scholarly journals Identifiability analysis for models of the translation kinetics after mRNA transfection

2021 ◽  
Author(s):  
Susanne Pieschner ◽  
Jan Hasenauer ◽  
Christiane Fuchs

Mechanistic models are a powerful tool to gain insights into biological processes. The parameters of such models, e.g. kinetic rate constants, usually cannot be measured directly but need to be inferred from experimental data. In this article, we study dynamical models of the translation kinetics after mRNA transfection and analyze their parameter identifiability. Previous studies have considered ordinary differential equation (ODE) models of the process, and here we formulate a stochastic differential equation (SDE) model. For both model types, we consider structural identifiability based on the model equations and practical identifiability based on simulated as well as experimental data and find that the SDE model provides better parameter identifiability than the ODE model. Moreover, our analysis shows that even for those parameters of the ODE model that are considered to be identifiable, the obtained estimates are sometimes unreliable. Overall, our study clearly demonstrates the relevance of considering different modeling approaches and that stochastic models can provide more reliable and informative results.

2020 ◽  
Author(s):  
Alexander P Browning ◽  
David J Warne ◽  
Kevin Burrage ◽  
Ruth E Baker ◽  
Matthew J Simpson

AbstractMathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly-adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically-motivated synthetic data and Markov-chain Monte Carlo (MCMC) methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.


2020 ◽  
Vol 17 (173) ◽  
pp. 20200652
Author(s):  
Alexander P. Browning ◽  
David J. Warne ◽  
Kevin Burrage ◽  
Ruth E. Baker ◽  
Matthew J. Simpson

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability , we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github .


2012 ◽  
Vol 19 (2) ◽  
pp. 175-196 ◽  
Author(s):  
Hanna Kierzkowska-Pawlak

Determination of Kinetics in Gas-Liquid Reaction Systems. An Overview The aim of this paper is to present a brief review of the determination methods of reaction kinetics in gas-liquid systems with a special emphasis on CO2 absorption in aqueous alkanolamine solutions. Both homogenous and heterogeneous experimental techniques are described with the corresponding theoretical background needed for the interpretation of the results. The case of CO2 reaction in aqueous solutions of methyldiethanolamine is discussed as an illustrative example. It was demonstrated that various measurement techniques and methods of analyzing the experimental data can result in different expressions for the kinetic rate constants.


2020 ◽  
Author(s):  
Sajad Shafiekhani ◽  
Amir. H. Jafari ◽  
L. Jafarzadeh ◽  
N. Gheibi

Abstract Background: Ordinary differential equation (ODE) models widely have been used in mathematical oncology to capture dynamics of tumor and immune cells and evaluate the efficacy of treatments. However, for dynamic models of tumor-immune system (TIS), some parameters are uncertain due to inaccurate, missing or incomplete data, which has hindered the application of ODEs that require accurate parameters. Methods: We extended an available ODE model of TIS interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. Fuzzy ODE (FODE) models, in comparison with the stochastic differential equation (SDE) models, assigns a fuzzy number instead of a random number (from a specific probability density function) to the parameters, to capture parametric uncertainty. We used FODE model to predict tumor and immune cells dynamics and assess the efficacy of 5-FU. The present model is configurable for 5-FU chemotherapy injection timing and propose testable hypothesis in vitro/ in vivo experiments. Result: FODE model was used to explore the uncertainty of cells dynamics resulting from parametric uncertainty in presence and absence of 5-FU therapy. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and NK cells, and decreasing that of myeloid-derived suppressor (MDSC) cells. We investigate the effect of perturbation on model parameters on dynamics of cells through global sensitivity analysis (GSA) and compute correlation between model parameters and cell dynamics. Conclusion: ODE models with fuzzy uncertain kinetic parameters cope with insufficient experimental data in the field of mathematical oncology and can predict cells dynamics uncertainty band. In silico assessment of treatments considering parameter uncertainty and investigating the effect of the drugs on movement of cells dynamics uncertainty band may be more appropriate than in crisp setting.


1986 ◽  
Vol 64 (11) ◽  
pp. 2199-2204
Author(s):  
François Hamon ◽  
Danielle Carrier ◽  
Jan A. Herman

An analysis of the kinetic rate constants for ion/molecule reactions of allene by use of the Laplace–Carson transform is performed and the results are compared with experimental data.


1992 ◽  
Vol 26 (3-4) ◽  
pp. 763-772 ◽  
Author(s):  
H. H. Tabak ◽  
C. Gao ◽  
S. Desai ◽  
R. Govind

Biodegradation is an important mechanism determining the fate of chemicals in the aquatic environment. In this paper, experimental data, determined from electrolytic respirometry, for 27 compounds were analyzed using first order and Monod kinetics. Additional data from the literature were also used in our analysis. A method based on group contribution to predict first-order and Monod kinetic rate constants was developed and validated. The group contribution approach gave reasonable results for a variety of compounds. More kinetic data are required to extend the group contribution approach.


