Dynamics Of Gene Regulatory Networks Research Articles

Single-cell multi-modal integrative analyses highlight functional dynamic gene regulatory networks directing human cardiac development

Illuminating the precise stepwise genetic programs directing cardiac development provides insights into the mechanisms of congenital heart disease and strategies for cardiac regenerative therapies. Here, we integrate invitro and invivo human single-cell multi-omic studies with high-throughput functional genomic screening to reveal dynamic, cardiac-specific gene regulatory networks (GRNs) and transcriptional regulators during human cardiomyocyte development. Interrogating developmental trajectories reconstructed from single-cell data unexpectedly reveal divergent cardiomyocyte lineages with distinct gene programs based on developmental signaling pathways. High-throughput functional genomic screens identify key transcription factors from inferred GRNs that are functionally relevant for cardiomyocyte lineages derived from each pathway. Notably, we discover a critical heat shock transcription factor 1 (HSF1)-mediated cardiometabolic GRN controlling cardiac mitochondrial/metabolic function and cell survival, also observed in fetal human cardiomyocytes. Overall, these multi-modal genomic studies enable the systematic discovery and validation of coordinated GRNs and transcriptional regulators controlling the development of distinct human cardiomyocyte populations.

Optimal transport reveals dynamic gene regulatory networks via gene velocity estimation.

Inferring gene regulatory networks from gene expression data is an important and challenging problem in the biology community. We propose OTVelo, a methodology that takes time-stamped single-cell gene expression data as input and predicts gene regulation across two time points. It is known that the rate of change of gene expression, which we will refer to as gene velocity, provides crucial information that enhances such inference; however, this information is not always available due to the limitations in sequencing depth. Our algorithm overcomes this limitation by estimating gene velocities using optimal transport. We then infer gene regulation using time-lagged correlation and Granger causality via regularized linear regression. Instead of providing an aggregated network across all time points, our method uncovers the underlying dynamical mechanism across time points. We validate our algorithm on 13 simulated datasets with both synthetic and curated networks and demonstrate its efficacy on 4 experimental data sets.

Inferring Gene Regulatory Networks from Single-Cell Time-Course Data Based on Temporal Convolutional Networks

Background: Time-course single-cell RNA sequencing (scRNA-seq) data represent dynamic gene expression values that change over time, which can be used to infer causal relationships between genes and construct dynamic gene regulatory networks (GRNs). However, most of the existing methods are designed for bulk RNA sequencing (bulk RNA-seq) data and static scRNA-seq data, and only a few methods, such as CNNC and DeepDRIM can be directly applied to time-course scRNA-seq data. Objective: This work aims to infer causal relationships between genes and construct dynamic gene regulatory networks using time-course scRNA-seq data. Methods: We propose an analytical method for inferring GRNs from single-cell time-course data based on temporal convolutional networks (scTGRN), which provides a supervised learning approach to infer causal relationships among genes. scTGRN constructs a 4D tensor representing gene expression features for each gene pair, then inputs the constructed 4D tensor into the temporal convolutional network to train and infer the causal relationship between genes. Results: We validate the performance of scTGRN on five real datasets and four simulated datasets, and the experimental results show that scTGRN outperforms existing models in constructing GRNs. In addition, we test the performance of scTGRN on gene function assignment, and scTGRN outperforms other models. Conclusion: The analysis shows that scTGRN can not only accurately identify the causal relationship between genes, but also can be used to achieve gene function assignment.

Deciphering the dynamic expression network of fiber elongation and the functional role of the GhTUB5 gene for fiber length in cotton based on an introgression population of upland cotton

