Modelling in biology becomes necessary when systems are complex. However, the more complex the systems are, the harder models become to read and write. The most common ways of writing models are by writing reactions on species (discrete objects), or by writing rate equations for the populations of such species. One problem with such approaches is that the number of species is often so large that the model cannot be realistically enumerated. Another problem is that the number of species and reactions often fixed by default, whereas new variations of species and reactions are constantly being improvised by evolution in the long-term and moment to moment by the changing chemical environments and compartments living organisms inhabit and create within. Here we develop a modelling language Chromar that provides an extension to the representation of reactions, in which objects, called agents, carry attributes with associated types — for example, Leaf agents all have a mass attribute. Dynamics are given by stochastic rules defined on groups of agents — for example all agents of a specific type — and so enumerating the dynamics of each agent is not necessary. This compact representation addresses the first problem. Having a more compact representation can also help make models a tool for knowledge representation and exchange instead of just simulation. Further, if we think of agents as the analogue of species in reactions, then creating a new agent of some type effectively creates a new species, thereby addressing the second problem. We then develop an extension of Chromar equipped with deterministically changing time-dependent values (fluents) and aggregate values computed from the state of the system (observables). Fluents are useful for describing the context of the system, which is rarely static; observables are useful in abstracting away details of system behaviour and providing a way to observe the system during simulation. Finally, we develop an embedding of Chromar (and its extensions) in the programming language Haskell and demonstrate its applicability via two examples. Embedding Chromar in a general purpose programming language such as Haskell eases some of the constraints of modelling languages while still maintaining the naturalness of a domain-specific language.

MOTIVATION: Oscillations lie at the core of many biological processes, from the cell cycle, to circadian oscillations and developmental processes. Time-keeping mechanisms are essential to enable organisms to adapt to varying conditions in environmental cycles, from day/night to seasonal. Transcriptional regulatory networks are one of the mechanisms behind these biological oscillations. However, while identifying cyclically expressed genes from time series measurements is relatively easy, determining the structure of the interaction network underpinning the oscillation is a far more challenging problem. RESULTS: Here, we explicitly leverage the oscillatory nature of the transcriptional signals and present a method for reconstructing network interactions tailored to this special but important class of genetic circuits. Our method is based on projecting the signal onto a set of oscillatory basis functions using a Discrete Fourier Transform. We build a Bayesian Hierarchical model within a frequency domain linear model in order to enforce sparsity and incorporate prior knowledge about the network structure. Experiments on real and simulated data show that the method can lead to substantial improvements over competing approaches if the oscillatory assumption is met, and remains competitive also in cases it is not. AVAILABILITY: DSS, experiment scripts and data are available at http://homepages.inf.ed.ac.uk/gsanguin/DSS.zip. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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.

MOTIVATION: Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. RESULTS: Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. AVAILABILITY AND IMPLEMENTATION: http://homepages.inf.ed.ac.uk/gsanguin/software.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Promoter-driven reporter genes, notably luciferase and green fluorescent protein, provide a tool for the generation of a vast array of time-course data sets from living cells and organisms. The aim of this study is to introduce a modeling framework based on stochastic differential equations (SDEs) and ordinary differential equations (ODEs) that addresses the problem of reconstructing transcription time-course profiles and associated degradation rates. The dynamical model is embedded into a Bayesian framework and inference is performed using Markov chain Monte Carlo algorithms. RESULTS: We present three case studies where the methodology is used to reconstruct unobserved transcription profiles and to estimate associated degradation rates. We discuss advantages and limits of fitting either SDEs ODEs and address the problem of parameter identifiability when model variables are unobserved. We also suggest functional forms, such as on/off switches and stimulus response functions to model transcriptional dynamics and present results of fitting these to experimental data.

METHOD: The objective of the present article is to propose and evaluate a probabilistic approach based on Bayesian networks for modelling non-homogeneous and non-linear gene regulatory processes. The method is based on a mixture model, using latent variables to assign individual measurements to different classes. The practical inference follows the Bayesian paradigm and samples the network structure, the number of classes and the assignment of latent variables from the posterior distribution with Markov Chain Monte Carlo (MCMC), using the recently proposed allocation sampler as an alternative to RJMCMC. RESULTS: We have evaluated the method using three criteria: network reconstruction, statistical significance and biological plausibility. In terms of network reconstruction, we found improved results both for a synthetic network of known structure and for a small real regulatory network derived from the literature. We have assessed the statistical significance of the improvement on gene expression time series for two different systems (viral challenge of macrophages, and circadian rhythms in plants), where the proposed new scheme tends to outperform the classical BGe score. Regarding biological plausibility, we found that the inference results obtained with the proposed method were in excellent agreement with biological findings, predicting dichotomies that one would expect to find in the studied systems. AVAILABILITY: Two supplementary papers on theoretical (T) and experi-mental (E) aspects and the datasets used in our study are available from http://www.bioss.ac.uk/associates/marco/supplement/

Eukaryotes and some prokaryotes have adapted to the 24 h day/night cycle by evolving circadian clocks. The circadian clock now controls 24-hour rhythms in very many aspects of metabolism, physiology and behaviour. Day-length (photoperiod) measurement depends on the circadian clock, so the 24 h clock mechanism also governs seasonal rhythms, such as reproduction. In the model plant species, Arabidopsis thaliana, the clock controls the expression of about 10% of genes, and this proportion is similar in other eukaryotes. Fundamental properties of the clock are shared across taxonomic groups, such as phase resetting by light signals and temperature compensation of the circadian period. All the known clock mechanisms include a gene circuit with negative feedback, involving 24 h rhythms in the levels of positive- and negatively-acting transcriptional regulators. Molecular genetics has identified 5–15 genes that are involved in constructing these regulatory loops in cyanobacteria, Drosophila, Neurospora, Arabidopsis and mouse, though other components almost certainly remain to be discovered. The protein sequences of the clock components are largely distinct to each taxonomic group but some features of the regulatory circuits are shared among groups, suggesting that the circuit architecture may be important for clock function. Circadian regulation is ubiquitous, pervasive and has complex properties, yet the number of components in the clock is relatively small, making this an excellent prototype for reverse engineering of a genetic sub-network. My experimental group has identified new components of the plant circadian clock, using the bioluminescent reporter gene luciferase (LUC) to reveal gene expression rhythms with high spatial and temporal resolution. As the details revealed by molecular genetics do not necessarily lead to greater understanding of a regulatory circuit, we have also developed differential equation models for the plant clock and photoperiod sensor, together with our collaborators in IPCR. The models incorporate molecular components in a realistic manner, so numerical simulations using the models are now directing the design and evaluation of molecular experiments. We have developed an experimentalist-friendly interface for the models, to allow other groups to use these methods (free online at http://www.amillar.org/Downloads.html webcite). David Rand and colleagues have established a novel analytical method to assess the contribution of each component of the model (RNA or protein) at each phase of the cycle. This work indicates a general explanation for the evolution of multi-loop structures, to allow flexible regulation, providing one of the design principles that may underlie the architecture of the circadian clock gene circuits. Funded by BBSRC, EPSRC and DTI. More information can be found at http://www.amillar.org webcite.