1,720,973 research outputs found
Wavelet-Based Segmentation and Convex Hull Approaches for Quantitative Analysis of Biological Imaging Data
No full textImaging-based analysis of developmental processes are crucial to understand the mechanisms controlling plant and animal development. In vertebrate embryos such as the zebrafish embryo, nuclei segmentation plays an important role to detect and quantify nuclei over space and time. However, limitations of the image quality and segmentation methods may affect the segmentation performance. In plant including studies on Arabidopsis epidermis growth, cellular shape change dictates organ size control and growth behavior, and quantitative image analysis of dynamics cell patterning is needed to link the cause and effect between cells and organs. Here we provide a series of new quantitative biological imaging methods a series of new quantitative biological imaging methods and tools including wavelet-based segmentation method in zebrafish embryo development studies and convex hull approach for quantitative shape analyses of lobed plant cells.Identification of individual cells in tissues, organs, and in various developing systems is a well-studied problem because it is an essential part of objectively analyzing quantitative images in numerous biological contexts. In this paper we present a size dependent wavelet-based segmentation method that provides robust segmentation without any preprocessing, filtering or fine-tuning steps, and is robust to the signal-to-noise ratio (SNR). The program separates overlapping nuclei, identifies cell cycle states and minimizes intensity attenuation in object identification. The wavelet-based methods presented herein achieves robust segmentation results with respect to True Positive rate, Precision, and segmentation accuracy compared with other commonly used methods. We applied the segmentation program to Zebrafish embryonic development IN TOTO quantification and developed an automatic interactive imaging analysis platform named WaveletSEG, that integrates nuclei segmentation, image registration, and nuclei shape analysis. A set of additional functions we developed include a 3D ground truth annotation tool, a synthetic image generator, a segmented training datasets export tool, and data visualization interfaces are also incorporated in WaveletSEG for additional data analysis and data validation.In addition to our work in Zebrafish, we developed image analysis tools for quantitative studies of cell-to-organ in plants. Given the importance of the epidermis and this particular cell type for leaf expansion, there is a strong need to understand how pavement cells morph from a simple polyhedral shape into highly lobed and interdigitated cells. Currently, it is still unclear how and when patterns of lobing are initiated in pavement cells, and one major technological bottleneck to address the problem is the lack of a robust and objective methodology to identify and track lobing events during the transition from simple cell geometry to lobed cells. We develop a convex-hullbased algorithm termed LobeFinder to identify lobes, quantify geometric properties, and create a useful graphical output for further analysis. The algorithm is validated against manually curated cell images of pavement cells of widely varying sizes and shapes. The ability to objectively count and detect new lobe initiation events provides an improved quantitative framework to analyze mutant phenotypes, detect symmetry-breaking events in time-lapse image data, and quantify the time-dependent correlation between cell shape change and intracellular factors that may play a role in the morphogenesis process
Combined Physics and BMP Signaling Network Dynamics to Model Early Embryonic Development in Zebrafish
No full textEmbryonic development is a complicated phenomenon influenced by genetic regulation and biomechanical cellular behaviors. However, the relative influence of these factors on spatiotemporal morphogen distributions is not well understood. Bone Morphogenetic Proteins (BMPs) are the primary morphogen guiding the dorsal-ventral (DV) patterning of the early zebrafish embryo, and BMP signaling is regulated by a network of extracellular and intracellular factors that impact the range and signaling of BMP ligands. Recent advances in understanding the mechanism of pattern formation support a source-sink mechanism, however, it is not clear how the source-sink mechanism shapes patterns in 3D, nor how sensitive the pattern is to biophysical rates and boundary conditions along both the anteroposterior (AP) and DV axes of the embryo.Throughout blastulation and gastrulation, major cell movement, known as epiboly, happens along with the BMP mediated DV patterning. The layer of epithelial cells begins to thin as it spreads toward the vegetal pole of the embryo until it has completely engulfed the yolk cell. This dynamic domain may influence the distributions of BMP network members. This project aims to investigate the multiscale regulatory network of the BMP signaling dynamics along with the biophysical deformation of the embryo tissue during epiboly.In this study, we present a three-dimensional (3D) growing domain mathematical modeling framework to simulate the BMP patterning and epiboly process during the blastula to gastrula stage zebrafish embryo, with both finite difference and finite element approaching. These models provide a starting point to elucidate how different mechanisms and components work together in 3D to create and maintain the BMP gradient in the zebrafish embryo. We are interested in how the cellular movements impact the formation of gradients by contributing an advective term