IntroductionInterspecific introgression between Gossypium hirsutum and G. barbadense allows breeding cotton with outstanding fiber length (FL). However, the dynamic gene regulatory network of FL-related genes has not been characterized, and the functional mechanism through which the hub gene GhTUB5 mediates fiber elongation has yet to be determined. MethodsCoexpression analyses of 277 developing fiber transcriptomes integrated with QTL mapping using 250 introgression lines of different FL phenotypes were conducted to identify genes related to fiber elongation. The function of GhTUB5 was determined by ectopic expression of two TUB5 alleles in Arabidopsis and knockout of GhTUB5 in upland cotton. Yeast two-hybrid, split-luciferase and pull-down assays were conducted to screen for interacting proteins, and upstream genes were identified by yeast one-hybrid, dual-LUC and electrophoretic mobility shift assays. ResultsThe 32,612, 30,837 and 30,277 genes expressed at 5, 10 and 15 days postanthesis (dpa) were grouped into 19 distinct coexpression modules, and 988 genes in the MEblack module were enriched in the cell wall process and exhibited significant associations with FL. A total of 20 FL-QTLs were identified, each explaining 3.34–16.04 % of the phenotypic variance in the FL. Furthermore, several FL-QTLs contained 15 genes that were differentially expressed in the MEblack module including the tubulin beta gene (TUB5). Compared with the wild type, the overexpression of GhTUB5 and GbTUB5 in Arabidopsis suppressed root cell length but promoted cellulose synthesis. Knockout of GhTUB5 resulted in longer fiber lines. Protein-based experiments revealed that GhTUB5 interacts with GhZFP6. Additionally, GhTUB5 was directly activated by GhHD-ZIP7, a homeobox-leucine zipper transcription factor, and its paralogous gene was previously reported to mediate fiber elongation. ConclusionThis study opens a new avenue to dissect functional mechanism of cotton fiber elongation. Our findings provide some molecular details on how GhTUB5 mediates the FL phenotype in cotton.

DeepIMAGER: Deeply Analyzing Gene Regulatory Networks from scRNA-seq Data.

Understanding the dynamics of gene regulatory networks (GRNs) across diverse cell types poses a challenge yet holds immense value in unraveling the molecular mechanisms governing cellular processes. Current computational methods, which rely solely on expression changes from bulk RNA-seq and/or scRNA-seq data, often result in high rates of false positives and low precision. Here, we introduce an advanced computational tool, DeepIMAGER, for inferring cell-specific GRNs through deep learning and data integration. DeepIMAGER employs a supervised approach that transforms the co-expression patterns of gene pairs into image-like representations and leverages transcription factor (TF) binding information for model training. It is trained using comprehensive datasets that encompass scRNA-seq profiles and ChIP-seq data, capturing TF-gene pair information across various cell types. Comprehensive validations on six cell lines show DeepIMAGER exhibits superior performance in ten popular GRN inference tools and has remarkable robustness against dropout-zero events. DeepIMAGER was applied to scRNA-seq datasets of multiple myeloma (MM) and detected potential GRNs for TFs of RORC, MITF, and FOXD2 in MM dendritic cells. This technical innovation, combined with its capability to accurately decode GRNs from scRNA-seq, establishes DeepIMAGER as a valuable tool for unraveling complex regulatory networks in various cell types.

SAILoR: Structure-Aware Inference of Logic Rules.

Boolean networks provide an effective mechanism for describing interactions and dynamics of gene regulatory networks (GRNs). Deriving accurate Boolean descriptions of GRNs is a challenging task. The number of experiments is usually much smaller than the number of genes. In addition, binarization leads to a loss of information and inconsistencies arise in binarized time-series data. The inference of Boolean networks from binarized time-series data alone often leads to complex and overfitted models. To obtain relevant Boolean models of gene regulatory networks, inference methods could incorporate data from multiple sources and prior knowledge in terms of general network structure and/or exact interactions. We propose the Boolean network inference method SAILoR (Structure-Aware Inference of Logic Rules). SAILoR incorporates time-series gene expression data in combination with provided reference networks to infer accurate Boolean models. SAILoR automatically extracts topological properties from reference networks. These can describe a more general structure of the GRN or can be more precise and describe specific interactions. SAILoR infers a Boolean network by learning from both continuous and binarized time-series data. It navigates between two main objectives, topological similarity to reference networks and correspondence with gene expression data. By incorporating the NSGA-II multi-objective genetic algorithm, SAILoR relies on the wisdom of crowds. Our results indicate that SAILoR can infer accurate and biologically relevant Boolean descriptions of GRNs from both a static and a dynamic perspective. We show that SAILoR improves the static accuracy of the inferred network compared to the network inference method dynGENIE3. Furthermore, we compared the performance of SAILoR with other Boolean network inference approaches including Best-Fit, REVEAL, MIBNI, GABNI, ATEN, and LogBTF. We have shown that by incorporating prior knowledge about the overall network structure, SAILoR can improve the structural correctness of the inferred Boolean networks while maintaining dynamic accuracy. To demonstrate the applicability of SAILoR, we inferred context-specific Boolean subnetworks of female Drosophila melanogaster before and after mating.

