Stochastic modelling of biochemical systems of multi-step reactions using a simplified two-variable model

Background

A fundamental issue in systems biology is how to design simplified mathematical models for describing the dynamics of complex biochemical reaction systems. Among them, a key question is how to use simplified reactions to describe the chemical events of multi-step reactions that are ubiquitous in biochemistry and biophysics. To address this issue, a widely used approach in literature is to use one-step reaction to represent the multi-step chemical events. In recent years, a number of modelling methods have been designed to improve the accuracy of the one-step reaction method, including the use of reactions with time delay. However, our recent research results suggested that there are still deviations between the dynamics of delayed reactions and that of the multi-step reactions. Therefore, more sophisticated modelling methods are needed to accurately describe the complex biological systems in an efficient way.

Results

This work designs a two-variable model to simplify chemical events of multi-step reactions. In addition to the total molecule number of a species, we first introduce a new concept regarding the location of molecules in the multi-step reactions, which is the second variable to represent the system dynamics. Then we propose a simulation algorithm to compute the probability for the firing of the last step reaction in the multi-step events. This probability function is evaluated using a deterministic model of ordinary differential equations and a stochastic model in the framework of the stochastic simulation algorithm. The efficiency of the proposed two-variable model is demonstrated by the realization of mRNA degradation process based on the experimentally measured data.

Conclusions

Numerical results suggest that the proposed new two-variable model produces predictions that match the multi-step chemical reactions very well. The successful realization of the mRNA degradation dynamics indicates that the proposed method is a promising approach to reduce the complexity of biological systems.

     

Statistical model comparison applied to common network motifs

Background  

Network motifs are small modules that show interesting functional and dynamic properties, and are believed to be the building blocks of complex cellular processes. However, the mechanistic details of such modules are often unknown: there is uncertainty about the motif architecture as well as the functional form and parameter values when converted to ordinary differential equations (ODEs). This translates into a number of candidate models being compatible with the system under study. A variety of statistical methods exist for ranking models including maximum likelihood-based and Bayesian methods. Our objective is to show how such methods can be applied in a typical systems biology setting.     

Bifurcation analysis informs Bayesian inference in the Hes1 feedback loop

Background  

Ordinary differential equations (ODEs) are an important tool for describing the dynamics of biological systems. However, for ODE models to be useful, their parameters must first be calibrated. Parameter estimation, that is, finding parameter values given experimental data, is an inference problem that can be treated systematically through a Bayesian framework.     

Stochastic and deterministic multiscale models for systems biology: an auxin-transport case study

Background  

Stochastic and asymptotic methods are powerful tools in developing multiscale systems biology models; however, little has been done in this context to compare the efficacy of these methods. The majority of current systems biology modelling research, including that of auxin transport, uses numerical simulations to study the behaviour of large systems of deterministic ordinary differential equations, with little consideration of alternative modelling frameworks.     

The ups and downs of biological timers

Background  

The need to execute a sequence of events in an orderly and timely manner is central to many biological processes, including cell cycle progression and cell differentiation. For self-perpetuating systems, such as the cell cycle oscillator, delay times between events are defined by the network of interacting proteins that propagates the system. However, protein levels inside cells are subject to genetic and environmental fluctuations, raising the question of how reliable timing is maintained.     

Parameter estimation for stiff equations of biosystems using radial basis function networks

Background  

The modeling of dynamic systems requires estimating kinetic parameters from experimentally measured time-courses. Conventional global optimization methods used for parameter estimation, e.g. genetic algorithms (GA), consume enormous computational time because they require iterative numerical integrations for differential equations. When the target model is stiff, the computational time for reaching a solution increases further.     

Genome-wide analysis of mRNA decay patterns during early <Emphasis Type="Italic">Drosophila</Emphasis>development

Background  

The modulation of mRNA levels across tissues and time is key for the establishment and operation of the developmental programs that transform the fertilized egg into a fully formed embryo. Although the developmental mechanisms leading to differential mRNA synthesis are heavily investigated, comparatively little attention is given to the processes of mRNA degradation and how these relate to the molecular programs controlling development.     

Odefy - From discrete to continuous models

Background  

Phenomenological information about regulatory interactions is frequently available and can be readily converted to Boolean models. Fully quantitative models, on the other hand, provide detailed insights into the precise dynamics of the underlying system. In order to connect discrete and continuous modeling approaches, methods for the conversion of Boolean systems into systems of ordinary differential equations have been developed recently. As biological interaction networks have steadily grown in size and complexity, a fully automated framework for the conversion process is desirable.     