whereby the morphogens are swept with the moving cells as they move vegetally. Dynamic cell imaging data are used to quantify the cell movement during the epiboly. We evaluated the accuracy of the mesh updating compared to the advection caused by cell movement and its role in embryonic patterning. Quantitative whole-mount RNA scope data of BMP2b, Chordin, Noggin, Sizzled, and phosphorylated-SMAD data are collected and analyzed precisely to test the hypotheses of the gradient formation mechanism in our model. We also present a novel approach of Neuro Network model to accelerate the computationally intensive PDE simulations. Our goal is to develop a complete advection-diffusion-reaction model that incorporates all stages of zebrafish embryonic development data. By combining the biophysics of epiboly with the regulatory dynamics of the BMP network, we can test complex models to investigate the consistent spatiotemporal DV patterning in the early zebrafish embryo
Computational Modeling of Transforming Growth Factor-β2 Receptor Complex Assembly
No full textTransforming growth factor (TGF)-β1, TGF-β2, and TGF-β3 are secreted signaling proteins that play an essential role in tissue development, immune response, and physiological homeostasis. TGF-β ligands signal through a tetrameric complex made up of two type I receptors (TβRI) and two type II receptors (TβRII). Dysregulation of TGF-β signaling has been linked to uncontrolled cell proliferation and cancer metastasis. An accurate understanding of TGF-β’s receptor complex assembly pathway may allow for pharmacological intervention and/or preservation of proper TGF-β signaling.Amongst the ligand types, TGF-β1 and TGF-β3 are efficient signalers, presumably by strong binding to both type I and II receptors. However, TGF-β2 has a very weak affinity for TβRII and requires an additional membrane-bound protein called betaglycan (BG) to achieve similar levels of downstream signaling. While computational modeling has been performed on the signaling pathway of the TGF-β system, to date no computational modeling has aimed to decipher BG’s role in the potentiation of TGF-β2 signal. To determine the role of BG in selectively facilitating signaling by TGF-β2, we developed computational models with different assumptions based on the levels of cooperativity between receptor subtypes and types of BG behavior (No Receptor Recruitment model, Single-stage Receptor Recruitment model, and Twostage Receptor Recruitment model).With each of the receptor recruitment models we hypothesized that BG uses two domains to successfully enhance TGF-β2 signaling. This model was first proposed in Villarreal et al., 2016 and is further investigated in this work using a two-step computational approach. First, a root mean square error (RMSE) calculation was performed between our computational models with no BG present and published experimental signaling data in cell lines with no BG present. Lower RMSE values indicate the simulated data is more representative of experimental signaling behavior when no BG is present. The second round of model validation was performed by adding BG into the simulations and comparing its behavior to experimentally determined and hypothesized behaviors of BG.In summary, the simulations indicate there may be more cooperative receptor recruitment present in the system then stated in literature. Furthermore, it appears that BG binding to TGF-β2 ligand through two domains provides an effective transfer mechanism that can be tuned to control differential signaling between TGF-β ligand subtypes. Experiments were then suggested in order to support or refute one of the models offered in this thesis. For the purpose of uncovering how BG enhances TGF-β2 signaling, the computational work performed in this thesis highlights the areas where researchers should focus their experimental efforts and provides a baseline model for further computational work in the TGF-β system
Analysis of stochastic receptor signaling in BMP pathways
No full textMany patterning processes that produce an intricate body pattern from a single cell embryo rely on the precise interpretation of the local concentration of a class of secreted molecules known as morphogens. Morphogens play a crucial role in organismal development by specifying cell fate organization in developing tissues. Patterns of gene expressions or signalling immediately downstream of many morphogens such as the Bone Morphogenetic Proteins(BMPs) are highly reproducible despite the presence of various forms of perturbations. This starkly contrasts with our expectation of a noisy interpretation due to stochastic fluctuations that would arise due to biophysical reasons such as: 1) experimentally determined low concentration (approximately picomolar) BMP activity, 2) tight receptor binding, and 3) very slow kinetic rates. To investigate mechanisms by which this intrinsic noise can be attenuated in BMP-mediated patterning, we focus on a class of secreted molecules that bind to BMPs extracellularly and play an active role in the mediation of BMP/receptor interactions. We developed a stochastic model of BMP signaling in Drosophila melanogaster and used the model to quantify the extent that stochastic fluctuations would lead to errors in spatial patterning. The model was extended to investigate how a surface–associated BMP binding protein (SBP) like Crossveinless-2 (Cv-2) may buffer out signaling noise in the context of BMP signaling. We find that in the presence of SBPs, fluctuations in the level of ligand-bound receptor can be reduced by more than 2-fold depending on the associated dynamics for the intermediate transition states. In order to screen the model based on