STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python

Crosstalk between biochemical signalling network architecture and trafficking governs AMPAR dynamics in synaptic plasticity

Synaptic plasticity involves modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; an increase in AMPAR corresponds to strengthening of synapses while a decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signalling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Previous work in the field of deterministic modelling of CaMKII dynamics has assumed bistable kinetics, while experiments and rule-based modelling have revealed that CaMKII dynamics can be either monostable or ultrasensitive. This raises the following question: how does the choice of model assumptions involving CaMKII dynamics influence AMPAR dynamics at the synapse? To answer this question, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of different signalling and trafficking variations, along with their coupled effects, on AMPAR dynamics at the synaptic site. We find that the properties of the model including network architecture describing different stability features of CaMKII and parameters that capture the endocytosis and exocytosis of AMPAR significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (1) the choice of signalling model (bistable CaMKII or monostable CaMKII dynamics), (2) trafficking versus influx contributions and (3) frequency of stimulus. KEY POINTS: The density of AMPA receptors (AMPARs) at the postsynaptic density of the synapse provides a readout of synaptic plasticity, which involves crosstalk between complex biochemical signalling networks including CaMKII dynamics and trafficking pathways including exocytosis and endocytosis. Here we build a model that integrates CaMKII dynamics and AMPAR trafficking to explore this crosstalk. We compare different models of CaMKII that result in monostable or bistable kinetics and their impact on AMPAR dynamics. Our results show that AMPAR density depends on the coupling between aspects of biochemical signalling and trafficking. Specifically, assumptions regarding CaMKII dynamics and its stability features can alter AMPAR density at the synapse. Our model also predicts that the kinetics of trafficking versus influx of AMPAR from the extrasynaptic space can further impact AMPAR density. Thus, the contributions of both signalling and trafficking should be considered in computational models.

Ultraliser: a framework for creating multiscale, high-fidelity and geometrically realistic 3D models for in silico neuroscience

Ultraliser is a neuroscience-specific software framework capable of creating accurate and biologically realistic 3D models of complex neuroscientific structures at intracellular (e.g. mitochondria and endoplasmic reticula), cellular (e.g. neurons and glia) and even multicellular scales of resolution (e.g. cerebral vasculature and minicolumns). Resulting models are exported as triangulated surface meshes and annotated volumes for multiple applications in in silico neuroscience, allowing scalable supercomputer simulations that can unravel intricate cellular structure-function relationships. Ultraliser implements a high-performance and unconditionally robust voxelization engine adapted to create optimized watertight surface meshes and annotated voxel grids from arbitrary non-watertight triangular soups, digitized morphological skeletons or binary volumetric masks. The framework represents a major leap forward in simulation-based neuroscience, making it possible to employ high-resolution 3D structural models for quantification of surface areas and volumes, which are of the utmost importance for cellular and system simulations. The power of Ultraliser is demonstrated with several use cases in which hundreds of models are created for potential application in diverse types of simulations. Ultraliser is publicly released under the GNU GPL3 license on GitHub (BlueBrain/Ultraliser).

SIGNIFICANCE

There is crystal clear evidence on the impact of cell shape on its signaling mechanisms. Structural models can therefore be insightful to realize the function; the more realistic the structure can be, the further we get insights into the function. Creating realistic structural models from existing ones is challenging, particularly when needed for detailed subcellular simulations. We present Ultraliser, a neuroscience-dedicated framework capable of building these structural models with realistic and detailed cellular geometries that can be used for simulations.

HillTau: A fast, compact abstraction for model reduction in biochemical signaling networks

Signaling networks mediate many aspects of cellular function. The conventional, mechanistically motivated approach to modeling such networks is through mass-action chemistry, which maps directly to biological entities and facilitates experimental tests and predictions. However such models are complex, need many parameters, and are computationally costly. Here we introduce the HillTau form for signaling models. HillTau retains the direct mapping to biological observables, but it uses far fewer parameters, and is 100 to over 1000 times faster than ODE-based methods. In the HillTau formalism, the steady-state concentration of signaling molecules is approximated by the Hill equation, and the dynamics by a time-course tau. We demonstrate its use in implementing several biochemical motifs, including association, inhibition, feedforward and feedback inhibition, bistability, oscillations, and a synaptic switch obeying the BCM rule. The major use-cases for HillTau are system abstraction, model reduction, scaffolds for data-driven optimization, and fast approximations to complex cellular signaling.

