Dynamic publication media with the COPASI R Connector (CoRC).

In this article we show how dynamic publication media and the COPASI R Connector (CoRC) can be combined in a natural and synergistic way to communicate (biochemical) models. Dynamic publication media are becoming a popular tool for authors to effectively compose and publish their work. They are built from templates and the final documents are created dynamically. In addition, they can also be interactive. Working with dynamic publication media is made easy with the programming environment R via its integration with tools such as R Markdown, Jupyter and Shiny. Additionally, the COmplex PAthway SImulator COPASI (http://www.copasi.org), a widely used biochemical modelling toolkit, is available in R through the use of the COPASI R Connector (CoRC, https://jpahle.github.io/CoRC). Models are a common tool in the mathematical biosciences, in particular kinetic models of biochemical networks in (computational) systems biology. We focus on three application areas of dynamic publication media and CoRC: Documentation (reproducible workflows), Teaching (creating self-paced lessons) and Science Communication (immersive and engaging presentation). To illustrate these, we created six dynamic document examples in the form of R Markdown and Jupyter notebooks, hosted on the platforms GitHub, shinyapps.io, Google Colaboratory. Having code and output in one place, creating documents in template-form and the option of interactivity make the combination of dynamic documents and CoRC a versatile tool. All our example documents are freely available at https://jpahle.github.io/DynamiCoRC under the Creative Commons BY 4.0 licence.

CoRC: the COPASI R Connector.

MOTIVATION: COPASI is a biochemical simulator and model analyzer which has found widespread use in academic research, teaching and beyond. One of COPASI's strengths is its graphical user interface, and this is what most users work with. COPASI also provides a command-line tool. So far, an intuitive scripting interface that allows the creation and documentation of systems biology workflows was missing though. RESULTS: We have developed CoRC, the COPASI R Connector, an R package which provides a high-level scripting interface for COPASI. It closely mirrors the thought process of a (graphical interface) user and should therefore be very easy to use. This allows for complex workflows to be reproducibly scripted, utilizing COPASI's powerful analytic toolset in combination with R's extensive analysis and package ecosystem. AVAILABILITY AND IMPLEMENTATION: CoRC is a free and open-source R package, available via GitHub at https://jpahle.github.io/CoRC/ under the Artistic-2.0 license. SUPPLEMENTARY INFORMATION: We provide tutorial articles as well as several example scripts on the project's website.

Data Management in Computational Systems Biology: Exploring Standards, Tools, Databases, and Packaging Best Practices.

Computational systems biology involves integrating heterogeneous datasets in order to generate models. These models can assist with understanding and prediction of biological phenomena. Generating datasets and integrating them into models involves a wide range of scientific expertise. As a result these datasets are often collected by one set of researchers, and exchanged with others researchers for constructing the models. For this process to run smoothly the data and models must be FAIR-findable, accessible, interoperable, and reusable. In order for data and models to be FAIR they must be structured in consistent and predictable ways, and described sufficiently for other researchers to understand them. Furthermore, these data and models must be shared with other researchers, with appropriately controlled sharing permissions, before and after publication. In this chapter we explore the different data and model standards that assist with structuring, describing, and sharing. We also highlight the popular standards and sharing databases within computational systems biology.

Requirements for band-pass activation of Ca2+-sensitive proteins such as NFAT.

Several proteins are sensitive to frequency-modulated oscillations of calcium levels. Most of them exhibit increased activities for faster frequencies, a characteristic here referred to as high-pass activation. In contrast, the transcription factor NFAT is optimally activated at a specific frequency, a behaviour we call band-pass activation. We constructed a kinetic model of NFAT activation, confirming its ability for band-pass activation at experimentally observed frequencies. To characterise the requirements for band-pass activation further, we developed a minimal model, identifying antagonistic, calcium-dependent regulation with differently responsive regulators as essential for band-pass activation. Further, in optimisations cooperative binding proved to be an important feature for distinct frequency-decoding in models of high- and band-pass activation. A subsequent analysis of the optimised parameter sets revealed the most sensitive parameters along with additional preconditions for efficient decoding. Our analysis is not limited to NFAT, but potentially applies to any protein showing high- or band-pass activation.

COPASI and its applications in biotechnology.

COPASI is software used for the creation, modification, simulation and computational analysis of kinetic models in various fields. It is open-source, available for all major platforms and provides a user-friendly graphical user interface, but is also controllable via the command line and scripting languages. These are likely reasons for its wide acceptance. We begin this review with a short introduction describing the general approaches and techniques used in computational modeling in the biosciences. Next we introduce the COPASI package, and its capabilities, before looking at typical applications of COPASI in biotechnology.

Exploiting intrinsic fluctuations to identify model parameters.