the parameter values of intermediate transition rates, we developed a comparatively easy, yet efficient and accurate, way of finding the steady-state(SS) distribution of ligand-bound receptor assuming the existence of a unique deterministic SS (unimodal) of the system. To find the approximate SS, we first use the truncated-state space representation to reduce the system to a finite dimension, and subsequently reformulate an eigenvalue problem into a linear system. We used this approach to 1) estimate the steady state probability distribution, 2) calculate the standard deviation (σ) and mean of all the interacting species and 3) quantify the dynamic properties of SBP-mediated receptor regulation. Screening of the network yields three primary qualitative subclasses for Cv-2 behavior in the regulation of extracellular BR (C) fluctuation amplitude: i) reduced amplitude ii) increased amplitude and iii) mixed amplitude behavior [1]. Regulation of receptor-ligand interactions by SBPs may also increase the frequency of stochastic fluctuations providing a separation of time-scales between high frequency receptor equilibration and slower morphogen patterning. High frequency noise generated by SBP regulation is easily attenuated by the intracellular pMad network creating a system that imitates the performance of a simple low pass filter common in audio and communication applications. Together, these data indicate that one of the benefits of receptor-ligand regulation by secreted non-receptors may be greater reliability of BMP-mediated signaling
Quantification of Morphogen Gradients and Patterning Scale Invariance along Dorsal-ventral Embryonic Axis
Full text linkMorphogen gradients provide positional information to underlying cells that translate the information into differential gene expression and eventually different cell fates. Scale invariance is the property where the gradients of the morphogen adjust proportionately to the size of the domain. Scale invariance of morphogen gradients or patterns of differentiation is a common phenomenon observed between individuals within the same species and between homologous tissues or structures in different species. To determine whether a pattern is scale invariant, we and others developed definitions and measurements of gradient scaling. These include point-wise and global scaling errors as well as global scaling power. Furthermore, there are several mathematical conditions for scale invariance of advection-diffusion-reaction models that inform mechanisms of scaling. Herein we provide a deeper perspective on modeling and measurement of scale-invariance of morphogen gradients. Scale invariance of DV patterning has been investigated in invertebrates but remains poorly-understood in vertebrates. In both vertebrates and invertebrates, spatial patterning progression along Dorsal-ventral (DV) embryonic axis depends on a morphogen gradient of Bone Morphogenetic Protein (BMP) signaling. Here, we introduce a method for studying DV patterning scale invariance by precisely altering the size of zebrafish embryos by reducing vegetal yolk. Use of this method in scaling experiments indicated that the degree of scaling for intraspecies scaling within zebrafish is greater than that between Danioninae species. Specifically, through analysis of experimentally re-sized embryos, we determined that DV patterning and its underlying morphogen gradients are scale invariant within species of zebrafish. We then extended our study to investigate DV patterning between Danioninae species (zebrafish and giant danio) and found that morphogen gradients do not scale between Danioninae species. In the process of developing tools to quantify morphogen gradients from fluorescent images, we created a novel method to match points in two partially overlapping images. Point cloud data sets, or simply point clouds (PCs), originating from a common specimen but containing different measurement parameters (i.e. using different sensors, times, depths, viewpoints, etc.) usually contain both overlapping and non-overlapping points. Registration aligns these distinct PCs into one coordinate system by assigning point-by-point correspondence between PCs and applying a transformation. Registration shows great potential for practical applications, but the effectiveness of current methods is limited in PCs having large differences in relative initial positions, low overlapping ratios, and excessive noise. We introduce a point matching algorithm called Signature that relaxes these constraints. We approach the problem of identifying corresponding points between PCs by assigning and matching point identification (ID), or the distance of a point to a select number of closest points in the same PC. Signature has been tested on both computationally generated images and experimentally generated images from confocal microscopy of biological samples. Signature accurately identifies point correspondence in PCs with any initial angles, with overlapping ratios as low as 15%, and shows some improvement in aligning noisy PCs. Preprocessing with Signature also intelligently relaxes point-wise registration of initial point positions. Furthermore, combining Signature with Anchor Point Alignment allows for robust alignment of noise-free PCs under any initial position
Network Analysis of Extracellular Matrix Microenvironment Signaling in Vasculogenesis
