Alida Palmisano

A new probabilistic generative model of parameter inference in biochemical networks

We present a new method for estimating rate coefficients and level of noise in models of biochemical networks from noisy observations of concentration levels at discrete time points. Its probabilistic formulation, based on maximum likelihood estimation, is key to a principled handling of the noise inherent in biological data, and it allows for a number of further extensions, such as a fully Bayesian treatment of the parameter inference and automated model selection strategies based on the comparison between marginal likelihoods of different models. We developed KInfer (Knowlegde Inference), a tool implementing our inference model. KInfer is downloadable for free at http://www.cosbi.eu.

The critical size is set at a single-cell level by growth rate to attain homeostasis and adaptation

Budding yeast cells are assumed to trigger Start and enter the cell cycle only after they attain a critical size set by external conditions. However, arguing against deterministic models of cell size control, cell volume at Start displays great individual variability even under constant conditions. Here we show that cell size at Start is robustly set at a single-cell level by the volume growth rate in G1, which explains the observed variability. We find that this growth-rate-dependent sizer is intimately hardwired into the Start network and the Ydj1 chaperone is key for setting cell size as a function of the individual growth rate. Mathematical modelling and experimental data indicate that a growth-rate-dependent sizer is sufficient to ensure size homeostasis and, as a remarkable advantage over a rigid sizer mechanism, it reduces noise in G1 length and provides an immediate solution for size adaptation to external conditions at a population level.

Calibration of dynamic models of biological systems with KInfer

Methods for parameter estimation that are robust to experimental uncertainties and to stochastic and biological noise and that require a minimum of a priori input knowledge are of key importance in computational systems biology. The new method presented in this paper aims to ensure an inference model that deduces the rate constants of a system of biochemical reactions from experimentally measured time courses of reactants. This new method was applied to some challenging parameter estimation problems of nonlinear dynamic biological systems and was tested both on synthetic and real data. The synthetic case studies are the 12-state model of the SERCA pump and a model of a genetic network containing feedback loops of interaction between regulator and effector genes. The real case studies consist of a model of the reaction between the inhibitor κB kinase enzyme and its substrate in the signal transduction pathway of NF-κB, and a stiff model of the fermentation pathway of Lactococcus lactis.

FROM ODES TO LANGUAGE-BASED, EXECUTABLE MODELS OF BIOLOGICAL SYSTEMS

Modeling in biology is mainly grounded in mathematics, and specifically on ordinary differential equations (ODE). The programming language approach is a complementary and emergent tool to analyze the dynamics of biological networks. Here we focus on BlenX showing how it is possible to easily re-use ODE models within this framework. A budding yeast cell cycle example demonstrates the advantages of using a stochastic approach. Finally, some hints are provided on how the automatically translated model can take advantage of the full power of BlenX to analyze the control mechanisms of the cell cycle machinery.

Programming Biology in BlenX

We introduce a programming language called BlenX. It has been specifically designed and implemented to model and simulate biological systems and is strongly inspired to process calculi. We describe all the features of BlenX together with its supporting tools and show the application of the language on real case studies.

Multistate Model Builder (MSMB): a flexible editor for compact biochemical models.

BackgroundBuilding models of molecular regulatory networks is challenging not just because of the intrinsic difficulty of describing complex biological processes. Writing a model is a creative effort that calls for more flexibility and interactive support than offered by many of today’s biochemical model editors. Our model editor MSMB — Multistate Model Builder — supports multistate models created using different modeling styles.ResultsMSMB provides two separate advances on existing network model editors. (1) A simple but powerful syntax is used to describe multistate species. This reduces the number of reactions needed to represent certain molecular systems, thereby reducing the complexity of model creation. (2) Extensive feedback is given during all stages of the model creation process on the existing state of the model. Users may activate error notifications of varying stringency on the fly, and use these messages as a guide toward a consistent, syntactically correct model. MSMB default values and behavior during model manipulation (e.g., when renaming or deleting an element) can be adapted to suit the modeler, thus supporting creativity rather than interfering with it. MSMB’s internal model representation allows saving a model with errors and inconsistencies (e.g., an undefined function argument; a syntactically malformed reaction). A consistent model can be exported to SBML or COPASI formats. We show the effectiveness of MSMB’s multistate syntax through models of the cell cycle and mRNA transcription.ConclusionsUsing multistate reactions reduces the number of reactions need to encode many biochemical network models. This reduces the cognitive load for a given model, thereby making it easier for modelers to build more complex models. The many interactive editing support features provided by MSMB make it easier for modelers to create syntactically valid models, thus speeding model creation. Complete information and the installation package can be found at http://www.copasi.org/SoftwareProjects. MSMB is based on Java and the COPASI API.

