Neural mass models (NMMs) are important for helping us interpret observations of brain dynamics. They provide a means to understand data in terms of mechanisms such as synaptic interactions between excitatory and inhibitory neuronal populations. To interpret data using NMMs we need to quantitatively compare the output of NMMs with data, and thereby find parameter values for which the model can produce the observed dynamics. Mapping dynamics to NMM parameter values in this way has the potential to improve our understanding of the brain in health and disease. Though abstract, NMMs still comprise of many parameters that are difficult to constrain a priori. This makes it challenging to explore the dynamics of NMMs and elucidate regions of parameter space in which their dynamics best approximate data. Existing approaches to overcome this challenge use a combination of linearising models, constraining the values they can take and exploring restricted subspaces by fixing the values of many parameters a priori. As such, we have little knowledge of the extent to which different regions of parameter space of NMMs can yield dynamics that approximate data, how nonlinearities in models can affect parameter mapping or how best to quantify similarities between model output and data. These issues need to be addressed in order to fully understand the potential and limitations of NMMs, and to aid the development of new models of brain dynamics in the future. To begin to overcome these issues, we present a global nonlinear approach to recovering parameters of NMMs from data. We use global optimisation to explore all parameters of nonlinear NMMs simultaneously, in a minimally constrained way. We do this using multi-objective optimisation (multi-objective evolutionary algorithm, MOEA) so that multiple data features can be quantified. In particular, we use the weighted horizontal visibility graph (wHVG), which is a flexible framework for quantifying different aspects of time series, by converting them into networks. We study EEG alpha activity recorded during the eyes closed resting state from 20 healthy individuals and demonstrate that the MOEA performs favourably compared to single objective approaches. The addition of the wHVG objective allows us to better constrain the model output, which leads to the recovered parameter values being restricted to smaller regions of parameter space, thus improving the practical identifiability of the model. We then use the MOEA to study differences in the alpha rhythm observed in EEG recorded from 20 people with epilepsy. We find that a small number of parameters can explain this difference and that, counterintuitively, the mean excitatory synaptic gain parameter is reduced in people with epilepsy compared to control. In addition, we propose that the MOEA could be used to mine for the presence of pathological rhythms, and demonstrate the application of this to epileptiform spike-wave discharges.

The circadian clock orchestrates biological processes so that they occur at specific times of the day, thereby facilitating adaptation to diurnal and seasonal environmental changes. In plants, mathematical modelling has been comprehensively integrated with experimental studies to gain a better mechanistic understanding of the complex genetic regulatory network comprising the clock. However, with an increasing number of circadian genes being discovered, there is a pressing need for methods facilitating the expansion of computational models to incorporate these newly-discovered components. Conventionally, plant clock models have comprised differential equation systems based on Michaelis-Menten kinetics. However, the difficulties associated with modifying interactions using this approach-and the concomitant problem of robustly identifying regulation types-has contributed to a complexity bottleneck, with quantitative fits to experimental data rapidly becoming computationally intractable for models possessing more than ≈50 parameters. Here, we address these issues by constructing the first plant clock models based on the S-System formalism originally developed by Savageau for analysing biochemical networks. We show that despite its relative simplicity, this approach yields clock models with comparable accuracy to the conventional Michaelis-Menten formalism. The S-System formulation also confers several key advantages in terms of model construction and expansion. In particular, it simplifies the inclusion of new interactions, whilst also facilitating the modification of regulation types, thereby making it well-suited to network inference. Furthermore, S-System models mitigate the issue of parameter identifiability. Finally, by applying linear systems theory to the models considered, we provide some justification for the increased use of aggregated protein equations in recent plant clock modelling, replacing the separate cytoplasmic/nuclear protein compartments that were characteristic of the earlier models. We conclude that as well as providing a simplified framework for model development, the S-System formalism also possesses significant potential as a robust modelling method for designing synthetic gene circuits.

Stochastic differential equations (SDEs) are widely used to model systems affected by random processes. In general, the analysis of an SDE model requires numerical solutions to be generated many times over multiple parameter combinations. However, this process often requires considerable computational resources to be practicable. Due to the embarrassingly parallel nature of the task, devices such as multi-core processors and graphics processing units (GPUs) can be employed for acceleration. Here, we present SODECL (https://github.com/avramidis/sodecl), a software library that utilizes such devices to calculate multiple orbits of an SDE model. To evaluate the acceleration provided by SODECL, we compared the time required to calculate multiple orbits of an exemplar stochastic model when one CPU core is used, to the time required when using all CPU cores or a GPU. In addition, to assess scalability, we investigated how model size affected execution time on different parallel compute devices. Our results show that when using all 32 CPU cores of a high-end high-performance computing node, the task is accelerated by a factor of up to ≈6.7, compared to when using a single CPU core. Executing the task on a high-end GPU yielded accelerations of up to ≈4.5, compared to a single CPU core.

MOTIVATION: Model selection and parameter inference are complex problems of long-standing interest in systems biology. Selecting between competing models arises commonly as underlying biochemical mechanisms are often not fully known, hence alternative models must be considered. Parameter inference yields important information on the extent to which the data and the model constrain parameter values. RESULTS: We report Dizzy-Beats, a graphical Java Bayesian evidence analysis tool implementing nested sampling - an algorithm yielding an estimate of the log of the Bayesian evidence Z and the moments of model parameters, thus addressing two outstanding challenges in systems modelling. A likelihood function based on the L1-norm is adopted as it is generically applicable to replicated time series data. AVAILABILITY AND IMPLEMENTATION: http://sourceforge.net/p/bayesevidence/home/Home/.

SUMMARY: Complex computational experiments in Systems Biology, such as fitting model parameters to experimental data, can be challenging to perform. Not only do they frequently require a high level of computational power, but the software needed to run the experiment needs to be usable by scientists with varying levels of computational expertise, and modellers need to be able to obtain up-to-date experimental data resources easily. We have developed a software suite, the Systems Biology Software Infrastructure (SBSI), to facilitate the parameter-fitting process. SBSI is a modular software suite composed of three major components: SBSINumerics, a high-performance library containing parallelized algorithms for performing parameter fitting; SBSIDispatcher, a middleware application to track experiments and submit jobs to back-end servers; and SBSIVisual, an extensible client application used to configure optimization experiments and view results. Furthermore, we have created a plugin infrastructure to enable project-specific modules to be easily installed. Plugin developers can take advantage of the existing user-interface and application framework to customize SBSI for their own uses, facilitated by SBSI's use of standard data formats. AVAILABILITY AND IMPLEMENTATION: All SBSI binaries and source-code are freely available from http://sourceforge.net/projects/sbsi under an Apache 2 open-source license. The server-side SBSINumerics runs on any Unix-based operating system; both SBSIVisual and SBSIDispatcher are written in Java and are platform independent, allowing use on Windows, Linux and Mac OS X. The SBSI project website at http://www.sbsi.ed.ac.uk provides documentation and tutorials.