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

Bridging Hierarchies in Multi-Scale Models of Neural Systems: Look-Up Tables Enable Computationally Efficient Simulations of Non-linear Synaptic Dynamics

Synapses are critical actors of neuronal transmission as they form the basis of chemical communication between neurons. Accurate computational models of synaptic dynamics may prove important in elucidating emergent properties across hierarchical scales. Yet, in large-scale neuronal network simulations, synapses are often modeled as highly simplified linear exponential functions due to their small computational footprint. However, these models cannot capture the complex non-linear dynamics that biological synapses exhibit and thus, are insufficient in representing synaptic behavior accurately. Existing detailed mechanistic synapse models can replicate these non-linear dynamics by modeling the underlying kinetics of biological synapses, but their high complexity prevents them from being a suitable option in large-scale models due to long simulation times. This motivates the development of more parsimonious models that can capture the complex non-linear dynamics of synapses accurately while maintaining a minimal computational cost. We propose a look-up table approach that stores precomputed values thereby circumventing most computations at runtime and enabling extremely fast simulations for glutamatergic receptors AMPAr and NMDAr. Our results demonstrate that this methodology is capable of replicating the dynamics of biological synapses as accurately as the mechanistic synapse models while offering up to a 56-fold increase in speed. This powerful approach allows for multi-scale neuronal networks to be simulated at large scales, enabling the investigation of how low-level synaptic activity may lead to changes in high-level phenomena, such as memory and learning.

Modeling Nonlinear Synaptic Dynamics: A Laguerre-Volterra Network Framework for Improved Computational Efficiency in Large Scale Simulations

Synapses are key components in signal transmission in the brain, often exhibiting complex non-linear dynamics. Yet, they are often crudely modelled as linear exponential equations in large-scale neuron network simulations. Mechanistic models that use detailed channel receptor kinetics more closely replicate the nonlinear dynamics observed at synapses, but use of such models are generally restricted to small scale simulations due to their computational complexity. Previously, we have developed an ``input-output'' (IO) synapse model using the Volterra functional series to estimate nonlinear synaptic dynamics. Here, we present an improvement on the IO synapse model using the extbf{Laguerre-Volterra network (LVN) framework. We demonstrate that utilization of the LVN framework helps reduce memory requirements and improves the simulation speed in comparison to the previous iteration of the IO synapse model. We present results that demonstrate the accuracy, memory efficiency, and speed of the LVN model that can be extended to simulations with large numbers of synapses. Our efforts enable complex nonlinear synaptic dynamics to be modelled in large-scale network models, allowing us to explore how synaptic activity may influence network behavior and affects memory, learning, and neurodegenerative diseases.

A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics

In synapses, calcium is required for modulating synaptic transmission, plasticity, synaptogenesis, and synaptic pruning. The regulation of calcium dynamics within neurons involves cellular mechanisms such as synaptically activated channels and pumps, calcium buffers, and calcium sequestrating organelles. Many experimental studies tend to focus on only one or a small number of these mechanisms, as technical limitations make it difficult to observe all features at once. Computational modeling enables incorporation of many of these properties together, allowing for more complete and integrated studies. However, the scale of existing detailed models is often limited to synaptic and dendritic compartments as the computational burden rapidly increases when these models are integrated in cellular or network level simulations. In this article we present a computational model of calcium dynamics at the postsynaptic spine of a CA1 pyramidal neuron, as well as a methodology that enables its implementation in multi-scale, large-scale simulations. We first present a mechanistic model that includes individually validated models of various components involved in the regulation of calcium at the spine. We validated our mechanistic model by comparing simulated calcium levels to experimental data found in the literature. We performed additional simulations with the mechanistic model to determine how the simulated calcium activity varies with respect to presynaptic-postsynaptic stimulation intervals and spine distance from the soma. We then developed an input-output (IO) model that complements the mechanistic calcium model and provide a computationally efficient representation for use in larger scale modeling studies; we show the performance of the IO model compared to the mechanistic model in terms of accuracy and speed. The models presented here help achieve two objectives. First, the mechanistic model provides a comprehensive platform to describe spine calcium dynamics based on individual contributing factors. Second, the IO model is trained on the main dynamical features of the mechanistic model and enables nonlinear spine calcium modeling on the cell and network level simulation scales. Utilizing both model representations provide a multi-level perspective on calcium dynamics, originating from the molecular interactions at spines and propagating the effects to higher levels of activity involved in network behavior.

