TWO-LAYER MATHEMATICAL MODELING OF GENE EXPRESSION: INCORPORATING DNA-LEVEL INFORMATION AND SYSTEM DYNAMICS

Dynamics of BMP signaling and stable gene expression in the early Drosophila embryo

In developing tissues, morphogen gradients are thought to initialize gene expression patterns. However, the relationship between the dynamics of morphogen-encoded signals and gene expression decisions is largely unknown. Here we examine the dynamics of the Bone Morphogenetic Protein (BMP) pathway in Drosophila blastoderm-stage embryos. In this tissue, the BMP pathway is highly dynamic: it begins as a broad and weak signal on the dorsal half of the embryo, then 20-30 min later refines into a narrow, intense peak centered on the dorsal midline. This dynamical progression of the BMP signal raises questions of how it stably activates target genes. Therefore, we performed live imaging of the BMP signal and found that dorsal-lateral cells experience only a short transient in BMP signaling, after which the signal is lost completely. Moreover, we measured the transcriptional response of the BMP target gene pannier in live embryos and found it to remain activated in dorsal-lateral cells, even after the BMP signal is lost. Our findings may suggest that the BMP pathway activates a memory, or 'ratchet' mechanism that may sustain gene expression.

Order-of-Mutation Effects on Cancer Progression: Models for Myeloproliferative Neoplasm

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found: JAK2 V617F and one in the TET2 gene. Whether one mutation is present influences how the other subsequent mutation will affect the regulation of gene expression. In other words, when a patient carries both mutations, the order of when they first arose has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation, the Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. Combined, these observations are used to shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Fitting thermodynamic-based models: Incorporating parameter sensitivity improves the performance of an evolutionary algorithm

A detailed comprehension of transcriptional regulation is critical to understanding the genetic control of development and disease across many different organisms. To more fully investigate the complex molecular interactions controlling the precise expression of genes, many groups have constructed mathematical models to complement their experimental approaches. A critical step in such studies is choosing the most appropriate parameter estimation algorithm to enable detailed analysis of the parameters that contribute to the models. In this study, we develop a novel set of evolutionary algorithms that use a pseudo-random Sobol Set to construct the initial population and incorporate parameter sensitivities into the adaptation of mutation rates, using local, global, and hybrid strategies. Comparison of the performance of these new algorithms to a number of current state-of-the-art global parameter estimation algorithms on a range of continuous test functions, as well as synthetic biological data representing models of gene regulatory systems, reveals improved performance of the new algorithms in terms of runtime, error and reproducibility. In addition, by analyzing the ability of these algorithms to fit datasets of varying quality, we provide the experimentalist with a guide to how the algorithms perform across a range of noisy data. These results demonstrate the improved performance of the new set of parameter estimation algorithms and facilitate meaningful integration of model parameters and predictions in our understanding of the molecular mechanisms of gene regulation.

Deciphering enhancer sequence using thermodynamics-based models and convolutional neural networks

Deciphering the sequence-function relationship encoded in enhancers holds the key to interpreting non-coding variants and understanding mechanisms of transcriptomic variation. Several quantitative models exist for predicting enhancer function and underlying mechanisms; however, there has been no systematic comparison of these models characterizing their relative strengths and shortcomings. Here, we interrogated a rich data set of neuroectodermal enhancers in Drosophila, representing cis- and trans- sources of expression variation, with a suite of biophysical and machine learning models. We performed rigorous comparisons of thermodynamics-based models implementing different mechanisms of activation, repression and cooperativity. Moreover, we developed a convolutional neural network (CNN) model, called CoNSEPT, that learns enhancer 'grammar' in an unbiased manner. CoNSEPT is the first general-purpose CNN tool for predicting enhancer function in varying conditions, such as different cell types and experimental conditions, and we show that such complex models can suggest interpretable mechanisms. We found model-based evidence for mechanisms previously established for the studied system, including cooperative activation and short-range repression. The data also favored one hypothesized activation mechanism over another and suggested an intriguing role for a direct, distance-independent repression mechanism. Our modeling shows that while fundamentally different models can yield similar fits to data, they vary in their utility for mechanistic inference. CoNSEPT is freely available at: https://github.com/PayamDiba/CoNSEPT.

