SensA: web-based sensitivity analysis of SBML models.

SUMMARY: SensA is a web-based application for sensitivity analysis of mathematical models. The sensitivity analysis is based on metabolic control analysis, computing the local, global and time-dependent properties of model components. Interactive visualization facilitates interpretation of usually complex results. SensA can contribute to the analysis, adjustment and understanding of mathematical models for dynamic systems. AVAILABILITY AND IMPLEMENTATION: SensA is available at http://gofid.biologie.hu-berlin.de/ and can be used with any modern browser. The source code can be found at https://bitbucket.org/floettma/sensa/ (MIT license)

Long-term model predictive control of gene expression at the population and single-cell levels.

Gene expression plays a central role in the orchestration of cellular processes. The use of inducible promoters to change the expression level of a gene from its physiological level has significantly contributed to the understanding of the functioning of regulatory networks. However, from a quantitative point of view, their use is limited to short-term, population-scale studies to average out cell-to-cell variability and gene expression noise and limit the nonpredictable effects of internal feedback loops that may antagonize the inducer action. Here, we show that, by implementing an external feedback loop, one can tightly control the expression of a gene over many cell generations with quantitative accuracy. To reach this goal, we developed a platform for real-time, closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells' environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmostress responsive promoter and playing with the osmolarity of the cells environment, we show that long-term control can, indeed, be achieved for both time-constant and time-varying target profiles at the population and even the single-cell levels. Importantly, we provide evidence that real-time control can dynamically limit the effects of gene expression stochasticity. We anticipate that our method will be useful to quantitatively probe the dynamic properties of cellular processes and drive complex, synthetically engineered networks.

Modular rate laws for enzymatic reactions: thermodynamics, elasticities and implementation.

MOTIVATION: Standard rate laws are a key requisite for systematically turning metabolic networks into kinetic models. They should provide simple, general and biochemically plausible formulae for reaction velocities and reaction elasticities. At the same time, they need to respect thermodynamic relations between the kinetic constants and the metabolic fluxes and concentrations. RESULTS: We present a family of reversible rate laws for reactions with arbitrary stoichiometries and various types of regulation, including mass-action, Michaelis-Menten and uni-uni reversible Hill kinetics as special cases. With a thermodynamically safe parameterization of these rate laws, parameter sets obtained by model fitting, sampling or optimization are guaranteed to lead to consistent chemical equilibrium states. A reformulation using saturation values yields simple formulae for rates and elasticities, which can be easily adjusted to the given stationary flux distributions. Furthermore, this formulation highlights the role of chemical potential differences as thermodynamic driving forces. We compare the modular rate laws to the thermodynamic-kinetic modelling formalism and discuss a simplified rate law in which the reaction rate directly depends on the reaction affinity. For automatic handling of modular rate laws, we propose a standard syntax and semantic annotations for the Systems Biology Markup Language. AVAILABILITY: An online tool for inserting the rate laws into SBML models is freely available at www.semanticsbml.org. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Annotation and merging of SBML models with semanticSBML.

SUMMARY: Systems Biology Markup Language (SBML) is the leading exchange format for mathematical models in Systems Biology. Semantic annotations link model elements with external knowledge via unique database identifiers and ontology terms, enabling software to check and process models by their biochemical meaning. Such information is essential for model merging, one of the key steps towards the construction of large kinetic models. SemanticSBML is a tool that helps users to check and edit MIRIAM annotations and SBO terms in SBML models. Using a large collection of biochemical names and database identifiers, it supports modellers in finding the right annotations and in merging existing models. Initially, an element matching is derived from the MIRIAM annotations and conflicting element attributes are categorized and highlighted. Conflicts can then be resolved automatically or manually, allowing the user to control the merging process in detail. AVAILABILITY: SemanticSBML comes as a free software written in Python and released under the GPL 3. A Debian package, a source package for other Linux distributions, a Windows installer and an online version of semanticSBML with limited functionality are available at http://www.semanticsbml.org. A preinstalled version can be found on the Linux live DVD SB.OS, available at http://www.sbos.eu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Osmolyte homeostasis controls single-cell growth rate and maximum cell size of Saccharomyces cerevisiae.

Cell growth is well described at the population level, but precisely how nutrient and water uptake and cell wall expansion drive the growth of single cells is poorly understood. Supported by measurements of single-cell growth trajectories and cell wall elasticity, we present a single-cell growth model for yeast. The model links the thermodynamic quantities, such as turgor pressure, osmolarity, cell wall elasto-plasticity, and cell size, applying concepts from rheology and thin shell theory. It reproduces cell size dynamics during single-cell growth, budding, and hyper-osmotic or hypo-osmotic stress. We find that single-cell growth rate and final size are primarily governed by osmolyte uptake and consumption, while bud expansion requires additionally different cell wall extensibilities between mother and bud. Based on first principles the model provides a more accurate description of size dynamics than previous attempts and its analytical simplification allows for easy combination with models for other cell processes.

Automatically generated model of a metabolic network.

We demonstrate an approach to automatically generating kinetic models of metabolic networks. In a first step, the metabolic network is characterised by its stoichiometric structure. Then to each reaction a kinetic equation is associated describing the metabolic flux. For the kinetics we use a formula that is universally applicable to reactions with arbitrary numbers of substrates and products. Last, the kinetics of the reactions are assigned parameters. The resulting model in SBML format can be fed into standard simulation tools. The approach is applied to the sulphur-glutathione-pathway in Saccharomyces cerevisiae.

