scholarly journals The finite state projection based Fisher information matrix approach to estimate information and optimize single-cell experiments

2018 ◽  
Author(s):  
Zachary Fox ◽  
Brian Munsky
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Fisher Information ◽  
Single Molecule ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Model Parameters ◽  
Gaussian Fluctuations ◽  
Cellular Environment ◽  
Finite State

AbstractModern optical imaging experiments not only measure single-cell and single-molecule dynamics with high precision, but they can also perturb the cellular environment in myriad controlled and novel settings. Techniques, such as single-molecule fluorescence in-situ hybridization, microfluidics, and optogenetics, have opened the door to a large number of potential experiments, which begs the question of how best to choose the best possible experiment. The Fisher information matrix (FIM) estimates how well potential experiments will constrain model parameters and can be used to design optimal experiments. Here, we introduce the finite state projection (FSP) based FIM, which uses the formalism of the chemical master equation to derive and compute the FIM. The FSP-FIM makes no assumptions about the distribution shapes of single-cell data, and it does not require precise measurements of higher order moments of such distributions. We validate the FSP-FIM against well-known Fisher information results for the simple case of constitutive gene expression. We then use numerical simulations to demonstrate the use of the FSP-FIM to optimize the timing of single-cell experiments with more complex, non-Gaussian fluctuations. We validate optimal simulated experiments determined using the FSP-FIM with Monte-Carlo approaches and contrast these to experiment designs chosen by traditional analyses that assume Gaussian fluctuations or use the central limit theorem. By systematically designing experiments to use all of the measurable fluctuations, our method enables a key step to improve co-design of experiments and quantitative models.Author summaryA main objective of quantitative modeling is to predict the behaviors of complex systems under varying conditions. In a biological context, stochastic fluctuations in expression levels among isogenic cell populations have required modeling efforts to incorporate and even rely upon stochasticity. At the same time, new experimental variables such as chemical induction and optogenetic control have created vast opportunities to probe and understand gene expression, even at single-molecule and single-cell precision. With many possible measurements or perturbations to choose from, researchers require sophisticated approaches to choose which experiment to perform next. In this work, we provide a new tool, the finite state projection based Fisher information matrix (FSP-FIM), which considers all cell-to-cell fluctuations measured in modern data sets, and can design optimal experiments under these conditions. Unlike previous approaches, the FSP-FIM does not make any assumptions about the shape of the distribution being measured. This new tool will allow experimentalists to optimally perturb systems to learn as much as possible about single-cell processes with a minimum of experimental cost or effort.

scholarly journals On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

2021 ◽  
Author(s):  
Matthias Himmelsbach ◽  
Andreas Kroll
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Parameter Estimate ◽  
Model Parameters ◽  
Signal Design ◽  
Optimal Test ◽  
Identification Schemes ◽  
Fuzzy Models ◽  
Takagi Sugeno

AbstractThis paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

scholarly journals Multi-Objective Optimization of Experiments Using Curvature and Fisher Information Matrix

2017 ◽  
Author(s):  
Erica Manesso ◽  
Sridharan Srinath ◽  
Rudiyanto Gunawan
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Dynamic Models ◽  
Information Matrix ◽  
Model Parameters ◽  
Multi Objective Optimization ◽  
Experimental Conditions ◽  
Maximum Information ◽  
Multi Objective ◽  
Highly Nonlinear

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

scholarly journals Optimal Design of Single-Cell Experiments within Temporally Fluctuating Environments

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zachary R. Fox ◽  
Gregor Neuert ◽  
Brian Munsky
Keyword(s):  
Single Cell ◽  
Computational Models ◽  
Osmotic Shock ◽  
Information Matrix ◽  
Specific Model ◽  
Model Parameters ◽  
Prediction Errors ◽  
Estimation Uncertainty ◽  
Regulatory Systems ◽  
Finite State