Cell cycle specific, differentially tagged ribosomal proteins to measure phase specific transcriptomes from asynchronously cycling cells

Asynchronously cycling cells pose a challenge to the accurate characterization of phase-specific gene expression. Current strategies, including RNAseq, survey the steady state gene expression across the cell cycle and are inherently limited by their inability to resolve dynamic gene regulatory networks. Single cell RNAseq (scRNAseq) can identify different cell cycle transcriptomes if enough cycling cells are present, however some cells are not amenable to scRNAseq. Therefore, we merged two powerful strategies, the CDT1 and GMNN degrons used in Fluorescent Ubiquitination-based Cell Cycle Indicator (FUCCI) cell cycle sensors and the ribosomal protein epitope tagging used in RiboTrap/Tag technologies to isolate cell cycle phase-specific mRNA for sequencing. The resulting cell cycle dependent, tagged ribosomal proteins (ccTaggedRP) were differentially expressed during the cell cycle, had similar subcellular locations as endogenous ribosomal proteins, incorporated into ribosomes and polysomes, and facilitated the recovery of cell cycle phase-specific RNA for sequencing. ccTaggedRP has broad applications to investigate phase-specific gene expression in complex cell populations.

A gene regulatory network critical for axillary bud dormancy directly controlled by Arabidopsis BRANCHED1.

The Arabidopsis thaliana transcription factor BRANCHED1 (BRC1) plays a pivotal role in the control of shoot branching as it integrates environmental and endogenous signals that influence axillary bud growth. Despite its remarkable activity as a growth inhibitor, the mechanisms by which BRC1 promotes bud dormancy are largely unknown. We determined the genome-wide BRC1 binding sites in vivo and combined these with transcriptomic data and gene co-expression analyses to identify bona fide BRC1 direct targets. Next, we integrated multi-omics data to infer the BRC1 gene regulatory network (GRN) and used graph theory techniques to find network motifs that control the GRN dynamics. We generated an open online tool to interrogate this network. A group of BRC1 target genes encoding transcription factors (BTFs) orchestrate this intricate transcriptional network enriched in abscisic acid-related components. Promoter::β-GLUCURONIDASE transgenic lines confirmed that BTFs are expressed in axillary buds. Transient co-expression assays and studies in planta using mutant lines validated the role of BTFs in modulating the GRN and promoting bud dormancy. This knowledge provides access to the developmental mechanisms that regulate shoot branching and helps identify candidate genes to use as tools to adapt plant architecture and crop production to ever-changing environmental conditions.

A multiscale model of the role of microenvironmental factors in cell segregation and heterogeneity in breast cancer development.

We analyzed a quantitative multiscale model that describes the epigenetic dynamics during the growth and evolution of an avascular tumor. A gene regulatory network (GRN) formed by a set of ten genes that are believed to play an important role in breast cancer development was kinetically coupled to the microenvironmental agents: glucose, estrogens, and oxygen. The dynamics of spontaneous mutations was described by a Yule-Furry master equation whose solution represents the probability that a given cell in the tissue undergoes a certain number of mutations at a given time. We assumed that the mutation rate is modified by a spatial gradient of nutrients. The tumor mass was simulated by means of cellular automata supplemented with a set of reaction diffusion equations that described the transport of microenvironmental agents. By analyzing the epigenetic state space described by the GRN dynamics, we found three attractors that were identified with cellular epigenetic states: normal, precancer and cancer. For two-dimensional (2D) and three-dimensional (3D) tumors we calculated the spatial distribution of the following quantities: (i) number of mutations, (ii) mutation of each gene and, (iii) phenotypes. Using estrogen as the principal microenvironmental agent that regulates cell proliferation process, we obtained tumor shapes for different values of estrogen consumption and supply rates. It was found that he majority of mutations occurred in cells that were located close to the 2D tumor perimeter or close to the 3D tumor surface. Also, it was found that the occurrence of different phenotypes in the tumor are controlled by estrogen concentration levels since they can change the individual cell threshold and gene expression levels. All results were consistently observed for 2D and 3D tumors.

