Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network

<p>Abstract</p> <p>Background</p> <p>Gene Regulatory Networks (GRNs) control the differentiation, specification and function of cells at the genomic level. The levels of interactions within large GRNs are of enormous depth and complexity. Details about many GRNs are emerging, but in most cases it is unknown to what extent they control a given process, i.e. the grade of completeness is uncertain. This uncertainty stems from limited experimental data, which is the main bottleneck for creating detailed dynamical models of cellular processes. Parameter estimation for each node is often infeasible for very large GRNs. We propose a method, based on random parameter estimations through Monte-Carlo simulations to measure completeness grades of GRNs.</p> <p>Results</p> <p>We developed a heuristic to assess the completeness of large GRNs, using ODE simulations under different conditions and randomly sampled parameter sets to detect parameter-invariant effects of perturbations. To test this heuristic, we constructed the first ODE model of the whole sea urchin endomesoderm GRN, one of the best studied large GRNs. We find that nearly 48% of the parameter-invariant effects correspond with experimental data, which is 65% of the expected optimal agreement obtained from a submodel for which kinetic parameters were estimated and used for simulations. Randomized versions of the model reproduce only 23.5% of the experimental data.</p> <p>Conclusion</p> <p>The method described in this paper enables an evaluation of network topologies of GRNs without requiring any parameter values. The benefit of this method is exemplified in the first mathematical analysis of the complete Endomesoderm Network Model. The predictions we provide deliver candidate nodes in the network that are likely to be erroneous or miss unknown connections, which may need additional experiments to improve the network topology. This mathematical model can serve as a scaffold for detailed and more realistic models. We propose that our method can be used to assess a completeness grade of any GRN. This could be especially useful for GRNs involved in human diseases, where often the amount of connectivity is unknown and/or many genes/interactions are missing.</p

Automated Translation and Accelerated Solving of Differential Equations on Multiple GPU Platforms

We demonstrate a high-performance vendor-agnostic method for massively parallel solving of ensembles of ordinary differential equations (ODEs) and stochastic differential equations (SDEs) on GPUs. The method is integrated with a widely used differential equation solver library in a high-level language (Julia's DifferentialEquations.jl) and enables GPU acceleration without requiring code changes by the user. Our approach achieves state-of-the-art performance compared to hand-optimized CUDA-C++ kernels, while performing $20-100\times$ faster than the vectorized-map (\texttt{vmap}) approach implemented in JAX and PyTorch. Performance evaluation on NVIDIA, AMD, Intel, and Apple GPUs demonstrates performance portability and vendor-agnosticism. We show composability with MPI to enable distributed multi-GPU workflows. The implemented solvers are fully featured, supporting event handling, automatic differentiation, and incorporating of datasets via the GPU's texture memory, allowing scientists to take advantage of GPU acceleration on all major current architectures without changing their model code and without loss of performance.Comment: 11 figure

Experimental and computation approaches reveal mechanisms of evolution of gene regulatory networks underlying echinoderm skeletogenesis

The evolutionary mechanisms in distantly related animals involved in shaping complex gene regulatory networks (GRN) that encode morphologically similar structures remain elusive. In this context, echinoderm larval skeletons found only in brittle stars and sea urchins out of the five classes provide an ideal system. Here, we characterise for the first time the development of the larval skeleton in the poorly described class of echinoderms, the ophiuroid Amphiura filiformis, and we compare it systematically with the well-established sea urchin. In the first part of this study, we show that ophiuroids and euechinoids, that split at least 480 Million years ago (Mya), have remarkable similarities in tempo and mode of skeletal development. Despite morphological and ontological similarities, our high-resolution study of the dynamics of regulatory states using 24 sea urchin candidates highlights that gene duplication, protein function diversification and cis-regulatory element evolution all contributed to shape the regulatory program for larval skeletogenesis in different branches of echinoderms. Our data allows to comment on the independent or homologous evolution of the larval skeleton in light of the recently established phylogeny of echinoderm classes. In the second part of this study, we employ mRNA sequencing to establish a transcriptome and analyse its content quantitatively and qualitatively. We identify a core set of skeletogenic genes that is highly conserved using various comparative genomic analyses including other three classes of echinoderms. Additionally, from a differential screen on samples with inhibited skeleton we obtain a list of candidates specific for brittle star skeleton development and analyse their expression using experimental techniques. Finally, we provide access to all transcriptomic and expression data via a customised web interface. In conclusion, we establish the brittle star A. filiformis as new developmental model system and provide novel insights into evolution of GRNs

Unraveling the Complex Regulatory Relationships between Metabolism and Signal Transduction in Breast Cancer.