Chemical signals mediate many computations in cells, from housekeeping functions in all cells to memory and pattern selectivity in neurons. These signals form complex networks of interactions. Computer models are a powerful way to study how such networks behave, but it is hard to get all the chemical details for typical models, and it is slow to run them with standard numerical approaches to chemical kinetics. We introduce HillTau as a simplified way to model complex chemical networks. HillTau models condense multiple reaction steps into single steps defined by a small number of parameters for activation and settling time. As a result the models are simple, easy to find values for, and they run quickly. Remarkably, they fit the full chemical formulations rather well. We illustrate the utility of HillTau for modeling several signaling network functions, and for fitting complicated signaling networks.

Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

A novel approach to simulate simple protein-ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein-protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein-protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package.

Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Deep learning of the role of interleukin IL-17 and its action in promoting cancer

In breast cancer patients, metastasis remains a major cause of death. The metastasis formation process is given by an interaction between the cancer cells and the microenvironment that surrounds them. In this article, we develop a mathematical model that analyzes the role of interleukin IL-17 and its action in promoting cancer and in facilitating tissue metastasis in breast cancer, using a dynamic analysis based on a stochastic process that accounts for the local and global action of this molecule. The model uses the Ornstein–Uhlembeck and Markov process in continuous time. It focuses on the oncological expansion and the interaction between the interleukin IL-17 and cell populations This analysis tends to clarify the processes underlying the metastasis expansion mechanism both for a better understanding of the pathological event and for a possible better control of therapeutic strategies.

IL-17 is a proinflammatory interleukin that acts when there is tissue damage or when there is a pathological situation caused by an external pathogen or by a pathological condition such as cancer.

This research is focused on the role of interleukin IL-17 which, especially in the case of breast cancer, turns out to be a dominant “communication pin” since it interconnects with the activity of different cell populations affected by the oncological phenomenon. Stochastic modeling strategies, specially the Ornstein-Uhlenbeck process, with the aid of numerical algorithms are elaborated in this review.

The role of IL-17 is discussed in this manuscript at all the stages of cancer. It is discussed that IL-17 also acts as “metastasis promoter” as a result of its proinflammatory nature. The stochastic nature of IL-17 is discussed based on the evidence provided by recent literature.

The resulting dynamical analysis can help to select the most appropriate therapeutic strategy.

Cancer cells, in the case of breast cancer, have high level of IL-17 receptors (IL-17R); therefore the interleukin itself has direct effects on these cells. Immunotherapy research, focused on this cytokine and interlinked with the stochastic modeling, seems to be a promising avenue.

Gibbs free energy change of a discrete chemical reaction event

In modeling the interior of cells by simulating a reaction-diffusion master equation over a grid of compartments, one employs the assumption that the copy numbers of various chemical species are small, discrete quantities. We show that, in this case, textbook expressions for the change in Gibbs free energy accompanying a chemical reaction or diffusion between adjacent compartments are inaccurate. We derive exact expressions for these free energy changes for the case of discrete copy numbers and show how these expressions reduce to traditional expressions under a series of successive approximations leveraging the relative sizes of the stoichiometric coefficients and the copy numbers of the solutes and solvent. Numerical results are presented to corroborate the claim that if the copy numbers are treated as discrete quantities, then only these more accurate expressions lead to correct behavior. Thus, the newly derived expressions are critical for correctly computing entropy production in mesoscopic simulations based on the reaction-diffusion master equation formalism.

