Mikael Djurfeldt

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016 ), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

In multi-scale models, multiple scales, and even physical formalisms, are used in a single model [1] while simulation tools in computational neuroscience are usually specialized for a single scale and formalism [2, 3, 4]. One possibility when solving such models is to use a co-simulation methodology. Co-simulation allows model components to be simulated by different tools, running simultaneously while exchanging data. However, a naive coupling of numerical methods for different models may lead to unexpected numerical problems going far beyond those which could be expected from the individual components. With the ultimate goal of extending the MUSIC API [5] for multi-scale modeling through co-simulation by integration of numerical solvers, we have examined ways of moving beyond trial-and-error and ad-hoc methods [6, 7] when coupling solvers. We show techniques for how synchronization in bi-directional communication as well as error control [8] can be achieved in a framework motivated by waveform relaxation methods. We apply these techniques when simulating a reduced MAPK model [6] in a spine in the context of the electrical activity of the whole neuron. The model exhibits bistability. It switches from the inactive to the active stable state after current injection to the soma. In our model, the stimulus of 0.09 nA causes a Ca2+ elevation of 1 uM in the spine during the stimulation period of 5 s. This condition is sufficient to switch on P-MAPK and phosphorylate potassium channels. The electrical part of the model is formulated using Hodgkin-Huxley formalism while biochemistry is formulated by the reaction-rate equations. This model gives us a stiff problem with a coupling strength varying along the integration. We compare different techniques for achieving a balance between efficiency of coupling and accuracy of integration. This analysis will be used to set up the requirements for a generic API to perform co-simulation and, in particular, identify the signals which need to be propagated by a multi-scale API.

MUSIC [1] is a tool for co-simulation. It provides a communication API which allows neuronal simulators and other tools to ship data between each other on-line during simulation. It supports simulations in a supercomputer cluster or on a desktop. MUSIC enables the construction of simulations encompassing multiple tools and combining model components written for different simulators. MUSIC is compatible with common MPI implementations such as OpenMPI and MPICH and is known to run on a variety of machines such as IBM BG/Q, Cray XC30 and the Japan K computer. It has been used on up to 32 K processors. Here, we give an update on the status of the latest MUSIC release which includes a new scheduler and support for multiple communication algorithms. MUSIC has also been extended to allow for simultaneous use of different communication layers, e.g. combining MPI-based communication with communication over UDP. This is useful when connecting simulations to external equipment. New Python bindings enables MUSIC-connected Python scripts. Another development is integration with PyNN [2], which is a simulator-independent language for building neuronal network models. PyNN release 0.8 includes a MUSIC interface enabling scripting of MUSIC co-simulations in PyNN. MUSIC has been benchmarked on multiple architectures. This includes benchmarks with artificial neurons, focusing on communication performance, and simulations of a cortical network using the NEST simulator [3]. We present some of these results and discuss strengths, shortcomings and potential future improvements. The next development steps are outlined, including a test suite, continuous integration, a multi-scale API and opening up the MUSIC project for collaborative development, with the aim of turning MUSIC into a community-based open source software project.

The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31–42, 2008b) and an implementation in Python has been publicly released.

MUSIC is a standard API allowing large scale neuron simulators to exchange data within a parallel computer during runtime. A pilot implementation of this API has been released as open source. We provide experiences from the implementation of MUSIC interfaces for two neuronal network simulators of different kinds, NEST and MOOSE. A multi-simulation of a cortico-striatal network model involving both simulators is performed, demonstrating how MUSIC can promote inter-operability between models written for different simulators and how these can be re-used to build a larger model system. Benchmarks show that the MUSIC pilot implementation provides efficient data transfer in a cluster computer with good scaling. We conclude that MUSIC fulfills the design goal that it should be simple to adapt existing simulators to use MUSIC. In addition, since the MUSIC API enforces independence of the applications, the multi-simulation could be built from pluggable component modules without adaptation of the components to each other in terms of simulation time-step or topology of connections between the modules.

The connection-set algebra is a novel notation for the description of connectivity in neuronal network models. Both the connection structure, that is which connections exist, and parameters associated with connections can be described. An elementary set of connection patterns, connection-sets, are provided as well as a set of rules for how to compute new connection-sets from elementary ones. The design goals are to provide a description which is close to how we think about the connection pattern, is expressive enough to describe a wide range of connectivities, and, is still possible to implement in a neuronal network simulator with reasonable time and memory complexity. Special consideration is given to parallel simulators. A C++ version of the algebra has been implemented and used in a large-scale neuronal network simulation.

Is there any hope of achieving a thorough understanding of higher functions such as perception, memory, thought and emotion or is the stunning complexity of the brain a barrier which will limit such efforts for the foreseeable future? In this perspective we discuss methods to handle complexity, approaches to model building, and point to detailed large-scale models as a new contribution to the toolbox of the computational neuroscientist. We elucidate some aspects which distinguishes large-scale models and some of the technological challenges which they entail.

Background: In previous work [1], a biologically detailed model of cortical layers II/III was presented. The model exhibits phenomena such as UP/DOWN-states and states with alpha- and gamma-like rythms [2]. Although the model is based on current knowledge of cortical microcircuitry, the structure of long-range connections is determined using the working hypothesis that these layers function similarly to a recurrent attractor network. More specifically, groups of pyramidal cells within minicolumns stretching through the layers constitute functional units. Long-range connections between minicolumns collectively form a set of attractors in the network dynamics, each representing a latent memory. When the dynamic state of the network approaches an attractor, the state moves towards the attractor. Close to the attractor the memory pattern has become fully recalled; the latent memory has become active. The present work is, thus, based on the simplifying assumption that memory patterns are static. To what extent can this type of model match artificial recurrent networks with regard to memory capacity? Methods: Minicolumns in our models are further grouped into hypercolumns, each hypercolumn operating as a winner-take-all module through the mechanism of lateral inhibition. We ran simulations using two network sizes, one with 9 hypercolumns and 9 minicolumns per hypercolumn and the other with 25x25 minicolumns. Long-range connections were determined by a weight matrix obtained by training an artificial neural network. In previous models [1,2], the ANN was trained with orthogonal, non-overlapping, patterns. Here, patterns were random and overlapping. A pattern was considered correctly recalled if activation of 2/3 of the pattern resulted in recall of the full pattern with error in at most one minicolumn. Results: Figure 1 shows the number of correctly recalled patterns for weight matrices trained with different numbers of stored patterns. Ideal performance is a straight line. Results are shown for the cortex model and for an ANN with matching connection weights. For both network sizes, memory breaks down at the same point for both types of model indicating that the cortex model can match the ANN with regard to memory capacity.