scholarly journals Simulating tubulin-associated unit transport in an axon: using bootstrapping for estimating confidence intervals of best-fit parameter values obtained from indirect experimental data

2017 ◽  
Vol 473 (2201) ◽  
pp. 20170045 ◽  
Author(s):  
I. A. Kuznetsov ◽  
A. V. Kuznetsov
Keyword(s):  
Experimental Data ◽  
Confidence Intervals ◽  
Surrogate Data ◽  
Model Parameters ◽  
Model Predictions ◽  
Estimate Parameter ◽  
Minimum Number ◽  
Percentile Bootstrap ◽  
Parameter Values ◽  
Best Fit

In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping. Model parameters were estimated by minimizing the objective function that simulates the discrepancy between the model predictions and experimental data. Residuals were then identified by calculating the differences between the experimental data and model predictions. New, surrogate ‘experimental’ data were generated by randomly resampling residuals. By finding sets of best-fit parameters for a large number of surrogate data the histograms for the model parameters were produced. These histograms were then used to estimate confidence intervals for the model parameters, by using the percentile bootstrap. Once the model was calibrated, we applied it to analysing some features of tau transport that are not accessible to current experimental techniques.

scholarly journals Statistics of nascent and mature RNA fluctuations in a stochastic model of transcriptional initiation, elongation, pausing, and termination

2020 ◽  
Author(s):  
Tatiana Filatova ◽  
Nikola Popovic ◽  
Ramon Grima
Keyword(s):  
Experimental Data ◽  
Fluorescence Microscopy ◽  
Stochastic Model ◽  
Explicit Dependence ◽  
Transcriptional Initiation ◽  
Estimate Parameter ◽  
Mean And Variance ◽  
The Mean ◽  
Nascent Rna ◽  
Parameter Values

AbstractRecent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

scholarly journals The chaos in calibrating crop models

2020 ◽  
Author(s):  
Daniel Wallach ◽  
Taru Palosuo ◽  
Peter Thorburn ◽  
Zvi Hochman ◽  
Emmanuelle Gourdain ◽  
...  
Keyword(s):  
Experimental Data ◽  
Model Calibration ◽  
Crop Model ◽  
Process Models ◽  
Model Parameters ◽  
Model Structure ◽  
Crop Models ◽  
Estimation Of Model Parameters ◽  
Parameter Values ◽  
Made In

Calibration, that is the estimation of model parameters based on fitting the model to experimental data, is among the first steps in essentially every application of crop models and process models in other fields and has an important impact on simulated values. The goal of this study is to develop a comprehensive list of the decisions involved in calibration and to identify the range of choices made in practice, as groundwork for developing guidelines for crop model calibration starting with phenology. Three groups of decisions are identified; the criterion for choosing the parameter values, the choice of parameters to estimate and numerical aspects of parameter estimation. It is found that in practice there is a large diversity of choices for every decision, even among modeling groups using the same model structure. These findings are relevant to process models in other fields.

scholarly journals Model-Based Design and Optimization of Blood Oxygenators

2020 ◽  
Vol 14 (4) ◽  
Author(s):  
Ge He ◽  
Tao Zhang ◽  
Jiafeng Zhang ◽  
Bartley P. Griffith ◽  
Zhongjun J. Wu
Keyword(s):  
Experimental Data ◽  
Carbon Dioxide ◽  
Fiber Bundle ◽  
Cfd Modeling ◽  
Design Parameters ◽  
Model Parameters ◽  
Transfer Rates ◽  
Design And Optimization ◽  
Model Based ◽  
Model Predictions

Abstract Blood oxygenators, also known as artificial lungs, are widely used in cardiopulmonary bypass surgery to maintain physiologic oxygen (O2) and carbon dioxide (CO2) levels in blood, and also serve as respiratory assist devices to support patients with lung failure. The time- and cost-consuming method of trial and error is initially used to optimize the oxygenator design, and this method is followed by the introduction of the computational fluid dynamics (CFD) that is employed to reduce the number of prototypes that must be built as the design is optimized. The CFD modeling method, while having progress in recent years, still requires complex three-dimensional (3D) modeling and experimental data to identify the model parameters and validate the model. In this study, we sought to develop an easily implemented mathematical models to predict and optimize the performance (oxygen partial pressure/saturation, oxygen/carbon dioxide transfer rates, and pressure loss) of hollow fiber membrane-based oxygenators and this model can be then used in conjunction with CFD to reduce the number of 3D CFD iteration for further oxygenator design and optimization. The model parameters are first identified by fitting the model predictions to the experimental data obtained from a mock flow loop experimental test on a mini fiber bundle. The models are then validated through comparing the theoretical results with the experimental data of seven full-size oxygenators. The comparative analysis show that the model predictions and experimental results are in good agreement. Based on the verified models, the design curves showing the effects of parameters on the performance of oxygenators and the guidelines detailing the optimization process are established to determine the optimal design parameters (fiber bundle dimensions and its porosity) under specific system design requirements (blood pressure drop, oxygen pressure/saturation, oxygen/carbon dioxide transfer rates, and priming volume). The results show that the model-based optimization method is promising to derive the optimal parameters in an efficient way and to serve as an intermediate modeling approach prior to complex CFD modeling.

