Brain metabolism after therapeutic hypothermia for murine hypoxia-ischemia using hyperpolarized [1-13C] pyruvate magnetic resonance spectroscopy.

Hypoxic-ischemic encephalopathy (HIE) is a common neurological syndrome in newborns with high mortality and morbidity. Therapeutic hypothermia (TH), which is standard of care for HIE, mitigates brain injury by suppressing anaerobic metabolism. However, more than 40% of HIE neonates have a poor outcome, even after TH. This study aims to provide metabolic biomarkers for predicting the outcomes of hypoxia-ischemia (HI) after TH using hyperpolarized [1-13C] pyruvate magnetic resonance spectroscopy. Postnatal day 10 (P10) mice with HI underwent TH at 1 h and were scanned at 6-8 h (P10), 24 h (P11), 7 days (P17), and 21 days (P31) post-HI on a 14.1-T NMR spectrometer. The metabolic images were collected, and the conversion rate from pyruvate to lactate and the ratio of lactate to pyruvate in the injured left hemisphere (kPL(L) and Lac/Pyr(L), respectively) were calculated at each timepoint. The outcomes of TH were determined by the assessments of brain injury on T2-weighted images and behavioral tests at later timepoint. kPL(L) and Lac/Pyr(L) over time between the good-outcome and poor-outcome groups and across timepoints within groups were analyzed. We found significant differences in temporal trends of kPL(L) and Lac/Pyr(L) between groups. In the good-outcome group, kPL(L) increased until P31 with a significantly higher value at P31 compared with that at P10, while the level of Lac/Pyr(L) at P31 was notably higher than those at all other timepoints. In the poor-outcome group, kPL(L) and Lac/Pyr(L) increased within 24 h. The kPL(L) value at P11 was considerably higher compared with P10. Discrete temporal changes of kPL(L) and Lac/Pyr(L) after TH between the good-outcome and poor-outcome groups were seen as early as 24 h after HI, reflecting various TH effects on brain anaerobic metabolism, which may provide insights for early screening for response to TH.

CellRemorph: A Toolkit for Transforming, Selecting, and Slicing 3D Cell Structures on the Road to Morphologically Detailed Astrocyte Simulations.

Understanding functions of astrocytes can be greatly enhanced by building and simulating computational models that capture their morphological details. Novel computational tools enable utilization of existing morphological data of astrocytes and building models that have appropriate level of details for specific simulation purposes. In addition to analyzing existing computational tools for constructing, transforming, and assessing astrocyte morphologies, we present here the CellRemorph toolkit implemented as an add-on for Blender, a 3D modeling platform increasingly recognized for its utility for manipulating 3D biological data. To our knowledge, CellRemorph is the first toolkit for transforming astrocyte morphologies from polygonal surface meshes into adjustable surface point clouds and vice versa, precisely selecting nanoprocesses, and slicing morphologies into segments with equal surface areas or volumes. CellRemorph is an open-source toolkit under the GNU General Public License and easily accessible via an intuitive graphical user interface. CellRemorph will be a valuable addition to other Blender add-ons, providing novel functionality that facilitates the creation of realistic astrocyte morphologies for different types of morphologically detailed simulations elucidating the role of astrocytes both in health and disease.

Analysis of Network Models with Neuron-Astrocyte Interactions.

Neural networks, composed of many neurons and governed by complex interactions between them, are a widely accepted formalism for modeling and exploring global dynamics and emergent properties in brain systems. In the past decades, experimental evidence of computationally relevant neuron-astrocyte interactions, as well as the astrocytic modulation of global neural dynamics, have accumulated. These findings motivated advances in computational glioscience and inspired several models integrating mechanisms of neuron-astrocyte interactions into the standard neural network formalism. These models were developed to study, for example, synchronization, information transfer, synaptic plasticity, and hyperexcitability, as well as classification tasks and hardware implementations. We here focus on network models of at least two neurons interacting bidirectionally with at least two astrocytes that include explicitly modeled astrocytic calcium dynamics. In this study, we analyze the evolution of these models and the biophysical, biochemical, cellular, and network mechanisms used to construct them. Based on our analysis, we propose how to systematically describe and categorize interaction schemes between cells in neuron-astrocyte networks. We additionally study the models in view of the existing experimental data and present future perspectives. Our analysis is an important first step towards understanding astrocytic contribution to brain functions. However, more advances are needed to collect comprehensive data about astrocyte morphology and physiology in vivo and to better integrate them in data-driven computational models. Broadening the discussion about theoretical approaches and expanding the computational tools is necessary to better understand astrocytes' roles in brain functions.