Towards the virtual human patient. Quantitative Systems Pharmacology in Alzheimer's disease

Development of successful therapeutic interventions in Central Nervous Systems (CNS) disorders is a daunting challenge with a low success rate. Probable reasons include the lack of translation from preclinical animal models, the individual variability of many pathological processes converging upon the same clinical phenotype, the pharmacodynamical interaction of various comedications and last but not least the complexity of the human brain. This paper argues for a re-engineering of the pharmaceutical CNS Research & Development strategy using ideas focused on advanced computer modeling and simulation from adjacent engineering-based industries. We provide examples that such a Quantitative Systems Pharmacology approach based on computer simulation of biological processes and that combines the best of preclinical research with actual clinical outcomes can enhance translation to the clinical situation. We will expand upon (1) the need to go from Big Data to Smart Data and develop predictive and quantitative algorithms that are actionable for the pharma industry, (2) using this platform as a "knowledge machine" that captures community-wide expertise in an active hypothesis-testing approach, (3) learning from failed clinical trials and (4) the need to go beyond simple linear hypotheses and embrace complex non-linear hypotheses. We will propose a strategy for applying these concepts to the substantial individual variability of AD patient subgroups and the treatment of neuropsychiatric problems in AD. Quantitative Systems Pharmacology is a new 'humanized' tool for supporting drug discovery and development in general and CNS disorders in particular.

Calcium Hypothesis of Alzheimer's disease and brain aging: A framework for integrating new evidence into a comprehensive theory of pathogenesis

This article updates the Calcium Hypothesis of Alzheimer's disease and brain aging on the basis of emerging evidence since 1994 (The present article, with the subtitle "New evidence for a central role of Ca²⁺ in neurodegeneration," includes three appendices that provide context and further explanations for the rationale for the revisions in the updated hypothesis-the three appendices are as follows: Appendix I "Emerging concepts on potential pathogenic roles of [Ca²⁺]," Appendix II "Future studies to validate the central role of dysregulated [Ca²⁺] in neurodegeneration," and Appendix III "Epilogue: towards a comprehensive hypothesis.") (Marx J. Fresh evidence points to an old suspect: calcium. Science 2007; 318:384-385). The aim is not only to re-evaluate the original key claims of the hypothesis with a critical eye but also to identify gaps in knowledge required to validate relevant claims and delineate additional studies and/or data that are needed. Some of the key challenges for this effort included examination of questions regarding (1) the temporal and spatial relationships of molecular mechanisms that regulate neuronal calcium ion (Ca²⁺), (2) the role of changes in concentration of calcium ion [Ca²⁺] in various subcellular compartments of neurons, (3) how alterations in Ca²⁺ signaling affect the performance of neurons under various conditions, ranging from optimal functioning in a healthy state to conditions of decline and deterioration in performance during aging and in disease, and (4) new ideas about the contributions of aging, genetic, and environmental factors to the causal relationships between dysregulation of [Ca²⁺] and the functioning of neurons (see Appendices I and II). The updated Calcium Hypothesis also includes revised postulates that are intended to promote further crucial experiments to confirm or reject the various predictions of the hypothesis (see Appendix III).

A comparison between direct and indirect measurements of neurotransmitter vesicle release dynamics: a computational study

Presynaptic vesicular release of neurotransmitters is a stochastic process involving complex mechanisms triggered by an elevation of calcium concentration. The mechanisms behind neurotransmitters release play a critical role in synaptic function and plasticity. Understanding its properties, both in term of its dynamics and its underlying mechanisms, may therefore help further our understanding of synaptic plasticity. However, measuring vesicle release dynamics is experimentally challenging. One experimental protocol used to determine the dynamic properties of vesicle release is to measure postsynaptic current. However, this method inherently not only captures properties of the release itself, but also the contributions from the postsynaptic receptors. Here we propose to use a synapse simulation platform known as EONS/RHENOMS to capture the functional properties of vesicle release, separate from the dynamics known to be associated with postsynaptic receptors, and compare the results with those determined experimentally. We find that despite attempts to reduce interference of postsynaptic dynamics, the receptor channel properties, particularly desensitization, may influence the overall measured results significantly. Re-estimating release rate by taking into account the contributions of postsynaptic receptors may give further insight into release dynamics and further our overall understanding on synaptic plasticity.

