Drug effects are difficult to investigate in detail in vivo. However, a mechanistic understanding of drug action is clearly beneficial for both pharmaceutical development as well as for optimization of treatment designs. We here established a quantitative systems pharmacology (QSP) mouse model which simultaneously describes whole-body pharmacokinetics of murine IFN-α as well as the cellular pharmacodynamic effect through the antiviral response biomarker Mx2. To this end, a dynamic model of intracellular IFN-α signalling in the JAK/STAT pathway was combined with a whole-body physiologically-based pharmacokinetic model of IFN-α in mice. The pharmacodynamic behaviour of the resulting mouse IFN-α QSP model was first compared to a cellular model of the JAK/STAT pathway to compare in vitro and in vivo drug effects and to identify functional differences. It was found that the in vitro drug effect in the cellular model overestimates the in vivo response in mice at least by a factor of two which is partly due to the missing drug clearance in vitro. Also, the drug responses in the in vitro model were time delayed. Interspecies analyses in murine and a previously published human QSP model of IFN-α next show a similar dynamic behavior. However, our models demonstrate eight to 16-fold stronger response levels in mice than in humans due to more efficient interferon binding. Our analysis supports a mechanistic analysis of both upstream pharmacokinetic as well as downstream pharmacodynamic drug effects through the combination of physiological knowledge and quantitative computational models. The study hence shows potential applications for QSP modelling in terms of study planning, for example by choosing physiologically relevant in vitro concentrations. Also, the QSP model allows inter-species comparisons of the effect strength in specific functional readouts, which in humans are otherwise not possible due to the limited sampling possibilities. We expect QSP modelling to play an increasingly important role in drug development and research in the future.

Interferon (IFN) activates the transcription of several hundred of IFN stimulated genes (ISGs) that constitute a highly effective antiviral defense program. Cell-to-cell variability in the induction of ISGs is well documented, but its source and effects are not completely understood. The molecular mechanisms behind this heterogeneity have been related to randomness in molecular events taking place during the JAK-STAT signaling pathway. Here, we study the sources of variability in the induction of the IFN-alpha response by using MxA and IFIT1 activation as read-out. To this end, we integrate time-resolved flow cytometry data and stochastic modeling of the JAK-STAT signaling pathway. The complexity of the IFN response was matched by fitting probability distributions to time-course flow cytometry snapshots. Both, experimental data and simulations confirmed that the MxA and IFIT1 induction circuits generate graded responses rather than all-or-none responses. Subsequently, we quantify the size of the intrinsic variability at different steps in the pathway. We found that stochastic effects are transiently strong during the ligand-receptor activation steps and the formation of the ISGF3 complex, but negligible for the final induction of the studied ISGs. We conclude that the JAK-STAT signaling pathway is a robust biological circuit that efficiently transmits information under stochastic environments.

BACKGROUND: Computational modelling of cell biological processes is a frequently used technique to analyse the underlying mechanisms and to generally understand the behaviour of these processes in the context of a pathway, network or even the whole cell. The most common technique in this context is the usage of ordinary differential equations that describe the kinetics of the relevant processes in mechanistic detail. Here, it is usually assumed that the content of the cell is well-stirred and thus homogeneous - which is of course an over-simplification, but often worked in the past. However, many processes happen at membranes and thus not in 3D, but in 2D. The scaling of the rates of these processes poses a special problem, if volumes of compartments are changed. They will typically scale with an area, but not with the volume of the involved compartment. However, commonly, this is neglected when setting up models and/or volume scaling also sometimes automatically happens when using modelling software in the field. RESULTS: Here, we investigate generic as well as specific, realistic cases to find out, how strong the impact of the wrong scaling is for the outcome of simulations. We show that the importance of correct area scaling depends on the architecture of the reaction site and its changes upon volume alterations and it is hard to foresee, if it has a significant impact or not just by looking at the original model set-up. Moreover, scaled rates might exhibit more or less control over the behaviour of the system and therefore, accordingly, incorrect scaling will have more or less influence. CONCLUSIONS: Working with multi-compartment reactions requires a careful consideration of the correct scaling of the rates when changing the volumes of the involved compartments. The error following incorrect scaling - often done by scaling with the volume of the respective compartments can lead to significant aberrations of model behaviour.