Stochastic self-tuning hybrid algorithm for reaction-diffusion systems

Many biochemical phenomena involve reactants with vastly different concentrations, some of which are amenable to continuum-level descriptions, while the others are not. We present a hybrid self-tuning algorithm to model such systems. The method combines microscopic (Brownian) dynamics for diffusion with mesoscopic (Gillespie-type) methods for reactions and remains efficient in a wide range of regimes and scenarios with large variations of concentrations. Its accuracy, robustness, and versatility are balanced by redefining propensities and optimizing the mesh size and time step. We use a bimolecular reaction to demonstrate the potential of our method in a broad spectrum of scenarios: from almost completely reaction-dominated systems to cases where reactions rarely occur or take place very slowly. The simulation results show that the number of particles present in the system does not degrade the performance of our method. This makes it an accurate and computationally efficient tool to model complex multireaction systems.

CoreNEURON : An Optimized Compute Engine for the NEURON Simulator

The NEURON simulator has been developed over the past three decades and is widely used by neuroscientists to model the electrical activity of neuronal networks. Large network simulation projects using NEURON have supercomputer allocations that individually measure in the millions of core hours. Supercomputer centers are transitioning to next generation architectures and the work accomplished per core hour for these simulations could be improved by an order of magnitude if NEURON was able to better utilize those new hardware capabilities. In order to adapt NEURON to evolving computer architectures, the compute engine of the NEURON simulator has been extracted and has been optimized as a library called CoreNEURON. This paper presents the design, implementation, and optimizations of CoreNEURON. We describe how CoreNEURON can be used as a library with NEURON and then compare performance of different network models on multiple architectures including IBM BlueGene/Q, Intel Skylake, Intel MIC and NVIDIA GPU. We show how CoreNEURON can simulate existing NEURON network models with 4-7x less memory usage and 2-7x less execution time while maintaining binary result compatibility with NEURON.

A Closed-Loop Toolchain for Neural Network Simulations of Learning Autonomous Agents

Neural network simulation is an important tool for generating and evaluating hypotheses on the structure, dynamics, and function of neural circuits. For scientific questions addressing organisms operating autonomously in their environments, in particular where learning is involved, it is crucial to be able to operate such simulations in a closed-loop fashion. In such a set-up, the neural agent continuously receives sensory stimuli from the environment and provides motor signals that manipulate the environment or move the agent within it. So far, most studies requiring such functionality have been conducted with custom simulation scripts and manually implemented tasks. This makes it difficult for other researchers to reproduce and build upon previous work and nearly impossible to compare the performance of different learning architectures. In this work, we present a novel approach to solve this problem, connecting benchmark tools from the field of machine learning and state-of-the-art neural network simulators from computational neuroscience. The resulting toolchain enables researchers in both fields to make use of well-tested high-performance simulation software supporting biologically plausible neuron, synapse and network models and allows them to evaluate and compare their approach on the basis of standardized environments with various levels of complexity. We demonstrate the functionality of the toolchain by implementing a neuronal actor-critic architecture for reinforcement learning in the NEST simulator and successfully training it on two different environments from the OpenAI Gym. We compare its performance to a previously suggested neural network model of reinforcement learning in the basal ganglia and a generic Q-learning algorithm.

Multiscale Stochastic Reaction-Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations

Two multiscale algorithms for stochastic simulations of reaction-diffusion processes are analysed. They are applicable to systems which include regions with significantly different concentrations of molecules. In both methods, a domain of interest is divided into two subsets where continuous-time Markov chain models and stochastic partial differential equations (SPDEs) are used, respectively. In the first algorithm, Markov chain (compartment-based) models are coupled with reaction-diffusion SPDEs by considering a pseudo-compartment (also called an overlap or handshaking region) in the SPDE part of the computational domain right next to the interface. In the second algorithm, no overlap region is used. Further extensions of both schemes are presented, including the case of an adaptively chosen boundary between different modelling approaches.