On the computation of a retina resistivity profile for applications in multi-scale modeling of electrical stimulation and absorption

This study proposes a methodology for computationally estimating resistive properties of tissue in multi-scale computational models, used for studying the interaction of electromagnetic fields with neural tissue, with applications to both dosimetry and neuroprosthetics. Traditionally, models at bulk tissue- and cellular-level scales are solved independently, linking resulting voltage from existing resistive tissue-scale models as extracellular sources to cellular models. This allows for solving the effects that external electric fields have on cellular activity. There are two major limitations to this approach: first, the resistive properties of the tissue need to be chosen, of which there are contradicting measurements in literature; second, the measurements of resistivity themselves may be inaccurate, leading to the mentioned contradicting results found across different studies. Our proposed methodology allows for constructing computed resistivity profiles using knowledge of only the neural morphology within the multi-scale model, resulting in a practical implementation of the effective medium theory; this bypasses concerns regarding the choice of resistive properties and accuracy of measurement setups. A multi-scale model of retina is constructed with an external electrode to serve as a test bench for analyzing existing and resulting resistivity profiles, and validation is presented through the reconstruction of a published resistivity profile of retina tissue. Results include a computed resistivity profile of retina tissue for use with a retina multi-scale model used to analyze effects of external electric fields on neural activity.

Modeling and simulation of organophosphate-induced neurotoxicity: Prediction and validation by experimental studies

Exposure to organophosphorus (OP) compounds, either pesticides or chemical warfare agents, represents a major health problem. As potent irreversible inhibitors of cholinesterase, OP may induce seizures, as in status epilepticus, and occasionally brain lesions. Although these compounds are extremely toxic agents, the search for novel antidotes remains extremely limited. In silico modeling constitutes a useful tool to identify pharmacological targets and to develop efficient therapeutic strategies. In the present work, we developed a new in silico simulator in order to predict the neurotoxicity of irreversible inhibitors of acetyl- and/or butyrylcholinesterase (ChE) as well as the potential neuroprotection provided by antagonists of cholinergic muscarinic and glutamate N-methyl-d-aspartate (NMDA) receptors. The simulator reproduced firing of CA1 hippocampal neurons triggered by exposure to paraoxon (POX), as found in patch-clamp recordings in in vitro mouse hippocampal slices. In the case of POX intoxication, it predicted a preventing action of the muscarinic receptor antagonist atropine sulfate, as well as a synergistic action with the non-competitive NMDA receptor antagonist memantine. These in silico predictions relative to beneficial effects of atropine sulfate combined with memantine were recapitulated experimentally in an in vivo model of POX in adult male Swiss mice using electroencephalic (EEG) recordings. Thus, our simulator is a new powerful tool to identify protective therapeutic strategies against OP central effects, by screening various combinations of muscarinic and NMDA receptor antagonists.

A multi-scale computational model for the study of retinal prosthetic stimulation

An implantable retinal prosthesis has been developed to restore vision to patients who have been blinded by degenerative diseases that destroy photoreceptors. By electrically stimulating the surviving retinal cells, the damaged photoreceptors may be bypassed and limited vision can be restored. While this has been shown to restore partial vision, the understanding of how cells react to this systematic electrical stimulation is largely unknown. Better predictive models and a deeper understanding of neural responses to electrical stimulation is necessary for designing a successful prosthesis. In this work, a computational model of an epi-retinal implant was built and simulated, spanning multiple spatial scales, including a large-scale model of the retina and implant electronics, as well as underlying neuronal networks.