Inferring delays in partially observed gene regulation processes.

Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality. We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: an activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components. Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.

ScGRN: a comprehensive single-cell gene regulatory network platform of human and mouse.

Gene regulatory networks (GRNs) are interpretable graph models encompassing the regulatory interactions between transcription factors (TFs) and their downstream target genes. Making sense of the topology and dynamics of GRNs is fundamental to interpreting the mechanisms of disease etiology and translating corresponding findings into novel therapies. Recent advances in single-cell multi-omics techniques have prompted the computational inference of GRNs from single-cell transcriptomic and epigenomic data at an unprecedented resolution. Here, we present scGRN (https://bio.liclab.net/scGRN/), a comprehensive single-cell multi-omics gene regulatory network platform of human and mouse. The current version of scGRN catalogs 237051 cell type-specific GRNs (62 999692 TF-target gene pairs), covering 160 tissues/cell lines and 1324 single-cell samples. scGRN is the first resource documenting large-scale cell type-specific GRN information of diverse human and mouse conditions inferred from single-cell multi-omics data. We have implemented multiple online tools for effective GRN analysis, including differential TF-target network analysis, TF enrichment analysis, and pathway downstream analysis. We also provided details about TF binding to promoters, super-enhancers and typical enhancers of target genes in GRNs. Taken together, scGRN is an integrative and useful platform for searching, browsing, analyzing, visualizingand downloading GRNs of interest, enabling insight into the differences in regulatory mechanisms across diverse conditions.

Computing Minimal Boolean Models of Gene Regulatory Networks.

Models of gene regulatory networks (GRNs) capture the dynamics of the regulatory processes that occur within the cell as a means to understanding the variability observed in gene expression between different conditions. Arguably the simplest mathematical construct used for modeling is the Boolean network, which dictates a set of logical rules for transition between states described as Boolean vectors. Due to the complexity of gene regulation and the limitations of experimental technologies, in most cases knowledge about regulatory interactions and Boolean states is partial. In addition, the logical rules themselves are not known a priori. Our goal in this work is to create an algorithm that finds the network that fits the data optimally, and identify the network states that correspond to the noise-free data. We present a novel methodology for integrating experimental data and performing a search for the optimal consistent structure via optimization of a linear objective function under a set of linear constraints. In addition, we extend our methodology into a heuristic that alleviates the computational complexity of the problem for datasets that are generated by single-cell RNA-Sequencing (scRNA-Seq). We demonstrate the effectiveness of these tools using simulated data, and in addition a publicly available scRNA-Seq dataset and the GRN that is associated with it. Our methodology will enable researchers to obtain a better understanding of the dynamics of GRNs and their biological role.

A digital twin reproducing gene regulatory network dynamics of early Ciona embryos indicates robust buffers in the network.

How gene regulatory networks (GRNs) encode gene expression dynamics and how GRNs evolve are not well understood, although these problems have been studied extensively. We created a digital twin that accurately reproduces expression dynamics of 13 genes that initiate expression in 32-cell ascidian embryos. We first showed that gene expression patterns can be manipulated according to predictions by this digital model. Next, to simulate GRN rewiring, we changed regulatory functions that represented their regulatory mechanisms in the digital twin, and found that in 55 of 100 cases, removal of a single regulator from a conjunctive clause of Boolean functions did not theoretically alter qualitative expression patterns of these genes. In other words, we found that more than half the regulators gave theoretically redundant temporal or spatial information to target genes. We experimentally substantiated that the expression pattern of Nodal was maintained without one of these factors, Zfpm, by changing the upstream regulatory sequence of Nodal. Such robust buffers of regulatory mechanisms may provide a basis of enabling developmental system drift, or rewiring of GRNs without changing expression patterns of downstream genes, during evolution.