Simulation of calcium signaling in fine astrocytic processes: Effect of spatial properties on spontaneous activity

Astrocytes, a glial cell type of the central nervous system, have emerged as detectors and regulators of neuronal information processing. Astrocyte excitability resides in transient variations of free cytosolic calcium concentration over a range of temporal and spatial scales, from sub-microdomains to waves propagating throughout the cell. Despite extensive experimental approaches, it is not clear how these signals are transmitted to and integrated within an astrocyte. The localization of the main molecular actors and the geometry of the system, including the spatial organization of calcium channels IP3R, are deemed essential. However, as most calcium signals occur in astrocytic ramifications that are too fine to be resolved by conventional light microscopy, most of those spatial data are unknown and computational modeling remains the only methodology to study this issue. Here, we propose an IP3R-mediated calcium signaling model for dynamics in such small sub-cellular volumes. To account for the expected stochasticity and low copy numbers, our model is both spatially explicit and particle-based. Extensive simulations show that spontaneous calcium signals arise in the model via the interplay between excitability and stochasticity. The model reproduces the main forms of calcium signals and indicates that their frequency crucially depends on the spatial organization of the IP3R channels. Importantly, we show that two processes expressing exactly the same calcium channels can display different types of calcium signals depending on the spatial organization of the channels. Our model with realistic process volume and calcium concentrations successfully reproduces spontaneous calcium signals that we measured in calcium micro-domains with confocal microscopy and predicts that local variations of calcium indicators might contribute to the diversity of calcium signals observed in astrocytes. To our knowledge, this model is the first model suited to investigate calcium dynamics in fine astrocytic processes and to propose plausible mechanisms responsible for their variability.

FindSim: A Framework for Integrating Neuronal Data and Signaling Models

Current experiments touch only small but overlapping parts of very complex subcellular signaling networks in neurons. Even with modern optical reporters and pharmacological manipulations, a given experiment can only monitor and control a very small subset of the diverse, multiscale processes of neuronal signaling. We have developed FindSim (Framework for Integrating Neuronal Data and SIgnaling Models) to anchor models to structured experimental datasets. FindSim is a framework for integrating many individual electrophysiological and biochemical experiments with large, multiscale models so as to systematically refine and validate the model. We use a structured format for encoding the conditions of many standard physiological and pharmacological experiments, specifying which parts of the model are involved, and comparing experiment outcomes with model output. A database of such experiments is run against successive generations of composite cellular models to iteratively improve the model against each experiment, while retaining global model validity. We suggest that this toolchain provides a principled and scalable way to tackle model complexity and diversity of data sources.

Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics

Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. The extracellular medium of neural tissue is an active medium of neuromodulators, ions, inflammatory cells, oxygen, NO and other gases, with additional physiological, pharmacological and pathological agents. These extracellular agents influence, and are influenced by, cellular electrophysiology, and cellular chemophysiology-the complex internal cellular milieu of second-messenger signaling and cascades. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction-the proportion of space in which species are able to diffuse, and tortuosity-the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke. Simulation results were verified against analytic results and against the extracellular portion of the simulation run under FiPy. The creation of this NEURON interface provides a pathway for interoperability that can be used to automatically export this class of models into complex intracellular/extracellular simulations and future cross-simulator standardization.

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.

Extremely Scalable Spiking Neuronal Network Simulation Code: From Laptops to Exascale Computers

State-of-the-art software tools for neuronal network simulations scale to the largest computing systems available today and enable investigations of large-scale networks of up to 10 % of the human cortex at a resolution of individual neurons and synapses. Due to an upper limit on the number of incoming connections of a single neuron, network connectivity becomes extremely sparse at this scale. To manage computational costs, simulation software ultimately targeting the brain scale needs to fully exploit this sparsity. Here we present a two-tier connection infrastructure and a framework for directed communication among compute nodes accounting for the sparsity of brain-scale networks. We demonstrate the feasibility of this approach by implementing the technology in the NEST simulation code and we investigate its performance in different scaling scenarios of typical network simulations. Our results show that the new data structures and communication scheme prepare the simulation kernel for post-petascale high-performance computing facilities without sacrificing performance in smaller systems.