Almost all cancer cells exhibit a metabolic phenotype characterized by high rates of glucose uptake known as the Warburg effect. Metabolic changes that are representative of distinct stages of breast cancer may suggest dependence by cancer cells on certain metabolic processes that are not relevant to normal cells. Importantly, these differences may help identify therapeutic targets that are non-lethal to normal cells. In this thesis, I present a set of models and methodologies developed using both experimental and theoretical approaches to investigate the complex intracellular signaling and metabolic networks associated with distinct stages of breast cancer. First, a detailed literature search was used to construct a logic network model of the PI3K signaling pathway, which is known to play an important regulatory role in glucose metabolism. Comparisons of experimental and simulated results suggest that the network model is well constructed but some regulatory crosstalk with MAPK requires additional refinement. Targeted therapeutic inhibitors frequently induce off-target effects. This thesis also explored the role of retroactivity in generating off-target effects in signaling networks using a computational model. The simulation results suggest that the kinetics governing covalently modified cycles in a cascade are more important for propagating an upstream off-target effect via retroactivity than the binding affinity of a drug to a targeted protein, which is a commonly optimized property in drug development. Finally, 13C tracer experiments were used to infer relative glucose and glutamine derived flux in cell lines representing distinct stages of breast cancer. Steady state metabolic flux analysis was also used to computationally fit the absolute TCA cycle flux in these cell lines. Variations in acetyl-CoA, citrate, pyruvate, and alpha-ketoglutarate flux were identified. A particularly important finding was a large reductive carboxylation flux from alpha-ketoglutarate to citrate in SUM-149 cells. Together, the models presented in this thesis provide a framework for identifying mechanistic drivers of the Warburg effect, which may represent important therapeutic targets for modulating cancer proliferation and progression.PHDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/98062/1/mlwynn_1.pd

Quantitative analysis of the receptor-induced apoptotic decision network

Thesis (Ph. D.)--Massachusetts Institute of Technology, Biological Engineering Division, 2008.Includes bibliographical references (p. 157-169).Cells use a complex web of protein signaling pathways to interpret extracellular cues and decide and execute cell fates such as survival, apoptosis, differentiation, and proliferation. Cell decisions can be triggered by subtle, transient signals that are context specific, making them hard to study by conventional experimental methods. In this thesis, we use a systems approach combining quantitative experiments with computational modeling and analysis to understand the regulation of the survival-vs-death decision. A second goal of this thesis was to develop modeling and analysis methods that enable study of signals that are transient or at intermediate activation levels. We addressed the challenge of balancing mechanistic detail and ease of interpretation in modeling by adapting fuzzy logic to analyze a previously published experimental dataset characterizing the dynamic behavior of kinase pathways governing apoptosis in human colon carcinoma cells. Simulations of our fuzzy logic model recapitulated most features of the data and generated several predictions involving pathway crosstalk and regulation. Fuzzy logic models are flexible, able to incorporate qualitative and noisy data, and powerful enough to generate not only quantitative predictions but also biological insights concerning operation of signaling networks. To study transient signals in differential-equation based models, we employed direct Lyapunov exponents (DLEs) to identify phase-space domains of high sensitivity to initial conditions. These domains delineate regions exhibiting qualitatively different transient activities that would be indistinguishable using steady-state analysis but which correspond to different outcomes.(cont.) We combine DLE analysis of a physicochemical model of receptor-mediated apoptosis with single cell data obtained by flow cytometry and FRET-based reporters in live-cell microscopy to classify conditions that alter the usage of two apoptosis pathways (Type I/II apoptosis). While it is generally thought that the control point for Type I/II occurs at the level of initiator caspase activation, we find that Type II cells can be converted to Type I by removal of XIAP, a regulator of effector caspases. Our study suggests that the classification of cells as Type I or II obscures a third variable category of cells that are highly sensitive to changes in the concentrations of key apoptotic network proteins.by Bree Beardsley Aldridge.Ph.D

Mathematical models of the gene regulatory networks underlying mesendoderm formation in amphibians

