From Solvable to Executable Models of Biological Systems

Classical modeling approaches for biology are mainly grounded in mathematics, and specifically on ordinary differential equations (ODE). Process calculi-based conceptual and computational tools are an alternative and emergent approach. Here we focus our analysis on BlenX (a beta-binders inspired programming language) showing how it is possible to easily re-use ODE models within this framework. An example will show then the advantages of moving into a stochastic approach. This is the preliminary version of a paper that was published in Proceedings of Pacific Symposium on Biocomputing (PSB 2009), January, 2009. The original publication is available at http://psb.stanford.edu/psb-online/proceedings/psb09

Inferring rate coefficents of biochemical reactions from noisy data with KInfer

Dynamical models of inter- and intra-cellular processes contain the rate constants of the biochemical reactions. These kinetic parameters are often not accessible directly through experiments, but they can be inferred from time-resolved data. Time resolved data, that is, measurements of reactant concentration at series of time points, are usually affected by different types of error, whose source can be both experimental and biological. The noise in the input data makes the estimation of the model parameters a very difficult task, as if the inference method is not sufficiently robust to the noise, the resulting estimates are not reliable. Therefore "noise-robust" methods that estimate rate constants with the maximum precision and accuracy are needed. In this report we present the probabilistic generative model of parameter inference implemented by the software prototype KInfer and we show the ability of this tool of estimating the rate coefficients of models of biochemical network with a good accuracy even from very noisy input data

Analyzing various models of Circadian Clock and Cell Cycle coupling

The daily rhythm can influence the proliferation rate of many cell types. In the mammalian system the transcription of the cell cycle regulatory protein Wee1 is controlled by the circadian clock. Zamborszky et al. (2007) present a computational model coupling the cell cycle and circadian rhythm, showing that this coupling can lead to multimodal cell cycle time distributions. Biological data points to additional couplings, including a link back from the cell cycle to the circadian clock. Proper modelling of this coupling requires a more detailed description of both parts of the model. Hence, we aim at further extending and analysing earlier models using a combination of modelling techniques and computer software, including CoSBI lab, BIOCHAM, and GINsim

Computational Modeling for the Activation Cycle of G-proteins by G-protein-coupled Receptors

In this paper, we survey five different computational modeling methods. For comparison, we use the activation cycle of G-proteins that regulate cellular signaling events downstream of G-protein-coupled receptors (GPCRs) as a driving example. Starting from an existing Ordinary Differential Equations (ODEs) model, we implement the G-protein cycle in the stochastic Pi-calculus using SPiM, as Petri-nets using Cell Illustrator, in the Kappa Language using Cellucidate, and in Bio-PEPA using the Bio-PEPA eclipse plug in. We also provide a high-level notation to abstract away from communication primitives that may be unfamiliar to the average biologist, and we show how to translate high-level programs into stochastic Pi-calculus processes and chemical reactions.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution

Calibration of biochemical network models

The estimation of parameter values (model calibration) is the bottleneck of the computational analysis of biological systems. Modeling approaches are central in systems biology, as they provide a rational framework to guide systematic strategies for key issues in medicine as well as the pharmaceutical and biotechnological industries. Inter- and intra-cellular processes require dynamic models, that contain the rate constants of the biochemical reactions. These kinetic parameters are often not accessible directly through experiments. Therefore methods that estimate rate constants with the maximum precision and accuracy are needed. We present here a new method for estimating rate coefficients from noisy observations of concentration levels at discrete time points. This is traditionally done by computing the least-squares estimator. However, estimation of the error function generally requires solving the reaction rate equations, which can become computationally unfeasible. We propose an alternative approach based on a probabilistic, generative model of the variations in reactant concentration. Our method returns the rate coefficients, the level of noise and an error range on the estimates of rate constants. Its probabilistic formulation is key to a principled handling of the noise inherent in biological data, and it allows for a number of further extensions. The mathematical procedure presented here has been implemented in a software tool, named KInfer

A new model for kinetic parameter estimation in biochemical reactions.

We present a novel method for estimating rate coefficients from noisy observations of concentration levels at discrete time points. This is traditionally done by computing the least-squares estimator. However, estimation of the error function generally requires solving the reaction rate equations, which can become computationally unfeasible. Here we present an alternative approach based on a probabilistic, generative model of the variations in reactant concentration. Our method returns the rate coefficients, the level of noise and an error range on the estimates of rate constants. Its probabilistic formulation is key to a principled handling of the noise inherent in biological data, and it allows a number of further extensions

Modelling and Inference Strategies for Biological Systems

For many years, computers have played an important role in helping scientists to store, manipulate, and analyze data coming from many different disciplines. In recent years, however, new technological capabilities and new ways of thinking about the usefulness of computer science is extending the reach of computers from simple analysis of collected data to hypothesis generation. The aim of this work is to provide a contribution in the Computational Systems Biology field. The main purpose of this recent discipline is to enhance the intertwined relationship connecting Biology and Computer Science, by developing tools and theoretical frameworks able to formally and quantitatively investigate the interactions among the components of biological systems. The final goal of these efforts is to assemble the different pieces into a working model of a living, responding, reproducing cell; a model that can be used for performing in-silico tests and simulations in order to understand and predict possible emergent properties. In this thesis we present the application to real biological case studies of a specific concurrent modelling language (derived by the metaphors of "molecules-as-object" -introduced by Fontana- and "cells-as-computations" -introduced by Regev and Shapiro- at the end of last century) and the development and implementation of a tool for inferring knowledge from experimental data in order to link the numerical aspects of a model to real wet-lab data

An analysis of irreversible transitions in a model of the buddying yeast cell cycle

Cells life follows a cycling behaviour which starts at cell birth and leads to cell division through a number of distinct phases. The transitions through the various cell cycle phases are controlled by a complex network of signalling pathways. Many cell cycle transitions are irreversible: once they are started they must reach completion. In this study we investigate the existence of conditions which lead to cases when irreversibility may be broken. Specifically, we characterise the elements of the cell cycle signalling network that are responsible for the irreversibility and we determine conditions for which the irreversible transitions may become reversible. We illustrate our results through a formal approach in which stochastic simulation analysis and model checking verification are combined. Through probabilistic model checking we provide a quantitative measure for the probability of irreversibility in the ``Start" transition of the cell cycle. This is the preliminary version of a paper that was published in Proceedings of the third International Workshop on Practical Applications of Stochastic Modelling (PASM 2008), ENTCS 232, pp. 39-53, 2009. (DOI:10.1016/j.entcs.2009.02.049