SBMLmerge, a system for combining biochemical network models.

The Systems Biology Markup Language (SBML) is an XML-based format for representing mathematical models of biochemical reaction networks, and it is likely to become a main standard in the systems biology community. As published mathematical models in cell biology are growing in number and size, modular modelling approaches will gain additional importance. The main issue to be addressed in computer-assisted model combination is the specification and handling of model semantics. The software SBMLmerge assists the user in combining models of biological subsystems to larger biochemical networks. First, the program helps the user in annotating all model elements with unique identifiers pointing to databases such as KEGG or Gene Ontology. Second, during merging, SBMLmerge detects and resolves various syntactic and semantic problems. Typical problems are conflicting variable names, elements which appear in more than one input model, and mathematical problems arising from the combination of equations. If the input models make contradicting statements about a biochemical quantity, the user is asked to choose between them. In the end the merging process results in a new, valid SBML model.

Dynamics of cell wall elasticity pattern shapes the cell during yeast mating morphogenesis.

The cell wall defines cell shape and maintains integrity of fungi and plants. When exposed to mating pheromone, Saccharomyces cerevisiae grows a mating projection and alters in morphology from spherical to shmoo form. Although structural and compositional alterations of the cell wall accompany shape transitions, their impact on cell wall elasticity is unknown. In a combined theoretical and experimental approach using finite-element modelling and atomic force microscopy (AFM), we investigated the influence of spatially and temporally varying material properties on mating morphogenesis. Time-resolved elasticity maps of shmooing yeast acquired with AFM in vivo revealed distinct patterns, with soft material at the emerging mating projection and stiff material at the tip. The observed cell wall softening in the protrusion region is necessary for the formation of the characteristic shmoo shape, and results in wider and longer mating projections. The approach is generally applicable to tip-growing fungi and plants cells.

Toward Community Standards and Software for Whole-Cell Modeling.

OBJECTIVE: Whole-cell (WC) modeling is a promising tool for biological research, bioengineering, and medicine. However, substantial work remains to create accurate comprehensive models of complex cells. METHODS: We organized the 2015 Whole-Cell Modeling Summer School to teach WC modeling and evaluate the need for new WC modeling standards and software by recoding a recently published WC model in the Systems Biology Markup Language. RESULTS: Our analysis revealed several challenges to representing WC models using the current standards. CONCLUSION: We, therefore, propose several new WC modeling standards, software, and databases. SIGNIFICANCE: We anticipate that these new standards and software will enable more comprehensive models.

In silico control of biomolecular processes.

By implementing an external feedback loop one can tightly control the expression of a gene over many cell generations with quantitative accuracy. Controlling precisely the level of a protein of interest will be useful to probe quantitatively the dynamical properties of cellular processes and to drive complex, synthetically-engineered networks. In this chapter we describe a platform for real-time closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmo-stress responsive promoter and playing with the osmolarity of the cells environment, we demonstrate that long-term control can indeed be achieved for both time-constant and time-varying target profiles, at the population level, and even at the single-cell level.

The Dynamical Systems Properties of the HOG Signaling Cascade.

The High Osmolarity Glycerol (HOG) MAP kinase pathway in the budding yeast Saccharomyces cerevisiae is one of the best characterized model signaling pathways. The pathway processes external signals of increased osmolarity into appropriate physiological responses within the yeast cell. Recent advances in microfluidic technology coupled with quantitative modeling, and techniques from reverse systems engineering have allowed yet further insight into this already well-understood pathway. These new techniques are essential for understanding the dynamical processes at play when cells process external stimuli into biological responses. They are widely applicable to other signaling pathways of interest. Here, we review the recent advances brought by these approaches in the context of understanding the dynamics of the HOG pathway signaling.

Towards real-time control of gene expression: controlling the HOG signaling cascade.

To decipher the dynamical functioning of cellular processes, the method of choice is to observe the time response of cells subjected to well controlled perturbations in time and amplitude. Efficient methods, based on molecular biology, are available to monitor quantitatively and dynamically many cellular processes. In contrast, it is still a challenge to perturb cellular processes - such as gene expression - in a precise and controlled manner. Here, we propose a first step towards in vivo control of gene expression: in real-time, we dynamically control the activity of a yeast signaling cascade thanks to an experimental platform combining a micro-fluidic device, an epi-fluorescence microscope and software implementing control approaches. We experimentally demonstrate the feasibility of this approach, and we investigate computationally some possible improvements of our control strategy using a model of the yeast osmo-adaptation response fitted to our data.

Integration of enzyme kinetic data from various sources.

We describe a workflow to translate a given metabolic network into a kinetic model; the model summarises kinetic information collected from different data sources. All reactions are modelled by convenience kinetics; where detailed kinetic laws are known, they can also be incorporated. Confidence intervals and correlations of the resulting model parameters are obtained from Bayesian parameter estimation; they can be used to sample parameter sets for Monte-Carlo simulations. The integration method ensures that the resulting parameter distributions are thermodynamically feasible. Here we summarise different previous works on this topic: we give an overview over the convenience kinetics, thermodynamic criteria for parameter sets, Bayesian parameter estimation, the collection of kinetic data, and different machine learning techniques that can be used to obtain prior distributions for kinetic parameters. All methods have been assembled into a workflow that facilitates the integration of biochemical data and the modelling of metabolic networks from scratch.