No full textAberrant blood vessel formation is implicated in many diseases. Physiological and pathological vascularization is governed by a balance of pro- and anti-neovascular signals in the microenvironment that control a neovascular switch. Several anti-neovascular drugs targeting specific molecules are under investigation; however, the dynamics of the neovascular switch are poorly understood, so it is difficult to predict how the vasculature will respond to particular therapeutic regimens. The purpose of the current research is to investigate the dynamics of the extracellular matrix molecules that promote and inhibit neovascularization through the mechanotransduction pathway. We focused on force-dependent signaling through β1 integrin and investigated the dynamics by building a computational model of the effects of pro-neovascular type I collagen, type IV collagen, and type IV collagen-derived anti-neovascular fragments on vessel growth in vivo and in vitro, including matrix metalloproteinase signaling important for the feedback between the endothelial cells and the matrix. Using data from a three-dimensional tissue culture system of endothelial colony forming cells embedded in type I oligomeric collagen, as well as various sources in the experimental literature, we used the computational model to understand the mechanism by which β1 integrin integrates the mechanical signals of interest. Because the available data is largely qualitative, we used optimal scaling and multi-objective optimization to facilitate its use with the computational model. We focused on two specific mechanisms: direct inhibition of matrix metalloproteinase (MMP) activation by type IV collagen fragments and positive autoregulation of recruitment of β1 integrin to the focal adhesion site. We found that in order to fit the experimental data, positive autoregulation is necessary for integrin dynamics and the dominant mechanism of inhibition of MMP activation by type IV collagen fragments is through indirect means. With further extension of this model, we can investigate downstream signaling that guides vasculogenesis and understand the dynamics of therapeutics that utilize this pathway
Quantitative analysis for complex biological models using qualitative data: Applications in developmental biology
No full textBetter understanding the many complex processes governing living organisms relies on the combination of efficient experimentation and careful consideration in a theoretical framework. Informed by experimental data, mathematical modeling offers many tools to aid comprehension of complex systems, providing critical support throughout biological sciences. However, the technical challenges to performing precise experiments and making many molecular measurements, all in fragile living systems, limit the ability to quantify data. Much biological data is instead qualitative, especially in fields such as developmental biology, which emphasizes imaging molecular distributions across many cells or whole tissues. In contrast with quantitative measurements, there is an absence of tools to incorporate information from these qualitative data into the mathematical models used to understand complex interactions, compare and distinguish hypotheses, predict behavior, and plan experiments. The work presented in this dissertation develops strategies to address the technical limitations to quantitative modeling with qualitative data, applied in the context of developmental biology. Two parallel objectives are discussed. The theoretical objective is the development of a parameter estimation procedure for complex models that accommodates qualitative information, based on existing qualitative and quantitative techniques. The biological objective is the elucidation of stem cell regulatory mechanisms through study of the Drosophila germarium, a stem cell niche in the ovary. Mathematical representations of the germarium system are formulated based on experimental evidence, and employed to evaluate the viability and potential effects of several proposed mechanisms. Through the newly developed parameter estimation procedure, multiple hypothetical mechanisms are compared based on a compilation of published qualitative data from wild type flies and genetic mutants. The extent to which these experiments can distinguish hypotheses is shown, and the quantitatively tuned models are used to estimate the utility of feasible future experiments to refine models and better discriminate among them. The framework and procedure developed herein offer benefits to many applications of mathematical modeling in biology, biotechnology and other fields where qualitative data are prevalent
QUANTITATIVE MODELING OF SCALING OF PATTERNS AND RECEPTOR SIGNALING IN MORPHOGENESIS
Full text linkOrgans and tissue development often experience perturbations, but developmental processes seem to replicate a common body template to maintain appropriate proportions and positions. The key signaling factors that guide a number of those processes are known as morphogens. Developing cells sense their respective positional information from a graded morphogen profile, and differentiate into patterns. Remarkably, patterns are highly robust and reproducible among species, and the underlying mechanisms associated with such high degrees of precision are still enigmatic. In addition, details of the signal, such as the Bone Morphogenetic Protein (BMP) signal, that transmit patterning information to a group of homogenous cells to differentiate is not well understood. Determining how developmental processes ensure robust patterning in the presence of perturbations, and what regulatory mechanisms act to ensure robust and reproducible patterning are two longstanding questions that need unraveling. Moreover, determining the mechanisms by which BMP heterodimers dominate signaling in developing zebrafish embryos and other contexts is a key factor in understanding developmental regulation for a classic morphogen patterning system.