Parameterisation of kinetic models plays a central role in computational systems biology. Besides the lack of experimental data of high enough quality, some of the biggest challenges here are identification issues. Model parameters can be structurally non-identifiable because of functional relationships. Noise in measured data is usually considered to be a nuisance for parameter estimation. However, it turns out that intrinsic fluctuations in particle numbers can make parameters identifiable that were previously non-identifiable. The authors present a method to identify model parameters that are structurally non-identifiable in a deterministic framework. The method takes time course recordings of biochemical systems in steady state or transient state as input. Often a functional relationship between parameters presents itself by a one-dimensional manifold in parameter space containing parameter sets of optimal goodness. Although the system's behaviour cannot be distinguished on this manifold in a deterministic framework it might be distinguishable in a stochastic modelling framework. Their method exploits this by using an objective function that includes a measure for fluctuations in particle numbers. They show on three example models, immigration-death, gene expression and Epo-EpoReceptor interaction, that this resolves the non-identifiability even in the case of measurement noise with known amplitude. The method is applied to partially observed recordings of biochemical systems with measurement noise. It is simple to implement and it is usually very fast to compute. This optimisation can be realised in a classical or Bayesian fashion.

PKC-mediated inhibitory feedback of the cholecystokinin 1 receptor controls the shape of oscillatory Ca²âº signals.

Translation of extracellular hormonal input into cellular responses is often mediated by repetitive increases in cytosolic free Ca(2+) concentration ([Ca(2+) ]c ). Amplitude, duration and frequency of these so-called [Ca(2+) ]c oscillations then carry information about the nature and concentration of the extracellular signalling molecule. At present, there are different hypotheses concerning the induction and control of these oscillations. Here, we investigated the role of agonist-induced receptor phosphorylation in this process using Chinese hamster ovary cells stably expressing a variant of the cholecystokinin 1 receptor (CCK1R) lacking the four consensus sites for protein kinase C (PKC) phosphorylation and deficient in CCK-induced receptor phosphorylation (CCK1R-mt cells). In the presence of cholecystokinin-(26-33)-peptide amide (CCK-8), these cells displayed Ca(2+) oscillations with a much more pronounced bursting dynamics rather than the dominant spiking dynamics observed in Chinese hamster ovary cells stably expressing the wild-type CCK1R. The bursting behaviour returned to predominantly spiking behaviour following removal of extracellular Ca(2+) , suggesting that CCK-8-induced, PKC-mediated CCK1R phosphorylation inhibits Ca(2+) influx across the plasma membrane. To gain mechanistic insight into the underlying mechanism we developed a mathematical model able to reproduce the experimental observations. From the model we conclude that binding of CCK-8 to the CCK1R leads to activation of PKC which subsequently phosphorylates the receptor to inhibit the receptor-mediated influx of Ca(2+) across the plasma membrane. Receptor-specific differences in this feedback mechanism may, at least in part, explain the observation that different agonists evoke [Ca(2+) ]c oscillations with different kinetics in the same cell type.

An in vivo control map for the eukaryotic mRNA translation machinery.

Rate control analysis defines the in vivo control map governing yeast protein synthesis and generates an extensively parameterized digital model of the translation pathway. Among other non-intuitive outcomes, translation demonstrates a high degree of functional modularity and comprises a non-stoichiometric combination of proteins manifesting functional convergence on a shared maximal translation rate. In exponentially growing cells, polypeptide elongation (eEF1A, eEF2, and eEF3) exerts the strongest control. The two other strong control points are recruitment of mRNA and tRNA(i) to the 40S ribosomal subunit (eIF4F and eIF2) and termination (eRF1; Dbp5). In contrast, factors that are found to promote mRNA scanning efficiency on a longer than-average 5'untranslated region (eIF1, eIF1A, Ded1, eIF2B, eIF3, and eIF5) exceed the levels required for maximal control. This is expected to allow the cell to minimize scanning transition times, particularly for longer 5'UTRs. The analysis reveals these and other collective adaptations of control shared across the factors, as well as features that reflect functional modularity and system robustness. Remarkably, gene duplication is implicated in the fine control of cellular protein synthesis.

Biochemical fluctuations, optimisation and the linear noise approximation.

BACKGROUND: Stochastic fluctuations in molecular numbers have been in many cases shown to be crucial for the understanding of biochemical systems. However, the systematic study of these fluctuations is severely hindered by the high computational demand of stochastic simulation algorithms. This is particularly problematic when, as is often the case, some or many model parameters are not well known. Here, we propose a solution to this problem, namely a combination of the linear noise approximation with optimisation methods. The linear noise approximation is used to efficiently estimate the covariances of particle numbers in the system. Combining it with optimisation methods in a closed-loop to find extrema of covariances within a possibly high-dimensional parameter space allows us to answer various questions. Examples are, what is the lowest amplitude of stochastic fluctuations possible within given parameter ranges? Or, which specific changes of parameter values lead to the increase of the correlation between certain chemical species? Unlike stochastic simulation methods, this has no requirement for small numbers of molecules and thus can be applied to cases where stochastic simulation is prohibitive. RESULTS: We implemented our strategy in the software COPASI and show its applicability on two different models of mitogen-activated kinases (MAPK) signalling -- one generic model of extracellular signal-regulated kinases (ERK) and one model of signalling via p38 MAPK. Using our method we were able to quickly find local maxima of covariances between particle numbers in the ERK model depending on the activities of phospho-MKKK and its corresponding phosphatase. With the p38 MAPK model our method was able to efficiently find conditions under which the coefficient of variation of the output of the signalling system, namely the particle number of Hsp27, could be minimised. We also investigated correlations between the two parallel signalling branches (MKK3 and MKK6) in this model. CONCLUSIONS: Our strategy is a practical method for the efficient investigation of fluctuations in biochemical models even when some or many of the model parameters have not yet been fully characterised.

