Constitutive and alternative splicing are necessary steps in mRNA processing that contributes to a diverse proteome, but errors in splicing machinery lead to numerous degenerative diseases and cancers. The SR proteins are essential splicing factors that control splice-site selection as well as the transport of processed mRNA for translation. The SR proteins consist of one or two RNA- binding domains and an RS domain rich in arginine-serine repeats. Processive poly-phosphorylation of the RS domain by splicing kinases such as SRPK1, and subsequent dephosphorylation by nuclear phosphatases such as PP1 regulate cellular localization and mRNA processing functions of SR proteins. In this thesis we focused on SRPK1-catalyzed phosphorylation and PP1-catalyzed dephosphorylation of the prototypical SR protein, ASF/SF2. Our overall goals were to establish whether these two enzymes add and remove phosphates in a directional manner and determine specific sequence elements that control initiation and sequential modification of the RS domain of ASF/SF2. A novel LysC digestion phosphomapping technique was developed to observe the order of phosphorylation. We found that SRPK1 phosphorylates ASF/SF2 in a C->N direction preferring to initiate between S221-S225 of ASF/ SF2, but the kinase can adapt to other start sequences if the initiation box is made dysfunctional through mutation. Having established that SRPK1 is a directional kinase with a strong preference for phosphorylation initiation in the center of the RS domain, we then explored structural determinants within the enzyme and substrate that might control this novel mechanism of phosphorylation. Mutagenesis within the RS domain revealed that an uninterrupted RS/SR stretch is necessary for initiation preference. Using the SRPK1:ASF/SF2 complex as a guide for mutagenesis studies, we found that RRM2 (but not RRM1) and N'-RS1 of the RS domain of ASF/SF2 form important and cooperative contacts with SRPK1 that guide directional phosphorylation. Thus, while RS/SR content in the RS domain alone governs regiospecificity, directional phosphorylation is controlled by distal structural elements offered by RRM2 and the docking groove in SRPK1. To analyze how phosphates are removed from the RS domain of ASF/SF2, we studied the dephosphorylation reaction catalyzed by the nuclear protein phosphatase, PP1. PP1 was found to remove phosphates from the RS1 segment of ASF/SF2 in a single kinetic phase suggesting that a common rate- limiting step exists. Deletion analyses indicated that RRM1 protects against dephosphorylation. Through digestion mapping, we found that PP1 dephosphorylates ASF/SF2 in an N->C direction and that removal of RRM1 leads to random dephosphorylation. These data suggest that while RRM2 is important for the directional phosphorylation of ASF/SF2, RRM1 is important for the directional dephosphorylation. Overall, the data suggest that the opposing directional activities of SRPK1 and PP1 may foster the preferential modification of serines in the C-terminal end of RS1 in ASF/SF2, with possible biological relevance

For a large ensemble of complex systems, a Many-System Problem (MSP) studies how heterogeneity constrains and hides structural mechanisms, and how to uncover and reveal hidden major factors from homogeneous parts. All member systems in an MSP share common governing principles of dynamics, but differ in idiosyncratic characteristics. A typical dynamic is found underlying response features with respect to covariate features of quantitative or qualitative data types. Neither all-system-as-one-whole nor individual system-specific functional structures are assumed in such response-vs-covariate (Re-Co) dynamics. We developed a computational protocol for identifying various collections of major factors of various orders underlying Re-Co dynamics. We first demonstrate the immanent effects of heterogeneity among member systems, which constrain compositions of major factors and even hide essential ones. Secondly, we show that fuller collections of major factors are discovered by breaking heterogeneity into many homogeneous parts. This process further realizes Andersons More is Different phenomenon. We employ the categorical nature of all features and develop a Categorical Exploratory Data Analysis (CEDA)-based major factor selection protocol. Information theoretical measurements-conditional mutual information and entropy-are heavily used in two selection criteria: C1-confirmable and C2-irreplaceable. All conditional entropies are evaluated through contingency tables with algorithmically computed reliability against the finite sample phenomenon. We study one artificially designed MSP and then two real collectives of Major League Baseball (MLB) pitching dynamics with 62 slider pitchers and 199 fastball pitchers, respectively. Finally, our MSP data analyzing techniques are applied to resolve a scientific issue related to the Rosenberg Self-Esteem Scale.

