations of channel and synaptic activation properties that could compensate for the effects of Aβ. The model predicts possible therapeutic treatments in terms of pharmacological manipulations of channels' kinetic and activation properties. The results also suggest how and which mechanisms can be targeted by a drug to restore the original firing conditions.

Modeling of the nervous system: from molecular dynamics and synaptic modulation to neuron spiking activity

The brain is a perfect example of an integrated multi-scale system, as the complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. In the present study we illustrate our approach to model and simulate the spatio-temporal complexity of the nervous system by developing a multi-scale model integrating synaptic models into the neuronal and ultimately network levels. We apply this approach to a concrete example and demonstrate how changes at the level of kinetic parameters of a receptor model are translated into significant changes in the firing of a pyramidal neuron. These results illustrate the abilities of our modeling approach and support its direct application to the evaluation of the effects of drugs, from functional target to integrated system.

Integrated multiscale modeling of the nervous system: predicting changes in hippocampal network activity by a positive AMPA receptor modulator

One of the fundamental characteristics of the brain is its hierarchical organization. Scales in both space and time that must be considered when integrating across hierarchies of the nervous system are sufficiently great as to have impeded the development of routine multilevel modeling methodologies. Complex molecular interactions at the level of receptors and channels regulate activity at the level of neurons; interactions between multiple populations of neurons ultimately give rise to complex neural systems function and behavior. This spatial complexity takes place in the context of a composite temporal integration of multiple, different events unfolding at the millisecond, second, minute, hour, and longer time scales. In this study, we present a multiscale modeling methodology that integrates synaptic models into single neuron, and multineuron, network models. We have applied this approach to the specific problem of how changes at the level of kinetic parameters of a receptor-channel model are translated into changes in the temporal firing pattern of a single neuron, and ultimately, changes in the spatiotemporal activity of a network of neurons. These results demonstrate how this powerful methodology can be applied to understand the effects of a given local process within multiple hierarchical levels of the nervous system.

Multiple firing patterns in deep dorsal horn neurons of the spinal cord: computational analysis of mechanisms and functional implications

Deep dorsal horn relay neurons (dDHNs) of the spinal cord are known to exhibit multiple firing patterns under the control of local metabotropic neuromodulation: tonic firing, plateau potential, and spontaneous oscillations. This work investigates the role of interactions between voltage-gated channels and the occurrence of different firing patterns and then correlates these two phenomena with their functional role in sensory information processing. We designed a conductance-based model using the NEURON software package, which successfully reproduced the classical features of plateau in dDHNs, including a wind-up of the neuronal response after repetitive stimulation. This modeling approach allowed us to systematically test the impact of conductance interactions on the firing patterns. We found that the expression of multiple firing patterns can be reproduced by changes in the balance between two currents (L-type calcium and potassium inward rectifier conductances). By investigating a possible generalization of the firing state switch, we found that the switch can also occur by varying the balance of any hyperpolarizing and depolarizing conductances. This result extends the control of the firing switch to neuromodulators or to network effects such as synaptic inhibition. We observed that the switch between the different firing patterns occurs as a continuous function in the model, revealing a particular intermediate state called the accelerating mode. To characterize the functional effect of a firing switch on information transfer, we used correlation analysis between a model of peripheral nociceptive afference and the dDHN model. The simulation results indicate that the accelerating mode was the optimal firing state for information transfer.