Modern biological experiments are becoming increasingly complex, and designing these experiments to yield the greatest possible quantitative insight is an open challenge. Increasingly, computational models of complex stochastic biological systems are being used to understand and predict biological behaviors or to infer biological parameters. Such quantitative analyses can also help to improve experiment designs for particular goals, such as to learn more about specific model mechanisms or to reduce prediction errors in certain situations. A classic approach to experiment design is to use the Fisher information matrix (FIM), which quantifies the expected information a particular experiment will reveal about model parameters. The finite state projection-based FIM (FSP-FIM) was recently developed to compute the FIM for discrete stochastic gene regulatory systems, whose complex response distributions do not satisfy standard assumptions of Gaussian variations. In this work, we develop the FSP-FIM analysis for a stochastic model of stress response genes in S. cerevisiae under time-varying MAPK induction. We verify this FSP-FIM analysis and use it to optimize the number of cells that should be quantified at particular times to learn as much as possible about the model parameters. We then extend the FSP-FIM approach to explore how different measurement times or genetic modifications help to minimize uncertainty in the sensing of extracellular environments, and we experimentally validate the FSP-FIM to rank single-cell experiments for their abilities to minimize estimation uncertainty of NaCl concentrations during yeast osmotic shock. This work demonstrates the potential of quantitative models to not only make sense of modern biological datasets but to close the loop between quantitative modeling and experimental data collection.

scholarly journals Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 35
Author(s):  
Jianping Zhu ◽  
Hua Xin ◽  
Chenlu Zheng ◽  
Tzong-Ru Tsai
Keyword(s):  
Normal Distribution ◽  
Fisher Information ◽  
Performance Index ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Estimation Method ◽  
Parametric Bootstrap ◽  
Quality Characteristic ◽  
Model Parameters ◽  
Process Performance

The process performance index (PPI) can be a simple metric to connect the conforming rate of products. The properties of the PPI have been well studied for the normal distribution and other widely used lifetime distributions, such as the Weibull, Gamma, and Pareto distributions. Assume that the quality characteristic of product follows power-normal distribution. Statistical inference procedures for the PPI are established. The maximum likelihood estimation method for the model parameters and PPI is investigated and the exact Fisher information matrix is derived. We discuss the drawbacks of using the exact Fisher information matrix to obtain the confidence interval of the model parameters. The parametric bootstrap percentile and bootstrap bias-corrected percentile methods are proposed to obtain approximate confidence intervals for the model parameters and PPI. Monte Carlo simulations are conducted to evaluate the performance of the proposed methods. One example about the flow width of the resist in the hard-bake process is used for illustration.

scholarly journals Optimal Design of Single-Cell Experiments within Temporally Fluctuating Environments

2019 ◽  
Author(s):  
Zachary R Fox ◽  
Gregor Neuert ◽  
Brian Munsky
Keyword(s):  
Single Cell ◽  
Computational Models ◽  
Osmotic Shock ◽  
Information Matrix ◽  
Specific Model ◽  
Biological Data ◽  
Model Parameters ◽  
Prediction Errors ◽  
Estimation Uncertainty ◽  
Finite State

AbstractModern biological experiments are becoming increasingly complex, and designing these experiments to yield the greatest possible quantitative insight is an open challenge. Increasingly, computational models of complex stochastic biological systems are being used to understand and predict biological behaviors or to infer biological parameters. Such quantitative analyses can also help to improve experiment designs for particular goals, such as to learn more about specific model mechanisms or to reduce prediction errors in certain situations. A classic approach to experiment design is to use the Fisher information matrix (FIM), which quantifies the expected information a particular experiment will reveal about model parameters. The Finite State Projection based FIM (FSP-FIM) was recently developed to compute the FIM for discrete stochastic gene regulatory systems, whose complex response distributions do not satisfy standard assumptions of Gaussian variations. In this work, we develop the FSP-FIM analysis for a stochastic model of stress response genes in S. cerevisae under time-varying MAPK induction. We verify this FSP-FIM analysis and use it to optimize the number of cells that should be quantified at particular times to learn as much as possible about the model parameters. We then extend the FSP-FIM approach to explore how different measurement times or genetic modifications help to minimize uncertainty in the sensing of extracellular environments, and we experimentally validate the FSP-FIM to rank single-cell experiments for their abilities to minimize estimation uncertainty of NaCl concentrations during yeast osmotic shock. This work demonstrates the potential of quantitative models to not only make sense of modern biological data sets, but to close the loop between quantitative modeling and experimental data collection.