B anomalies with unparticles

2021 ◽  
Vol 36 (30) ◽  
Author(s):  
Jong-Phil Lee
Keyword(s):  
Experimental Data ◽  
Standard Model ◽  
Branching Ratio ◽  
Branching Ratios ◽  
The Standard Model ◽  
Model Predictions ◽  
Best Fit

We analyze the [Formula: see text] anomalies associated with the [Formula: see text] decays in the unparticle model. The fraction of the branching ratios [Formula: see text] and other parameters related to the polarization are fitted to the experimental data by minimizing [Formula: see text]. The best-fit values are [Formula: see text] and [Formula: see text] which are still larger than the standard model predictions. We find that our results safely render the branching ratio [Formula: see text] below [Formula: see text].

Improving Model Parameters in Vibrating Systems Using Neumann Series

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Alyssa T. Liem ◽  
J. Gregory McDaniel ◽  
Andrew S. Wixom
Keyword(s):  
Longitudinal Vibration ◽  
Dynamic Stiffness ◽  
Neumann Series ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Experimental Measurements ◽  
Resonance Frequencies ◽  
Model Predictions ◽  
Parameter Values ◽  
Vibrating Systems

A method is presented to improve the estimates of material properties, dimensions, and other model parameters for linear vibrating systems. The method improves the estimates of a single model parameter of interest by finding parameter values that bring model predictions into agreement with experimental measurements. A truncated Neumann series is used to approximate the inverse of the dynamic stiffness matrix. This approximation avoids the need to directly solve the equations of motion for each parameter variation. The Neumman series is shown to be equivalent to a Taylor series expansion about nominal parameter values. A recursive scheme is presented for computing the associated derivatives, which are interpreted as sensitivities of displacements to parameter variations. The convergence of the Neumman series is studied in the context of vibrating systems, and it is found that the spectral radius is strongly dependent on system resonances. A homogeneous viscoelastic bar in longitudinal vibration is chosen as a test specimen, and the complex-valued Young's modulus is chosen as an uncertain parameter. The method is demonstrated on simulated experimental measurements computed from the model. These demonstrations show that parameter values estimated by the method agree with those used to simulate the experiment when enough terms are included in the Neumann series. Similar results are obtained for the case of an elastic plate with clamped boundary conditions. The method is also demonstrated on experimental data, where it produces improved parameter estimates that bring the model predictions into agreement with the measured response to within 1% at a point on the bar across a frequency range that includes three resonance frequencies.

A Model for Vortex Induced Oscillation of Structures

1974 ◽  
Vol 41 (3) ◽  
pp. 581-586 ◽  
Author(s):  
W. D. Iwan ◽  
R. D. Blevins
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Analytical Model ◽  
Vortex Shedding ◽  
Fluid Dynamic ◽  
Model Parameters ◽  
Structural Systems ◽  
Dynamic Effects ◽  
Hidden Variable ◽  
Model Predictions

A model is presented for the analysis of the response of structural systems excited by vortex shedding. The model is based on the introduction of a hidden variable to describe the fluid dynamic effects. Model parameters may be determined from experimental data for fixed and forced elements and the model used to predict the response of elastically mounted elements. Analytical model predictions are compared with experimental results for a circular cylinder.

scholarly journals Simulating intervertebral disc cell behaviour within 3D multifactorial environments

2020 ◽  
Author(s):  
L Baumgartner ◽  
J J Reagh ◽  
M A González Ballester ◽  
J Noailly
Keyword(s):  
Experimental Data ◽  
Intervertebral Disc ◽  
Cell Viability ◽  
Mrna Expression ◽  
Collagen Type ◽  
Supplementary Information ◽  
Model Parameters ◽  
Type I ◽  
Cell Behaviour ◽  
Model Predictions

