Mathematical modeling of gene expression: a guide for the perplexed biologist

Ay, Ahmet; Arnosti, David N.

doi:10.3109/10409238.2011.556597

Cited by 130 publications

(120 citation statements)

References 91 publications

(172 reference statements)

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“…To simulate gene expression, we used a simple linear production-degradation model for each of the four species ( sna, vnd, sog, zen ) in nucleus h :

\frac{d}{d t} {[m R N A]}_{i}^{h} = \frac{1}{τ_{i}} true(f_{i} (U_{n u c}^{h}, {[s n a]}^{h}) - {false[m R N A false]}_{i}^{h} true)

, where f is the production rate of species i , and

U_{n u c}^{h}

is the scaled concentration of nuclear dl in nucleus h [10, 19]. For simplicity, f is formulated as a hard-threshold on/off switch for each species (Hill function with Hill exponent of n H = 100), where production is unity when the concentration of dl is above (for sna/sog/vnd ) or below (for zen ) a threshold θ dl : mRNA i .…”

Section: Methodsmentioning

confidence: 99%

The Presence of Nuclear Cactus in the Early Drosophila Embryo May Extend the Dynamic Range of the Dorsal Gradient

O'Connell

Reeves

2015

PLoS Comput Biol

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In a developing embryo, the spatial distribution of a signaling molecule, or a morphogen gradient, has been hypothesized to carry positional information to pattern tissues. Recent measurements of morphogen distribution have allowed us to subject this hypothesis to rigorous physical testing. In the early Drosophila embryo, measurements of the morphogen Dorsal, which is a transcription factor responsible for initiating the earliest zygotic patterns along the dorsal-ventral axis, have revealed a gradient that is too narrow to pattern the entire axis. In this study, we use a mathematical model of Dorsal dynamics, fit to experimental data, to determine the ability of the Dorsal gradient to regulate gene expression across the entire dorsal-ventral axis. We found that two assumptions are required for the model to match experimental data in both Dorsal distribution and gene expression patterns. First, we assume that Cactus, an inhibitor that binds to Dorsal and prevents it from entering the nuclei, must itself be present in the nuclei. And second, we assume that fluorescence measurements of Dorsal reflect both free Dorsal and Cactus-bound Dorsal. Our model explains the dynamic behavior of the Dorsal gradient at lateral and dorsal positions of the embryo, the ability of Dorsal to regulate gene expression across the entire dorsal-ventral axis, and the robustness of gene expression to stochastic effects. Our results have a general implication for interpreting fluorescence-based measurements of signaling molecules.

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“…To simulate gene expression, we used a simple linear production-degradation model for each of the four species ( sna, vnd, sog, zen ) in nucleus h :

\frac{d}{d t} {[m R N A]}_{i}^{h} = \frac{1}{τ_{i}} true(f_{i} (U_{n u c}^{h}, {[s n a]}^{h}) - {false[m R N A false]}_{i}^{h} true)

, where f is the production rate of species i , and

U_{n u c}^{h}

Section: Methodsmentioning

confidence: 99%

The Presence of Nuclear Cactus in the Early Drosophila Embryo May Extend the Dynamic Range of the Dorsal Gradient

O'Connell

Reeves

2015

PLoS Comput Biol

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“…These are not the only informative studies we could have chosen; there is an extensive literature on modeling the anterior/posterior and dorsal/ ventral patterning networks operating in the blastoderm [21,22]. The three studies we chose interrogate TRNs at different scales and therefore provide a good illustration of how the goals of the analysis dictate the type of input 712 Genetics of system biology data and the nature of the computational framework used in the study.…”

Section: Quantitative Studies Of Early Drosophila Developmentmentioning

confidence: 99%

Modeling transcriptional networks in Drosophila development at multiple scales

Wunderlich

DePace

2011

Current Opinion in Genetics & Development

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Quantitative models of developmental processes can provide insights at multiple scales. Ultimately, models may be particularly informative for key questions about network level behavior during development such as how does the system respond to environmental perturbation, or operate reliably in different genetic backgrounds? The transcriptional networks that pattern the Drosophila embryo have been the subject of numerous quantitative experimental studies coupled to modeling frameworks in recent years. In this review, we describe three studies that consider these networks at different levels of molecular detail and therefore result in different types of insights. We also discuss other developmental transcriptional networks operating in Drosophila, with the goal of highlighting what additional insights they may provide.

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“…In the field of gene regulation, three different mathematical models have been applied most frequently: Boolean models, thermodynamic-based (also termed “fractional occupancy”) models, and differential equation models [6]. More recently, a fourth approach, which involves stochastic dynamical models together with a modified Gillespie algorithm, has been proposed for this problem [18, 26].…”

Section: Introductionmentioning

confidence: 99%

Two-Layer Mathematical Modeling of Gene Expression: Incorporating DNA-Level Information and System Dynamics

Dresch

Thompson

Arnosti

et al. 2013

SIAM J. Appl. Math.

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High-throughput genome sequencing and transcriptome analysis have provided researchers with a quantitative basis for detailed modeling of gene expression using a wide variety of mathematical models. Two of the most commonly employed approaches used to model eukaryotic gene regulation are systems of differential equations, which describe time-dependent interactions of gene networks, and thermodynamic equilibrium approaches that can explore DNA-level transcriptional regulation. To combine the strengths of these approaches, we have constructed a new two-layer mathematical model that provides a dynamical description of gene regulatory systems, using detailed DNA-based information, as well as spatial and temporal transcription factor concentration data. We also developed a semi-implicit numerical algorithm for solving the model equations and demonstrate here the efficiency of this algorithm through stability and convergence analyses. To test the model, we used it together with the semi-implicit algorithm to simulate a Drosophila gene regulatory circuit that drives development in the dorsal-ventral axis of the blastoderm-stage embryo, involving three genes. For model validation, we have done both mathematical and statistical comparisons between the experimental data and the model’s simulated data. Where protein and cis-regulatory information is available, our two-layer model provides a method for recapitulating and predicting dynamic aspects of eukaryotic transcriptional systems that will greatly improve our understanding of gene regulation at a global level.

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Mathematical modeling of gene expression: a guide for the perplexed biologist

Cited by 130 publications

References 91 publications

The Presence of Nuclear Cactus in the Early Drosophila Embryo May Extend the Dynamic Range of the Dorsal Gradient

The Presence of Nuclear Cactus in the Early Drosophila Embryo May Extend the Dynamic Range of the Dorsal Gradient

Modeling transcriptional networks in Drosophila development at multiple scales

Two-Layer Mathematical Modeling of Gene Expression: Incorporating DNA-Level Information and System Dynamics

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