Spatially extended hybrid methods: a review

Many biological and physical systems exhibit behaviour at multiple spatial, temporal or population scales. Multiscale processes provide challenges when they are to be simulated using numerical techniques. While coarser methods such as partial differential equations are typically fast to simulate, they lack the individual-level detail that may be required in regions of low concentration or small spatial scale. However, to simulate at such an individual level throughout a domain and in regions where concentrations are high can be computationally expensive. Spatially coupled hybrid methods provide a bridge, allowing for multiple representations of the same species in one spatial domain by partitioning space into distinct modelling subdomains. Over the past 20 years, such hybrid methods have risen to prominence, leading to what is now a very active research area across multiple disciplines including chemistry, physics and mathematics. There are three main motivations for undertaking this review. Firstly, we have collated a large number of spatially extended hybrid methods and presented them in a single coherent document, while comparing and contrasting them, so that anyone who requires a multiscale hybrid method will be able to find the most appropriate one for their need. Secondly, we have provided canonical examples with algorithms and accompanying code, serving to demonstrate how these types of methods work in practice. Finally, we have presented papers that employ these methods on real biological and physical problems, demonstrating their utility. We also consider some open research questions in the area of hybrid method development and the future directions for the field.

ViSimpl: Multi-View Visual Analysis of Brain Simulation Data

After decades of independent morphological and functional brain research, a key point in neuroscience nowadays is to understand the combined relationships between the structure of the brain and its components and their dynamics on multiple scales, ranging from circuits of neurons at micro or mesoscale to brain regions at macroscale. With such a goal in mind, there is a vast amount of research focusing on modeling and simulating activity within neuronal structures, and these simulations generate large and complex datasets which have to be analyzed in order to gain the desired insight. In such context, this paper presents ViSimpl, which integrates a set of visualization and interaction tools that provide a semantic view of brain data with the aim of improving its analysis procedures. ViSimpl provides 3D particle-based rendering that allows visualizing simulation data with their associated spatial and temporal information, enhancing the knowledge extraction process. It also provides abstract representations of the time-varying magnitudes supporting different data aggregation and disaggregation operations and giving also focus and context clues. In addition, ViSimpl tools provide synchronized playback control of the simulation being analyzed. Finally, ViSimpl allows performing selection and filtering operations relying on an application called NeuroScheme. All these views are loosely coupled and can be used independently, but they can also work together as linked views, both in centralized and distributed computing environments, enhancing the data exploration and analysis procedures.

Reproducibility in Computational Neuroscience Models and Simulations

OBJECTIVE

Like all scientific research, computational neuroscience research must be reproducible. Big data science, including simulation research, cannot depend exclusively on journal articles as the method to provide the sharing and transparency required for reproducibility.

METHODS

Ensuring model reproducibility requires the use of multiple standard software practices and tools, including version control, strong commenting and documentation, and code modularity.

RESULTS

Building on these standard practices, model-sharing sites and tools have been developed that fit into several categories: 1) standardized neural simulators; 2) shared computational resources; 3) declarative model descriptors, ontologies, and standardized annotations; and 4) model-sharing repositories and sharing standards.

CONCLUSION

A number of complementary innovations have been proposed to enhance sharing, transparency, and reproducibility. The individual user can be encouraged to make use of version control, commenting, documentation, and modularity in development of models. The community can help by requiring model sharing as a condition of publication and funding.

SIGNIFICANCE

Model management will become increasingly important as multiscale models become larger, more detailed, and correspondingly more difficult to manage by any single investigator or single laboratory. Additional big data management complexity will come as the models become more useful in interpreting experiments, thus increasing the need to ensure clear alignment between modeling data, both parameters and results, and experiment.

BluePyOpt: Leveraging Open Source Software and Cloud Infrastructure to Optimise Model Parameters in Neuroscience

At many scales in neuroscience, appropriate mathematical models take the form of complex dynamical systems. Parameterizing such models to conform to the multitude of available experimental constraints is a global non-linear optimisation problem with a complex fitness landscape, requiring numerical techniques to find suitable approximate solutions. Stochastic optimisation approaches, such as evolutionary algorithms, have been shown to be effective, but often the setting up of such optimisations and the choice of a specific search algorithm and its parameters is non-trivial, requiring domain-specific expertise. Here we describe BluePyOpt, a Python package targeted at the broad neuroscience community to simplify this task. BluePyOpt is an extensible framework for data-driven model parameter optimisation that wraps and standardizes several existing open-source tools. It simplifies the task of creating and sharing these optimisations, and the associated techniques and knowledge. This is achieved by abstracting the optimisation and evaluation tasks into various reusable and flexible discrete elements according to established best-practices. Further, BluePyOpt provides methods for setting up both small- and large-scale optimisations on a variety of platforms, ranging from laptops to Linux clusters and cloud-based compute infrastructures. The versatility of the BluePyOpt framework is demonstrated by working through three representative neuroscience specific use cases.