2020 ◽  
Author(s):  
Yinglong Miao ◽  
Apurba Bhattarai ◽  
Jinan Wang

AbstractCalculations of ligand binding free energies and kinetic rates are important for drug design. However, such tasks have proven challenging in computational chemistry and biophysics. To address this challenge, we have developed a new computational method “LiGaMD”, which selectively boosts the ligand non-bonded interaction potential energy based on the Gaussian accelerated molecular dynamics (GaMD) enhanced sampling technique. Another boost potential could be applied to the remaining potential energy of the entire system in a dual-boost algorithm (LiGaMD_Dual) to facilitate ligand binding. LiGaMD has been demonstrated on host-guest and protein-ligand binding model systems. Repetitive guest binding and unbinding in the β-cyclodextrin host were observed in hundreds-of-nanosecond LiGaMD simulations. The calculated binding free energies of guest molecules with sufficient sampling agreed excellently with experimental data (< 1.0 kcal/mol error). In comparison with previous microsecond-timescale conventional molecular dynamics simulations, accelerations of ligand kinetic rate constants in LiGaMD simulations were properly estimated using Kramers’ rate theory. Furthermore, LiGaMD allowed us to capture repetitive dissociation and binding of the benzamidine inhibitor in trypsin within 1 μs simulations. The calculated ligand binding free energy and kinetic rate constants compared well with the experimental data. In summary, LiGaMD provides a promising approach for characterizing ligand binding thermodynamics and kinetics simultaneously, which is expected to facilitate computer-aided drug design.


2020 ◽  
Author(s):  
Francoise Mazet ◽  
Marcus J. Tindall ◽  
Jonathan M. Gibbins ◽  
Michael J. Fry

AbstractThe phosphatidylinositol (PI) cycle is central to eukaryotic cell signaling. Its complexity, due to the number of reactions and lipid and inositol phosphate intermediates involved makes it difficult to analyze experimentally. Computational modelling approaches are seen as a way forward to elucidate complex biological regulatory mechanisms when this cannot be achieved solely through experimental approaches. Whilst mathematical modelling is well established in informing biological systems, many models are often informed by data sourced from different cell types (mosaic data), to inform model parameters. For instance, kinetic rate constants are often determined from purified enzyme data in vitro or use experimental concentrations obtained from multiple unrelated cell types. Thus they do not represent any specific cell type nor fully capture cell specific behaviours. In this work, we develop a model of the PI cycle informed by in-vivo omics data taken from a single cell type, namely platelets. Our model recapitulates the known experimental dynamics before and after stimulation with different agonists and demonstrates the importance of lipid- and protein-binding proteins in regulating second messenger outputs. Furthermore, we were able to make a number of predictions regarding the regulation of PI cycle enzymes and the importance of the number of receptors required for successful GPCR signaling. We then consider how pathway behavior differs, when fully informed by data for HeLa cells and show that model predictions remain relatively consistent. However, when informed by mosaic experimental data model predictions greatly vary. Our work illustrates the risks of using mosaic datasets from unrelated cell types which leads to over 75% of outputs not fitting with expected behaviors.Authors summaryComputational models of cellular complexity offer much in terms of understanding cell behaviors and in informing experimental design, but their usefulness is limited in them being built with mosaic data not representing specific cell types and tested against limited experimental outputs. In this work we demonstrate an approach using quantitative proteomic datasets and temporal experimental data from a single cell type (platelets) to inform kinetic rate constants and protein concentrations for a mathematical model of a key signaling pathway - the phosphatidylinositol (PI) cycle; known for its central role in numerous cell functions and diseases. After using our model to make novel predictions regarding how aspects of the pathway are regulated, we demonstrate its versatile nature by utilising proteomic data from other cell types to generate similar predictions for those cells while highlighting the pitfalls of using mosaic data when constructing computational models.


2020 ◽  
Vol 21 (11) ◽  
pp. 1054-1059
Author(s):  
Bin Yang ◽  
Yuehui Chen

: Reconstruction of gene regulatory networks (GRN) plays an important role in understanding the complexity, functionality and pathways of biological systems, which could support the design of new drugs for diseases. Because differential equation models are flexible androbust, these models have been utilized to identify biochemical reactions and gene regulatory networks. This paper investigates the differential equation models for reverse engineering gene regulatory networks. We introduce three kinds of differential equation models, including ordinary differential equation (ODE), time-delayed differential equation (TDDE) and stochastic differential equation (SDE). ODE models include linear ODE, nonlinear ODE and S-system model. We also discuss the evolutionary algorithms, which are utilized to search the optimal structures and parameters of differential equation models. This investigation could provide a comprehensive understanding of differential equation models, and lead to the discovery of novel differential equation models.


Sign in / Sign up

Export Citation Format

Share Document