Without assuming any functional or distributional structure, we select collections of major factors embedded within response-versus-covariate (Re-Co) dynamics via selection criteria [C1: confirmable] and [C2: irrepaceable], which are based on information theoretic measurements. The two criteria are constructed based on the computing paradigm called Categorical Exploratory Data Analysis (CEDA) and linked to Wiener-Granger causality. All the information theoretical measurements, including conditional mutual information and entropy, are evaluated through the contingency table platform, which primarily rests on the categorical nature within all involved features of any data types: quantitative or qualitative. Our selection task identifies one chief collection, together with several secondary collections of major factors of various orders underlying the targeted Re-Co dynamics. Each selected collection is checked with algorithmically computed reliability against the finite sample phenomenon, and so is each members major factor individually. The developments of our selection protocol are illustrated in detail through two experimental examples: a simple one and a complex one. We then apply this protocol on two data sets pertaining to two somewhat related but distinct pitching dynamics of two pitch types: slider and fastball. In particular, we refer to a specific Major League Baseball (MLB) pitcher and we consider data of multiple seasons.

We investigate the dynamic characteristics of Covid-19 daily infection rates in Taiwan during its initial surge period, focusing on 79 districts within the seven largest cities. By employing computational techniques, we extract 18 features from each district-specific curve, transforming unstructured data into structured data. Our analysis reveals distinct patterns of asymmetric growth and decline among the curves. Utilizing theoretical information measurements such as conditional entropy and mutual information, we identify major factors of order-1 and order-2 that influence the peak value and curvature at the peak of the curves, crucial features characterizing the infection rates. Additionally, we examine the impact of geographic and socioeconomic factors on the curves by encoding each of the 79 districts with two binary characteristics: North-vs-South and Urban-vs-Suburban. Furthermore, leveraging this data-driven understanding at the district level, we explore the fine-scale behavioral effects on disease spread by examining the similarity among 96 age-group-specific curves within urban districts of Taipei and suburban districts of New Taipei City, which collectively represent a substantial portion of the nations population. Our findings highlight the implicit influence of human behaviors related to living, traveling, and working on the dynamics of Covid-19 transmission in Taiwan.

We develop Categorical Exploratory Data Analysis (CEDA) with mimicking to explore and exhibit the complexity of information content that is contained within any data matrix: categorical, discrete, or continuous. Such complexity is shown through visible and explainable serial multiscale structural dependency with heterogeneity. CEDA is developed upon all features' categorical nature via histogram and it is guided by all features' associative patterns (order-2 dependence) in a mutual conditional entropy matrix. Higher-order structural dependency of k(≥3) features is exhibited through block patterns within heatmaps that are constructed by permuting contingency-kD-lattices of counts. By growing k, the resultant heatmap series contains global and large scales of structural dependency that constitute the data matrix's information content. When involving continuous features, the principal component analysis (PCA) extracts fine-scale information content from each block in the final heatmap. Our mimicking protocol coherently simulates this heatmap series by preserving global-to-fine scales structural dependency. Upon every step of mimicking process, each accepted simulated heatmap is subject to constraints with respect to all of the reliable observed categorical patterns. For reliability and robustness in sciences, CEDA with mimicking enhances data visualization by revealing deterministic and stochastic structures within each scale-specific structural dependency. For inferences in Machine Learning (ML) and Statistics, it clarifies, upon which scales, which covariate feature-groups have major-vs.-minor predictive powers on response features. For the social justice of Artificial Intelligence (AI) products, it checks whether a data matrix incompletely prescribes the targeted system.