Revealing neuronal function through microelectrode array recordings

Microelectrode arrays and microprobes have been widely utilized to measure neuronal activity, both in vitro and in vivo. The key advantage is the capability to record and stimulate neurons at multiple sites simultaneously. However, unlike the single-cell or single-channel resolution of intracellular recording, microelectrodes detect signals from all possible sources around every sensor. Here, we review the current understanding of microelectrode signals and the techniques for analyzing them. We introduce the ongoing advancements in microelectrode technology, with focus on achieving higher resolution and quality of recordings by means of monolithic integration with on-chip circuitry. We show how recent advanced microelectrode array measurement methods facilitate the understanding of single neurons as well as network function.

Python-based geometry preparation and simulation visualization toolkits for STEPS

STEPS is a stochastic reaction-diffusion simulation engine that implements a spatial extension of Gillespie's Stochastic Simulation Algorithm (SSA) in complex tetrahedral geometries. An extensive Python-based interface is provided to STEPS so that it can interact with the large number of scientific packages in Python. However, a gap existed between the interfaces of these packages and the STEPS user interface, where supporting toolkits could reduce the amount of scripting required for research projects. This paper introduces two new supporting toolkits that support geometry preparation and visualization for STEPS simulations.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

Computational modeling of diffusion in the cerebellum

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.

Approaches and tools for modeling signaling pathways and calcium dynamics in neurons

Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.

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.

Single molecule simulations in complex geometries with embedded dynamic one-dimensional structures

Stochastic models of reaction-diffusion systems are important for the study of biochemical reaction networks where species are present in low copy numbers or if reactions are highly diffusion limited. In living cells many such systems include reactions and transport on one-dimensional structures, such as DNA and microtubules. The cytoskeleton is a dynamic structure where individual fibers move, grow, and shrink. In this paper we present a simulation algorithm that combines single molecule simulations in three-dimensional space with single molecule simulations on one-dimensional structures of arbitrary shape. Molecules diffuse and react with each other in space, they associate with and dissociate from one-dimensional structures as well as diffuse and react with each other on the one-dimensional structure. A general curve embedded in space can be approximated by a piecewise linear curve to arbitrary accuracy. The resulting algorithm is hence very flexible. Molecules bound to a curve can move by pure diffusion or via active transport, and the curve can move in space as well as grow and shrink. The flexibility and accuracy of the algorithm is demonstrated in five numerical examples.

Integration of biochemical and electrical signaling-multiscale model of the medium spiny neuron of the striatum

Neuron behavior results from the interplay between networks of biochemical processes and electrical signaling. Synaptic plasticity is one of the neuronal properties emerging from such an interaction. One of the current approaches to study plasticity is to model either its electrical aspects or its biochemical components. Among the chief reasons are the different time scales involved, electrical events happening in milliseconds while biochemical cascades respond in minutes or hours. In order to create multiscale models taking in consideration both aspects simultaneously, one needs to synchronize the two models, and exchange relevant variable values. We present a new event-driven algorithm to synchronize different neuronal models, which decreases computational time and avoids superfluous synchronizations. The algorithm is implemented in the TimeScales framework. We demonstrate its use by simulating a new multiscale model of the Medium Spiny Neuron of the Neostriatum. The model comprises over a thousand dendritic spines, where the electrical model interacts with the respective instances of a biochemical model. Our results show that a multiscale model is able to exhibit changes of synaptic plasticity as a result of the interaction between electrical and biochemical signaling. Our synchronization strategy is general enough to be used in simulations of other models with similar synchronization issues, such as networks of neurons. Moreover, the integration between the electrical and the biochemical models opens up the possibility to investigate multiscale process, like synaptic plasticity, in a more global manner, while taking into account a more realistic description of the underlying mechanisms.

