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Additional file 1. contains all supplementary materials and figures referenced in the main manuscript. Section 1 1.1 describes more in depth th paralle sampling performance, Section 1 1.2 describes the stability of empirical null distributions, Section 1 1.3 describes the geneset network association bootstrapprocedures, Section 1 1.4 describes materials and preprocessing stepts for the TCGA data analysis. Section 2 is instead dedicated to the supplementary figures that are referenced in the main text.

We describe construction of the 660 kilobase synthetic yeast chromosome XI (synXI) and reveal how synthetic redesign of non-coding DNA elements impact the cell. To aid construction from synthesized 5 to 10 kilobase DNA fragments, we implemented CRISPR-based methods for synthetic crossovers in vivo and used these methods in an extensive process of bug discovery, redesign and chromosome repair, including for the precise removal of 200 kilobases of unexpected repeated sequence. In synXI, the underlying causes of several fitness defects were identified as modifications to non-coding DNA, including defects related to centromere function and mitochondrial activity that were subsequently corrected. As part of synthetic yeast chromosome design, loxPsym sequences for Cre-mediated recombination are inserted between most genes. Using the GAP1 locus from chromosome XI, we show here that targeted insertion of these sites can be used to create extrachromosomal circular DNA on demand, allowing direct study of the effects and propagation of these important molecules. Construction and characterization of synXI has uncovered effects of non-coding and extrachromosomal circular DNA, contributing to better understanding of these elements and informing future synthetic genome design.

Modeling dynamics of gene regulatory networks using ordinary differential equations (ODEs) allow a deeper understanding of disease progression and response to therapy, thus aiding in intervention optimization. Although there exist methods to infer regulatory ODEs, these are generally limited to small networks, rely on dimensional reduction, or impose non-biological parametric restrictions - all impeding scalability and explainability. PHOENIX is a neural ODE framework incorporating prior domain knowledge as soft constraints to infer sparse, biologically interpretable dynamics. Extensive experiments - on simulated and real data - demonstrate PHOENIX's unique ability to learn key regulatory dynamics while scaling to the whole genome.

Gene regulatory networks (GRNs) are effective tools for inferring complex interactions between molecules that regulate biological processes and hence can provide insights into drivers of biological systems. Inferring co-expression networks is a critical element of GRN inference as the correlation between expression patterns may indicate that genes are coregulated by common factors. However, methods that estimate co-expression networks generally derive an aggregate network representing the mean regulatory properties of the population and so fail to fully capture population heterogeneity. To address these concerns, we introduce BONOBO (Bayesian Optimized Networks Obtained By assimilating Omics data), a scalable Bayesian model for deriving individual sample-specific co-expression networks by recognizing variations in molecular interactions across individuals. For every sample, BONOBO assumes a Gaussian distribution on the log-transformed centered gene expression and a conjugate prior distribution on the sample-specific co-expression matrix constructed from all other samples in the data. Combining the sample-specific gene expression with the prior distribution, BONOBO yields a closed-form solution for the posterior distribution of the sample-specific co-expression matrices, thus making the method extremely scalable. We demonstrate the utility of BONOBO in several contexts, including analyzing gene regulation in yeast transcription factor knockout studies, prognostic significance of miRNA-mRNA interaction in human breast cancer subtypes, and sex differences in gene regulation within human thyroid tissue. We find that BONOBO outperforms other sample-specific co-expression network inference methods and provides insight into individual differences in the drivers of biological processes.

Lung adenocarcinoma (LUAD) has been observed to have significant sex differences in incidence, prognosis, and response to therapy. However, the molecular mechanisms responsible for these disparities have not been investigated extensively. Sample-specific gene regulatory network methods were used to analyze RNA sequencing data from non-cancerous human lung samples from The Genotype Tissue Expression Project (GTEx) and lung adenocarcinoma primary tumor samples from The Cancer Genome Atlas (TCGA); results were validated on independent data. We observe that genes associated with key biological pathways including cell proliferation, immune response and drug metabolism are differentially regulated between males and females in both healthy lung tissue, as well as in tumor, and that these regulatory differences are further perturbed by tobacco smoking. We also uncovered significant sex bias in transcription factor targeting patterns of clinically actionable oncogenes and tumor suppressor genes, including AKT2 and KRAS . Using differentially regulated genes between healthy and tumor samples in conjunction with a drug repurposing tool, we identified several small-molecule drugs that might have sex-biased efficacy as cancer therapeutics and further validated this observation using an independent cell line database. These findings underscore the importance of including sex as a biological variable and considering gene regulatory processes in developing strategies for disease prevention and management., Competing Interests: Declaration of interests The authors declare no competing interests.

Models that are formulated as ordinary differential equations (ODEs) can accurately explain temporal gene expression patterns and promise to yield new insights into important cellular processes, disease progression, and intervention design. Learning such ODEs is challenging, since we want to predict the evolution of gene expression in a way that accurately encodes the causal gene-regulatory network (GRN) governing the dynamics and the nonlinear functional relationships between genes. Most widely used ODE estimation methods either impose too many parametric restrictions or are not guided by meaningful biological insights, both of which impedes scalability and/or explainability. To overcome these limitations, we developed PHOENIX, a modeling framework based on neural ordinary differential equations (NeuralODEs) and Hill-Langmuir kinetics, that can flexibly incorporate prior domain knowledge and biological constraints to promote sparse, biologically interpretable representations of ODEs. We test accuracy of PHOENIX in a series of in silico experiments benchmarking it against several currently used tools for ODE estimation. We also demonstrate PHOENIX's flexibility by studying oscillating expression data from synchronized yeast cells and assess its scalability by modelling genome-scale breast cancer expression for samples ordered in pseudotime. Finally, we show how the combination of user-defined prior knowledge and functional forms from systems biology allows PHOENIX to encode key properties of the underlying GRN, and subsequently predict expression patterns in a biologically explainable way., Competing Interests: Declarations. The authors declare the following: Conflict of interest: All authors declare no competing interests.