Quantifying cancer cell plasticity with gene regulatory networks and single-cell dynamics.

Phenotypic plasticity of cancer cells can lead to complex cell state dynamics during tumor progression and acquired resistance. Highly plastic stem-like states may be inherently drug-resistant. Moreover, cell state dynamics in response to therapy allow a tumor to evade treatment. In both scenarios, quantifying plasticity is essential for identifying high-plasticity states or elucidating transition paths between states. Currently, methods to quantify plasticity tend to focus on 1) quantification of quasi-potential based on the underlying gene regulatory network dynamics of the system; or 2) inference of cell potency based on trajectory inference or lineage tracing in single-cell dynamics. Here, we explore both of these approaches and associated computational tools. We then discuss implications of each approach to plasticity metrics, and relevance to cancer treatment strategies.

Dictys: dynamic gene regulatory network dissects developmental continuum with single-cell multiomics.

Gene regulatory networks (GRNs) are key determinants of cell function and identity and are dynamically rewired during development and disease. Despite decades of advancement, challenges remain in GRN inference, including dynamic rewiring, causal inference, feedback loop modeling and context specificity. To address these challenges, we develop Dictys, a dynamic GRN inference and analysis method that leverages multiomic single-cell assays of chromatin accessibility and gene expression, context-specific transcription factor footprinting, stochastic process network and efficient probabilistic modeling of single-cell RNA-sequencing read counts. Dictys improves GRN reconstruction accuracy and reproducibility and enables the inference and comparative analysis of context-specific and dynamic GRNs across developmental contexts. Dictys' network analyses recover unique insights in human blood and mouse skin development with cell-type-specific and dynamic GRNs. Its dynamic network visualizations enable time-resolved discovery and investigation of developmental driver transcription factors and their regulated targets. Dictys is available as a free, open-source and user-friendly Python package.

Diffusion-enhanced characterization of 3D chromatin structure reveals its linkage to gene regulatory networks and the interactome.

The interactome networks at the DNA, RNA, and protein levels are crucial for cellular functions, and the diverse variations of these networks are heavily involved in the establishment of different cell states. We have developed a diffusion-based method, Hi-C to geometry (CTG), to obtain reliable geometric information on the chromatin from Hi-C data. CTG produces a consistent and reproducible framework for the 3D genomic structure and provides a reliable and quantitative understanding of the alterations of genomic structures under different cellular conditions. The genomic structure yielded by CTG serves as an architectural blueprint of the dynamic gene regulatory network, based on which cell-specific correspondence between gene-gene and corresponding protein-protein physical interactions, as well as transcription correlation, is revealed. We also find that gene fusion events are significantly enriched between genes of short CTG distances and are thus close in 3D space. These findings indicate that 3D chromatin structure is at least partially correlated with downstream processes such as transcription, gene regulation, and even regulatory networking through affecting protein-protein interactions.

Dynamic gene regulatory networks improving spike fertility through regulation of floret primordia fate in wheat.

The developmental process of spike is critical for spike fertility through affecting floret primordia fate in wheat; however, the genetic regulation of this dynamic and complex developmental process remains unclear. Here, we conducted a high temporal-resolution analysis of spike transcriptomes and monitored the number and morphology of floret primordia within spike. The development of all floret primordia in a spike was clearly separated into three distinct phases: differentiation, pre-dimorphism and dimorphism. Notably, we identified that floret primordia with meiosis ability at the pre-dimorphism phase usually develop into fertile floret primordia in the next dimorphism phase. Compared to control, increasing plant space treatment achieved the maximum increasement range (i.e., 50%) in number of fertile florets by accelerating spike development. The process of spike fertility improvement was directed by a continuous and dynamic regulatory network involved in transcription factor and genes interaction. This was based on the coordination of genes related to heat shock protein and jasmonic acid biosynthesis during differentiation phase, and genes related to lignin, anthocyanin and chlorophyll biosynthesis during dimorphism phase. The multi-dimensional association with high temporal-resolution approach reported here allows rapid identification of genetic resource for future breeding studies to realise the maximum spike fertility potential in more cereal crops.