Neuronize: a tool for building realistic neuronal cell morphologies

This study presents a tool, Neuronize, for building realistic three-dimensional models of neuronal cells from the morphological information extracted through computer-aided tracing applications. Neuronize consists of a set of methods designed to build 3D neural meshes that approximate the cell membrane at different resolution levels, allowing a balance to be reached between the complexity and the quality of the final model. The main contribution of the present study is the proposal of a novel approach to build a realistic and accurate 3D shape of the soma from the incomplete information stored in the digitally traced neuron, which usually consists of a 2D cell body contour. This technique is based on the deformation of an initial shape driven by the position and thickness of the first order dendrites. The addition of a set of spines along the dendrites completes the model, building a final 3D neuronal cell suitable for its visualization in a wide range of 3D environments.

Comparison of models for IP3 receptor kinetics using stochastic simulations

Inositol 1,4,5-trisphosphate receptor (IP₃R) is a ubiquitous intracellular calcium (Ca²⁺) channel which has a major role in controlling Ca²⁺ levels in neurons. A variety of computational models have been developed to describe the kinetic function of IP₃R under different conditions. In the field of computational neuroscience, it is of great interest to apply the existing models of IP₃R when modeling local Ca²⁺ transients in dendrites or overall Ca²⁺ dynamics in large neuronal models. The goal of this study was to evaluate existing IP₃R models, based on electrophysiological data. This was done in order to be able to suggest suitable models for neuronal modeling. Altogether four models (Othmer and Tang, 1993; Dawson etal., 2003; Fraiman and Dawson, 2004; Doi etal., 2005) were selected for a more detailed comparison. The selection was based on the computational efficiency of the models and the type of experimental data that was used in developing the model. The kinetics of all four models were simulated by stochastic means, using the simulation software STEPS, which implements the Gillespie stochastic simulation algorithm. The results show major differences in the statistical properties of model functionality. Of the four compared models, the one by Fraiman and Dawson (2004) proved most satisfactory in producing the specific features of experimental findings reported in literature. To our knowledge, the present study is the first detailed evaluation of IP₃R models using stochastic simulation methods, thus providing an important setting for constructing a new, realistic model of IP₃R channel kinetics for compartmental modeling of neuronal functions. We conclude that the kinetics of IP₃R with different concentrations of Ca²⁺ and IP₃ should be more carefully addressed when new models for IP₃R are developed.

Spatial simulations in systems biology: from molecules to cells

Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusion-controlled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multi-scale simulation methods.

STEPS: efficient simulation of stochastic reaction-diffusion models in realistic morphologies

Background

Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins), conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems.

Results

We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation.

Conclusion

STEPS simulates models of cellular reaction–diffusion systems with complex boundaries with high accuracy and high performance in C/C++, controlled by a powerful and user-friendly Python interface. STEPS is free for use and is available at http://steps.sourceforge.net/

Python as a federation tool for GENESIS 3.0

The GENESIS simulation platform was one of the first broad-scale modeling systems in computational biology to encourage modelers to develop and share model features and components. Supported by a large developer community, it participated in innovative simulator technologies such as benchmarking, parallelization, and declarative model specification and was the first neural simulator to define bindings for the Python scripting language. An important feature of the latest version of GENESIS is that it decomposes into self-contained software components complying with the Computational Biology Initiative federated software architecture. This architecture allows separate scripting bindings to be defined for different necessary components of the simulator, e.g., the mathematical solvers and graphical user interface. Python is a scripting language that provides rich sets of freely available open source libraries. With clean dynamic object-oriented designs, they produce highly readable code and are widely employed in specialized areas of software component integration. We employ a simplified wrapper and interface generator to examine an application programming interface and make it available to a given scripting language. This allows independent software components to be 'glued' together and connected to external libraries and applications from user-defined Python or Perl scripts. We illustrate our approach with three examples of Python scripting. (1) Generate and run a simple single-compartment model neuron connected to a stand-alone mathematical solver. (2) Interface a mathematical solver with GENESIS 3.0 to explore a neuron morphology from either an interactive command-line or graphical user interface. (3) Apply scripting bindings to connect the GENESIS 3.0 simulator to external graphical libraries and an open source three dimensional content creation suite that supports visualization of models based on electron microscopy and their conversion to computational models. Employed in this way, the stand-alone software components of the GENESIS 3.0 simulator provide a framework for progressive federated software development in computational neuroscience.

