MEANS: python package for Moment Expansion Approximation, iNference and Simulation

MomentClosure.jl: automated moment closure approximations in Julia

SUMMARY

MomentClosure.jl is a Julia package providing automated derivation of the time-evolution equations of the moments of molecule numbers for virtually any chemical reaction network using a wide range of moment closure approximations. It extends the capabilities of modelling stochastic biochemical systems in Julia and can be particularly useful when exact analytic solutions of the chemical master equation are unavailable and when Monte Carlo simulations are computationally expensive.

AVAILABILITY AND IMPLEMENTATION

MomentClosure.jl is freely accessible under the MIT licence. Source code and documentation are available at https://github.com/augustinas1/MomentClosure.jl.

Compartor: A toolbox for the automatic generation of moment equations for dynamic compartment populations

Summary

Many biochemical processes in living organisms take place inside compartments that can interact with each other and remodel over time. In a recent work, we have shown how the stochastic dynamics of a compartmentalized biochemical system can be effectively studied using moment equations. With this technique, the time evolution of a compartment population is summarized using a finite number of ordinary differential equations, which can be analyzed very efficiently. However, the derivation of moment equations by hand can become time-consuming for systems comprising multiple reactants and interactions. Here we present Compartor, a toolbox that automatically generates the moment equations associated with a user-defined compartmentalized system. Through the moment equation method, Compartor renders the analysis of stochastic population models accessible to a broader scientific community.

Availability and implementation

Compartor is provided as a Python package and is available at https://pypi.org/project/compartor/. Source code and usage tutorials for Compartor are available at https://github.com/zechnerlab/Compartor.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Tellurium notebooks-An environment for reproducible dynamical modeling in systems biology

The considerable difficulty encountered in reproducing the results of published dynamical models limits validation, exploration and reuse of this increasingly large biomedical research resource. To address this problem, we have developed Tellurium Notebook, a software system for model authoring, simulation, and teaching that facilitates building reproducible dynamical models and reusing models by 1) providing a notebook environment which allows models, Python code, and narrative to be intermixed, 2) supporting the COMBINE archive format during model development for capturing model information in an exchangeable format and 3) enabling users to easily simulate and edit public COMBINE-compliant models from public repositories to facilitate studying model dynamics, variants and test cases. Tellurium Notebook, a Python–based Jupyter–like environment, is designed to seamlessly inter-operate with these community standards by automating conversion between COMBINE standards formulations and corresponding in–line, human–readable representations. Thus, Tellurium brings to systems biology the strategy used by other literate notebook systems such as Mathematica. These capabilities allow users to edit every aspect of the standards–compliant models and simulations, run the simulations in–line, and re–export to standard formats. We provide several use cases illustrating the advantages of our approach and how it allows development and reuse of models without requiring technical knowledge of standards. Adoption of Tellurium should accelerate model development, reproducibility and reuse.

There is considerable value to systems and synthetic biology in creating reproducible models. An essential element of reproducibility is the use of community standards, an often challenging undertaking for modelers. This article describes Tellurium Notebook, a tool for developing dynamical models that provides an intuitive approach to building and reusing models built with community standards. Tellurium automates embedding human–readable representations of COMBINE archives in literate coding notebooks, bringing to systems biology this strategy central to other literate notebook systems such as Mathematica. We show that the ability to easily edit this human–readable representation enables users to test models under a variety of conditions, thereby providing a way to create, reuse, and modify standard–encoded models and simulations, regardless of the user’s level of technical knowledge of said standards.

Efficient simulation of intrinsic, extrinsic and external noise in biochemical systems

Motivation

Biological cells operate in a noisy regime influenced by intrinsic, extrinsic and external noise, which leads to large differences of individual cell states. Stochastic effects must be taken into account to characterize biochemical kinetics accurately. Since the exact solution of the chemical master equation, which governs the underlying stochastic process, cannot be derived for most biochemical systems, approximate methods are used to obtain a solution.

Results

In this study, a method to efficiently simulate the various sources of noise simultaneously is proposed and benchmarked on several examples. The method relies on the combination of the sigma point approach to describe extrinsic and external variability and the τ-leaping algorithm to account for the stochasticity due to probabilistic reactions. The comparison of our method to extensive Monte Carlo calculations demonstrates an immense computational advantage while losing an acceptable amount of accuracy. Additionally, the application to parameter optimization problems in stochastic biochemical reaction networks is shown, which is rarely applied due to its huge computational burden. To give further insight, a MATLAB script is provided including the proposed method applied to a simple toy example of gene expression.

Availability and implementation

MATLAB code is available at Bioinformatics online.

Supplementary information

Supplementary data are available at Bioinformatics online.

Control mechanisms for stochastic biochemical systems via computation of reachable sets

Controlling the behaviour of cells by rationally guiding molecular processes is an overarching aim of much of synthetic biology. Molecular processes, however, are notoriously noisy and frequently nonlinear. We present an approach to studying the impact of control measures on motifs of molecular interactions that addresses the problems faced in many biological systems: stochasticity, parameter uncertainty and nonlinearity. We show that our reachability analysis formalism can describe the potential behaviour of biological (naturally evolved as well as engineered) systems, and provides a set of bounds on their dynamics at the level of population statistics: for example, we can obtain the possible ranges of means and variances of mRNA and protein expression levels, even in the presence of uncertainty about model parameters.

Computational Model Reveals Limited Correlation between Germinal Center B-Cell Subclone Abundancy and Affinity: Implications for Repertoire Sequencing

Immunoglobulin repertoire sequencing has successfully been applied to identify expanded antigen-activated B-cell clones that play a role in the pathogenesis of immune disorders. One challenge is the selection of the Ag-specific B cells from the measured repertoire for downstream analyses. A general feature of an immune response is the expansion of specific clones resulting in a set of subclones with common ancestry varying in abundance and in the number of acquired somatic mutations. The expanded subclones are expected to have BCR affinities for the Ag higher than the affinities of the naive B cells in the background population. For these reasons, several groups successfully proceeded or suggested selecting highly abundant subclones from the repertoire to obtain the Ag-specific B cells. Given the nature of affinity maturation one would expect that abundant subclones are of high affinity but since repertoire sequencing only provides information about abundancies, this can only be verified with additional experiments, which are very labor intensive. Moreover, this would also require knowledge of the Ag, which is often not available for clinical samples. Consequently, in general we do not know if the selected highly abundant subclone(s) are also the high(est) affinity subclones. Such knowledge would likely improve the selection of relevant subclones for further characterization and Ag screening. Therefore, to gain insight in the relation between subclone abundancy and affinity, we developed a computational model that simulates affinity maturation in a single GC while tracking individual subclones in terms of abundancy and affinity. We show that the model correctly captures the overall GC dynamics, and that the amount of expansion is qualitatively comparable to expansion observed from B cells isolated from human lymph nodes. Analysis of the fraction of high- and low-affinity subclones among the unexpanded and expanded subclones reveals a limited correlation between abundancy and affinity and shows that the low abundant subclones are of highest affinity. Thus, our model suggests that selecting highly abundant subclones from repertoire sequencing experiments would not always lead to the high(est) affinity B cells. Consequently, additional or alternative selection approaches need to be applied.