Neuron-Glia Interactions and Brain Circuits.

Recent evidence suggests that glial cells take an active role in a number of brain functions that were previously attributed solely to neurons. For example, astrocytes, one type of glial cells, have been shown to promote coordinated activation of neuronal networks, modulate sensory-evoked neuronal network activity, and influence brain state transitions during development. This reinforces the idea that astrocytes not only provide the "housekeeping" for the neurons, but that they also play a vital role in supporting and expanding the functions of brain circuits and networks. Despite this accumulated knowledge, the field of computational neuroscience has mostly focused on modeling neuronal functions, ignoring the glial cells and the interactions they have with the neurons. In this chapter, we introduce the biology of neuron-glia interactions, summarize the existing computational models and tools, and emphasize the glial properties that may be important in modeling brain functions in the future.

Astrocyte-mediated spike-timing-dependent long-term depression modulates synaptic properties in the developing cortex.

Astrocytes have been shown to modulate synaptic transmission and plasticity in specific cortical synapses, but our understanding of the underlying molecular and cellular mechanisms remains limited. Here we present a new biophysicochemical model of a somatosensory cortical layer 4 to layer 2/3 synapse to study the role of astrocytes in spike-timing-dependent long-term depression (t-LTD) in vivo. By applying the synapse model and electrophysiological data recorded from rodent somatosensory cortex, we show that a signal from a postsynaptic neuron, orchestrated by endocannabinoids, astrocytic calcium signaling, and presynaptic N-methyl-D-aspartate receptors coupled with calcineurin signaling, induces t-LTD which is sensitive to the temporal difference between post- and presynaptic firing. We predict for the first time the dynamics of astrocyte-mediated molecular mechanisms underlying t-LTD and link complex biochemical networks at presynaptic, postsynaptic, and astrocytic sites to the time window of t-LTD induction. During t-LTD a single astrocyte acts as a delay factor for fast neuronal activity and integrates fast neuronal sensory processing with slow non-neuronal processing to modulate synaptic properties in the brain. Our results suggest that astrocytes play a critical role in synaptic computation during postnatal development and are of paramount importance in guiding the development of brain circuit functions, learning and memory.

Cerebellar Purkinje cells control eye movements with a rapid rate code that is invariant to spike irregularity.

The rate and temporal pattern of neural spiking each have the potential to influence computation. In the cerebellum, it has been hypothesized that the irregularity of interspike intervals in Purkinje cells affects their ability to transmit information to downstream neurons. Accordingly, during oculomotor behavior in mice and rhesus monkeys, mean irregularity of Purkinje cell spiking varied with mean eye velocity. However, moment-to-moment variations revealed a tight correlation between eye velocity and spike rate, with no additional information conveyed by spike irregularity. Moreover, when spike rate and irregularity were independently controlled using optogenetic stimulation, the eye movements elicited were well-described by a linear population rate code with 3-5 ms temporal precision. Biophysical and random-walk models identified biologically realistic parameter ranges that determine whether spike irregularity influences responses downstream. The results demonstrate cerebellar control of movements through a remarkably rapid rate code, with no evidence for an additional contribution of spike irregularity.

Challenges in Reproducibility, Replicability, and Comparability of Computational Models and Tools for Neuronal and Glial Networks, Cells, and Subcellular Structures.

The possibility to replicate and reproduce published research results is one of the biggest challenges in all areas of science. In computational neuroscience, there are thousands of models available. However, it is rarely possible to reimplement the models based on the information in the original publication, let alone rerun the models just because the model implementations have not been made publicly available. We evaluate and discuss the comparability of a versatile choice of simulation tools: tools for biochemical reactions and spiking neuronal networks, and relatively new tools for growth in cell cultures. The replicability and reproducibility issues are considered for computational models that are equally diverse, including the models for intracellular signal transduction of neurons and glial cells, in addition to single glial cells, neuron-glia interactions, and selected examples of spiking neuronal networks. We also address the comparability of the simulation results with one another to comprehend if the studied models can be used to answer similar research questions. In addition to presenting the challenges in reproducibility and replicability of published results in computational neuroscience, we highlight the need for developing recommendations and good practices for publishing simulation tools and computational models. Model validation and flexible model description must be an integral part of the tool used to simulate and develop computational models. Constant improvement on experimental techniques and recording protocols leads to increasing knowledge about the biophysical mechanisms in neural systems. This poses new challenges for computational neuroscience: extended or completely new computational methods and models may be required. Careful evaluation and categorization of the existing models and tools provide a foundation for these future needs, for constructing multiscale models or extending the models to incorporate additional or more detailed biophysical mechanisms. Improving the quality of publications in computational neuroscience, enabling progressive building of advanced computational models and tools, can be achieved only through adopting publishing standards which underline replicability and reproducibility of research results.