To answer these questions, this work has developed a set of mathematical models to evaluate and interrogate potential signaling networks and regulatory motifs. These models identify scaling mechanisms, test hypotheses on heterodimer dominance during signal transduction, and show how patterning systems function. For the scaling problem, this research proposes a Two Component System (TCS) mechanism, where a morphogen (m) and a modulator (M) interact to alter the transport and reaction properties of each other spatially. An exhaustive parametric and network motif screen is conducted for several TCS variants under the reaction-diffusion-advection paradigm with spatially varying coefficients. Our analysis revealed a number of candidate networks and minimal regulatory motifs that achieve the precision needed for a developing species to ensure perfect development. Computational models of patterning signal, namely the Bone Morphogenetic Protein (BMP) mediated signal, were developed to analyze the receptor oligomerization that forms heterotetrameric receptor associations in BMP signaling. The oligomerization model disproves previous kinetic based hypotheses of heterodimer dominance, and identifies other theoretical conditions to acquire heterodimer dominance. Finally, the model predicts that heterodimer dominance provides a larger dynamic range and a higher concentration of morphogen activity, making it a robust sensor responding wide ranges of morphogen concentrations fundamental to a morphogen gradient system. Moreover, stochastic analysis of oligomerization steps reveal that recruitment of type II receptors during the receptor oligomerization by itself does not tend to lower noise in receptor signaling. This outcome can be applied to develop a complete probabilistic model of receptor oligomerization events.
The computational arrangements and frameworks developed in this research have wider applications - for instance, illustration of a large-scale screen of a reaction-diffusion-advection systems with spatially varying coefficients is an efficient strategy to perform a large-scale screen of such system and could have wider applications in other areas. Additionally, our mathematical framework on the dynamics of a tetrameric complex formation and oligomerization steps could be applicable to other signaling pathways that require trimeric/tetrameric complex formation on the cell surface to elicit signaling
Estimation and Regulation of Spatially Distributed Signals
No full textDetection and estimation of unknown parameters in random systems, and regulation of signal sensing, are both important in the study of a wide range of systems including communication, ecological, biological, and manufacturing systems. For instance, the rate of photons hitting at the array of photon detectors, the number of cells of interest in a fluorescence cell sorting experiment, and identifying faulty products through random inspection in manufacturing, are all examples of randomly occurring phenomena that are analogous to detection of random objects using a randomly distributed set of detectors or detection attempts. Additionally, an efficient and cost-effective detection system for random targets requires precise knowledge of the number of detectors, position of the detectors, or the rate of detection attempts that can detect the targets with sufficient accuracy. Moreover, many systems, such as biochemical systems, require signal sensing with remarkable resilience in response to various forms of intrinsic and extrinsic variations. One such system is pattern formation by morphogen during different stages of species development. A morphogen gradient transmits positional information to a homogeneous field of cells and differentiates them into distinct patterns. Many factors, such as modulators, regulate morphogen signaling to ensure reproducibility of patterns. During signal transduction, morphogen always degrades, and an important question that needs unraveling is how different degradation mechanisms of morphogen affect system\u27s ability to scale. To study these problems, we use point processes to approximate the detection of randomly arriving targets by randomly distributed detection attempts, and the analysis of the impact of degradation schemes on scaling is done using a partial differential equation (PDE) model. Specifically, we propose a Maximum Likelihood Estimator (MLE) framework to estimate the rate of random targets by detecting the targets using randomly distributed set of detectors. In this analysis, both the random targets, and the detectors, are modeled as Poisson processes. With the assumption that detection is certain when targets and detection attempts are within a fixed detection window, the proposed MLE successfully estimates the underlying rate of the targets, and the performance of the MLE is shown to be largely dependent on the detection window considered. In addition, research reveals that with a sufficiently large rate of detection attempts, bias of the estimation reduces to a negligibly low value. It is worth mentioning that this MLE is applicable to estimate rate of random arrival in any given continuum, and the MLE formulation can be used for non-Poisson processes as well. Furthermore, to study the role of degradation schemes on morphogen signaling and its ability to scale, we use a partial differential equation (PDE) model for a two component system (TCS) comprising of a morphogen and a modulator. Using the model, we compare the role of two different degradation mechanisms-- i) linear degradation of morphogen, ii) linear + quadratic degradation of morphogen. A large-scale parametric screen reveals that both decay mechanisms are able to achieve scaling, and a quadratic decay of morphogen is not mandatory to achieve scaling in patterning systems. These findings increase our understanding of how morphogen gradient scales in many species
- …