Synaptic Efficacy as a Function of Ionotropic Receptor Distribution: A Computational Study

Glutamatergic synapses are the most prevalent functional elements of information processing in the brain. Changes in pre-synaptic activity and in the function of various post-synaptic elements contribute to generate a large variety of synaptic responses. Previous studies have explored postsynaptic factors responsible for regulating synaptic strength variations, but have given far less importance to synaptic geometry, and more specifically to the subcellular distribution of ionotropic receptors. We analyzed the functional effects resulting from changing the subsynaptic localization of ionotropic receptors by using a hippocampal synaptic computational framework. The present study was performed using the EONS (Elementary Objects of the Nervous System) synaptic modeling platform, which was specifically developed to explore the roles of subsynaptic elements as well as their interactions, and that of synaptic geometry. More specifically, we determined the effects of changing the localization of ionotropic receptors relative to the presynaptic glutamate release site, on synaptic efficacy and its variations following single pulse and paired-pulse stimulation protocols. The results indicate that changes in synaptic geometry do have consequences on synaptic efficacy and its dynamics.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

AMPA receptor potentiators: from drug design to cognitive enhancement

Positive allosteric modulators of ionotropic glutamate receptors have emerged as a target for treating cognitive impairment and neurodegeneration, but also mental illnesses such as major depressive disorder. The possibility of creating a new class of pharmaceutical agent to treat refractive mental health issues has compelled researchers to redouble their efforts to develop a safe, effective treatment for memory and cognition impairments. Coupled with the more robust research methodologies that have emerged, including more sophisticated high-throughput-screens, higher resolution structural biology techniques, and more focused assessment on pharmacokinetics, the development of positive modulators of AMPA receptors holds great promise. We describe recent approaches that improve our understanding of the basic physiology underlying memory and cognition, and their application toward promoting human health.

Pharmacological enhancement of memory or cognition in normal subjects

The possibility of expanding memory or cognitive capabilities above the levels in high functioning individuals is a topic of intense discussion among scientists and in society at large. The majority of animal studies use behavioral endpoint measures; this has produced valuable information but limited predictability for human outcomes. Accordingly, several groups are pursuing a complementary strategy with treatments targeting synaptic events associated with memory encoding or forebrain network operations. Transcription and translation figure prominently in substrate work directed at enhancement. Notably, the question of why new proteins would be needed for a now-forming memory given that learning-driven synthesis presumably occurred throughout the immediate past has been largely ignored. Despite this conceptual problem, and some controversy, recent studies have reinvigorated the idea that selective gene manipulation is a plausible route to enhancement. Efforts to improve memory by facilitating synaptic encoding of information have also progressed, in part due of breakthroughs on mechanisms that stabilize learning-related, long-term potentiation (LTP). These advances point to a reductionistic hypothesis for a diversity of experimental results on enhancement, and identify under-explored possibilities. Cognitive enhancement remains an elusive goal, in part due to the difficulty of defining the target. The popular view of cognition as a collection of definable computations seems to miss the fluid, integrative process experienced by high functioning individuals. The neurobiological approach obviates these psychological issues to directly test the consequences of improving throughput in networks underlying higher order behaviors. The few relevant studies testing drugs that selectively promote excitatory transmission indicate that it is possible to expand cortical networks engaged by complex tasks and that this is accompanied by capabilities not found in normal animals.

Hypothesizing the body's genius to trigger and self-organize its healing: 25 years using a standardized neurophysics therapy

We aim for this contribution to operate bi-directionally, both as a "bedside to bench" reverse-translational fractal physiological hypothesis and as a methodological innovation to inform clinical practice. In 25 years using gym equipment therapeutically in non-research settings, the standardized therapy is consistently observed to trigger universal responses of micro to macro waves of system transition dynamics in the human nervous system. These are associated with observably desirable impacts on disorders, injuries, diseases, and athletic performance. Requisite conditions are therapeutic coaching, erect posture, extremely slow movements in mild resistance exercises, and executive control over arousal and attention. To motivate research into the physiological improvements and in validation studies, we integrate from across disciplines to hypothesize explanations for the relationships among the methods, the system dynamics, and evident results. Key hypotheses include: (1) Correctly-directed system efforts may reverse a system's heretofore misdirected efforts, restoring healthier neurophysiology. (2) The enhanced information processing accompanying good posture is an essential initial condition. (3) Behaviors accompanying exercises performed with few degrees of freedom amplify information processing, triggering destabilization and transition dynamics. (4) Executive control over arousal and attention is essential to release system constraints, amplifying and complexifying information. (5) The dynamics create necessary and in many cases evidently sufficient conditions for the body to resolve or improve its own conditions within often short time periods. Literature indicates how the human system possesses material self-awareness. A broad explanation for the nature and effects of the therapy appears rooted in the cascading recursions of the systems' dynamics, which appear to trigger health-fostering self-reorganizing processes when this therapy provides catalytic initial conditions.