Computational Models for Calcium-Mediated Astrocyte Functions.

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

Reproducibility and Comparability of Computational Models for Astrocyte Calcium Excitability.

The scientific community across all disciplines faces the same challenges of ensuring accessibility, reproducibility, and efficient comparability of scientific results. Computational neuroscience is a rapidly developing field, where reproducibility and comparability of research results have gained increasing interest over the past years. As the number of computational models of brain functions is increasing, we chose to address reproducibility using four previously published computational models of astrocyte excitability as an example. Although not conventionally taken into account when modeling neuronal systems, astrocytes have been shown to take part in a variety of in vitro and in vivo phenomena including synaptic transmission. Two of the selected astrocyte models describe spontaneous calcium excitability, and the other two neurotransmitter-evoked calcium excitability. We specifically addressed how well the original simulation results can be reproduced with a reimplementation of the models. Additionally, we studied how well the selected models can be reused and whether they are comparable in other stimulation conditions and research settings. Unexpectedly, we found out that three of the model publications did not give all the necessary information required to reimplement the models. In addition, we were able to reproduce the original results of only one of the models completely based on the information given in the original publications and in the errata. We actually found errors in the equations provided by two of the model publications; after modifying the equations accordingly, the original results were reproduced more accurately. Even though the selected models were developed to describe the same biological event, namely astrocyte calcium excitability, the models behaved quite differently compared to one another. Our findings on a specific set of published astrocyte models stress the importance of proper validation of the models against experimental wet-lab data from astrocytes as well as the careful review process of models. A variety of aspects of model development could be improved, including the presentation of models in publications and databases. Specifically, all necessary mathematical equations, as well as parameter values, initial values of variables, and stimuli used should be given precisely for successful reproduction of scientific results.

Sustainable computational science: the ReScience initiative.

Computer science offers a large set of tools for prototyping, writing, running, testing, validating, sharing and reproducing results; however, computational science lags behind. In the best case, authors may provide their source code as a compressed archive and they may feel confident their research is reproducible. But this is not exactly true. James Buckheit and David Donoho proposed more than two decades ago that an article about computational results is advertising, not scholarship. The actual scholarship is the full software environment, code, and data that produced the result. This implies new workflows, in particular in peer-reviews. Existing journals have been slow to adapt: source codes are rarely requested and are hardly ever actually executed to check that they produce the results advertised in the article. ReScience is a peer-reviewed journal that targets computational research and encourages the explicit replication of already published research, promoting new and open-source implementations in order to ensure that the original research can be replicated from its description. To achieve this goal, the whole publishing chain is radically different from other traditional scientific journals. ReScience resides on GitHub where each new implementation of a computational study is made available together with comments, explanations, and software tests.

Computational study of noise in a large signal transduction network.

BACKGROUND: Biochemical systems are inherently noisy due to the discrete reaction events that occur in a random manner. Although noise is often perceived as a disturbing factor, the system might actually benefit from it. In order to understand the role of noise better, its quality must be studied in a quantitative manner. Computational analysis and modeling play an essential role in this demanding endeavor. RESULTS: We implemented a large nonlinear signal transduction network combining protein kinase C, mitogen-activated protein kinase, phospholipase A2, and ß isoform of phospholipase C networks. We simulated the network in 300 different cellular volumes using the exact Gillespie stochastic simulation algorithm and analyzed the results in both the time and frequency domain. In order to perform simulations in a reasonable time, we used modern parallel computing techniques. The analysis revealed that time and frequency domain characteristics depend on the system volume. The simulation results also indicated that there are several kinds of noise processes in the network, all of them representing different kinds of low-frequency fluctuations. In the simulations, the power of noise decreased on all frequencies when the system volume was increased. CONCLUSIONS: We concluded that basic frequency domain techniques can be applied to the analysis of simulation results produced by the Gillespie stochastic simulation algorithm. This approach is suited not only to the study of fluctuations but also to the study of pure noise processes. Noise seems to have an important role in biochemical systems and its properties can be numerically studied by simulating the reacting system in different cellular volumes. Parallel computing techniques make it possible to run massive simulations in hundreds of volumes and, as a result, accurate statistics can be obtained from computational studies.