4 Molecularly guided multiplexed digital spatial analysis reveals differential gene expression profiles in the WNT-β-catenin pathway between melanoma and prostate tumors

2020 ◽  
Vol 8 (Suppl 3) ◽  
pp. A4-A4
Author(s):  
Anushka Dikshit ◽  
Dan Zollinger ◽  
Karen Nguyen ◽  
Jill McKay-Fleisch ◽  
Kit Fuhrman ◽  
...  
Keyword(s):  
Gene Expression ◽  
Single Cell ◽  
Single Molecule ◽  
Spatial Information ◽  
Expression Profiles ◽  
Gene Expression Profiles ◽  
Fluorescence Assay ◽  
Differentially Expressed ◽  
Tumor Type ◽  
Prostate Tumors

BackgroundThe canonical WNT-β-catenin signaling pathway is vital for development and tissue homeostasis but becomes strongly tumorigenic when dysregulated. and alter the transcriptional signature of a cell to promote malignant transformation. However, thorough characterization of these transcriptomic signatures has been challenging because traditional methods lack either spatial information, multiplexing, or sensitivity/specificity. To overcome these challenges, we developed a novel workflow combining the single molecule and single cell visualization capabilities of the RNAscope in situ hybridization (ISH) assay with the highly multiplexed spatial profiling capabilities of the GeoMx™ Digital Spatial Profiler (DSP) RNA assays. Using these methods, we sought to spatially profile and compare gene expression signatures of tumor niches with high and low CTNNB1 expression.MethodsAfter screening 120 tumor cores from multiple tumors for CTNNB1 expression by the RNAscope assay, we identified melanoma as the tumor type with the highest CTNNB1 expression while prostate tumors had the lowest expression. Using the RNAscope Multiplex Fluorescence assay we selected regions of high CTNNB1 expression within 3 melanoma tumors as well as regions with low CTNNB1 expression within 3 prostate tumors. These selected regions of interest (ROIs) were then transcriptionally profiled using the GeoMx DSP RNA assay for a set of 78 genes relevant in immuno-oncology. Target genes that were differentially expressed were further visualized and spatially assessed using the RNAscope Multiplex Fluorescence assay to confirm GeoMx DSP data with single cell resolution.ResultsThe GeoMx DSP analysis comparing the melanoma and prostate tumors revealed that they had significantly different gene expression profiles and many of these genes showed concordance with CTNNB1 expression. Furthermore, immunoregulatory targets such as ICOSLG, CTLA4, PDCD1 and ARG1, also demonstrated significant correlation with CTNNB1 expression. On validating selected targets using the RNAscope assay, we could distinctly visualize that they were not only highly expressed in melanoma compared to the prostate tumor, but their expression levels changed proportionally to that of CTNNB1 within the same tumors suggesting that these differentially expressed genes may be regulated by the WNT-β-catenin pathway.ConclusionsIn summary, by combining the RNAscope ISH assay and the GeoMx DSP RNA assay into one joint workflow we transcriptionally profiled regions of high and low CTNNB1 expression within melanoma and prostate tumors and identified genes potentially regulated by the WNT- β-catenin pathway. This novel workflow can be fully automated and is well suited for interrogating the tumor and stroma and their interactions.GeoMx Assays are for RESEARCH ONLY, not for diagnostics.

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