A Review of Using Mathematical Modeling to Improve Our Understanding of Bacteriophage, Bacteria, and Eukaryotic Interactions

Phage therapy, the therapeutic usage of viruses to treat bacterial infections, has many theoretical benefits in the ‘post antibiotic era.’ Nevertheless, there are currently no approved mainstream phage therapies. One reason for this is a lack of understanding of the complex interactions between bacteriophage, bacteria and eukaryotic hosts. These three-component interactions are complex, with non-linear or synergistic relationships, anatomical barriers and genetic or phenotypic heterogeneity all leading to disparity between performance and efficacy in in vivo versus in vitro environments. Realistic computer or mathematical models of these complex environments are a potential route to improve the predictive power of in vitro studies for the in vivo environment, and to streamline lab work. Here, we introduce and review the current status of mathematical modeling and highlight that data on genetic heterogeneity and mutational stochasticity, time delays and population densities could be critical in the development of realistic phage therapy models in the future. With this in mind, we aim to inform and encourage the collaboration and sharing of knowledge and expertise between microbiologists and theoretical modelers, synergising skills and smoothing the road to regulatory approval and widespread use of phage therapy.

Expression pattern determines regulatory logic

Large amounts of effort have been invested in trying to understand how a single genome is able to specify the identity of hundreds of cell types. Inspired by some aspects of Caenorhabditis elegans biology, we implemented an in silico evolutionary strategy to produce gene regulatory networks (GRNs) that drive cell-specific gene expression patterns, mimicking the process of terminal cell differentiation. Dynamics of the gene regulatory networks are governed by a thermodynamic model of gene expression, which uses DNA sequences and transcription factor degenerate position weight matrixes as input. In a version of the model, we included chromatin accessibility. Experimentally, it has been determined that cell-specific and broadly expressed genes are regulated differently. In our in silico evolved GRNs, broadly expressed genes are regulated very redundantly and the architecture of their cis-regulatory modules is different, in accordance to what has been found in C. elegans and also in other systems. Finally, we found differences in topological positions in GRNs between these two classes of genes, which help to explain why broadly expressed genes are so resilient to mutations. Overall, our results offer an explanatory hypothesis on why broadly expressed genes are regulated so redundantly compared to cell-specific genes, which can be extrapolated to phenomena such as ChIP-seq HOT regions.

Analyzing the stability of gene expression using a simple reaction-diffusion model in an early Drosophila embryo

In all complex organisms, the precise levels and timing of gene expression controls vital biological processes. In higher eukaryotes, including the fruit fly Drosophila melanogaster, the complex molecular control of transcription (the synthesis of RNA from DNA) and translation (the synthesis of proteins from RNA) events driving this gene expression are not fully understood. In particular, for Drosophila melanogaster, there is a plethora of experimental data, including quantitative measurements of both RNA and protein concentrations, but the precise mechanisms that control the dynamics of gene expression during early development and the processes which lead to steady-state levels of certain proteins remain elusive. This study analyzes a current mathematical modeling approach in an attempt to better understand the long-term behavior of gene regulation. The model is a modified reaction-diffusion equation which has been previously employed in predicting gene expression levels and studying the relative contributions of transcription and translation events to protein abundance [10,11,24]. Here, we use Matrix Algebra and Analysis techniques to study the stability of the gene expression system and analyze equilibria, using very general assumptions regarding the parameter values incorporated into the model. We prove that, given realistic biological parameter values, the system will result in a unique, stable equilibrium solution. Additionally, we give an example of this long-term behavior using the model alongside actual experimental data obtained from Drosophila embryos.

Sig2GRN: a software tool linking signaling pathway with gene regulatory network for dynamic simulation

Background

Linking computational models of signaling pathways to predicted cellular responses such as gene expression regulation is a major challenge in computational systems biology. In this work, we present Sig2GRN, a Cytoscape plugin that is able to simulate time-course gene expression data given the user-defined external stimuli to the signaling pathways.

Methods

A generalized logical model is used in modeling the upstream signaling pathways. Then a Boolean model and a thermodynamics-based model are employed to predict the downstream changes in gene expression based on the simulated dynamics of transcription factors in signaling pathways.

Results

Our empirical case studies show that the simulation of Sig2GRN can predict changes in gene expression patterns induced by DNA damage signals and drug treatments.

Conclusions

As a software tool for modeling cellular dynamics, Sig2GRN can facilitate studies in systems biology by hypotheses generation and wet-lab experimental design.

