From ODES to Language-Based, Executable Models of Biological Systems (original) (raw)
Related papers
2006
ABSTRACT Cellular processes are governed by complex networks of interacting genes and proteins. Theoretical molecular biologists attempt to describe these processes via mathematical models by writing biochemical reaction equations. Modellers are building increasingly larger and complex mathematical models to describe these cellular processes, making model evaluation a time consuming and difficult task. We describe an automatable process for model evaluation and a software system that implements this process.
A data integration approach for cell cycle analysis oriented to model simulation in systems biology
BMC systems biology, 2007
The cell cycle is one of the biological processes most frequently investigated in systems biology studies and it involves the knowledge of a large number of genes and networks of protein interactions. A deep knowledge of the molecular aspect of this biological process can contribute to making cancer research more accurate and innovative. In this context the mathematical modelling of the cell cycle has a relevant role to quantify the behaviour of each component of the systems. The mathematical modelling of a biological process such as the cell cycle allows a systemic description that helps to highlight some features such as emergent properties which could be hidden when the analysis is performed only from a reductionism point of view. Moreover, in modelling complex systems, a complete annotation of all the components is equally important to understand the interaction mechanism inside the network: for this reason data integration of the model components has high relevance in systems biology studies.
An Intuitive Automated Modelling Interface for Systems Biology
We introduce a natural language interface for building stochastic pi calculus models of biological systems. In this language, complex constructs describing biochemical events are built from basic primitives of association, dissociation and transformation. This language thus allows us to model biochemical systems modularly by describing their dynamics in a narrative-style language, while making amendments, refinements and extensions on the models easy. We demonstrate the language on a model of Fc-gamma receptor phosphorylation during phagocytosis. We provide a tool implementation of the translation into a stochastic pi calculus language, Microsoft Research's SPiM.
Mathematical modeling as a tool for investigating cell cycle control networks
Methods, 2007
Although not a traditional experimental ''method,'' mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.
Modelling the dynamics of biosystems
Briefings in Bioinformatics, 2004
The need for a more formal handling of biological information processing with stochastic and mobile process algebras is addressed. Biology can benefit this approach, yielding a better understanding of behavioural properties of cells, and computer science can benefit this approach, obtaining new computational models inspired by nature.
Modelling Cell Cycle using Different Levels of Representation
Computing Research Repository - CORR, 2009
Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform computerised simulations of biological systems, which are called in silico experiments, to attain important insights and predictions about the system behaviour with a considerably lower cost. Computer visualisation is an important part of this approach, since it provides a realistic representation of the system behaviour. We define a formal methodology to model biological systems using different levels of representation: a purely formal representation, which we call molecular level, models the biochemical dynamics of the system; visualisation-oriented representations, which we call visual levels, provide views of the biological system at a higher level of organisation and are equipped with the necessary spatial information to generate the appropriate vis...
Mathematical Strategies for Programming Biological Cells
2012
Masters Thesis Advisers: Cherryl O. Talaue, Ph.D. (University of the Philippines Diliman) and Baltazar D. Aguda, Ph.D. (National Cancer Institute, USA) In this thesis, we study a phenomenological gene regulatory network (GRN) of a mesenchymal cell differentiation system. The GRN is composed of four nodes consisting of pluripotency and differentiation modules. The differentiation module represents a circuit of transcription factors (TFs) that activate osteogenesis, chondrogenesis, and adipogenesis. We investigate the dynamics of the GRN using Ordinary Differential Equations (ODE). The ODE model is based on a non-binary simultaneous decision model with autocatalysis and mutual inhibition. The simultaneous decision model can represent a cellular differentiation process that involves more than two possible cell lineages. We prove some mathematical properties of the ODE model such as positive invariance and existence-uniqueness of solutions. We employ geometric techniques to analyze the qualitative behavior of the ODE model. We determine the location and the maximum number of equilibrium points given a set of parameter values. The solutions to the ODE model always converge to a stable equilibrium point. Under some conditions, the solution may converge to the zero state. We are able to show that the system can induce multistability that may give rise to co-expression or to domination by some TFs. We illustrate cases showing how the behavior of the system changes when we vary some of the parameter values. Varying the values of some parameters, such as the degradation rate and the amount of exogenous stimulus, can decrease the size of the basin of attraction of an undesirable equilibrium point as well as increase the size of the basin of attraction of a desirable equilibrium point. A sufficient change in some parameter values can make a trajectory of the ODE model escape an inactive or a dominated state. Sufficient amounts of exogenous stimuli affect the potency of cells. The introduction of an exogenous stimulus is a possible strategy for controlling cell fate. A dominated TF can exceed a dominating TF by adding a corresponding exogenous stimulus. Moreover, increasing the amount of exogenous stimulus can shutdown multistability of the system such that only one stable equilibrium point remains. We observe the case where a random noise is present in our system. We add a Gaussian white noise term to our ODE model making the model a system of stochastic DEs. Simulations reveal that it is possible for cells to switch lineages when the system is multistable. We are able to show that a sole attractor can regulate the effect of moderate stochastic noise in gene expression.
Models in biology: lessons from modeling regulation of the eukaryotic cell cycle
BMC biology, 2015
In this essay we illustrate some general principles of mathematical modeling in biology by our experiences in studying the molecular regulatory network underlying eukaryotic cell division. We discuss how and why the models moved from simple, parsimonious cartoons to more complex, detailed mechanisms with many kinetic parameters. We describe how the mature models made surprising and informative predictions about the control system that were later confirmed experimentally. Along the way, we comment on the 'parameter estimation problem' and conclude with an appeal for a greater role for mathematical models in molecular cell biology.
Structure, function, and behaviour of computational models in systems biology
BMC Systems Biology, 2013
Background: Systems Biology develops computational models in order to understand biological phenomena. The increasing number and complexity of such "bio-models" necessitate computer support for the overall modelling task. Computer-aided modelling has to be based on a formal semantic description of bio-models. But, even if computational bio-models themselves are represented precisely in terms of mathematical expressions their full meaning is not yet formally specified and only described in natural language. Results: We present a conceptual framework -the meaning facets -which can be used to rigorously specify the semantics of bio-models. A bio-model has a dual interpretation: On the one hand it is a mathematical expression which can be used in computational simulations (intrinsic meaning). On the other hand the model is related to the biological reality (extrinsic meaning). We show that in both cases this interpretation should be performed from three perspectives: the meaning of the model's components (structure), the meaning of the model's intended use (function), and the meaning of the model's dynamics (behaviour). In order to demonstrate the strengths of the meaning facets framework we apply it to two semantically related models of the cell cycle. Thereby, we make use of existing approaches for computer representation of bio-models as much as possible and sketch the missing pieces. Conclusions: The meaning facets framework provides a systematic in-depth approach to the semantics of biomodels. It can serve two important purposes: First, it specifies and structures the information which biologists have to take into account if they build, use and exchange models. Secondly, because it can be formalised, the framework is a solid foundation for any sort of computer support in bio-modelling. The proposed conceptual framework establishes a new methodology for modelling in Systems Biology and constitutes a basis for computer-aided collaborative research.