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 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.

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 Determination of exothermic batch reactor specific model parameters

2019 ◽  
Vol 292 ◽  
pp. 01063
Author(s):  
Lubomír Macků
Keyword(s):  
Rate Constant ◽  
Reaction Rate ◽  
Batch Reactor ◽  
Specific Model ◽  
Reaction Rate Constant ◽  
Order Reaction ◽  
First Order Reaction ◽  
Model Parameters ◽  
Reactor Model ◽  
First Order

An alternative method of determining exothermic reactor model parameters which include first order reaction rate constant is described in this paper. The method is based on known in reactor temperature development and is suitable for processes with changing quality of input substances. This method allows us to evaluate the reaction substances composition change and is also capable of the reaction rate constant (parameters of the Arrhenius equation) determination. Method can be used in exothermic batch or semi- batch reactors running processes based on the first order reaction. An example of such process is given here and the problem is shown on its mathematical model with the help of simulations.

Calibration of single-cell model parameters based on membrane resistance improves the accuracy of cardiac tissue simulations

2021 ◽  
pp. 101375
Author(s):  
Elnaz Pouranbarani ◽  
Lucas Arantes Berg ◽  
Rafael Sachetto Oliveira ◽  
Rodrigo Weber dos Santos ◽  
Anders Nygren
Keyword(s):  
Single Cell ◽  
Cardiac Tissue ◽  
Cell Model ◽  
Membrane Resistance ◽  
Model Parameters ◽  
Single Cell Model

scholarly journals Inflationary cosmology in unimodular F(T) gravity

2017 ◽  
Vol 32 (21) ◽  
pp. 1750114 ◽  
Author(s):  
Kazuharu Bamba ◽  
Sergei D. Odintsov ◽  
Emmanuel N. Saridakis
Keyword(s):  
Spectral Index ◽  
Teleparallel Gravity ◽  
Specific Model ◽  
Inflationary Cosmology ◽  
Model Parameters ◽  
De Sitter ◽  
Reconstruction Procedure ◽  
Additional Advantage ◽  
Slow Roll ◽  
Good Agreement

We investigate the inflationary realization in the context of unimodular F(T) gravity, which is based on the F(T) modification of teleparallel gravity, in which one imposes the unimodular condition through the use of Lagrange multipliers. We develop the general reconstruction procedure of the F(T) form that can give rise to a given scale-factor evolution, and then we apply it in the inflationary regime. We extract the Hubble slow-roll parameters that allow us to calculate various inflation-related observables, such as the scalar spectral index and its running, the tensor-to-scalar ratio, and the tensor spectral index. Then, we examine the particular cases of de Sitter and power-law inflation, of Starobinsky inflation, as well as inflation in a specific model of unimodular F(T) gravity. As we show, in all cases the predictions of our scenarios are in a very good agreement with Planck observational data. Finally, inflation in unimodular F(T) gravity has the additional advantage that it always allows for a graceful exit for specific regions of the model parameters.

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

Unknown Parameter Excitation and Estimation for Complex Systems With Dynamic Performances

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Yi-Ping Chen ◽  
Kuei-Yuan Chan
Keyword(s):  
Complex Systems ◽  
Simulation Models ◽  
Credible Interval ◽  
Specific Model ◽  
Model Parameters ◽  
Real Model ◽  
Dynamic Case ◽  
Dynamic Performances ◽  
Validation Stage ◽  
Setting Parameters

Abstract Simulation models play crucial roles in efficient product development cycles, therefore many studies aim to improve the confidence of a model during the validation stage. In this research, we proposed a dynamic model validation to provide accurate parameter settings for minimal output errors between simulation models and real model experiments. The optimal operations for setting parameters are developed to maximize the effects by specific model parameters while minimizing interactions. To manage the excessive costs associated with simulations of complex systems, we propose a procedure with three main features: the optimal excitation based on global sensitivity analysis (GSA) is done via metamodel techniques, for estimating parameters with the polynomial chaos-based Kalman filter, and validating the updated model based on hypothesis testing. An illustrative mathematical model was used to demonstrate the detail processes in our proposed method. We also apply our method on a vehicle dynamic case with a composite maneuver for exciting unknown model parameters such as inertial and coefficients of the tire model; the unknown model parameters were successfully estimated within a 95% credible interval. The contributions of this research are also underscored through multiple cases.

Hierarchical Bayesian Parameter Estimation for Modeling and Analysis of User Affective Influence

2013 ◽  
Author(s):  
Feng Zhou ◽  
Jianxin (Roger) Jiao
Keyword(s):  
Decision Making ◽  
Interior Design ◽  
Computational Models ◽  
Human Perception ◽  
Model Parameters ◽  
Hierarchical Bayesian ◽  
Affective States ◽  
Modeling And Analysis ◽  
Human Decision

Traditional user experience (UX) models are mostly qualitative in terms of its measurement and structure. This paper proposes a quantitative UX model based on cumulative prospect theory. It takes a decision making perspective between two alternative design profiles. However, affective elements are well-known to have influence on human decision making, the prevailing computational models for analyzing and simulating human perception on UX are mainly cognition-based models. In order to incorporate both affective and cognitive factors in the decision making process, we manipulate the parameters involved in the cumulative prospect model to show the affective influence. Specifically, three different affective states are induced to shape the model parameters. A hierarchical Bayesian model with a technique called Markov chain Monte Carlo is used to estimate the parameters. A case study of aircraft cabin interior design is illustrated to show the proposed methodology.

Cluster Analysis of Dynamic Parameters of Gene Expression

2003 ◽  
Vol 01 (03) ◽  
pp. 447-458 ◽  
Author(s):  
Xiwei Wu ◽  
T. Gregory Dewey
Keyword(s):  
Gene Expression ◽  
Cell Cycle ◽  
Cluster Analysis ◽  
Hierarchical Cluster ◽  
Specific Model ◽  
Model Parameters ◽  
Dynamic Parameters ◽  
Clustering Methods ◽  
Transition Matrices ◽  
Great Utility

Cluster analysis has proven to be a valuable statistical method for analyzing whole genome expression data. Although clustering methods have great utility, they do represent a lower level statistical analysis that is not directly tied to a specific model. To extend such methods and to allow for more sophisticated lines of inference, we use cluster analysis in conjunction with a specific model of gene expression dynamics. This model provides phenomenological dynamic parameters on both linear and non-linear responses of the system. This analysis determines the parameters of two different transition matrices (linear and nonlinear) that describe the influence of one gene expression level on another. Using yeast cell cycle microarray data as test set, we calculated the transition matrices and used these dynamic parameters as a metric for cluster analysis. Hierarchical cluster analysis of this transition matrix reveals how a set of genes influence the expression of other genes activated during different cell cycle phases. Most strikingly, genes in different stages of cell cycle preferentially activate or inactivate genes in other stages of cell cycle, and this relationship can be readily visualized in a two-way clustering image. The observation is prior to any knowledge of the chronological characteristics of the cell cycle process. This method shows the utility of using model parameters as a metric in cluster analysis.

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