Abstract Motivation Low back pain is responsible for more global disability than any other condition. Its incidence is closely related to intervertebral disc (IVD) failure, which is likely caused by an accumulation of microtrauma within the IVD. Crucial factors in microtrauma development are not entirely known yet, probably because their exploration in vivo or in vitro remains tremendously challenging. In silico modelling is, therefore, definitively appealing, and shall include approaches to integrate influences of multiple cell stimuli at the microscale. Accordingly, this study introduces a hybrid Agent-based (AB) model in IVD research and exploits network modelling solutions in systems biology to mimic the cellular behaviour of Nucleus Pulposus cells exposed to a 3D multifactorial biochemical environment, based on mathematical integrations of existing experimental knowledge. Cellular activity reflected by mRNA expression of Aggrecan, Collagen type I, Collagen type II, MMP-3 and ADAMTS were calculated for inflamed and non-inflamed cells. mRNA expression over long periods of time is additionally determined including cell viability estimations. Model predictions were eventually validated with independent experimental data. Results As it combines experimental data to simulate cell behaviour exposed to a multifactorial environment, the present methodology was able to reproduce cell death within 3 days under glucose deprivation and a 50% decrease in cell viability after 7 days in an acidic environment. Cellular mRNA expression under non-inflamed conditions simulated a quantifiable catabolic shift under an adverse cell environment, and model predictions of mRNA expression of inflamed cells provide new explanation possibilities for unexpected results achieved in experimental research. Availabilityand implementation The AB model as well as used mathematical functions were built with open source software. Final functions implemented in the AB model and complete AB model parameters are provided as Supplementary Material. Experimental input and validation data were provided through referenced, published papers. The code corresponding to the model can be shared upon request and shall be reused after proper training. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.

An independent quark model study of weak leptonic decays of pseudoscalar mesons

2015 ◽  
Vol 30 (16) ◽  
pp. 1550092
Author(s):  
S. N. Jena ◽  
P. K. Nanda ◽  
S. Sahoo ◽  
S. Panda
Keyword(s):  
Experimental Data ◽  
Quark Model ◽  
Decay Constant ◽  
Model Parameters ◽  
Decay Modes ◽  
Leptonic Decays ◽  
Model Study ◽  
Pseudoscalar Mesons ◽  
Model Predictions ◽  
Decay Widths

An independent quark model with a relativistic power-law potential is used to study the weak leptonic decays of light and heavy pseudoscalar mesons. The partial decay width and the decay constant for the weak leptonic decay are derived from the quark–antiquark momentum distribution amplitude which is obtained from the bound quark eigenfunction with the assumption of a strong correlation existing between quark–antiquark momenta inside the decaying meson in its rest frame. The model parameters are first determined from the application of the model to study the ground state hyperfine splitting of ρ, K, D, Ds, B, Bs and Bc mesons. The same model with no adjustable parameters is then used to evaluate the decay constants fM and the decay widths of pseudoscalar mesons. The model predictions agree quite well with the available experimental data as well as with those of several other models. The decay constant for pion and kaon are obtained as fπ = 132 MeV and fk = 161 MeV which closely agree with experimental values. But in case of heavier mesons for which experimental data are not yet available, the present model gives its predictions as fBC > fBS > fB, fDS > fD, fD > fB and fπ > fB which are in conformity with most of other model predictions. The model predictions of the corresponding decay widths and the branching ratios for the [Formula: see text] and [Formula: see text] decay modes are in close agreement with the available experimental data.

scholarly journals Estimating parameters from multiple time series of population dynamics using Bayesian inference

2018 ◽  
Author(s):  
Benjamin Rosenbaum ◽  
Michael Raatz ◽  
Guntram Weithoff ◽  
Gregor F. Fussmann ◽  
Ursula Gaedke
Keyword(s):  
Time Series ◽  
Population Dynamics ◽  
Bayesian Inference ◽  
Steady States ◽  
Series Data ◽  
Model Parameters ◽  
List Type ◽  
Model Predictions ◽  
Cyclic Dynamics ◽  
Parameter Values

AbstractEmpirical time series of interacting entities, e.g. species abundances, are highly useful to study ecological mechanisms. Mathematical models are valuable tools to further elucidate those mechanisms and underlying processes. However, obtaining an agreement between model predictions and experimental observations remains a demanding task. As models always abstract from reality one parameter often summarizes several properties. Parameter measurements are performed in additional experiments independent of the ones delivering the time series. Transferring these parameter values to different settings may result in incorrect parametrizations. On top of that, the properties of organisms and thus the respective parameter values may vary considerably. These issues limit the use of a priori model parametrizations.In this study, we present a method suited for a direct estimation of model parameters and their variability from experimental time series data. We combine numerical simulations of a continuous-time dynamical population model with Bayesian inference, using a hierarchical framework that allows for variability of individual parameters. The method is applied to a comprehensive set of time series from a laboratory predator-prey system that features both steady states and cyclic population dynamics.Our model predictions are able to reproduce both steady states and cyclic dynamics of the data. Additionally to the direct estimates of the parameter values, the Bayesian approach also provides their uncertainties. We found that fitting cyclic population dynamics, which contain more information on the process rates than steady states, yields more precise parameter estimates. We detected significant variability among parameters of different time series and identified the variation in the maximum growth rate of the prey as a source for the transition from steady states to cyclic dynamics.By lending more flexibility to the model, our approach facilitates parametrizations and shows more easily which patterns in time series can be explained also by simple models. Applying Bayesian inference and dynamical population models in conjunction may help to quantify the profound variability in organismal properties in nature.

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