Efficient discovery of anti-inflammatory small-molecule combinations using evolutionary computing.

The control of biochemical fluxes is distributed, and to perturb complex intracellular networks effectively it is often necessary to modulate several steps simultaneously. However, the number of possible permutations leads to a combinatorial explosion in the number of experiments that would have to be performed in a complete analysis. We used a multiobjective evolutionary algorithm to optimize reagent combinations from a dynamic chemical library of 33 compounds with established or predicted targets in the regulatory network controlling IL-1ß expression. The evolutionary algorithm converged on excellent solutions within 11 generations, during which we studied just 550 combinations out of the potential search space of ~9 billion. The top five reagents with the greatest contribution to combinatorial effects throughout the evolutionary algorithm were then optimized pairwise. A p38 MAPK inhibitor together with either an inhibitor of IκB kinase or a chelator of poorly liganded iron yielded synergistic inhibition of macrophage IL-1ß expression. Evolutionary searches provide a powerful and general approach to the discovery of new combinations of pharmacological agents with therapeutic indices potentially greater than those of single drugs.

Biochemical simulations: stochastic, approximate stochastic and hybrid approaches.

Computer simulations have become an invaluable tool to study the sometimes counterintuitive temporal dynamics of (bio-)chemical systems. In particular, stochastic simulation methods have attracted increasing interest recently. In contrast to the well-known deterministic approach based on ordinary differential equations, they can capture effects that occur due to the underlying discreteness of the systems and random fluctuations in molecular numbers. Numerous stochastic, approximate stochastic and hybrid simulation methods have been proposed in the literature. In this article, they are systematically reviewed in order to guide the researcher and help her find the appropriate method for a specific problem.

Information transfer in signaling pathways: a study using coupled simulated and experimental data.

BACKGROUND: The topology of signaling cascades has been studied in quite some detail. However, how information is processed exactly is still relatively unknown. Since quite diverse information has to be transported by one and the same signaling cascade (e.g. in case of different agonists), it is clear that the underlying mechanism is more complex than a simple binary switch which relies on the mere presence or absence of a particular species. Therefore, finding means to analyze the information transferred will help in deciphering how information is processed exactly in the cell. Using the information-theoretic measure transfer entropy, we studied the properties of information transfer in an example case, namely calcium signaling under different cellular conditions. Transfer entropy is an asymmetric and dynamic measure of the dependence of two (nonlinear) stochastic processes. We used calcium signaling since it is a well-studied example of complex cellular signaling. It has been suggested that specific information is encoded in the amplitude, frequency and waveform of the oscillatory Ca(2+)-signal. RESULTS: We set up a computational framework to study information transfer, e.g. for calcium signaling at different levels of activation and different particle numbers in the system. We stochastically coupled simulated and experimentally measured calcium signals to simulated target proteins and used kernel density methods to estimate the transfer entropy from these bivariate time series. We found that, most of the time, the transfer entropy increases with increasing particle numbers. In systems with only few particles, faithful information transfer is hampered by random fluctuations. The transfer entropy also seems to be slightly correlated to the complexity (spiking, bursting or irregular oscillations) of the signal. Finally, we discuss a number of peculiarities of our approach in detail. CONCLUSION: This study presents the first application of transfer entropy to biochemical signaling pathways. We could quantify the information transferred from simulated/experimentally measured calcium signals to a target enzyme under different cellular conditions. Our approach, comprising stochastic coupling and using the information-theoretic measure transfer entropy, could also be a valuable tool for the analysis of other signaling pathways.

COPASI--a COmplex PAthway SImulator.

MOTIVATION: Simulation and modeling is becoming a standard approach to understand complex biochemical processes. Therefore, there is a big need for software tools that allow access to diverse simulation and modeling methods as well as support for the usage of these methods. RESULTS: Here, we present COPASI, a platform-independent and user-friendly biochemical simulator that offers several unique features. We discuss numerical issues with these features; in particular, the criteria to switch between stochastic and deterministic simulation methods, hybrid deterministic-stochastic methods, and the importance of random number generator numerical resolution in stochastic simulation. AVAILABILITY: The complete software is available in binary (executable) for MS Windows, OS X, Linux (Intel) and Sun Solaris (SPARC), as well as the full source code under an open source license from http://www.copasi.org.

Transition from stochastic to deterministic behavior in calcium oscillations.

Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.