A Stochastic Model Correctly Predicts Changes in Budding Yeast Cell Cycle Dynamics upon Periodic Expression of CLN2

In this study, we focus on a recent stochastic budding yeast cell cycle model. First, we estimate the model parameters using extensive data sets: phenotypes of 110 genetic strains, single cell statistics of wild type and cln3 strains. Optimization of stochastic model parameters is achieved by an automated algorithm we recently used for a deterministic cell cycle model. Next, in order to test the predictive ability of the stochastic model, we focus on a recent experimental study in which forced periodic expression of CLN2 cyclin (driven by MET3 promoter in cln3 background) has been used to synchronize budding yeast cell colonies. We demonstrate that the model correctly predicts the experimentally observed synchronization levels and cell cycle statistics of mother and daughter cells under various experimental conditions (numerical data that is not enforced in parameter optimization), in addition to correctly predicting the qualitative changes in size control due to forced CLN2 expression. Our model also generates a novel prediction: under frequent CLN2 expression pulses, G1 phase duration is bimodal among small-born cells. These cells originate from daughters with extended budded periods due to size control during the budded period. This novel prediction and the experimental trends captured by the model illustrate the interplay between cell cycle dynamics, synchronization of cell colonies, and size control in budding yeast.

Molecular network dynamics of cell cycle control: transitions to start and finish.

The cell cycle is controlled by complex regulatory network to ensure that the phases of the cell cycle happen in the right order and transitions between phases happen only if the earlier phase is properly finished. This regulatory network receives signals from the environment, monitors the state of the DNA, and decides when the cell can proceed in its cycle. The transcriptional and post-translational regulatory interactions in this network can lead to complex dynamical responses. The cell cycle dependent oscillations in protein activities are driven by these interactions as the regulatory system moves between steady states that correspond to different phases of the cell cycle. The analysis of such complex molecular network behavior can be investigated with the tools of computational systems biology. Here we review the basic physiological and molecular transitions in the cell cycle and present how the system-level emergent properties were found by the help of mathematical/computational modeling.

Deducing Chemical Reaction Rate Constants and Their Regions of Confidence from Noisy Measurements of Time Series of Concentration

We present a new method for estimating rate coefficients from noisy observations of concentration levels at discrete time points. Our inference method is based on a new maximum likelihood approach to the estimation of probability density function of the variations in reactant concentration. The inference procedure returns the rate coefficients with their intervals of confidence, and the variance of noise in the input data.

JigCell Run Manager (JC-RM): a tool for managing large sets of biochemical model parametrizations

BackgroundMost biomolecular reaction modeling tools allow users to build models with a single list of parameter values. However, a common scenario involves different parameterizations of the model to account for the results of related experiments, for example, to define the phenotypes for a variety of mutations (gene knockout, over expression, etc.) of a specific biochemical network. This scenario is not well supported by existing model editors, forcing the user to manually generate, store, and maintain many variations of the same model.ResultsWe developed an extension to our modeling editor called the JigCell Run Manager (JC-RM). JC-RM allows the modeler to define a hierarchy of parameter values, simulations, and plot settings, and to save them together with the initial model. JC-RM supports generation of simulation plots, as well as export to COPASI and SBML (L3V1) for further analysis.ConclusionsDeveloping a model with its initial list of parameter values is just the first step in modeling a biological system. Models are often parameterized in many different ways to account for mutations of the organism and/or for sets of related experiments performed on the organism. JC-RM offers two critical features: it supports the everyday management of a large model, complete with its parameterizations, and it facilitates sharing this information before and after publication. JC-RM allows the modeler to define a hierarchy of parameter values, simulation, and plot settings, and to maintain a relationship between this hierarchy and the initial model. JC-RM is implemented in Java and uses the COPASI API. JC-RM runs on all major operating systems, with minimal system requirements. Installers, source code, user manual, and examples can be found at the COPASI website (http://www.copasi.org/Projects).