Dynamical modeling of microRNA (original) (raw)
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Dynamical modeling of microRNA action on the protein translation process
BMC systems …, 2010
Background: Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple mechanisms. It remains unclear what mechanisms of microRNA action are the most dominant: moreover, many experimental reports deliver controversial messages on what is the concrete mechanism actually observed in the experiment. Nissan and Parker have recently demonstrated that it might be impossible to distinguish alternative biological hypotheses using the steady state data on the rate of protein synthesis. For their analysis they used two simple kinetic models of protein translation. Results: In contrary to the study by Nissan and Parker, we show that dynamical data allow discriminating some of the mechanisms of microRNA action. We demonstrate this using the same models as developed by Nissan and Parker for the sake of comparison but the methods developed (asymptotology of biochemical networks) can be used for other models. We formulate a hypothesis that the effect of microRNA action is measurable and observable only if it affects the dominant system (generalization of the limiting step notion for complex networks) of the protein translation machinery. The dominant system can vary in different experimental conditions that can partially explain the existing controversy of some of the experimental data.
Dynamical Analysis of the MicroRNA – Mediated Protein Translation Process
BIOMATH, 2013
Mathematical modelling of kinetic processes with different time scales allows a reduction of the governing equations using quasi-steady-state approximations (QSSA). A QSSA theorem is applied to a modified mathematical model of the microRNA-mediated protein translation process. By an appropriate normalized procedure the system of seven nonlinear ordinary differential equations is rewritten in a form suitable for model reduction. In accordance with the terminology of the QSSA theorem, it is established that two of the protein concentrations are "fast varying", such that the corresponding kinetic equations form an attached system. The other four concentrations are "slow varying", and form a degenerate system. Another variable appears to be a constant. Analytical solutions, related to the steady-state values of the fast varying concentrations and the slow varying ones, are derived and interpreted as restrictions on the regulatory role of microRNAs on the protein tran...
Predictive Dynamical Modelling MicroRNAs Role in Complex Networks
Concepts, Methodologies, Tools, and Applications
The aim of this chapter is to give an extended analytical consideration of mathematical modelling of the microRNA role in cancer networks. For this purpose, ordinary and partial differential equations are used for synthesizing and analyzing the models of gene, microRNAs and mRNAs concentration alterations as time-dependent variables related by functional and differential relations. The architecture of the models and the definitions of their components are inspired by the qualitative theory of differential equations. This chapter’s analysis shows that it is able to ensure the authenticity and validity of the following qualitative conclusions: (a) the rates of protein production decrease with the increasing constant production rate of microRNA at microRNA-mediated target regulation on mRNAs; (b) time delay has a stabilizing role in the interaction between the miRNA-17-92 cluster and the transcription factors E2F and Myc.
Mathematical modeling of microRNA-mediated mechanisms of translation repression
2012
Abstract: MicroRNA can affect the protein translation using nine mechanistically different mechanisms, including repression of initiation and degradation of the transcript. There is a hot debate in the current literature about which mechanism and in which situations has a dominant role in living cells. The worst, same experimental systems dealing with the same pairs of mRNA and miRNA can provide controversial evidences about which is the actual mechanism of translation repression observed in the experiment.
2013
MicroRNAs (miRNAs) are involved in many regulatory pathways some of which are complex networks enriched in regulatory motifs like positive or negative feedback loops or coherent and incoherent feedforward loops. Their complexity makes the understanding of their regulation dif fi cult and the interpretation of experimental data cumbersome. In this book chapter we claim that systems biology is the appropriate approach to investigate the regulation of these miRNA-regulated networks. Systems biology is an interdisciplinary approach by which biomedical questions on biochemical networks are addressed by integrating experiments with mathematical modelling and simulation. We here introduce the foundations of the systems biology approach, the basic theoretical and computational tools used to perform model-based analyses of miRNA-regulated networks and review the scienti fi c literature in systems biology of miRNA regulation, with a focus on cancer. Keywords miRNA regulated networks • miRNA target hub • miRNA cluster • Feedback loop • Feedforward loop • Post-transcriptional regulation • miRNA network motifs • Kinetic models • Bistability • Ultrasensitivity
Mathematical and Computational Modellling of Post-Transcriptional Gene Regulation by Micrornas
2009
move on to a more general setting where the microRNA is simply treated as another species in the reaction network, with microRNA-mRNA binding forming the basis for the post-transcriptional repression. We include some speculative comments about the potential for kinetic modelling to add to the more widespread sequence and network based approaches in the qualitative investigation of microRNA based gene regulation. We also consider what new combinations of experimental data will be needed in order to make sense of the increased systems-level complexity introduced by microRNAs.
International Journal, 2009
The Quasi-Steady-State Approximation (QSSA) theorem is considered as a basic approach for reduction of dimensionality of a dynamical model of microRNA target regulation. On the basis of previously determined parameters, seven ordinary differential equations of the model are written in a form appropriate to evaluate their terms for further reduction. In accordance with the terminology of the QSSA theorem, it is established that five of the system components are fast varying such that the corresponding kinetic equations form an attached system. The other two variables are slow varying and their kinetic equations form a degenerate system.
Understanding microRNA-mediated gene regulatory networks through mathematical modelling
The discovery of microRNAs (miRNAs) has added a new player to the regulation of gene expression. With the increasing number of molecular species involved in gene regulatory networks, it is hard to obtain an intuitive understanding of network dynamics. Mathematical modelling can help dissecting the role of miRNAs in gene regulatory networks, and we shall here review the most recent developments that utilise different mathematical modelling approaches to provide quantitative insights into the function of miRNAs in the regulation of gene expression. Key miRNA regulation features that have been elucidated via modelling include: (i) the role of miRNA-mediated feedback and feedforward loops in fine-tuning of gene expression; (ii) the miRNA–target interaction properties determining the effectiveness of miRNA-mediated gene repression; and (iii) the competition for shared miRNAs leading to the cross-regulation of genes. However, there is still lack of mechanistic understanding of many other properties of miRNA regulation like unconventional miRNA–target interactions, miRNA regulation at different sub-cellular locations and functional miRNA variant, which will need future modelling efforts to deal with. This review provides an overview of recent developments and challenges in this field.
Oscillatory dynamics in a simple gene regulatory network mediated by small RNAs
Physica A-statistical Mechanics and Its Applications, 2009
More and more experiments show that small RNAs regulate gene expression by repressing translation of messenger RNAs (mRNAs) or degrading mRNAs. In this paper, we incorporate the small RNAs into a simple gene regulatory network and investigate its dynamical behaviors. In addition, we also derive the theoretical results of globally asymptotic stability and provide the sufficient conditions for the oscillation of the simple gene regulatory network, and further demonstrate that the amplitudes against the change of delay in the gene regulatory network are robust.