Pyruvate kinase (PYK) is a critical allosterically regulated enzyme that links glycolysis, the primary energy metabolism, to cellular metabolism. Lactic acid bacteria rely almost exclusively on glycolysis for their energy production under anaerobic conditions, which reinforces the key role of PYK in their metabolism. These organisms are closely related, but have adapted to a huge variety of native environments. They include food-fermenting organisms, important symbionts in the human gut, and antibiotic-resistant pathogens. In contrast to the rather conserved inhibition of PYK by inorganic phosphate, the activation of PYK shows high variability in the type of activating compound between different lactic acid bacteria. System-wide comparative studies of the metabolism of lactic acid bacteria are required to understand the reasons for the diversity of these closely related microorganisms. These require knowledge of the identities of the enzyme modifiers. Here, we predict potential allosteric activators of PYKs from three lactic acid bacteria which are adapted to different native environments. We used protein structure-based molecular modeling and enzyme kinetic modeling to predict and validate potential activators of PYK. Specifically, we compared the electrostatic potential and the binding of phosphate moieties at the allosteric binding sites, and predicted potential allosteric activators by docking. We then made a kinetic model of Lactococcus lactis PYK to relate the activator predictions to the intracellular sugar-phosphate conditions in lactic acid bacteria. This strategy enabled us to predict fructose 1,6-bisphosphate as the sole activator of the Enterococcus faecalis PYK, and to predict that the PYKs from Streptococcus pyogenes and Lactobacillus plantarum show weaker specificity for their allosteric activators, while still having fructose 1,6-bisphosphate play the main activator role in vivo. These differences in the specificity of allosteric activation may reflect adaptation to different environments with different concentrations of activating compounds. The combined computational approach employed can readily be applied to other enzymes.

MOTIVATION: The growing complexity of biochemical models asks for means to rationally dissect the networks into meaningful and rather independent subnetworks. Such foregoing should ensure an understanding of the system without any heuristics employed. Important for the success of such an approach is its accessibility and the clarity of the presentation of the results. RESULTS: In order to achieve this goal, we developed a method which is a modification of the classical approach of time-scale separation. This modified method as well as the more classical approach have been implemented for time-dependent application within the widely used software COPASI. The implementation includes different possibilities for the representation of the results including 3D-visualization. AVAILABILITY: The methods are included in COPASI which is free for academic use and available at www.copasi.org. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

UNLABELLED: SYCAMORE is a browser-based application that facilitates construction, simulation and analysis of kinetic models in systems biology. Thus, it allows e.g. database supported modelling, basic model checking and the estimation of unknown kinetic parameters based on protein structures. In addition, it offers some guidance in order to allow non-expert users to perform basic computational modelling tasks. AVAILABILITY: SYCAMORE is freely available for academic use at http://sycamore.eml.org. Commercial users may acquire a license. CONTACT: [email protected].

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.

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.

BACKGROUND: To study complex biochemical reaction networks in living cells researchers more and more rely on databases and computational methods. In order to facilitate computational approaches, visualisation techniques are highly important. Biochemical reaction networks, e.g. metabolic pathways are often depicted as graphs and these graphs should be drawn dynamically to provide flexibility in the context of different data. Conventional layout algorithms are not sufficient for every kind of pathway in biochemical research. This is mainly due to certain conventions to which biochemists/biologists are used to and which are not in accordance to conventional layout algorithms. A number of approaches has been developed to improve this situation. Some of these are used in the context of biochemical databases and make more or less use of the information in these databases to aid the layout process. However, visualisation becomes also more and more important in modelling and simulation tools which mostly do not offer additional connections to databases. Therefore, layout algorithms used in these tools have to work independently of any databases. In addition, all of the existing algorithms face some limitations with respect to the number of edge crossings when it comes to larger biochemical systems due to the interconnectivity of these. Last but not least, in some cases, biochemical conventions are not met properly. RESULTS: Out of these reasons we have developed a new algorithm which tackles these problems by reducing the number of edge crossings in complex systems, taking further biological conventions into account to identify and visualise cycles. Furthermore the algorithm is independent from database information in order to be easily adopted in any application. It can also be tested as part of the SimWiz package (free to download for academic users at 1). CONCLUSION: The new algorithm reduces the complexity of pathways, as well as edge crossings and edge length in the resulting graphical representation. It also considers existing and further biological conventions to create a drawing most biochemists are familiar with. A lot of examples can be found on 2.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/