Modeling signal transduction leading to synaptic plasticity: evaluation and comparison of five models.

An essential phenomenon of the functional brain is synaptic plasticity which is associated with changes in the strength of synapses between neurons. These changes are affected by both extracellular and intracellular mechanisms. For example, intracellular phosphorylation-dephosphorylation cycles have been shown to possess a special role in synaptic plasticity. We, here, provide the first computational comparison of models for synaptic plasticity by evaluating five models describing postsynaptic signal transduction networks. Our simulation results show that some of the models change their behavior completely due to varying total concentrations of protein kinase and phosphatase. Furthermore, the responses of the models vary when models are compared to each other. Based on our study, we conclude that there is a need for a general setup to objectively compare the models and an urgent demand for the minimum criteria that a computational model for synaptic plasticity needs to meet.

Effects of transmitters and amyloid-beta peptide on calcium signals in rat cortical astrocytes: Fura-2AM measurements and stochastic model simulations.

BACKGROUND: To better understand the complex molecular level interactions seen in the pathogenesis of Alzheimer's disease, the results of the wet-lab and clinical studies can be complemented by mathematical models. Astrocytes are known to become reactive in Alzheimer's disease and their ionic equilibrium can be disturbed by interaction of the released and accumulated transmitters, such as serotonin, and peptides, including amyloid- peptides (A). We have here studied the effects of small amounts of A25-35 fragments on the transmitter-induced calcium signals in astrocytes by Fura-2AM fluorescence measurements and running simulations of the detected calcium signals. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular calcium signals were measured in cultured rat cortical astrocytes following additions of serotonin and glutamate, or either of these transmitters together with A25-35. A25-35 increased the number of astrocytes responding to glutamate and exceedingly increased the magnitude of the serotonin-induced calcium signals. In addition to A25-35-induced effects, the contribution of intracellular calcium stores to calcium signaling was tested. When using higher stimulus frequency, the subsequent calcium peaks after the initial peak were of lower amplitude. This may indicate inadequate filling of the intracellular calcium stores between the stimuli. In order to reproduce the experimental findings, a stochastic computational model was introduced. The model takes into account the major mechanisms known to be involved in calcium signaling in astrocytes. Model simulations confirm the principal experimental findings and show the variability typical for experimental measurements. CONCLUSIONS/SIGNIFICANCE: Nanomolar A25-35 alone does not cause persistent change in the basal level of calcium in astrocytes. However, even small amounts of A25-35, together with transmitters, can have substantial synergistic effects on intracellular calcium signals. Computational modeling further helps in understanding the mechanisms associated with intracellular calcium oscillations. Modeling the mechanisms is important, as astrocytes have an essential role in regulating the neuronal microenvironment of the central nervous system.

Postsynaptic signal transduction models for long-term potentiation and depression.

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

Developing Itô stochastic differential equation models for neuronal signal transduction pathways.

Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the Itô stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain Itô stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the Itô stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the Itô stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The Itô stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values.

Discrete stochastic simulation of cell signaling: comparison of computational tools.

Several stochastic simulation tools have been developed recently for cell signaling. A comparative evaluation of the stochastic simulation tools is needed to highlight the current state of the development. In our study, we have chosen to evaluate three stochastic simulation tools: Dizzy, Systems Biology Toolbox, and Copasi, using our own MATLAB implementation as a benchmark. The Gillespie stochastic simulation algorithm is used in all tests. With all the tools, we are able to simulate stochastically the behavior of the selected test case and to produce similar results as our own MATLAB implementation. However, it is not possible to use time-dependent inputs in stochastic simulations in Systems Biology Toolbox and Copasi. The present study is one of the first evaluations of stochastic simulation tools for realistic signal transduction pathways.

Simulation tools for biochemical networks: evaluation of performance and usability.

MOTIVATION: Simulation of dynamic biochemical systems is receiving considerable attention due to increasing availability of experimental data of complex cellular functions. Numerous simulation tools have been developed for numerical simulation of the behavior of a system described in mathematical form. However, there exist only a few evaluation studies of these tools. Knowledge of the properties and capabilities of the simulation tools would help bioscientists in building models based on experimental data. RESULTS: We examine selected simulation tools that are intended for the simulation of biochemical systems. We choose four of them for more detailed study and perform time series simulations using a specific pathway describing the concentration of the active form of protein kinase C. We conclude that the simulation results are convergent between the chosen simulation tools. However, the tools differ in their usability, support for data transfer to other programs and support for automatic parameter estimation. From the experimentalists' point of view, all these are properties that need to be emphasized in the future.