Role of noise and parametric variation in the dynamics of gene regulatory circuits.

Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic simulations. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both the intrinsic and extrinsic noises, we develop a method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. RACIPE uniquely generates and analyzes an ensemble of models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. In sRACIPE we further develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several synthetic gene regulatory circuits and an epithelial-mesenchymal transition network in squamous cell carcinoma, we demonstrate that sRACIPE can interpret the experimental observations from single-cell gene expression data. We observe that parametric variation (the spread of parameters around a median value) increases the spread of the gene expression clusters, whereas high noise merges the states. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE as an R package

A quantitative evaluation of topological motifs and their coupling in gene circuit state distributions.

One of the major challenges in biology is to understand how gene interactions collaborate to determine overall functions of biological systems. Here, we present a new computational framework that enables systematic, high-throughput, and quantitative evaluation of how small transcriptional regulatory circuit motifs, and their coupling, contribute to functions of a dynamical biological system. We illustrate how this approach can be applied to identify four-node gene circuits, circuit motifs, and motif coupling responsible for various gene expression state distributions, including those derived from single-cell RNA sequencing data. We also identify seven major classes of four-node circuits from clustering analysis of state distributions. The method is applied to establish phenomenological models of gene circuits driving human neuron differentiation, revealing important biologically relevant regulatory interactions. Our study will shed light on a better understanding of gene regulatory mechanisms in creating and maintaining cellular states

Measurement of permeability for ferrous metallic plates using a novel lift-off compensation technique on phase signature

Lift-off of sensor affects the prediction of electromagnetic properties for both ferrous and non-ferrous steel plates. In this paper, we developed a strategy to address this issue for ferrous plates. With increased lift-off, the phase of the measured impedance for steel plates reduces. Meanwhile, the magnitude of the impedance signal decreases. Based on these facts, a phase compensation algorithm is developed which corrects the phase change due to lift-off considering the magnitude of the impedance signal. Further, a new magnetic permeability prediction technique is presented, which has been validated by analytical and measured results. With this new technique, the error in permeability prediction is less than 2% within the range of lift-offs tested

A data-driven optimization method for coarse-graining gene regulatory networks.

One major challenge in systems biology is to understand how various genes in a gene regulatory network (GRN) collectively perform their functions and control network dynamics. This task becomes extremely hard to tackle in the case of large networks with hundreds of genes and edges, many of which have redundant regulatory roles and functions. The existing methods for model reduction usually require the detailed mathematical description of dynamical systems and their corresponding kinetic parameters, which are often not available. Here, we present a data-driven method for coarse-graining large GRNs, named SacoGraci, using ensemble-based mathematical modeling, dimensionality reduction, and gene circuit optimization by Markov Chain Monte Carlo methods. SacoGraci requires network topology as the only input and is robust against errors in GRNs. We benchmark and demonstrate its usage with synthetic, literature-based, and bioinformatics-derived GRNs. We hope SacoGraci will enhance our ability to model the gene regulation of complex biological systems

Toward Modeling Context-Specific EMT Regulatory Networks Using Temporal Single Cell RNA-Seq Data.

Epithelial-mesenchymal transition (EMT) is well established as playing a crucial role in cancer progression and being a potential therapeutic target. To elucidate the gene regulation that drives the decision making of EMT, many previous studies have been conducted to model EMT gene regulatory circuits (GRCs) using interactions from the literature. While this approach can depict the generic regulatory interactions, it falls short of capturing context-specific features. Here, we explore the effectiveness of a combined bioinformatics and mathematical modeling approach to construct context-specific EMT GRCs directly from transcriptomics data. Using time-series single cell RNA-sequencing data from four different cancer cell lines treated with three EMT-inducing signals, we identify context-specific activity dynamics of common EMT transcription factors. In particular, we observe distinct paths during the forward and backward transitions, as is evident from the dynamics of major regulators such as NF-KB (e.g., NFKB2 and RELB) and AP-1 (e.g., FOSL1 and JUNB). For each experimental condition, we systematically sample a large set of network models and identify the optimal GRC capturing context-specific EMT states using a mathematical modeling method named Random Circuit Perturbation (RACIPE). The results demonstrate that the approach can build high quality GRCs in certain cases, but not others and, meanwhile, elucidate the role of common bioinformatics parameters and properties of network structures in determining the quality of GRCs. We expect the integration of top-down bioinformatics and bottom-up systems biology modeling to be a powerful and generally applicable approach to elucidate gene regulatory mechanisms of cellular state transitions

Random Parametric Perturbations of Gene Regulatory Circuit Uncover State Transitions in Cell Cycle.

Many biological processes involve precise cellular state transitions controlled by complex gene regulation. Here, we use budding yeast cell cycle as a model system and explore how a gene regulatory circuit encodes essential information of state transitions. We present a generalized random circuit perturbation method for circuits containing heterogeneous regulation types and its usage to analyze both steady and oscillatory states from an ensemble of circuit models with random kinetic parameters. The stable steady states form robust clusters with a circular structure that are associated with cell cycle phases. This circular structure in the clusters is consistent with single-cell RNA sequencing data. The oscillatory states specify the irreversible state transitions along cell cycle progression. Furthermore, we identify possible mechanisms to understand the irreversible state transitions from the steady states. We expect this approach to be robust and generally applicable to unbiasedly predict dynamical transitions of a gene regulatory circuit

Real transmission and reflection zeros of periodic structures with a bound state in the continuum

For lossless periodic structures with a proper symmetry, the transmission and reflection spectra often have peaks and dips that are truly $100\%$ and $0\%$, respectively. The full peaks and zero dips typically appear near resonant frequencies, and they are robust with respect to structural perturbations that preserve the required symmetry. However, current theories on the existence of full peaks and zero dips are incomplete and difficult to use. For periodic structures with a bound state in the continuum (BIC), we present a new theory on the existence of real transmission and reflection zeros that correspond to the zero dips in the transmission and reflection spectra. Our theory is relatively simple, complete, and easy to use. Numerical examples are presented to validate the new theory.Comment: 8 pages, 5 figure