Assessing biological network dynamics: comparing numerical simulations with analytical decomposition of parameter space

Mathematical modeling of the emergent dynamics of gene regulatory networks (GRN) faces a double challenge of (a) dependence of model dynamics on parameters, and (b) lack of reliable experimentally determined parameters. In this paper we compare two complementary approaches for describing GRN dynamics across unknown parameters: (1) parameter sampling and resulting ensemble statistics used by RACIPE (RAndom CIrcuit PErturbation), and (2) use of rigorous analysis of combinatorial approximation of the ODE models by DSGRN (Dynamic Signatures Generated by Regulatory Networks). We find a very good agreement between RACIPE simulation and DSGRN predictions for four different 2- and 3-node networks typically observed in cellular decision making. This observation is remarkable since the DSGRN approach assumes that the Hill coefficients of the models are very high while RACIPE assumes the values in the range 1-6. Thus DSGRN parameter domains, explicitly defined by inequalities between systems parameters, are highly predictive of ODE model dynamics within a biologically reasonable range of parameters.

Precisely timed regulation of enhancer activity defines the binary expression pattern of Fushi tarazu in the Drosophila embryo.

The genes that drive development each typically have many different enhancers. Properly coordinating the action of these different enhancers is crucial to correctly specifying cell-fate decisions, yet it remains poorly understood how their activity is choregraphed in time. To shed light on this question, we used recently developed single-cell live imaging tools to dissect the regulation of Fushi tarazu (Ftz) in Drosophila melanogaster embryos. Ftz is a transcription factor that is expressed in asymmetric stripes by two distinct enhancers: autoregulatory and zebra. The anterior edge of each stripe needs to be sharply defined to specify essential lineage boundaries. Here, we tracked how boundary cells commit to either a high-Ftz or low-Ftz fate by measuring Ftz protein traces in real time and simultaneously quantifying transcription from the endogenous locus and individual enhancers. This revealed that the autoregulatory enhancer does not establish this fate choice. Instead, it perpetuates the decision defined by zebra. This is contrary to the prevailing view that autoregulation drives the fate decision by causing bi-stable Ftz expression. Furthermore, we showed that the autoregulatory enhancer is not activated based on a Ftz-concentration threshold but through a timing-based mechanism. We hypothesize that this is regulated by several ubiquitously expressed pioneer-like transcription factors, which have recently been shown to act as timers in the embryo. Our work provides new insight into how precisely timed enhancer activity can directly regulate the dynamics of gene regulatory networks, which may be a general mechanism for ensuring that embryogenesis runs like clockwork.

ISRES+: an improved evolutionary strategy for function minimization to estimate the free parameters of systems biology models.

Mathematical models in systems biology help generate hypotheses, guide experimental design, and infer the dynamics of gene regulatory networks. These models are characterized by phenomenological or mechanistic parameters, which are typically hard to measure. Therefore, efficient parameter estimation is central to model development. Global optimization techniques, such as evolutionary algorithms (EAs), are applied to estimate model parameters by inverse modeling, i.e. calibrating models by minimizing a function that evaluates a measure of the error between model predictions and experimental data. EAs estimate model parameters "fittest individuals" by generating a large population of individuals using strategies like recombination and mutation over multiple "generations." Typically, only a few individuals from each generation are used to create new individuals in the next generation. Improved Evolutionary Strategy by Stochastic Ranking (ISRES), proposed by Runnarson and Yao, is one such EA that is widely used in systems biology to estimate parameters. ISRES uses information at most from a pair of individuals in any generation to create a new population to minimize the error. In this article, we propose an efficient evolutionary strategy, ISRES+, which builds on ISRES by combining information from all individuals across the population and across all generations to develop a better understanding of the fitness landscape. ISRES+ uses the additional information generated by the algorithm during evolution to approximate the local neighborhood around the best-fit individual using linear least squares fits in one and two dimensions, enabling efficient parameter estimation. ISRES+ outperforms ISRES and results in fitter individuals with a tighter distribution over multiple runs, such that a typical run of ISRES+ estimates parameters with a higher goodness-of-fit compared with ISRES. Algorithm and implementation: Github-https://github.com/gtreeves/isres-plus-bandodkar-2022.