42,984 research outputs found
Modeling Gene Expression with Differential Equations
Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in their technical report, “A Continuous Model of Gene Expression”, as wellas past models that inspired theirs. I solve the model by Hunt et al. for variousequilibrium points and analyze those points through eigenvalues and bifurcations to understand the biological relevance
Gene expression for simulation of biological tissue
BioDynaMo is a biological processes simulator developed by an international
community of researchers and software engineers working closely with
neuroscientists. The authors have been working on gene expression, i.e. the
process by which the heritable information in a gene - the sequence of DNA base
pairs - is made into a functional gene product, such as protein or RNA.
Typically, gene regulatory models employ either statistical or analytical
approaches, being the former already well understood and broadly used. In this
paper, we utilize analytical approaches representing the regulatory networks by
means of differential equations, such as Euler and Runge-Kutta methods. The two
solutions are implemented and have been submitted for inclusion in the
BioDynaMo project and are compared for accuracy and performance
Network estimation in State Space Model with L1-regularization constraint
Biological networks have arisen as an attractive paradigm of genomic science
ever since the introduction of large scale genomic technologies which carried
the promise of elucidating the relationship in functional genomics. Microarray
technologies coupled with appropriate mathematical or statistical models have
made it possible to identify dynamic regulatory networks or to measure time
course of the expression level of many genes simultaneously. However one of the
few limitations fall on the high-dimensional nature of such data coupled with
the fact that these gene expression data are known to include some hidden
process. In that regards, we are concerned with deriving a method for inferring
a sparse dynamic network in a high dimensional data setting. We assume that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some unknown or hidden process. We build an
input-dependent linear state space model from these hidden states and
demonstrate how an incorporated regularization constraint in an
Expectation-Maximization (EM) algorithm can be used to reverse engineer
transcriptional networks from gene expression profiling data. This corresponds
to estimating the model interaction parameters. The proposed method is
illustrated on time-course microarray data obtained from a well established
T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4,
CASP4, CD69, and C3X1 to have higher number of inwards directed connections and
FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed
connections. We recommend these genes to be object for further investigation.
Caspase 4 is also found to activate the expression of JunD which in turn
represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359
Feedback control of stochastic gene switches using PIDE models
[Abstract]: Achieving control of gene regulatory circuits is one of the goals of synthetic biology, as a way to regulate cellular functions for useful purposes (in biomedical, environmental or industrial applications). The inherent stochastic nature of gene expression makes it challenging to control the behavior of gene regulatory networks, and increasing efforts are being devoted in the field to address different control problems. In this work, we combine the efficient modeling of stochastic gene regulatory networks by means of Partial Integro-Differential Equations with feedback control, in order to keep protein levels at the target (pre-defined) stationary probability distribution. In particular, we achieve the closedloop stabilization of bi-modal toggle-switches in the stochastic regime within the region of low probability (around the minimum located between the two modes of the uncontrolled system).GAIN Oportunius Grant Xunta de Galici
Time-delayed models of gene regulatory networks
We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternativemodelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems
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