Availability: http://histone.scse.ntu.edu.sg/Sig2GRN/

Analysis of functional importance of binding sites in the Drosophila gap gene network model

BACKGROUND

The statistical thermodynamics based approach provides a promising framework for construction of the genotype-phenotype map in many biological systems. Among important aspects of a good model connecting the DNA sequence information with that of a molecular phenotype (gene expression) is the selection of regulatory interactions and relevant transcription factor bindings sites. As the model may predict different levels of the functional importance of specific binding sites in different genomic and regulatory contexts, it is essential to formulate and study such models under different modeling assumptions.

RESULTS

We elaborate a two-layer model for the Drosophila gap gene network and include in the model a combined set of transcription factor binding sites and concentration dependent regulatory interaction between gap genes hunchback and Kruppel. We show that the new variants of the model are more consistent in terms of gene expression predictions for various genetic constructs in comparison to previous work. We quantify the functional importance of binding sites by calculating their impact on gene expression in the model and calculate how these impacts correlate across all sites under different modeling assumptions.

CONCLUSIONS

The assumption about the dual interaction between hb and Kr leads to the most consistent modeling results, but, on the other hand, may obscure existence of indirect interactions between binding sites in regulatory regions of distinct genes. The analysis confirms the previously formulated regulation concept of many weak binding sites working in concert. The model predicts a more or less uniform distribution of functionally important binding sites over the sets of experimentally characterized regulatory modules and other open chromatin domains.

Global sensitivity analysis of a dynamic model for gene expression in Drosophila embryos

It is well known that gene regulation is a tightly controlled process in early organismal development. However, the roles of key processes involved in this regulation, such as transcription and translation, are less well understood, and mathematical modeling approaches in this field are still in their infancy. In recent studies, biologists have taken precise measurements of protein and mRNA abundance to determine the relative contributions of key factors involved in regulating protein levels in mammalian cells. We now approach this question from a mathematical modeling perspective. In this study, we use a simple dynamic mathematical model that incorporates terms representing transcription, translation, mRNA and protein decay, and diffusion in an early Drosophila embryo. We perform global sensitivity analyses on this model using various different initial conditions and spatial and temporal outputs. Our results indicate that transcription and translation are often the key parameters to determine protein abundance. This observation is in close agreement with the experimental results from mammalian cells for various initial conditions at particular time points, suggesting that a simple dynamic model can capture the qualitative behavior of a gene. Additionally, we find that parameter sensitivites are temporally dynamic, illustrating the importance of conducting a thorough global sensitivity analysis across multiple time points when analyzing mathematical models of gene regulation.

Sequence-based model of gap gene regulatory network

BACKGROUND

The detailed analysis of transcriptional regulation is crucially important for understanding biological processes. The gap gene network in Drosophila attracts large interest among researches studying mechanisms of transcriptional regulation. It implements the most upstream regulatory layer of the segmentation gene network. The knowledge of molecular mechanisms involved in gap gene regulation is far less complete than that of genetics of the system. Mathematical modeling goes beyond insights gained by genetics and molecular approaches. It allows us to reconstruct wild-type gene expression patterns in silico, infer underlying regulatory mechanism and prove its sufficiency.

RESULTS

We developed a new model that provides a dynamical description of gap gene regulatory systems, using detailed DNA-based information, as well as spatial transcription factor concentration data at varying time points. We showed that this model correctly reproduces gap gene expression patterns in wild type embryos and is able to predict gap expression patterns in Kr mutants and four reporter constructs. We used four-fold cross validation test and fitting to random dataset to validate the model and proof its sufficiency in data description. The identifiability analysis showed that most model parameters are well identifiable. We reconstructed the gap gene network topology and studied the impact of individual transcription factor binding sites on the model output. We measured this impact by calculating the site regulatory weight as a normalized difference between the residual sum of squares error for the set of all annotated sites and for the set with the site of interest excluded.

CONCLUSIONS

The reconstructed topology of the gap gene network is in agreement with previous modeling results and data from literature. We showed that 1) the regulatory weights of transcription factor binding sites show very weak correlation with their PWM score; 2) sites with low regulatory weight are important for the model output; 3) functional important sites are not exclusively located in cis-regulatory elements, but are rather dispersed through regulatory region. It is of importance that some of the sites with high functional impact in hb, Kr and kni regulatory regions coincide with strong sites annotated and verified in Dnase I footprint assays.