Cerebellar supervised learning revisited: biophysical modeling and degrees-of-freedom control

The biophysical models of spike-timing-dependent plasticity have explored dynamics with molecular basis for such computational concepts as coincidence detection, synaptic eligibility trace, and Hebbian learning. They overall support different learning algorithms in different brain areas, especially supervised learning in the cerebellum. Because a single spine is physically very small, chemical reactions at it are essentially stochastic, and thus sensitivity-longevity dilemma exists in the synaptic memory. Here, the cascade of excitable and bistable dynamics is proposed to overcome this difficulty. All kinds of learning algorithms in different brain regions confront with difficult generalization problems. For resolution of this issue, the control of the degrees-of-freedom can be realized by changing synchronicity of neural firing. Especially, for cerebellar supervised learning, the triangle closed-loop circuit consisting of Purkinje cells, the inferior olive nucleus, and the cerebellar nucleus is proposed as a circuit to optimally control synchronous firing and degrees-of-freedom in learning.

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.

Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology

In this paper, we present the Cellular Dynamic Simulator (CDS) for simulating diffusion and chemical reactions within crowded molecular environments. CDS is based on a novel event driven algorithm specifically designed for precise calculation of the timing of collisions, reactions and other events for each individual molecule in the environment. Generic mesh based compartments allow the creation / importation of very simple or detailed cellular structures that exist in a 3D environment. Multiple levels of compartments and static obstacles can be used to create a dense environment to mimic cellular boundaries and the intracellular space. The CDS algorithm takes into account volume exclusion and molecular crowding that may impact signaling cascades in small sub-cellular compartments such as dendritic spines. With the CDS, we can simulate simple enzyme reactions; aggregation, channel transport, as well as highly complicated chemical reaction networks of both freely diffusing and membrane bound multi-protein complexes. Components of the CDS are generally defined such that the simulator can be applied to a wide range of environments in terms of scale and level of detail. Through an initialization GUI, a simple simulation environment can be created and populated within minutes yet is powerful enough to design complex 3D cellular architecture. The initialization tool allows visual confirmation of the environment construction prior to execution by the simulator. This paper describes the CDS algorithm, design implementation, and provides an overview of the types of features available and the utility of those features are highlighted in demonstrations.

Effects of macromolecular crowding on intracellular diffusion from a single particle perspective

Compared to biochemical reactions taking place in relatively well-defined aqueous solutions in vitro, the corresponding reactions happening in vivo occur in extremely complex environments containing only 60-70% water by volume, with the remainder consisting of an undefined array of bio-molecules. In a biological setting, such extremely complex and volume-occupied solution environments are termed 'crowded'. Through a range of intermolecular forces and pseudo-forces, this complex background environment may cause biochemical reactions to behave differently to their in vitro counterparts. In this review, we seek to highlight how the complex background environment of the cell can affect the diffusion of substances within it. Engaging the subject from the perspective of a single particle's motion, we place the focus of our review on two areas: (1) experimental procedures for conducting single particle tracking experiments within cells along with methods for extracting information from these experiments; (2) theoretical factors affecting the translational diffusion of single molecules within crowded two-dimensional membrane and three-dimensional solution environments. We conclude by discussing a number of recent publications relating to intracellular diffusion in light of the reviewed material.

Trends in programming languages for neuroscience simulations

Neuroscience simulators allow scientists to express models in terms of biological concepts, without having to concern themselves with low-level computational details of their implementation. The expressiveness, power and ease-of-use of the simulator interface is critical in efficiently and accurately translating ideas into a working simulation. We review long-term trends in the development of programmable simulator interfaces, and examine the benefits of moving from proprietary, domain-specific languages to modern dynamic general-purpose languages, in particular Python, which provide neuroscientists with an interactive and expressive simulation development environment and easy access to state-of-the-art general-purpose tools for scientific computing.

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.