We reformulate and reframe a series of increasingly complex parametric statistical topics into a framework of response-vs.-covariate (Re-Co) dynamics that is described without any explicit functional structures. Then we resolve these topics' data analysis tasks by discovering major factors underlying such Re-Co dynamics by only making use of data's categorical nature. The major factor selection protocol at the heart of Categorical Exploratory Data Analysis (CEDA) paradigm is illustrated and carried out by employing Shannon's conditional entropy (CE) and mutual information (I[Re;Co]) as the two key Information Theoretical measurements. Through the process of evaluating these two entropy-based measurements and resolving statistical tasks, we acquire several computational guidelines for carrying out the major factor selection protocol in a do-and-learn fashion. Specifically, practical guidelines are established for evaluating CE and I[Re;Co] in accordance with the criterion called [C1:confirmable]. Following the [C1:confirmable] criterion, we make no attempts on acquiring consistent estimations of these theoretical information measurements. All evaluations are carried out on a contingency table platform, upon which the practical guidelines also provide ways of lessening the effects of the curse of dimensionality. We explicitly carry out six examples of Re-Co dynamics, within each of which, several widely extended scenarios are also explored and discussed.

Background

Physical scaffolds are useful for supporting cells to form three-dimensional (3D) tissue. However, it is non-trivial to develop a scheme that can robustly guide cells to self-organize into a tissue with the desired 3D spatial structures. To achieve this goal, the rational regulation of cellular self-organization in 3D extracellular matrix (ECM) such as hydrogel is needed.

Results

In this study, we integrated the Turing reaction-diffusion mechanism with the self-organization process of cells and produced multicellular 3D structures with the desired configurations in a rational manner. By optimizing the components of the hydrogel and applying exogenous morphogens, a variety of multicellular 3D architectures composed of multipotent vascular mesenchymal cells (VMCs) were formed inside hyaluronic acid (HA) hydrogels. These 3D architectures could mimic the features of trabecular bones and multicellular nodules. Based on the Turing reaction-diffusion instability of morphogens and cells, a theoretical model was proposed to predict the variations observed in 3D multicellular structures in response to exogenous factors. It enabled the feasibility to obtain diverse types of 3D multicellular structures by addition of Noggin and/or BMP2.

Conclusions

The morphological consistency between the simulation prediction and experimental results probably revealed a Turing-type mechanism underlying the 3D self-organization of VMCs in HA hydrogels. Our study has provided new ways to create a variety of self-organized 3D multicellular architectures for regenerating biomaterial and tissues in a Turing mechanism-based approach.

Our computational developments and analyses on experimental images are designed to evaluate the effectiveness of chemical spraying via unmanned aerial vehicle (UAV). Our evaluations are in accord with the two perspectives of color-complexity: color variety within a color system and color distributional geometry on an image. First, by working within RGB and HSV color systems, we develop a new color-identification algorithm relying on highly associative relations among three color-coordinates to lead us to exhaustively identify all targeted color-pixels. A color-dot is then identified as one isolated network of connected color-pixel. All identified color-dots vary in shapes and sizes within each image. Such a pixel-based computing algorithm is shown robustly and efficiently accommodating heterogeneity due to shaded regions and lighting conditions. Secondly, all color-dots with varying sizes are categorized into three categories. Since the number of small color-dot is rather large, we spatially divide the entire image into a 2D lattice of rectangular. As such, each rectangle becomes a collective of color-dots of various sizes and is classified with respect to its color-dots intensity. We progressively construct a series of minimum spanning trees (MST) as multiscale 2D distributional spatial geometries in a decreasing-intensity fashion. We extract the distributions of distances among connected rectangle-nodes in the observed MST and simulated MSTs generated under the spatial uniformness assumption. We devise a new algorithm for testing 2D spatial uniformness based on a Hierarchical clustering tree upon all involving MSTs. This new tree-based p-value evaluation has the capacity to become exact.