Multiscale modeling of dorsoventral patterning in Drosophila

The role of mathematical models of signaling networks is showcased by examples from Drosophila development. Three models of consecutive stages in dorsoventral patterning are presented. We begin with a compartmental model of intracellular reactions that generates a gradient of nuclear-localized Dorsal, exhibiting constant shape and dynamic amplitude. A simple thermodynamic model of equilibrium binding explains how a spatially uniform transcription factor, Zelda, can act in combination with a graded factor, Dorsal, to cooperatively regulate gene expression borders. Finally, we formulate a dynamic and stochastic model that predicts spatiotemporal patterns of Sog expression based on known patterns of its transcription factor, Dorsal. The future of coupling multifarious models across multiple temporal and spatial scales is discussed.

Old cell, new trick? Cnidocytes as a model for the evolution of novelty

Understanding how new cell types arise is critical for understanding the evolution of organismal complexity. Questions of this nature, however, can be difficult to answer due to the challenge associated with defining the identity of a truly novel cell. Cnidarians (anemones, jellies, and their allies) provide a unique opportunity to investigate the molecular regulation and development of cell-novelty because they possess a cell that is unique to the cnidarian lineage and that also has a very well-characterized phenotype: the cnidocyte (stinging cell). Because cnidocytes are thought to differentiate from the cell lineage that also gives rise to neurons, cnidocytes can be expected to express many of the same genes expressed in their neural "sister" cells. Conversely, only cnidocytes posses a cnidocyst (the explosive organelle that gives cnidocytes their sting); therefore, those genes or gene-regulatory relationships required for the development of the cnidocyst can be expected to be expressed uniquely (or in unique combination) in cnidocytes. This system provides an important opportunity to: (1) construct the gene-regulatory network (GRN) underlying the differentiation of cnidocytes, (2) assess the relative contributions of both conserved and derived genes in the cnidocyte GRN, and (3) test hypotheses about the role of novel regulatory relationships in the generation of novel cell types. In this review, we summarize common challenges to studying the evolution of novelty, introduce the utility of cnidocyte differentiation in the model cnidarian, Nematostella vectensis, as a means of overcoming these challenges, and describe an experimental approach that leverages comparative tissue-specific transcriptomics to generate hypotheses about the GRNs underlying the acquisition of the cnidocyte identity.

Quantitative modeling of a gene's expression from its intergenic sequence

Modeling a gene's expression from its intergenic locus and trans-regulatory context is a fundamental goal in computational biology. Owing to the distributed nature of cis-regulatory information and the poorly understood mechanisms that integrate such information, gene locus modeling is a more challenging task than modeling individual enhancers. Here we report the first quantitative model of a gene's expression pattern as a function of its locus. We model the expression readout of a locus in two tiers: 1) combinatorial regulation by transcription factors bound to each enhancer is predicted by a thermodynamics-based model and 2) independent contributions from multiple enhancers are linearly combined to fit the gene expression pattern. The model does not require any prior knowledge about enhancers contributing toward a gene's expression. We demonstrate that the model captures the complex multi-domain expression patterns of anterior-posterior patterning genes in the early Drosophila embryo. Altogether, we model the expression patterns of 27 genes; these include several gap genes, pair-rule genes, and anterior, posterior, trunk, and terminal genes. We find that the model-selected enhancers for each gene overlap strongly with its experimentally characterized enhancers. Our findings also suggest the presence of sequence-segments in the locus that would contribute ectopic expression patterns and hence were "shut down" by the model. We applied our model to identify the transcription factors responsible for forming the stripe boundaries of the studied genes. The resulting network of regulatory interactions exhibits a high level of agreement with known regulatory influences on the target genes. Finally, we analyzed whether and why our assumption of enhancer independence was necessary for the genes we studied. We found a deterioration of expression when binding sites in one enhancer were allowed to influence the readout of another enhancer. Thus, interference between enhancer activities was a possible factor necessitating enhancer independence in our model.

A primer on thermodynamic-based models for deciphering transcriptional regulatory logic

A rigorous analysis of transcriptional regulation at the DNA level is crucial to the understanding of many biological systems. Mathematical modeling has offered researchers a new approach to understanding this central process. In particular, thermodynamic-based modeling represents the most biophysically informed approach aimed at connecting DNA level regulatory sequences to the expression of specific genes. The goal of this review is to give biologists a thorough description of the steps involved in building, analyzing, and implementing a thermodynamic-based model of transcriptional regulation. The data requirements for this modeling approach are described, the derivation for a specific regulatory region is shown, and the challenges and future directions for the quantitative modeling of gene regulation are discussed.