An early event in embryo development is the formation of mesoderm, endoderm and ectoderm, known as the primary germ layers. The gene regulatory network (GRN) consisting of the regulatory mechanisms underlying the formation of mesoderm and endoderm (the mesendoderm GRN) has been extensively studied both experimentally and using mathematical models. The Xenopus GRN is complex, with much of this complexity due to large numbers of Mix and Nodal genes. Mice and humans have only single Mix and Nodal genes, meaning that the Xenopus GRN is overly complex compared with higher vertebrates. Urodele amphibians, for example the axolotl, have single Mix and Nodal genes required for mesoderm and endoderm formation giving a model organism for the study of a simplified mesendoderm GRN. We study the axolotl mesendoderm GRN by developing mathematical models that encompass the time evolution of transcription factors in a cell. A detailed investigation reveals that, despite differences in the axolotl mesendoderm GRN compared with the Xenopus, the model can qualitatively reproduce experimental observations. We obtain experimental data to estimate model parameters using a computational algorithm, then test the behaviour of the resulting mathematical model using independent data. We extend mathematical models of the Xenopus mesendoderm GRN to include transcription factors involved in patterning the DV axis. An investigation of this model shows that it can account for the formation of mesoderm, endoderm and anterior mesendoderm forming in regions of the embryo consistent wth experimental data. In the final section of this thesis, we extend a multicellular model of the Xenopus mesendoderm GRN into a grid of cells

Mathematical models of the gene regulatory networks underlying mesendoderm formation in amphibians

An early event in embryo development is the formation of mesoderm, endoderm and ectoderm, known as the primary germ layers. The gene regulatory network (GRN) consisting of the regulatory mechanisms underlying the formation of mesoderm and endoderm (the mesendoderm GRN) has been extensively studied both experimentally and using mathematical models. The Xenopus GRN is complex, with much of this complexity due to large numbers of Mix and Nodal genes. Mice and humans have only single Mix and Nodal genes, meaning that the Xenopus GRN is overly complex compared with higher vertebrates. Urodele amphibians, for example the axolotl, have single Mix and Nodal genes required for mesoderm and endoderm formation giving a model organism for the study of a simplified mesendoderm GRN. We study the axolotl mesendoderm GRN by developing mathematical models that encompass the time evolution of transcription factors in a cell. A detailed investigation reveals that, despite differences in the axolotl mesendoderm GRN compared with the Xenopus, the model can qualitatively reproduce experimental observations. We obtain experimental data to estimate model parameters using a computational algorithm, then test the behaviour of the resulting mathematical model using independent data. We extend mathematical models of the Xenopus mesendoderm GRN to include transcription factors involved in patterning the DV axis. An investigation of this model shows that it can account for the formation of mesoderm, endoderm and anterior mesendoderm forming in regions of the embryo consistent wth experimental data. In the final section of this thesis, we extend a multicellular model of the Xenopus mesendoderm GRN into a grid of cells

SYSTEMATIC INVESTIGATION OF QUORUM SENSING IN Escherichia coli

High throughput techniques and advanced mathematical tools have enabled systematic investigations of biological systems with unparalleled precision. Not only molecular interactions between components but mechanisms and the dynamic behaviors associated with these systems are revealed, suggesting that comprehensive systems biology can be realized in the near future. Quorum sensing, especially the auto-inducer2 (AI-2) system, has been extensively studied due to its commonality among bacteria and connections to pathogenic phenotypes. In this study, the E. coli quorum sensing AI-2 system was studied combing system-based mathematical modeling and high throughput genomic profiling. First, a Stochastic Petri Network (SPN) model was constructed based on available regulatory information. Simulations together with experimental data demonstrated that the apparent stimulation of AI-2 in the presence of glucose is not from the increased transcriptional or translational expression of AI-2 synthases luxS and pfs, nor from the increased metabolic flux associated with LuxS-related pathways but from an alternative AI-2 synthesis pathway. The conversion of adenosine with cellular extracts from both luxS and pfs mutants validated our prediction about the existence of an alternative non-LuxS related AI-2 synthesis pathway. Second, AI-2 uptake regulatory network was investigated in detail: lsrR-lacZ, lsrK-lacZ fusion reporters were constructed and the analysis found that lsrR is subject to its own repression and is induced by both lsrK and luxS. Further transcriptome analysis demonstrated that lsrR and lsrK, together with quorum signal AI-2, coregulate lsrRK regulon, which influences phenotypes (biofilm, small RNAs). Importantly, this regulation is in a distinctly different manner than that mediating the lsr operon. We hypothesize that lsrR acts together with AI-2 to mediate cellular processes and that the phosphorylation of AI-2 molecule through lsrK triggers different response pathways. These investigations demonstrated that lsrR, lsrK are indispensable for AI-2 uptake. These newly elucidated regulatory mechanisms and associations undoubtedly broaden the scope of the AI-2 quorum sensing system, and provide a solid foundation for further mathematical modeling of the dynamics and system behaviors in E. coli . Finally, a tight coupling of experimental manipulation with mathematical analysis, as demonstrated in this study, provides a good example for systematically investigating biological systems