General functions to transform associate data to host data,and their use in phylogenetic inference from sequences with intra-individual variability

Background  

Amongst the most commonly used molecular markers for plant phylogenetic studies are the nuclear ribosomal internal transcribed spacers (ITS). Intra-individual variability of these multicopy regions is a very common phenomenon in plants, the causes of which are debated in literature. Phylogenetic reconstruction under these conditions is inherently difficult. Our approach is to consider this problem as a special case of the general biological question of how to infer the characteristics of hosts (represented here by plant individuals) from features of their associates (represented by cloned sequences here).     

TiGER: A database for tissue-specific gene expression and regulation

Background  

Understanding how genes are expressed and regulated in different tissues is a fundamental and challenging question. However, most of currently available biological databases do not focus on tissue-specific gene regulation.     

MZmine 2: Modular framework for processing,visualizing, and analyzing mass spectrometry-based molecular profile data

Background  

Mass spectrometry (MS) coupled with online separation methods is commonly applied for differential and quantitative profiling of biological samples in metabolomic as well as proteomic research. Such approaches are used for systems biology, functional genomics, and biomarker discovery, among others. An ongoing challenge of these molecular profiling approaches, however, is the development of better data processing methods. Here we introduce a new generation of a popular open-source data processing toolbox, MZmine 2.     

Identifying interactions in the time and frequency domains in local and global networks - A Granger Causality Approach

Background  

Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality.     

Formin homology 2 domains occur in multiple contexts in angiosperms

Background  

Involvement of conservative molecular modules and cellular mechanisms in the widely diversified processes of eukaryotic cell morphogenesis leads to the intriguing question: how do similar proteins contribute to dissimilar morphogenetic outputs. Formins (FH2 proteins) play a central part in the control of actin organization and dynamics, providing a good example of evolutionarily versatile use of a conserved protein domain in the context of a variety of lineage-specific structural and signalling interactions.     

DOTcvpSB, a software toolbox for dynamic optimization in systems biology

Background  

Mathematical optimization aims to make a system or design as effective or functional as possible, computing the quality of the different alternatives using a mathematical model. Most models in systems biology have a dynamic nature, usually described by sets of differential equations. Dynamic optimization addresses this class of systems, seeking the computation of the optimal time-varying conditions (control variables) to minimize or maximize a certain performance index. Dynamic optimization can solve many important problems in systems biology, including optimal control for obtaining a desired biological performance, the analysis of network designs and computer aided design of biological units.     

Cancer as a dynamical phase transition

Background

We review and extend the work of Rosen and Casti who discuss category theory with regards to systems biology and manufacturing systems, respectively.

Results

We describe anticipatory systems, or long-range feed-forward chemical reaction chains, and compare them to open-loop manufacturing processes. We then close the loop by discussing metabolism-repair systems and describe the rationality of the self-referential equation f = f (f). This relationship is derived from some boundary conditions that, in molecular systems biology, can be stated as the cardinality of the following molecular sets must be about equal: metabolome, genome, proteome. We show that this conjecture is not likely correct so the problem of self-referential mappings for describing the boundary between living and nonliving systems remains an open question. We calculate a lower and upper bound for the number of edges in the molecular interaction network (the interactome) for two cellular organisms and for two manufacturomes for CMOS integrated circuit manufacturing.

Conclusions

We show that the relevant mapping relations may not be Abelian, and that these problems cannot yet be resolved because the interactomes and manufacturomes are incomplete.     

Propagation of kinetic uncertainties through a canonical topology of the TLR4 signaling network in different regions of biochemical reaction space

Background  

Signal transduction networks represent the information processing systems that dictate which dynamical regimes of biochemical activity can be accessible to a cell under certain circumstances. One of the major concerns in molecular systems biology is centered on the elucidation of the robustness properties and information processing capabilities of signal transduction networks. Achieving this goal requires the establishment of causal relations between the design principle of biochemical reaction systems and their emergent dynamical behaviors.     

An editor for pathway drawing and data visualization in the Biopathways Workbench

Background  

Pathway models serve as the basis for much of systems biology. They are often built using programs designed for the purpose. Constructing new models generally requires simultaneous access to experimental data of diverse types, to databases of well-characterized biological compounds and molecular intermediates, and to reference model pathways. However, few if any software applications provide all such capabilities within a single user interface.