A machine learning method for the prediction of receptor activation in the simulation of synapses

Chemical synaptic transmission involves the release of a neurotransmitter that diffuses in the extracellular space and interacts with specific receptors located on the postsynaptic membrane. Computer simulation approaches provide fundamental tools for exploring various aspects of the synaptic transmission under different conditions. In particular, Monte Carlo methods can track the stochastic movements of neurotransmitter molecules and their interactions with other discrete molecules, the receptors. However, these methods are computationally expensive, even when used with simplified models, preventing their use in large-scale and multi-scale simulations of complex neuronal systems that may involve large numbers of synaptic connections. We have developed a machine-learning based method that can accurately predict relevant aspects of the behavior of synapses, such as the percentage of open synaptic receptors as a function of time since the release of the neurotransmitter, with considerably lower computational cost compared with the conventional Monte Carlo alternative. The method is designed to learn patterns and general principles from a corpus of previously generated Monte Carlo simulations of synapses covering a wide range of structural and functional characteristics. These patterns are later used as a predictive model of the behavior of synapses under different conditions without the need for additional computationally expensive Monte Carlo simulations. This is performed in five stages: data sampling, fold creation, machine learning, validation and curve fitting. The resulting procedure is accurate, automatic, and it is general enough to predict synapse behavior under experimental conditions that are different to the ones it has been trained on. Since our method efficiently reproduces the results that can be obtained with Monte Carlo simulations at a considerably lower computational cost, it is suitable for the simulation of high numbers of synapses and it is therefore an excellent tool for multi-scale simulations.

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.

Has the time come for predictive computer modeling in CNS drug discovery and development?

We discuss whether a new paradigm, quantitative systems pharmacology (QSP), based on computational neuroscience modeling combined with proper drug target engagement and pharmacology, human pathology, imaging studies, and calibration and validation using clinical studies in human subjects might improve the success rate of central nervous systems research and development (CNS R&D) projects. We suggest that an improved understanding of neuronal circuit interactions using a humanized computer-based integration of physiology and pharmacology knowledge can substantially de-risk new CNS projects.

A computational model to investigate astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking

Over the past decades, our view of astrocytes has switched from passive support cells to active processing elements in the brain. The current view is that astrocytes shape neuronal communication and also play an important role in many neurodegenerative diseases. Despite the growing awareness of the importance of astrocytes, the exact mechanisms underlying neuron-astrocyte communication and the physiological consequences of astrocytic-neuronal interactions remain largely unclear. In this work, we define a modeling framework that will permit to address unanswered questions regarding the role of astrocytes. Our computational model of a detailed glutamatergic synapse facilitates the analysis of neural system responses to various stimuli and conditions that are otherwise difficult to obtain experimentally, in particular the readouts at the sub-cellular level. In this paper, we extend a detailed glutamatergic synaptic model, to include astrocytic glutamate transporters. We demonstrate how these glial transporters, responsible for the majority of glutamate uptake, modulate synaptic transmission mediated by ionotropic AMPA and NMDA receptors at glutamatergic synapses. Furthermore, we investigate how these local signaling effects at the synaptic level are translated into varying spatio-temporal patterns of neuron firing. Paired pulse stimulation results reveal that the effect of astrocytic glutamate uptake is more apparent when the input inter-spike interval is sufficiently long to allow the receptors to recover from desensitization. These results suggest an important functional role of astrocytes in spike timing dependent processes and demand further investigation of the molecular basis of certain neurological diseases specifically related to alterations in astrocytic glutamate uptake, such as epilepsy.